Patterson, Margaret Becker; Higgins, Jennifer; Bozman, Martha; Katz, Michael
We conducted a pilot study to see how the GED Mathematics Test could be administered on computer with embedded accessibility tools. We examined test scores and test-taker experience. Nineteen GED test centers across five states and 216 randomly assigned GED Tests candidates participated in the project. GED candidates completed two GED mathematics…
Ezzelle, Carol; Setzer, J. Carl
This manual was written to provide technical information regarding the 2002 Series GED (General Educational Development) Tests. Throughout this manual, documentation is provided regarding the development of the GED Tests, data collection activities, as well as reliability and validity evidence. The purpose of this manual is to provide evidence…
Larson, Kara; Gaeta, Cristina; Sager, Lou
In January 2014, the GED Testing Service significantly redesigned the GED test to incorporate the Common Core State Standards and the College and Career Readiness Standards for Adult Education. The purpose of this study was to examine the significant changes made to the test in 2014, examine the impact of the changes on Washingtonians, and make…
Heckman, James J.; LaFontaine, Paul A.; Rodriguez, Pedro L.
We exploit an exogenous increase in General Educational Development (GED) testing requirements to determine whether raising the difficulty of the test causes students to finish high school rather than drop out and GED certify. We find that a six point decrease in GED pass rates induces a 1.3 point decline in overall dropout rates. The effect size…
Heckman, James J.; Humphries, John Eric; LaFontaine, Paul A.; Rodríguez, Pedro L.
The option to obtain a General Education Development (GED) certificate changes the incentives facing high school students. This paper evaluates the effect of three different GED policy innovations on high school graduation rates. A six point decrease in the GED pass rate due to an increase in passing standards produced a 1.3 point decline in overall dropout rates. The introduction of a GED certification program in high schools in Oregon produced a four percent decrease in graduation rates. Introduction of GED certificates in California increased dropout rates by 3 points. The GED program induces high school students to drop out. PMID:24634564
CASAS - Comprehensive Adult Student Assessment Systems (NJ1), 2003
CASAS, in cooperation with the CASAS National Consortium Policy Council, conducted a study to provide guidance to program and instructional staff regarding student readiness to take the GED Tests. The study looked at the relationship of CASAS reading and math scores to official 2002 GED test results from five states--California, Hawaii, Iowa,…
Full Text Available Since 2014, there have been admission tests in mathematics for applicants to the Estonian University of Life Sciences for Geodesy, Land Management and Real Estate Planning; Civil Engineering; Hydraulic Engineering and Water Pollution Control; Engineering and Technetronics curricula. According to admission criteria, the test must be taken by students who have not passed the specific mathematics course state exam or when the score was less than 20 points. The admission test may also be taken by those who wish to improve their state exam score. In 2016, there were 126 such applicants of whom 63 took the test. In 2015, the numbers were 129 and 89 and in 2014 150 and 47 accordingly. The test was scored on scale of 100. The arithmetic average of the score was 30.6 points in 2016, 29.03 in 2015 and 18.84 in 2014. The test was considered to be passed with 1 point in 2014 and 20 points in 2015 and 2016. We analyzed test results and gave examples of problems which were solved exceptionally well or not at all.
Clark, Renee Smith
The tests of General Education Development (GED) provide adults with opportunities to attend and graduate from postsecondary institutions. A study investigated the academic achievement of GED recipients compared to that of high school diploma (HSD) students graduating from the Community College of Allegheny County (Pennsylvania) between June 1985…
Vernon, P. E.; And Others
The Mathematics Competency Test is a 46-question written test assessing mathematics achievement for groups or individuals aged 11 to adult. It is suitable for use with groups or individuals in school, college and workplace contexts. The questions are open-ended and require constructed responses rather than recognition of a correct answer in a…
Poppei, J.; Mayer, G.; Schwarz, R.
This final report for the Swiss Federal Office of Energy (SFOE) takes a look at a computer-aided dimensioning tool (Groundwater Energy Designer, GED) for use in the calculation work involved in designing systems for the thermal use of groundwater. The interactive tool is designed to support those involved in the analysis of heating and cooling demands and the direct use of groundwater to help meet such needs. The program and its user interface in German and French are described in detail, as are the basic models and data used in the calculations. Simulation aspects and the verification of the software are also discussed. Results of tests made are presented and discussed.
Hariharan, Joya Reena
The General Educational Development (GED) tests enable people to earn a high school equivalency diploma and help them to qualify for more jobs and opportunities. Apart from this main goal, GED courses aim at enabling adults to improve the condition of their lives and to cope with a changing society. In today's world, science and technology play an exceedingly important role in helping people better their lives and in promoting the national goals of informed citizenship. Despite the current efforts in the field of secondary science education directed towards scientific literacy and the concept of "Science for all Americans", the literature does not reflect any corresponding efforts in the field of adult education. Science education research appears to have neglected a population that could possibly benefit from it. The purpose of this study is to explore: the science component of GED programs, significant features of the science portion of GED curricula and GED science materials, and adult learners' attitudes toward various aspects of science. Data collection methods included interviews with GED students and instructors, content analysis of relevant materials, and classroom observations. Data indicate that the students in general feel that the science they learn should be relevant to their lives and have direct applications in everyday life. Student understanding of science and interest in it appears to be contingent to their perceiving it as relevant to their lives and to society. Findings indicate that the instructional approaches used in GED programs influence students' perceptions about the relevance of science. Students in sites that use strategies such as group discussions and field trips appear to be more aware of science in the world around them and more enthusiastic about increasing this awareness. However, the dominant strategy in most GED programs is individual reading. The educational strategies used in GED programs generally focus on developing reading
Minor, Elizabeth Covay
Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…
Boesen, Jesper; Lithner, Johan; Palm, Torulf
Internationally, education reform has been directed towards describing educational goals that go beyond topic and content descriptions. The idea of mathematical competencies describes such goals. National tests have been seen as one way of communicating these goals and influence teaching. The present study analyses Swedish national tests in…
Tempel, Tobias; Neumann, Roland
We investigated the combined effects of stereotype threat and trait test anxiety on mathematics test performance. Stereotype threat and test anxiety interacted with each other in affecting performance. Trait test anxiety predicted performance only in a diagnostic condition that prevented stereotype threat by stereotype denial. A state measure of…
McCune, Ennis Donice
Your guide to a higher score on the Praxis II?: Mathematics Content Knowledge Test (0061) Why CliffsTestPrep Guides? Go with the name you know and trust Get the information you need--fast! Written by test-prep specialists About the contents: Introduction * Overview of the exam * How to use this book * Proven study strategies and test-taking tips Part I: Subject Review * Focused review of all exam topics: arithmetic and basic algebra, geometry, trigonometry, analytic geometry, functions and their graphs, calculus, probability and statistics, discrete mathematics, linear algebra, compute
Riffle, Billy Joe
When discussing issues relating to students in General Educational Development (GED) Option and pre-GED programs with educators, the contention exists that it is possible to make reasonably accurate predictions on the success or failure of a student by observing a number of items. Looking at their cumulative records shows their academic and…
Based on the results of a prior case-study analysis of mathematics placement at one university, the mathematics department developed and piloted a mathematics placement test. This article describes the implementation process for a mathematics placement test and further analyzes the test results for the pilot group. As an unexpected result, the…
This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students' knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to…
Seng, Ernest Lim Kok
This study examines the relationship between mathematics test anxiety and numerical anxiety on students' mathematics achievement. 140 pre-university students who studied at one of the institutes of higher learning were being investigated. Gender issue pertaining to mathematics anxieties was being addressed besides investigating the magnitude of…
This is an excerpt from "Back to School: Why Everyone Deserves a Second Chance at Education" (The New Press, 2012). It concludes that GED programs need more resources, not less. The programs tend to be populated by low-to-modest income people who failed school the first time around and now are considered less worthy of investment. GED…
Tyler, John H.; Murnane, Richard J.; Willett, John B.
A study used data from a long-standing examination system, the General Educational Development (GED) certificate, to illustrate that the details of examination systems have marked impacts on the number of test takers who obtain the desired credential and on the racial/ethnic composition of passers. Data provided by the Florida Department of…
Groundwater Energy Designer (GED). Computerized design tool for use of groundwater as heating and cooling source - Final report; Groundwater Energy Designer (GED). Computergestuetztes Auslegungstool zur Waerme- und Kaeltenutzung von Grundwasser - Schlussbericht
Poppei, J.; Mayer, G.; Schwarz, R.
We have developed the graphic-based tool Groundwater Energy Designer (GED) for the dimensioning of groundwater withdrawal and reinjection facilities for the purpose of thermal energy exploitation. The tool is designed to support persons planning and constructing small and medium sized installations as well as licensing authorities. GED takes into account the site-specific energy demand and hydrogeological situation. Starting from the analysis of heating or cooling demand, the possibilities of a direct utilization of the groundwater are tested interactively. The well bores for groundwater withdrawal are dimensioned based on a simplified hydrogeological characterisation. The options for the reinjection of used water are investigated considering the local situation (available area and natural groundwater flow). The situation is assessed with consideration of: (i) the technical feasibility at the site (drawdown in the well, distance between production and reinjection wells); (ii) the potential thermal impact on the groundwater (delineation of the heat propagation front for an evaluation of licensing feasibility). GED combines interactive user interfaces for the input of data and characterisation of the local situation, a database with technical and hydrogeological parameters and a flow and heat transfer simulator based on a finite volume code with an automatic mesh generator. The program is available for purchase from the developer. (authors)
Full Text Available Abstract Background Mathematics anxiety (MA, a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA a construct related to MA but which is typically not controlled for in MA studies. Methods Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education
Devine, Amy; Fawcett, Kayleigh; Szűcs, Dénes; Dowker, Ann
Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys' mathematics performance is more negatively affected by MA than girls' performance is. The aim of the current study was to measure girls' and boys' mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on 'online' mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because
Background Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Methods Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in
Rosholm, Michael; Mikkelsen, Mai Bjørnskov; Gumede, Kamilla
We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1-3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students.
Rosholm, Michael; Mikkelsen, Mai Bjørnskov; Gumede, Kamilla Trille
We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1–3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We...... use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who...... are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students....
Full Text Available We analyse the effect of substituting a weekly mathematics lesson in primary school grades 1-3 with a lesson in mathematics based on chess instruction. We use data from the City of Aarhus in Denmark, combining test score data with a comprehensive data set obtained from administrative registers. We use two different methodological approaches to identify and estimate treatment effects and we tend to find positive effects, indicating that knowledge acquired through chess play can be transferred to the domain of mathematics. We also find larger impacts for unhappy children and children who are bored in school, perhaps because chess instruction facilitates learning by providing an alternative approach to mathematics for these children. The results are encouraging and suggest that chess may be an important and effective tool for improving mathematical capacity in young students.
This article discusses competing perspectives on the value of the General Educational Development (GED) credential. Although scholars and journalists debate the worth of the credential, urban youth continue to pursue the GED, especially as proxy for inadequate schooling. Using qualitative data from a participatory action research project, the…
Alberta Dept. of Education, Edmonton.
This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…
Ming Tsui; Xiao Y. Xu; Edmond Venator
Problem statement: Stereotype threat has repeatedly been shown to depress womens scores on difficult math tests. An attempt to replicate these findings in China found no support for the stereotype threat hypothesis. Our math test was characterized as being personally important for the student participants, an atypical condition in most stereotype threat laboratory research. Approach: To evaluate the effects of this personal demand, we conducted three experiments. Results: ...
Victoria Education Dept. (Australia).
This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…
Phillips, David S.; Hannon, James C.; Castelli, Darla M.
The effect of an acute bout of physical activity on academic performance in school-based settings is under researched. The purpose of this study was to examine associations between a single, vigorous (70-85%) bout of physical activity completed during physical education on standardized mathematics test performance among 72, eighth grade students…
Veldkamp, Bernard P.; van der Linden, Willem J.; Ariel, A.
This paper presents an approach to item pool design that has the potential to improve on the quality of current item pools in educational and psychological testing andhence to increase both measurement precision and validity. The approach consists of the application of mathematical programming
National Aeronautics and Space Administration — Place Germanium detectors (GeDs) in a few-MeV γ-ray Compton instrument on a satellite will enable unprecedented insight into nuclear astrophysics, key multimessenger...
Full Text Available Examination results are rather important for many students with regard to their future profession development. Results of exams should be carefully inspected by the teachers to help improve design and evaluation of tests and education process in general. Analysis of examination papers in mathematics taken by students of basic mathematics course at University of Economics in Prague is reported. The first issue addressed is identification of significant dependencies between performance in particular problem areas covered in the test and also between particular items and total score in test or ability level as a latent trait. The assessment is first performed with Spearman correlation coefficient, items in the test are then evaluated within Item Response Theory framework. The second analytical task addressed is a search for groups of students who are similar with respect to performance in test. Cluster analysis is performed using partitioning around medoids method and final model selection is made according to average silhouette width. Results of clustering, which may be also considered in connection with setting of the minimum score for passing the exam, show that two groups of students can be identified. The group which may be called "well-performers" is the more clearly defined one.
Fan, Ying; Wei, Yi-Ming; Zhang, Yue-Jun; Tsai, Hsien-Tang
Estimation has been carried out using GARCH-type models, based on the Generalized Error Distribution (GED), for both the extreme downside and upside Value-at-Risks (VaR) of returns in the WTI and Brent crude oil spot markets. Furthermore, according to a new concept of Granger causality in risk, a kernel-based test is proposed to detect extreme risk spillover effect between the two oil markets. Results of an empirical study indicate that the GED-GARCH-based VaR approach appears more effective than the well-recognized HSAF (i.e. historical simulation with ARMA forecasts). Moreover, this approach is also more realistic and comprehensive than the standard normal distribution-based VaR model that is commonly used. Results reveal that there is significant two-way risk spillover effect between WTI and Brent markets. Supplementary study indicates that at the 99% confidence level, when negative market news arises that brings about a slump in oil price return, historical information on risk in the WTI market helps to forecast the Brent market. Conversely, it is not the case when positive news occurs and returns rise. Historical information on risk in the two markets can facilitate forecasts of future extreme market risks for each other. These results are valuable for anyone who needs evaluation and forecasts of the risk situation in international crude oil markets. (author)
Pinto, J. S.; Oliveira, M. P.; Anjo, A. B.; Pais, S. I. Vieira; Isidro, R. O.; Silva, M. H.
Since 1989, the Mathematics Education Project (PmatE--Projecto Matematica Ensino) has developed several strategies to improve the success of students in Mathematics. The most important of these are mathematical games for all grades above primary school. The online evaluation of Mathematics subjects is one of PmatE's goals. The implementation of an…
Grant, M.W.; Langton, C.A.; Oblath, S.B.; Pepper, D.W.; Wallace, R.M.; Wilhite, E.L.; Yau, W.W.F.
A low-level alkaline salt solution will be a byproduct in the processing of high-level waste at the Savannah River Plant (SRP). This solution will be incorporated into a wasteform, saltstone, and disposed of in surface vaults. Laboratory and field leach testing and mathematical modeling have demonstrated the predictability of contaminant release from cement wasteforms. Saltstone disposal in surface vaults will meet the design objective, which is to meet drinking water standards in shallow groundwater at the disposal area boundary. Diffusion is the predominant mechanism for release of contaminants to the environment. Leach testing in unsaturated soil, at soil moisture levels above 1 wt %, has shown no difference in leach rate compared to leaching in distilled water. Field leach testing of three thirty-ton blocks of saltstone in lysimeters has been underway since January 1984. Mathematical models were applied to assess design features for saltstone disposal. One dimensional infinite-composite and semi-infinite analytical models were developed for assessing diffusion of nitrate from saltstone through a cement barrier. Numerical models, both finite element and finite difference, were validated by comparison of model predictions with the saltstone lysimeter results. Validated models were used to assess the long-term performance of the saltstone stored in surface vaults. The maximum concentrations of all contaminants released from saltstone to shallow groundwater are predicted to be below drinking water standards at the disposal area boundary. 5 refs., 11 figs., 5 tabs
Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...
Vranić, Edina; Mehmedagić, Aida; Hadzović, Sabira
In recent years, drug release/dissolution from solid dosage forms has been the subject of intense and profitable scientific developments. Whenever a new solid dosage form is developed or produced, it is necessary to ensure that drug dissolution occurs in an appropriate manner. The pharmaceutical industry and the registration authorities do focus, nowadays, on drug dissolution studies. The quantitative analysis of the values obtained in dissolution/release tests is easier when mathematical formulas that express the dissolution results as a function of some of the dosage forms characteristics are used. This work discusses the analysis of data obtained for dissolution profiles under different media pH conditions using mathematical methods of analysis described by Moore and Flanner. These authors have described difference factor (f1) and similarity factor (f2), which can be used to characterise drug dissolution/release profiles. In this work we have used these formulas for evaluation of dissolution profiles of the conventional tablets in different pH of dissolution medium (range of physiological variations).
Eringen, A Cemal
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Anis, Yasmeen; Krause, Jeremy A.; Blum, Emily N.
Mathematics anxiety typically involves apprehension toward activities that require computation, which can lead to complications in every-day-life activities (Ashcraft, 2002). Mathematics anxiety also has become accepted as an issue associated with academic success for both children and adults (Ashcraft, 2002; Ashcraft & Moore, 2009; Beilock,…
Patterson, Margaret Becker
Many adults with special needs, who did not finish high school, complete a GED® credential to go to college. As they prepare to transition, they may encounter barriers and likely require supports to succeed in college. The purpose of this qualitative research paper is to describe the college prospects of transitioning adults with a GED credential…
Full Text Available In recent years, drug release/dissolution from solid dosage forms has been the subject of intense and profitable scientific developments. Whenever a new solid dosage form is developed or produced, it is necessary to ensure that drug dissolutionoccurs in an appropriate manner. The pharmaceutical industry and the registration authorities do focus, nowadays, on drug dissolution studies. The quantitative analysis of the values obtained in dissolution/release tests is easier when mathematicalformulas that express the dissolution results as a function of some of the dosage forms characteristics are used. This work discusses the analysis of data obtained for dissolution profiles under different media pH conditions using mathematical methodsof analysis described by Moore and Flanner. These authors have described difference factor (f1 and similarity factor (f2, which can be used to characterise drug dissolution/release profiles. In this work we have used these formulas for evaluation of dissolution profiles of the conventional tablets in different pH of dissolution medium (range of physiological variations.
The Test of Early Mathematics Ability--Third Edition (TEMA-3) is a norm-referenced parallel forms test intended to identify the level of mathematical ability for children aged 3 years 0 months through 8 years 11 months. According to the authors, the instrument can also be used as a criterion referenced or diagnostic tool for older students who are…
Stein, Sherman K
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Hamid, Malai Hayati Sheikh; Shahrill, Masitah; Matzin, Rohani; Mahalle, Salwa; Mundia, Lawrence
The cross-sectional field survey examined the roles of mathematics anxiety, self-esteem, proactive coping, and test stress in mathematics achievement among 204 (151 females) randomly selected Year 8-10 Brunei secondary school students. The negative dimensions of mathematics anxiety, self-esteem, and proactive coping correlated negatively with…
Dass, Jane; Pine, Charles
The New Jersey College Basic Skills Placement Test (NJCBSPT) is designed to measure certain basic language and mathematics skills of students entering New Jersey colleges. The primary purpose of the two mathematics sections is to determine whether students are prepared to begin certain college-level work without a handicap in computation or…
This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive…
Carr, M.; Fidalgo, C.; Bigotte de Almeida, M. E.; Branco, J. R.; Santos, V.; Murphy, E.; Ní Fhloinn, E.
Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into…
Cornish, Greg; Wines, Robin
The Number Test of the ACER Mathematics Profile Series, contains 30 items, for each of three suggested grade levels: 7-8, 8-9, and 9-10. Raw scores on all tests in the ACER Mathematics Profile Series (Number, Operations, Space and Measurement) are converted to a common scale called MAPS, a major feature of the Series. Based on the Rasch Model,…
To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.
Campitelli, Guillermo; Gerrans, Paul
We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.
This study examined the impact of curricular factors and teaching practices on students' tested achievement in mathematics, explored the best predictors of the tested achievement, and examined differences in the tested achievement among student subgroups. The study utilized qualitative and quantitative methods and triangulated findings from…
Gamba, P.; Cavalca, D.; Jaiswal, K.S.; Huyck, C.; Crowley, H.
In order to quantify earthquake risk of any selected region or a country of the world within the Global Earthquake Model (GEM) framework (www.globalquakemodel.org/), a systematic compilation of building inventory and population exposure is indispensable. Through the consortium of leading institutions and by engaging the domain-experts from multiple countries, the GED4GEM project has been working towards the development of a first comprehensive publicly available Global Exposure Database (GED). This geospatial exposure database will eventually facilitate global earthquake risk and loss estimation through GEM’s OpenQuake platform. This paper provides an overview of the GED concepts, aims, datasets, and inference methodology, as well as the current implementation scheme, status and way forward.
Zhang, Yiyun; Zhou, Xinlin
Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD. © Hammill Institute on Disabilities 2014.
Hilgoe, Ellen; Brinkley, Jason; Hattingh, Johannes; Bernhardt, Robert
Since its establishment in 1996, the North Carolina Early Mathematics Placement Testing (NC EMPT) Program has provided a low stakes reality check of readiness for college-level mathematics to more than 600,000 high school students statewide. The program strives to help reduce the percentage of incoming college freshmen requiring mathematics…
King, Molly Elizabeth
The purpose of this quantitative, causal-comparative study was to compare the effect elementary music and visual arts lessons had on third through sixth grade standardized mathematics test scores. Inferential statistics were used to compare the differences between test scores of students who took in-school, elementary, music instruction during the…
Gadalla, Tahany M.
The equivalence of multiple-choice (MC) and constructed response (discrete) (CR-D) response formats as applied to mathematics computation at grade levels two to six was tested. The difference between total scores from the two response formats was tested for statistical significance, and the factor structure of items in both response formats was…
O'Dwyer, Laura M.; Russell, Michael; Bebell, Damian; Seeley, Kevon
Over the past decade, standardized test results have become the primary tool used to judge the effectiveness of schools and educational programs, and today, standardized testing serves as the keystone for educational policy at the state and federal levels. This paper examines the relationship between fourth grade mathematics achievement and…
Korhonen, Johan; Nyroos, Mikaela; Jonsson, Bert; Eklöf, Hanna
The aim of this study was to investigate the interplay between test anxiety and working memory (WM) on mathematics performance in younger children. A sample of 624 grade 3 students completed a test battery consisting of a test anxiety scale, WM tasks and the Swedish national examination in mathematics for grade 3. The main effects of test anxiety…
The present framework is developed under contract with the Smarter Balanced Assessment Consortium (SBAC) as a conceptual and methodological tool for guiding the reasonings and actions of contractors in charge of developing and providing test translation accommodations for English language learners. The framework addresses important challenges in…
Full Text Available Self-association of dynamin to form spiral structures around lipidic vesicles during endocytosis is largely mediated by its 'coiled coil' GTPase Effector Domain (GED, which, in vitro, self-associates into huge helical assemblies. Residue-level structural characterizations of these assemblies and understanding the process of association have remained a challenge. It is also impossible to get folded monomers in the solution phase. In this context, we have developed here a strategy to probe the self-association of GED by first dissociating the assembly using Dimethyl Sulfoxide (DMSO and then systematically monitoring the refolding into helix and concomitant re-association using NMR spectroscopy, as DMSO concentration is progressively reduced. The short segment, Arg109 - Met116, acts as the nucleation site for helix formation and self-association. Hydrophobic and complementary charge interactions on the surfaces drive self-association, as the helices elongate in both the directions resulting in an antiparallel stack. A small N-terminal segment remains floppy in the assembly. Following these and other published results on inter-domain interactions, we have proposed a plausible mode of dynamin self assembly.
Townsend, J T; Ashby, F G
A letter confusion experiment that used brief durations manipulated payoffs across the four stimulus letters, which were composed of line segments equal in length. The observers were required to report the features they perceived as well as to give a letter response. The early feature-sampling process is separated from the later letter-decision process in the substantive feature models, and predictions are thus obtained for the frequencies of feature report as well as letter report. Four substantive visual feature-processing models are developed and tested against one another and against three models of a more descriptive nature. The substantive models predict the decisional letter report phase much better than they do the feature-sampling phase, but the best overall 4 X 4 letter confusion matrix fits are obtained with one of the descriptive models, the similarity choice model. The present and other recent results suggest that the assumption that features are sampled in a stochastically independent manner may not be generally valid. The traditional high-threshold conceptualization of feature sampling is also falsified by the frequent reporting by observers of features not contained in the stimulus letter.
Toll, Sylke W. M.; Kroesbergen, Evelyn H.; Van Luit, Johannes E. H.
Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…
Pijls, M.; de Kramer, D.; Maj, B.; Pytlak, M.; Swoboda, E.
In an explorative research project, teachers experimented with new ideas to make their students discuss (i.e. show, explain, justify and reconstruct their work) their mathematical ideas with each other. Two kind of special tasks were developed: group tests and mind maps. Also, the role of the
Solano-Flores, Guillermo; Barnett-Clarke, Carne; Kachchaf, Rachel R.
We examined the performance of English language learners (ELLs) and non-ELLs on Grade 4 and Grade 5 mathematics content knowledge (CK) and academic language (AL) tests. CK and AL items had different semiotic loads (numbers of different types of semiotic features) and different semiotic structures (relative frequencies of different semiotic…
This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…
Sumantri, Mohamad Syarif; Satriani, Retni
The purpose of this research was to determine the effect of formative testing and self-directed learning on mathematics learning outcomes. The research was conducted at an elementary school in central Jakarta during the 2014/2015 school year. Seventy-two fourth-grade students who were selected using random sampling participated in this study. Data…
Dennison, E. W.; John, S. L.; Trentelman, G. F.
The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.
Nah, Kyeongah; Nishiura, Hiroshi; Tsuchiya, Naho; Sun, Xiaodan; Asai, Yusuke; Imamura, Akifumi
The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.
Toll, Sylke W M; Kroesbergen, Evelyn H; Van Luit, Johannes E H
Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. The aim of this study was to test the DD hypothesis within a longitudinal time span of 2 years. A total of 670 children participated. The mean age was 4.96 years at the start of the study and 7.02 years at the end of the study. At the end of the first year of kindergarten, both visual-spatial working memory and number sense were measured by two different tasks. At the end of first grade, mathematical performance was measured with two tasks, one for math facts and one for math problems. Multiple regressions revealed that both visual working memory and symbolic number sense are predictors of mathematical performance in first grade. Symbolic number sense appears to be the strongest predictor for both math areas (math facts and math problems). Non-symbolic number sense only predicts performance in math problems. Multivariate analyses of variance showed that a combination of visual working memory and number sense deficits (NSDs) leads to the lowest performance on mathematics. Our DD hypothesis was confirmed. Both visual working memory and symbolic number sense in kindergarten are related to mathematical performance 2 years later, and a combination of visual working memory and NSDs leads to low performance in mathematical performance. © 2016 The British Psychological Society.
Full Text Available This study examined individual differences in mathematics learning by combining antecedent (A, opportunity (O, and propensity (P indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD. Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6 with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task
Baten, Elke; Desoete, Annemie
This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers' experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O
Egorova, Marina S.
Full Text Available Academic achievement, which is inherently an indicator of progress in the curriculum, can also be viewed as an indirect measure of cognitive development, social adaptation, and motivational climate characteristics. In addition to its direct application, academic achievement is used as a mediating factor in the study of various phenomena, from the etiology of learning disabilities to social inequality. Analysis of sex differences in mathematical achievement is considered particularly important for exploring academic achievement, since creating an adequate educational environment with equal opportunities for boys and girls serves as a prerequisite for improving the overall mathematical and technical literacy that is crucial for modern society, creates balanced professional opportunities, and destroys traditional stereotypes about the roles of men and women in society. The objective of our research was to analyze sex differences in mathematical achievement among high school students and to compare various methods for diagnosing academic performance, such as school grades, test scores, and self-concept. The results were obtained through two population studies whose samples are representative of the Russian population in the relevant age group. Study 1 looked at sex differences in math grades among twins (n = 1,234 pairs and singletons (n = 2,227 attending high school. The sample of Study 2 comprised all twins who took the Unified State Examination in 2010–2012. The research analyzed sex differences in USE math scores across the entire sample and within the extreme subgroups. It also explored differences between boys and girls in opposite-sex dizygotic (DZ twin pairs. The key results were as follows. No difference in mathematical achievement was observed between twins and singletons. Sex differences were found in all measures of mathematical achievement. Girls had higher school grades in math than boys, while boys outperformed girls in USE math
Full Text Available This paper presents a novel methodology based on semistatic nondestructive testing of fish for the analytical computation of its textural characteristics via closed-form mathematical expressions. The novelty is that, unlike alternatives, explicit values for both stiffness and viscoelastic textural attributes may be computed, even if fish of different size/weight are tested. Furthermore, the testing procedure may be adapted to the specifications (sampling rate and accuracy of the available equipment. The experimental testing involves a fish placed on the pan of a digital weigh scale, which is subsequently tested with a ramp-like load profile in a custom-made installation. The ramp slope is (to some extent adjustable according to the specification (sampling rate and accuracy of the equipment. The scale’s reaction to fish loading, namely, the reactive force, is collected throughout time and is shown to depend on the fish textural attributes according to a closed-form mathematical formula. The latter is subsequently used along with collected data in order to compute these attributes rapidly and effectively. Four whole raw sea bass (Dicentrarchus labrax of various sizes and textures were tested. Changes in texture, related to different viscoelastic characteristics among the four fish, were correctly detected and quantified using the proposed methodology.
This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive conflicts. In the data analysis, one can identify three types of difficulties, relevant to object-level learning: namely regarding the frequently observed confusion between groups and sets, the object-level rules of visual mediators, and the object-level rules of contextual notions, such as permutations, exponentials, sets and matrices. In addition, data analysis suggests two types of difficulties, relevant to metalevel learning. The first refers to the actual proof that the three conditions of subgroup test hold, and the second is related to syntactic inaccuracies, incomplete argumentation and problematic use of visual mediators. Finally, this study suggests that there are clear links between object-level and metalevel learning, mainly due to the fact that objectification of the various relevant mathematical notions influences the endorsement of the governing metarules.
Klinglmayr, Eva; Wenger, Julia; Mayr, Sandra; Bossy-Wetzel, Ella; Puehringer, Sandra
The crystallization and initial diffraction analysis of human Drp1 GTPase-GED fusion protein are reported. The mechano-enzyme dynamin-related protein 1 plays an important role in mitochondrial fission and is implicated in cell physiology. Dysregulation of Drp1 is associated with abnormal mitochondrial dynamics and neuronal damage. Drp1 shares structural and functional similarities with dynamin 1 with respect to domain organization, ability to self-assemble into spiral-like oligomers and GTP-cycle-dependent membrane scission. Structural studies of human dynamin-1 have greatly improved the understanding of this prototypical member of the dynamin superfamily. However, high-resolution structural information for full-length human Drp1 covering the GTPase domain, the middle domain and the GTPase effector domain (GED) is still lacking. In order to obtain mechanistic insights into the catalytic activity, a nucleotide-free GTPase-GED fusion protein of human Drp1 was expressed, purified and crystallized. Initial X-ray diffraction experiments yielded data to 2.67 Å resolution. The hexagonal-shaped crystals belonged to space group P2 1 2 1 2, with unit-cell parameters a = 53.59, b = 151.65, c = 43.53 Å, one molecule per asymmetric unit and a solvent content of 42%. Expression of selenomethionine-labelled protein is currently in progress. Here, the expression, purification, crystallization and X-ray diffraction analysis of the Drp1 GTPase-GED fusion protein are presented, which form a basis for more detailed structural and biophysical analysis
Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
This report provides documentation of the mathematical basis for a colloid-facilitated radionuclide transport modeling capability that can be incorporated into GDSA-PFLOTRAN. It also provides numerous test cases against which the modeling capability can be benchmarked once the model is implemented numerically in GDSA-PFLOTRAN. The test cases were run using a 1-D numerical model developed by the author, and the inputs and outputs from the 1-D model are provided in an electronic spreadsheet supplement to this report so that all cases can be reproduced in GDSA-PFLOTRAN, and the outputs can be directly compared with the 1-D model. The cases include examples of all potential scenarios in which colloid-facilitated transport could result in the accelerated transport of a radionuclide relative to its transport in the absence of colloids. Although it cannot be claimed that all the model features that are described in the mathematical basis were rigorously exercised in the test cases, the goal was to test the features that matter the most for colloid-facilitated transport; i.e., slow desorption of radionuclides from colloids, slow filtration of colloids, and equilibrium radionuclide partitioning to colloids that is strongly favored over partitioning to immobile surfaces, resulting in a substantial fraction of radionuclide mass being associated with mobile colloids.
Full Text Available The study deals with the possibility of substituting time- and material-demanding mechanical testing of a bone defect fixation by mathematical modelling. Based on the mechanical model, a mathematical model of bone-implant construct stabilizing experimental segmental femoral bone defect (segmental ostectomy in a miniature pig ex vivo model using 4.5 mm titanium LCP was created. It was subsequently computer-loaded by forces acting parallel to the long axis of the construct. By the effect of the acting forces the displacement vector sum of individual construct points occurred. The greatest displacement was noted in the end segments of the bone in close proximity to ostectomy and in the area of the empty central plate hole (without screw at the level of the segmental bone defect. By studying the equivalent von Mises stress σEQV on LCP as part of the tested construct we found that the greatest changes of stress occur in the place of the empty central plate hole. The distribution of this strain was relatively symmetrical along both sides of the hole. The exceeding of the yield stress value and irreversible plastic deformations in this segment of LCP occurred at the acting of the force of 360 N. These findings are in line with the character of damage of the same construct loaded during its mechanic testing. We succeeded in creating a mathematical model of the bone-implant construct which may be further used for computer modelling of real loading of similar constructs chosen for fixation of bone defects in both experimental and clinical practice.
It is well documented in both the British press and mathematics education literature that many consider A-levels (qualifications for secondary school leavers in England, Wales and Northern Ireland) to be insufficient preparation for undergraduate mathematics study in the UK. A-level Mathematics and Further Mathematics are not solely intended for…
Nazzal, Ali; Oki, Masato
Discomfort glare from daylight is a common problem without valid prediction methods so far. A new mathematical DGIN (New Daylight Glare Index) method tries to respond the challenge. This paper reports on experiments carried out in daylit office environment in Japan to test applicability of the method. Slight positive correlation was found between the DGIN and the subjective evaluation. Additionally, a high Ladaptation value together with the small ratio of Lwindow to Ladaptation was obviously experienced sufficient to neutralize the effect of glare discomfort. However, subjective assessments are poor glare indicators and not reliable in testing glare prediction methods. DGIN is a good indicator of daylight glare, and when the DGIN value is analyzed together with the measured illuminance ratios, discomfort glare from daylight can be analyzed in a quantitative manner. The DGIN method could serve architects and lighting designers in testing daylighting systems, and also guide the action of daylight responsive lighting controls.
Fişek, M Hamit; Barlas, Zeynep
This paper presents statistical procedures for improving the goodness-of-fit testing of theoretical models to data obtained from laboratory experiments. We use an experimental study in the expectation states research tradition which has been carried out in the "standardized experimental situation" associated with the program to illustrate the application of our procedures. We briefly review the expectation states research program and the fundamentals of resampling statistics as we develop our procedures in the resampling context. The first procedure we develop is a modification of the chi-square test which has been the primary statistical tool for assessing goodness of fit in the EST research program, but has problems associated with its use. We discuss these problems and suggest a procedure to overcome them. The second procedure we present, the "Average Absolute Deviation" test, is a new test and is proposed as an alternative to the chi square test, as being simpler and more informative. The third and fourth procedures are permutation versions of Jonckheere's test for ordered alternatives, and Kendall's tau(b), a rank order correlation coefficient. The fifth procedure is a new rank order goodness-of-fit test, which we call the "Deviation from Ideal Ranking" index, which we believe may be more useful than other rank order tests for assessing goodness-of-fit of models to experimental data. The application of these procedures to the sample data is illustrated in detail. We then present another laboratory study from an experimental paradigm different from the expectation states paradigm - the "network exchange" paradigm, and describe how our procedures may be applied to this data set. Copyright © 2012 Elsevier Inc. All rights reserved.
Harackiewicz, Judith M; Rozek, Christopher S; Hulleman, Chris S; Hyde, Janet S
The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem.
Izzuddin, Nur; Sunarsih,; Priyanto, Agoes [Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor (Malaysia)
As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the target vessel’s speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel’s speed to obtain better characteristics and hence optimize the fuel saving rate.
Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming
Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.
Julie, Hongki; Sanjaya, Febi; Anggoro, Ant. Yudhi
One of purposes of this study was to describe the solution profile of the junior high school students for the PISA adaptation test. The procedures conducted by researchers to achieve this objective were (1) adapting the PISA test, (2) validating the adapting PISA test, (3) asking junior high school students to do the adapting PISA test, and (4) making the students' solution profile. The PISA problems for mathematics could be classified into four areas, namely quantity, space and shape, change and relationship, and uncertainty. The research results that would be presented in this paper were the result test for uncertainty problems. In the adapting PISA test, there were fifteen questions. Subjects in this study were 18 students from 11 junior high schools in Yogyakarta, Central Java, and Banten. The type of research that used by the researchers was a qualitative research. For the first uncertainty problem in the adapting test, 66.67% of students reached level 3. For the second uncertainty problem in the adapting test, 44.44% of students achieved level 4, and 33.33% of students reached level 3. For the third uncertainty problem in the adapting test n, 38.89% of students achieved level 5, 11.11% of students reached level 4, and 5.56% of students achieved level 3. For the part a of the fourth uncertainty problem in the adapting test, 72.22% of students reached level 4 and for the part b of the fourth uncertainty problem in the adapting test, 83.33% students achieved level 4.
Beck, T.; Bieler, A.; Thomas, N.
We present structural and thermal model (STM) tests of the BepiColombo laser altimeter (BELA) receiver baffle with emphasis on the correlation of the data with a thermal mathematical model. The test unit is a part of the thermal and optical protection of the BELA instrument being tested under infrared and solar irradiation at University of Bern. An iterative optimization method known as particle swarm optimization has been adapted to adjust the model parameters, mainly the linear conductivity, in such a way that model and test results match. The thermal model reproduces the thermal tests to an accuracy of 4.2 °C ± 3.2 °C in a temperature range of 200 °C after using only 600 iteration steps of the correlation algorithm. The use of this method brings major benefits to the accuracy of the results as well as to the computational time required for the correlation. - Highlights: ► We present model correlations of the BELA receiver baffle to thermal balance tests. ► Adaptive particle swarm optimization has been adapted for the correlation. ► The method improves the accuracy of the correlation and the computational time.
Carroll, William M.
Reports on the results of the reform curriculum of the University of Chicago School Mathematics Project's elementary curriculum, Everyday Mathematics, for third-grade students. Results included the fact that only 2% of UCSMP students failed to meet state goals. UCSMP students also scored well in all mathematical areas including number skills and…
Tsui, Joanne M.; Mazzocco, Michele M. M.
This study was designed to examine the effects of math anxiety and perfectionism on math performance, under timed testing conditions, among mathematically gifted sixth graders. We found that participants had worse math performance during timed versus untimed testing, but this difference was statistically significant only when the timed condition…
Full Text Available The study of Mathematics has been and is still a source of frustration and anxiety for a large number of students. The purpose of this study was to inquire systematically upon levels of test anxiety through behavioral and physiological procedures before and after a Math test, in 205 senior high school students. Academic worries were assessed by means of a computerized task based on the emotional version of the Stroop paradigm designed ex profeso to measure school anxiety (Hernández-Pozo, Macías & Torres, 2004. The Stroop task was administered, along with recordings of blood pressure and pulse, before and after the first Math test of the course. Academic general scores were inverse to the behavioral anxiety level, however the best Math scores were associated to middle levels of behavioral anxiety. Contradictory findings between academic performance in Math and global score, and the apparent lack of gender difference in anxiety measured through behavioral procedures suggests the need to review the generality of previous assertions relating academic performance inversely with levels of anxiety of high school students.
Westlund, Jonathan; Bostroem, Anders
Nondestructive testing with ultrasound is a standard procedure in the nuclear power industry. To develop and qualify the methods extensive experimental work with test blocks is usually required. This can be very time-consuming and costly and it also requires a good physical intuition of the situation. A reliable mathematical model of the testing situation can, therefore, be very valuable and cost-effective as it can reduce experimental work significantly. A good mathematical model enhances the physical intuition and is very useful for parametric studies, as a pedagogical tool, and for the qualification of procedures and personnel. The aim of the present report is to describe work that has been performed to model ultrasonic testing of components that contain a defect close to a nonplanar surface. For nuclear power applications this may be a crack or other defect on the inside of a pipe with a diameter change or connection. This is an extension of the computer program UTDefect, which previously only admits a planar back surface (which is often applicable also to pipes if the pipe diameter is large enough). The problems are investigated in both 2D and 3D, and in 2D both the simpler anti-plane (SH) and the in-plane (P-SV) problem are studied. The 2D investigations are primarily solved to get a 'feeling' for the solution procedure, the discretizations, etc. In all cases an integral equation approach with a Green's function in the kernel is taken. The nonplanar surface is treated by the boundary element method (BEM) where a division of the surface is made in small elements. The defects are mainly cracks, strip-like (in 2D) or rectangular (in 3D), and these are treated with more analytical methods. In 2D also more general defects are treated with the help of their transition (T) matrix. As in other parts of UTDefect the ultrasonic probes in transmission and reception are included in the model. In 3D normalization by a side drilled hole is possible. Some numerical results
Full Text Available Abstract Background Chiropractors use a variety of supine and prone leg checking procedures. Some, including the Allis test, purport to distinguish anatomic from functional leg length inequality. Although the reliability and to a lesser extent the validity of some leg checking procedures has been assessed, little is known on the Allis test. The present study mathematically models the test under a variety of hypothetical clinical conditions. In our search for historical and clinical information on the Allis test, nomenclatural and procedural issues became apparent. Methods The test is performed with the subject carefully positioned in the supine position, with the head, pelvis, and feet centered on the table. After an assessment for anatomic leg length inequality, the knees are flexed to approximately 90°. The examiner then sights the short leg side knee sequentially from both the foot and side of the table, noting its relative locations: both its height from the table and Y axis position. The traditional interpretation of the Allis test is that a low knee identifies a short tibia and a cephalad knee a short femur. Assuming arbitrary lengths and a tibio/femoral ratio of 1/1.26, and a hip to foot distance that placed the knee near 90°, we trigonometrically calculated changes in the location of the right knee that would result from hypothetical reductions in tibial and femoral length. We also modeled changes in the tibio/femoral ratio that did not change overall leg length, and also a change in hip location. Results The knee altitude diminishes with either femoral or tibial length reduction. The knee shifts cephalad when the femoral length is reduced, and caudally when the tibial length is reduced. Changes in the femur/tibia ratio also influence knee position, as does cephalad shifting of the hip. Conclusion The original Allis (aka Galeazzi test was developed to identify gross hip deformity in pediatric patients. The extension of this test to
Diamantopoulou, Sofia; Pina, Violeta; Valero-Garcia, Ana V.; Gonzalez-Salinas, Carmen; Fuentes, Luis J.
This study validated the four mathematics tests of the Spanish version of the Woodcock-Johnson III (WJ-III) Achievement (ACH) battery for use in the first six grades of school in Spain. Developmental effects and gender differences were also examined. Participants were a normal population sample of 424 (216 boys) children aged 6 to 13 years.…
Igbojinwaekwu, Patrick Chukwuemeka
This study investigated, using pretest-posttest quasi-experimental research design, the effectiveness of guided multiple choice objective questions test on students' academic achievement in Senior School Mathematics, by school location, in Delta State Capital Territory, Nigeria. The sample comprised 640 Students from four coeducation secondary…
Full Text Available Romania occupied a back position in the international tests on Mathematics and Sciences. Teachers stress out that one possible cause of this situation could be finding on the Mathematics and Sciences curricula. This paper presents the results of the comparisons of the Romanian curricula with the curricula promoted by the international testing (PISA 2000, 2003 and 2006, and TIMSS 1995, 1999, 2003, 2007 and the curricula of the countries occupied the first places in these tests. The comparisons underline those curricula approaches, which insure success on these tests and realize the reasons of the lack of success of the Romanian pupils. These results will be presented to the curriculum makers, universities and schools, to identify the specific and transferable competencies of the pupils with success in the above-mentioned disciplines.
Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.
The Mathematics Fluency and Calculation Tests (MFaCTs) are a series of measures designed to assess for arithmetic calculation skills and calculation fluency in children ages 6 through 18. There are five main purposes of the MFaCTs: (1) identifying students who are behind in basic math fact automaticity; (2) evaluating possible delays in arithmetic…
Steele, Marcee M.
This article reviews characteristics of high school students with learning disabilities and presents instructional modifications and study skills to help them succeed in algebra and geometry courses and on high stakes mathematics assessments.
This groundbreaking work features two essays written by the renowned mathematician Ilan Vardi. The first essay presents a thorough analysis of contrived problems suggested to "undesirable" applicants to the Department of Mathematics of Moscow University. His second essay gives an in-depth discussion of solutions to the Year 2000 International Mathematical Olympiad, with emphasis on the comparison of the olympiad problems to those given at the Moscow University entrance examinations. The second part of the book provides a historical background of a unique phenomenon in mathematics, which flourished in the 1970s-80s in the USSR. Specially designed math problems were used not to test students' ingenuity and creativity but, rather, as "killer problems," to deny access to higher education to "undesirable" applicants. The focus of this part is the 1980 essay, "Intellectual Genocide", written by B Kanevsky and V Senderov. It is being published for the first time. Also featured is a little-known page of the Soviet hi...
Pestman, Wiebe R
This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.
Ellington, Aimee J.; Whitenack, Joy W.; Inge, Vickie L.; Murray, Megan K.; Schneider, Patti J.
This article describes the design and implementation of an assessment instrument for Numbers and Operations, the first course in a program to train elementary mathematics specialists. We briefly describe the course and its content, and then we elaborate on the process we used to develop the assessment instrument and the corresponding rubric for…
Snyman, G.C.; Smith, S.W.
The application of mathematical models to evaluate tracer experiments is illustrated by examples of tests done in a variety of industrial plants, using radioactive tracers. Two basic models, the axial mixing model and the perfectly mixed tank model, as well as various applicational techniques, are described. It is concluded that many processes can be simulated to various degrees of accuracy by using the basic models, and that both quantitative and qualitative information can be obtained about the process [af
Donovan, Diane; Loch, Birgit
How can active learning, peer learning and prompt feedback be achieved in large first-year mathematics classes? Further, what technologies may support these aims? In this article, we assert that test revision sessions in first-year mathematics held in a technology-enhanced lecture theatre can be highly interactive with students solving problems, learning from each other and receiving immediate feedback. This is facilitated by pen-enabled screens and synchronization software. We argue that the educational benefits achievable through the technology do outweigh the technological distractions, and that these benefits can be achieved by focused, targeted one-off sessions and not only by a semester-long, regular approach. Repeat mid-semester test revision sessions were offered on a non-compulsory basis using pen-enabled screens for all students. Students worked practice test questions and marked solutions to mathematical problems on the screens. Students' work was then displayed anonymously for their peers to see. Answers were discussed with the whole class. We discuss outcomes from two offerings of these sessions using student feedback and lecturer reflections and show the impact of participation on self-reported student confidence. Pedagogical approaches that the technology allowed for the first time in a large class are highlighted. Students responded uniformly positively.
Full Text Available Skin factor is often regarded as a constant in most of the mathematical model for well test analysis in oilfields, but this is only a kind of simplified treatment with the actual skin factor changeable. This paper defined the average permeability of a damaged area as a function of time by using the definition of skin factor. Therefore a relationship between a variable skin factor and time was established. The variable skin factor derived was introduced into existing traditional models rather than using a constant skin factor, then, this newly derived mathematical model for well test analysis considering variable skin factor was solved by Laplace transform. The dimensionless wellbore pressure and its derivative changed with dimensionless time were plotted with double logarithm and these plots can be used for type curve fitting. The effects of all the parameters in the expression of variable skin factor were analyzed based on the dimensionless wellbore pressure and its derivative. Finally, actual well testing data were used to fit the type curves developed which validates the applicability of the mathematical model from Sheng-2 Block, Shengli Oilfield, China.
Callahan, Janet; Belcheir, Marcia
Methods that provide an early indicator of factors that affect student persistence are important to colleges and universities. This quantitative research focused on the role of level of entry mathematics and English and also on grades earned in those classes, as they relate to persistence after 1 year. The research showed that by far, the variable…
Ryan, Katherine E.; Fan, Meichu
Results for 3,244 female and 3,033 male junior high school students from the Second International Mathematics Study show that applied items in algebra, geometry, and computation were easier for males but arithmetic items were differentially easier for females. Implications of these findings for assessment and instruction are discussed. (SLD)
Doabler, Christian T.; Clarke, Ben; Kosty, Derek B.; Kurtz-Nelson, Evangeline; Fien, Hank; Smolkowski, Keith; Baker, Scott K.
The purpose of this closely aligned conceptual replication study was to investigate the efficacy of a Tier 2 kindergarten mathematics intervention. The replication study differed from the initial randomized controlled trial on three important elements: geographical region, timing of the intervention, and instructional context of the…
Sternberg, Robert J.; Jarvin, Linda; Birney, Damian P.; Naples, Adam; Stemler, Steven E.; Newman, Tina; Otterbach, Renate; Parish, Carolyn; Randi, Judy; Grigorenko, Elena L.
This study addressed whether prior successes with educational interventions grounded in the theory of successful intelligence could be replicated on a larger scale as the primary basis for instruction in language arts, mathematics, and science. A total of 7,702 4th-grade students in the United States, drawn from 223 elementary school classrooms in…
As the largest international study ever taken in history, the Trend in Mathematics and Science Study (TIMSS) has been held as a benchmark to measure U.S. student performance in the global context. In-depth analyses of the TIMSS project are conducted in this study to examine key issues of the comparative investigation: (1) item flaws in mathematics…
Toll, Sylke; Kroesbergen, Evelyn; Van Luit, Johannes E H
Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD)
Conclusion The results demonstrate that children with mathematical learning disorders were significantly worse than their normal peers in all three domains. Findings indicated that “Test of Everyday Attention for Children” has the potential to evaluate the attention deficits in mathematical learning disorder as compared with normal peers. Therefore, it can be an appropriate tool for the evaluation in this group.
Eighth-grade students in New Jersey take the Early Warning Test (EWT), which involves reading, writing, and mathematics. Students with EWT scores below the state level of competency take a remedial mathematics course that provides students with computer-assisted instruction (2 days per week) as well as regular classroom instruction (3 days per…
Full Text Available The purpose of this research is trying to identify epistemological obstacles which were experienced by Indonesian students in answering PISA test for mathematics literacy content uncertainty and data. Epistemological obstacles was identified by giving a test to the respondent, students of grade 7th and 8th who have studied data representation in the class. Respondents’ work analysed by qualitative method. The result showed that respondents have epistemological obstacles in reading the data, reading between the data, and reading beyond the data. To gain further understanding, some respondents chose to be interviewed.
Tsui, Joanne M.; Mazzocco, Michèle M. M.
This study was designed to examine the effects of math anxiety and perfectionism on math performance, under timed testing conditions, among mathematically gifted sixth graders. We found that participants had worse math performance during timed versus untimed testing, but this difference was statistically significant only when the timed condition preceded the untimed condition. We also found that children with higher levels of either math anxiety or perfectionism had a smaller performance discrepancy during timed versus untimed testing, relative to children with lower levels of math anxiety or perfectionism. There were no statistically significant gender differences in overall test performance, nor in levels of math anxiety or perfectionism; however, the difference between performance on timed and untimed math testing was statistically significant for girls, but not for boys. Implications for educators are discussed. PMID:20084180
Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.
Full Text Available This article describes the academic performance of students from urban and distant areas in the national mathematics test corresponding to the completion of secondary education, considering the specific test and according to the different types of schools: daytime (daytime scientific, daytime humanistic, nighttime, technical or integrated centers for education of young people and adults (CINDEA, in its Spanish acronym. The main objective is to describe the students academic performance in the national mathematics test issued to complete high-school level, for the year 2013 and according to the country educational areas. For the analysis of such information, the main source used was the High-School Education National Report, issued by the Ministry of Public Education for 2013 standardized tests. One of the conclusions from this study is the need to carry out a historical analysis of the performance of educational institutions which have recently obtained the highest and lowest average grades in the high-school diploma tests, in order to be able to delve into the causes of those performances.
Wiggs, G. F. S.
There are few empirical measurements of velocity, shear velocity, sand transport, morphological change on the windward slopes of dunes.This thesis compares field measurements on a barchan dune in Oman with calculations using a mathematical model (FLOWSTAR) and measurements in a wind tunnel. All three techniques demonstrate similar patterns of velocity, confirming the acceleration of flow up the windward slope, deceleration between the crest and brink and significant flow decele...
Full Text Available Functional magnetic resonance imaging (fMRI measures brain activity by detecting the blood-oxygen-level dependent (BOLD response to neural activity. The BOLD response depends on the neurovascular coupling, which connects cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level to neuronal activity. The exact mechanisms behind this neurovascular coupling are not yet fully investigated. There are at least three different ways in which these mechanisms are being discussed. Firstly, mathematical models involving the so-called Balloon model describes the relation between oxygen metabolism, cerebral blood volume, and cerebral blood flow. However, the Balloon model does not describe cellular and biochemical mechanisms. Secondly, the metabolic feedback hypothesis, which is based on experimental findings on metabolism associated with brain activation, and thirdly, the neurotransmitter feed-forward hypothesis which describes intracellular pathways leading to vasoactive substance release. Both the metabolic feedback and the neurotransmitter feed-forward hypotheses have been extensively studied, but only experimentally. These two hypotheses have never been implemented as mathematical models. Here we investigate these two hypotheses by mechanistic mathematical modeling using a systems biology approach; these methods have been used in biological research for many years but never been applied to the BOLD response in fMRI. In the current work, model structures describing the metabolic feedback and the neurotransmitter feed-forward hypotheses were applied to measured BOLD responses in the visual cortex of 12 healthy volunteers. Evaluating each hypothesis separately shows that neither hypothesis alone can describe the data in a biologically plausible way. However, by adding metabolism to the neurotransmitter feed-forward model structure, we obtained a new model structure which is able to fit the estimation data and successfully predict new
Malone, R.; Wang, X.J.
BY WRITING BOTH A CUSTOM WINDOWS(NTTM) DYNAMIC LINK LIBRARY AND GENERIC COMPANION SERVER SOFTWARE, THE INTRINSIC FUNCTIONS OF MATHSOFT MATHCAD(TM) HAVE BEEN EXTENDED WITH NEW CAPABILITIES WHICH PERMIT DIRECT ACCESS TO THE CONTROL SYSTEM DATABASES OF BROOKHAVEN NATIONAL LABORATORY ACCELERATOR TEST FACILITY. UNDER THIS SCHEME, A MATHCAD WORKSHEET EXECUTING ON A PERSONAL COMPUTER BECOMES A CLIENT WHICH CAN BOTH IMPORT AND EXPORT DATA TO A CONTROL SYSTEM SERVER VIA A NETWORK STREAM SOCKET CONNECTION. THE RESULT IS AN ALTERNATIVE, MATHEMATICALLY ORIENTED VIEW OF CONTROLLING THE ACCELERATOR INTERACTIVELY
Paulo Cesar Chagas Rodrigues
Full Text Available Acquire and produce what is strictly necessary are the goals of the organizations, since they aim companies more competitive and thereby reducing production costs. The research method is applied in nature, with a qualitative and quantitative approach, in which the objective of the research will be: exploratory and descriptive, with technical procedures, divided into: bibliographic, documentary, survey and concluding with a case study. On this assumption the main objective of this research is to develop and analyze a mathematical model that minimizes costs and maximizes the postponement of stocks in a company in the pulp, paper and paper products. Having been found only four papers, two articles and two theses that deal with the issue of demand management, supply chain and inventory postponement. These studies address the issue by modeling the productive time of the supply chain. For production segments this research may enable development of management practices demand and production strategy, allowing cost reductions and productivity gains possible. With the development of the mathematical model could ever analyze the behavior of demand and its influence on the productive strategy, strategy formulation regarding the purchase of raw materials and finished product storage in the last four years the company's results for the proposed model.
Hui, Eddie C. M.; Zheng, Xian; Wang, Hui
This study investigates property securities bubbles and crashes by using a dynamic mathematical methodology developed from the previous research (Watanabe et al. 2007a, b [31,32]). The improved model is used to detect the bubble and crash periods in five international countries/cities (namely, United States, United Kingdom, Japan, Hong Kong and Singapore) from Jan, 2000 to Oct, 2008. By this model definition, we are able to detect the beginning of each bubble period even before it bursts. Meanwhile, the empirical results show that most of property securities markets experienced bubble periods between 2003 and 2007, and crashes happened in Apr 2008 triggered by the Subprime Mortgage Crisis of US. In contrast, Japan suffered the shortest bubble period and no evidence has documented the existence of crash there.
Full Text Available This study used a randomized controlled trial design to investigate the ROOTS curriculum, a 50-lesson kindergarten mathematics intervention. Ten ROOTS-eligible students per classroom (n = 60 were randomly assigned to one of three conditions: a ROOTS five-student group, a ROOTS two-student group, and a no-treatment control group. Two primary research questions were investigated as part of this study: What was the overall impact of the treatment (the ROOTS intervention as compared with the control (business as usual? Was there a differential impact on student outcomes between the two treatment conditions (two- vs. five-student group? Initial analyses for the first research question indicated a significant impact on three outcomes and positive but nonsignificant impacts on three additional measures. Results for the second research question, comparing the two- and five-student groups, indicated negligible and nonsignificant differences. Implications for practice are discussed.
Suppression Test (DST) The dexamethasone suppression test (DST) is a pharmacological challenge test typically used to identify the cause of abnormal ...suppres- sion is in effect. One way to further probe the system is to combine a nonpharmacological, psychological stressor with the DST. The ensuing...second stage of our proposed test, we assume Iext(t) to be a positive constant when the external ( psychological ) stressor is on, and zero while off. In
Simzar, Rahila M; Martinez, Marcela; Rutherford, Teomara; Domina, Thurston; Conley, AnneMarie M
This study uses data from an urban school district to examine the relation between students' motivational beliefs about mathematics and high- versus low-stakes math test performance. We use ordinary least squares and quantile regression analyses and find that the association between students' motivation and test performance differs based on the stakes of the exam. Students' math self-efficacy and performance avoidance goal orientation were the strongest predictors for both exams; however, students' math self-efficacy was more strongly related to achievement on the low-stakes exam. Students' motivational beliefs had a stronger association at the low-stakes exam proficiency cutoff than they did at the high-stakes passing cutoff. Lastly, the negative association between performance avoidance goals and high-stakes performance showed a decreasing trend across the achievement distribution, suggesting that performance avoidance goals are more detrimental for lower achieving students. These findings help parse out the ways motivation influences achievement under different stakes.
Wilson, R. G.
The diffraction theory of the Foucault test provides an integral formula expressing the complex amplitude and irradiance distribution in the Foucault pattern of a test mirror (lens) as a function of wavefront error. Recent literature presents methods of inverting this formula to express wavefront error in terms of irradiance in the Foucault pattern. The present paper describes a study in which the inversion formulation was applied to photometric Foucault-test measurements on a nearly diffraction-limited mirror to determine wavefront errors for direct comparison with ones determined from scatter-plate interferometer measurements. The results affirm the practicability of the Foucault test for quantitative wavefront analysis of very small errors, and they reveal the fallacy of the prevalent belief that the test is limited to qualitative use only. Implications of the results with regard to optical testing and the potential use of the Foucault test for wavefront analysis in orbital space telescopes are discussed.
Takayanagi, M.; Suzuki, S.; Okamura, T.; Haas, E.E.; Krutzik, N.J.
To verify the beam-type and oval-type vibratory characteristics of a spherical shell structure, two test specimens were made and vibration tests were carried out. Results of these tests are compared with results of detailed analyses using 3-D FEM and 2-D axisymmetric FEM models. The analytical results of overall vibratory characteristics are in good agreement with the test results, has been found that the effect of the attached mass should be considered in evaluating local vibration. The replacing method into equivalent beam model is proposed
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
The purpose of this research is to determine mathematics teacher candidates' conceptual structures about the concept of "measurement" that is the one of the important learning fields of mathematics. Qualitative research method was used in this study. Participants of this study were 58 mathematics teacher candidates studying in one of the…
Townsend, Neal R.; Wheatley, Grayson H.
Sixteen beginning analytic geometry and calculus classes (442 students) followed eight testing regimes for one academic quarter. Three aptitude subgroups were identified in each class. Classes to which daily quizzes were given achieved significantly higher on a specially constructed test than those which had only a single midterm examination.…
Elkjær, Lars Skou; Bech, Bodil Hammer; Sun, Yuelian; Laursen, Thomas Munk; Christensen, Jakob
Valproate sodium is used for the treatment of epilepsy and other neuropsychiatric disorders in women of childbearing potential. However, there are concerns about impaired cognitive development in children who have been exposed to valproate during pregnancy. To estimate the association between long-term school performance and prenatal exposure to valproate and a number of other antiepileptic drugs (AEDs). In a prospective, population-based cohort study conducted from August 1, 2015, to May 31, 2017, data used in the study were provided by Statistics Denmark on April 15, 2016. All children born alive in Denmark between 1997 and 2006 (n = 656 496) were identified. From this cohort, children who did not participate in the national tests, with presumed coding errors in gestational age and children missing information on their mother's educational level or household income were excluded (n = 177 469) leaving 479 027 children for the analyses. Children were identified and linked across national registers that had information on exposure, covariates, and outcome. The primary outcome was performance in national tests, an academic test taken by students in Danish primary and lower secondary state schools. We assessed performance in Danish and mathematics at different grades among valproate-exposed children and compared their performance with that of unexposed children and children exposed to another AED (lamotrigine). Test scores were standardized to z scores and adjusted for risk factors. Difference in standardized z scores in Danish and mathematics tests among valproate-exposed children compared with unexposed and lamotrigine-exposed children. Of the 656 496 children identified, 479 027 children who participated in the national tests were evaluated, including children exposed to the following AEDs in monotherapy: valproate, 253; phenobarbital, 86; oxcarbazepine, 236; lamotrigine, 396; clonazepam, 188; and carbamazepine, 294. The mean (SD) age of the 244 095
Vogt, Natalja; Abaev, Maxim A.; Rykov, Anatolii N.; Shishkov, Igor F.
The molecular structure of succinic acid has been investigated by the gas-phase electron diffraction (GED) method for the first time. According to predictions of MP2/cc-pVTZ calculations, the molecule has 18 stable conformers with the C sbnd C sbnd C sbnd C chain in the gauche ( G) or anti ( A) configuration, and four of them, I ( G), II ( A), III ( G) and IV ( A) belonging to the C 2, C 2h, C 1 and C 1 point groups, respectively, with relative energies ΔE ZPE within 2.2 kcal/mol can be present at the experimental temperature of 445 K in noticeable amounts. The ratio of the conformers I:II:III:IV = 45(15):20(15):10(assumed):25(15) (in %) has been determined in the GED analysis guided by theoretical predictions. To take into account vibrational effects, the corrections Δ( r e - r a) to the experimental r a bond lengths were calculated from the MP2/cc-pVTZ quadratic and cubic force constants. The obtained equilibrium structural parameters of the dominant conformer I are the following (bond lengths in Å, angles in degrees): r e(C sp3sbnd C sp3) = 1.508(3), r e(C sp3sbnd C sp2) = 1.499(2), r e(C sbnd O) = 1.343(2), r e(C dbnd O) = 1.202(1), e(C sbnd C sbnd C) = 111.8(4), e(C sbnd C sbnd O) = 112.0(4), e(O sbnd C dbnd O) = 123.0(1), τ(C sbnd C sbnd C sbnd C) = 69.9(11). Yielding the best agreement with the GED structure, the MP2/cc-pVQZ approximation overestimates the C sbnd O and C dbnd O bond lengths by ca. 0.005(2) Å.
Goncalves, Marcio; Ceillier, Thierry
De nos jours, une entreprise est soumise à un flot d’informations continues plus ou moins important. Sur ce lot d’information, il faut savoir conserver l’information importante, la stocker et pouvoir la retrouver facilement et rapidement. Les outils de Gestion Electronique de Documents (GED) sont des solutions à cette problématique à laquelle les entreprises sont confrontées, d’autant plus si ces dernières font de l’EBuisness. Le but de ce rapport n’est pas de fournir une solution clef en mai...
Li, K.Y.; Xu, T.; Colapret, J.A.; Cawley, W.A.; Bonner, J.S.; Ernest, A.; Verramachaneni, P.B.
A fire-wall area (about 270 ft x 310 ft) with the Bunker C oil contaminated soil was selected for the bioremediation field test. This fire-wall area was separated into 18 plots by dirt dikes to test 6 bioremediation methods with three tests of each method. The six treatment methods were: (a) aeration with basic nutrients and indigenous organisms (BNIO); (b) aeration with basic nutrients and inoculation from a refinery wastewater treatment facility (BNSIWT); (c) aeration with an oleophilic fertilizer and indigenous organisms (INIPOL); (d) aeration with basic nutrients and biosurfactant organisms (EPA Seal Beach consortia) (EPA); (e) aeration with proprietary nutrients and organisms (PRO); and (f) aeration only for active control (CONTROL). This field test was conducted for 91 days. In general the oil contents in 18 plots were reduced, but the results showed significant fluctuations. A statistical method was used to examine if the oil reductions of six methods were the results from the random error of sampling and sample analysis or biodegradation. The results of the statistical analysis showed that oil reduction was concluded from all but the plots of PRO. From the data analysis, it may be concluded that the oil reduction rate in these studies is controlled by oil transfer from soil into the aqueous solution. An example of calculation was used to illustrate this conclusion
Bernard, Samuel [Universite de Lyon, Universite Lyon 1, INSA de Lyon, F-69621, Ecole Centrale de Lyon, CNRS, UMR5208, Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622 Villeurbanne-Cedex (France); Frisen, Jonas [Department of Cell and Molecular Biology, Karolinska Institute, SE-171 77 Stockholm (Sweden); Spalding, Kirsty L., E-mail: email@example.com [Department of Cell and Molecular Biology, Karolinska Institute, SE-171 77 Stockholm (Sweden)
Human tissues continually replace dying cells with newborn cells. However, the rate of renewal varies by orders of magnitudes between blood cells, which are renewed every day and neurons, for which renewal is non-existent or limited to specific regions of the brain. Between those extreme are many tissues that turnover on a time scale of years, although no direct measurements have been done. We present here a mathematical method to estimate cell turnover in slowly renewing biological systems. Age distribution of DNA can be estimated from the integration of radiocarbon derived from nuclear bomb-testing during the cold war (1955-1963). For slowly renewing tissues, this method provides a better estimate of the average age of the tissue than direct estimates from the bomb-curve. Moreover, death, birth and turnover rates can be estimated. We highlight this method with data from human fat cells.
Lombardi, Karen Ann
This mixed-methods case study focuses on the third through fifth grade classrooms at a public elementary school in a Midwestern urban school district where the Northwest Evaluation Association's (NWEA) Measures of Academic Progress (MAP) assessment is being implemented. According to the school district, the goals of these tests are: to show…
Although research has extensively documented sources for differential item functioning and stereotype threat--especially among women and black college students--little is known about group differences in test-taking strategies among black adolescent students. In this article, Arbuthnot presents findings from two studies that seek to explore how…
Zola, M.; Martelli, A.; Masoni, P.; Scandola, G.
This paper presents the main features and results of the on-site dynamic tests and the related numerical analyses carried out for the PEC reactor vessel. The purpose is to provide an example of on-site testing of large components, stressing the problems encountered during the experiments, as well as in the processing phase of the test results and for the comparisons between calculations and measurements. Tests, performed by ISMES on behalf of ENEA, allowed the dynamic response of the empty vessel to be measured, thus providing data for the verification of the numerical models of the vessel supporting structure adopted in the PEC reactor-block seismic analysis. An axisymmetric model of the vessel, implemented in the NOVAX code, had been developed in the framework of the detailed numerical studies performed by NOVATOME (again on behalf of ENEA), to check the beam schematization with fluid added mass model adopted by ANSALDO in SAP-IV and ANSYS for the reactor-block design calculations. Furthermore, a numerical model, describing vessel supporting structure in detail, was also developed by ANSALDO and implemented in the SAP-IV code. The test conditions were analysed by use of these and the design models. Comparisons between calculations and measurements showed particularly good agreement with regard to first natural frequency of the vessel and rocking stiffness of the vessel supporting structure, i.e. those parameters on which vessel seismic amplification mainly depends: this demonstrated the adequacy of the design analysis to correctly calculate the seismic motion at the PEC core diagrid. (author). 5 refs, 23 figs, 4 tabs
Zola, Maurizio; Martelli, Alessandro; Maresca, Giuseppe; Masoni, Paolo; Scandola, Giani; Descleves, Pierre
This paper presents the main features and results of the on-site dynamic tests and the related numerical analysis carried out for the PEC reactor vessel. The purpose is to provide an example of on-site testing of large components, stressing the problems encountered during the experiments, as well as in the processing phase of the test results and for the comparisons between calculations and measurements. Tests, performed by ISMES on behalf of ENEA, allowed the dynamic response of the empty vessel to be measured, thus providing data for the verification of the numerical models of the vessel supporting structure adopted in the PEC reactor-block seismic analysis. An axisymmetric model of the vessel, implemented in the vessel, implemented in the NOVAK code, had been developed in the framework of the detailed numerical studies performed by NOVATOME (again on behalf of ENEA), to check the beam schematization with fluid added mass model adopted by ANSALDO in SAP-IV and ANSYS for the reactor-block design calculations. Furthermore, a numerical model, describing vessel supporting structure in detail, was also developed by ANSALDO and implemented in the SAP-IV code. The test conditions were analysed by use of these and the design models. Comparisons between calculations and measurements showed particularly good agreement with regard to first natural frequency of the vessel and rocking stiffness of the vessel supporting structure, i.e. those parameters on which vessel seismic amplification mainly depends: this demonstrated the adequacy of the design analysis to correctly calculate the seismic motion at the PEC core diagrid. (author)
Julie, Hongki; Sanjaya, Febi; Yudhi Anggoro, Ant.
One of purposes of this study was to describe the solution profile of the junior high school students for the PISA adaptation test. The procedures conducted by researchers to achieve this objective were (1) adapting the PISA test, (2) validating the adapting PISA test, (3) asking junior high school students to do the adapting PISA test, and (4) making the students’ solution profile. The PISA problems for mathematics could be classified into four areas, namely quantity, space and shape, change and relationship, and uncertainty. The research results that would be presented in this paper were the result test for quantity, and change and relationship problems. In the adapting PISA test, there were fifteen questions that consist of two questions for the quantity group, six questions for space and shape group, three questions for the change and relationship group, and four questions for uncertainty. Subjects in this study were 18 students from 11 junior high schools in Yogyakarta, Central Java, and Banten. The type of research that used by the researchers was a qualitative research. For the first quantity problem, there were 38.89 % students who achieved level 3. For the second quantity problem, there were 88.89 % students who achieved level 2. For part a of the first change and relationship problem, there were 55.56 % students who achieved level 5. For part b of the first change and relationship problem, there were 77.78 % students who achieved level 2. For the second change and relationship problem, there were 38.89 % students who achieved level 2.
Lambert, Katharina; Spinath, Birgit
Intelligence measures play a pivotal role in the diagnosis of mathematical learning disabilities (MLD). Probably as a result of math-related material in IQ tests, children with MLD often display reduced IQ scores. However, it remains unclear whether the effects of math remediation extend to IQ scores. The present study investigated the impact of a special remediation program compared to a control group receiving private tutoring (PT) on the WISC IQ scores of children with MLD. We included N=45 MLD children (7-12 years) in a study with a pre- and post-test control group design. Children received remediation for two years on average. The analyses revealed significantly greater improvements in the experimental group on the Full-Scale IQ, and the Verbal Comprehension, Perceptual Reasoning, and Working Memory indices, but not Processing Speed, compared to the PT group. Children in the experimental group showed an average WISC IQ gain of more than ten points. Results indicate that the WISC IQ scores of MLD children might be underestimated and that an effective math intervention can improve WISC IQ test performance. Taking limitations into account, we discuss the use of IQ measures more generally for defining MLD in research and practice. Copyright © 2017 Elsevier Ltd. All rights reserved.
Karimah, R. K. N.; Kusmayadi, T. A.; Pramudya, I.
Learning in the current 2013 curriculum is based on contextual issues based on questions that can encourage students to think broadly. HOTS is a real-life based assessment of everyday life, but in practice, the students are having trouble completing the HOTS issue. Learning difficulty is also influenced by personality type Based on the fact that the real difference one can see from a person is behavior. Kersey classifies the personality into 4 types, namely Idealist, Rational, Artisan, and Guardian. The researcher focuses on the type of guardian personality that is the type of personality that does not like the picture. This study aims to describe the difficulty of learning mathematics in students with a type of guardian personality in the completion of Geometry materials especially in solving HOTS. This research type is descriptive qualitative research. Instruments used in this study were the researchers themselves, personality class test sheets, learning difficulty test sheets in the form of HOTS Geometry test, and interview guides. The results showed that students with guardian personality it was found that a total of 3.37 % difficulties of number fact skill, 4.49 % difficulties of arithmetics skill, 37.08 % difficulties of information skill, 31.46% difficulties of language skill, 23.60 % difficulties of visual-spatial skill.
Susan C. Gillmor
Full Text Available This study explores a new item-writing framework for improving the validity of math assessment items. The authors transfer insights from Cognitive Load Theory (CLT, traditionally used in instructional design, to educational measurement. Fifteen, multiple-choice math assessment items were modified using research-based strategies for reducing extraneous cognitive load. An experimental design with 222 middle-school students tested the effects of the reduced cognitive load items on student performance and anxiety. Significant findings confirm the main research hypothesis that reducing the cognitive load of math assessment items improves student performance. Three load-reducing item modifications are identified as particularly effective for reducing item difficulty: signalling important information, aesthetic item organization, and removing extraneous content. Load reduction was not shown to impact student anxiety. Implications for classroom assessment and future research are discussed.
Rajesh Kumar, K.; Vani, K.; Chakraborty, G.; Venkat Raj, V.
A dynamic analysis code to predict the time dependent behaviour of the reactor coolant system flow following the tripping and starting of Primary Circulating Pumps in the different operating modes has been developed for Indian Pressurised Heavy Water Reactor (PHWR) type power plants. The model is comprised of reactor coolant momentum equation, Primary Heat Transport (PHT) pump dynamic equation and pump characteristics. This model forms one of the modules of the integrated system code being developed for transient analysis of 220 MWe PHWR power plants. The Narora Atomic Power Station (NAPS) PHT system flow transient results for different combinations of pump operation predicted by the model have been compared with the experimental data obtained from a test carried out in NAPS-2 for validation of the model. The predicted results are in good agreement with the experimental data. (author). 3 refs., 5 figs
Arvustus: Sascha Möbius. Das Gedähtnis der Reichsstadt. Unruhen und Kriege in der lübeckischen Chronistik und Kriege und Erinnerungskultur des späten mittelalters und der frühen Neuzeit. (Göttingen, 2011)
Martins, Lurdes; Veiga, Paula
This paper measures and decomposes socioeconomic-related inequality in mathematics achievement in 15 European Union member states. Data is taken from the 2003 wave of the OECD Programme for International Student Assessment (PISA). There is socioeconomic-related inequality in mathematics achievement, favoring the higher socioeconomic groups in each…
Choi, Youn-Jeng; Alexeev, Natalia; Cohen, Allan S.
The purpose of this study was to explore what may be contributing to differences in performance in mathematics on the Trends in International Mathematics and Science Study 2007. This was done by using a mixture item response theory modeling approach to first detect latent classes in the data and then to examine differences in performance on items…
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…
Luther, Kenneth H.
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Full Text Available The article presents a comparative analysis of the results of computer mathematical modelling of the motion of the underwater robot-fish implemented by using the MATLAB / Simulink package and fullscale tests of an experimental model developed in the laboratory of mechatronics and robotics of the SouthWest State University.
MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.
Full Text Available The purpose of the South African Mathematics Olympiad is to generate interest in mathematics and to identify the most talented mathematical minds. Our focus is on how the handling of missing data affects the selection of the ‘best’ contestants. Two approaches handling missing data, applying the Rasch model, are described. The issue of guessing is investigated through a tailored analysis. We present two microanalyses to illustate how missing data may impact selection; the first investigates groups of contestants that may miss selection under particular conditions; the second focuses on two contestants each of whom answer 14 items correctly. This comparison raises questions about the proportion of correct to incorrect answers. Recommendations are made for future scoring of the test, which include reconsideration of negative marking and weighting as well as considering the inclusion of 150 or 200 contestants as opposed to 100 contestants for participation in the final round.
MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent
Approximate methods used to interpret the results of tests based on radioactive tracer dilution in a single water well by labelling the whole piezometric column are described; these simple mathematical models have been used to obtain semi-quantitative data on the apparent velocity (horizontal) in non-homogeneous aquifers with flow rates of metres daily. Measurements have also been made in a homogeneous aquifer with velocities of centimetres daily. Interpretation is based on determination of the average concentration for the various well zones; this involves recognition of a mean velocity for each region. All the tracer dilution effects that are not due to horizontal or vertical flow between two zones, i.e. convection, artificial mixing, diffusion and so on, are grouped together as a single term, which is taken arbitrarily to be proportional to the difference in concentration between the regions under consideration; its value is obtained from the experimental dilution curve. The model was applied to the solution of the three cases encountered most frequently during our measurements in Colombia: (a) when the well penetrates a permeable zone and adjacent impermeable zone; (b) when the well penetrates a permeable zone contained between impermeable regions; and (c) when the well traverses an aquifer with two adjacent zones of different permeability contained between impermeable zones. The shape of the dilution curve (logarithm of concentration versus time, usually with two or more slopes) is predicted by the model, the approximate nature of which is consistent with the fact that the method of labelling the whole piezometric column is semi-quantitative. The results obtained for measurements made when there are considerable vertical flows are apparently correct, but there is no other experimental measurement available to confirm them. (author) [es
Morsanyi, Kinga; Primi, Caterina; Handley, Simon J; Chiesi, Francesca; Galli, Silvia
In two experiments, we tested some of the central claims of the empathizing-systemizing (E-S) theory. Experiment 1 showed that the systemizing quotient (SQ) was unrelated to performance on a mathematics test, although it was correlated with statistics-related attitudes, self-efficacy, and anxiety. In Experiment 2, systemizing skills, and gender differences in these skills, were more strongly related to spatial thinking styles than to SQ. In fact, when we partialled the effect of spatial thinking styles, SQ was no longer related to systemizing skills. Additionally, there was no relationship between the Autism Spectrum Quotient (AQ) and the SQ, or skills and interest in mathematics and mechanical reasoning. We discuss the implications of our findings for the E-S theory, and for understanding the autistic cognitive profile. ©2011 The British Psychological Society.
Brankaer, Carmen; Ghesquière, Pol; De Smedt, Bert
The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills. PMID:24699664
Andreescu, Titu; Tetiva, Marian
Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...
This article addresses some important issues in mathematics instruction at the middle and secondary levels, including the structuring of a district's mathematics program; the choice of textbooks and use of calculators in the classroom; the need for more rigorous lesson planning practices; and the dangers of teaching to standardized tests rather…
Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4–8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4–8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Codding, Robin S; Petscher, Yaacov; Truckenmiller, Adrea
A paucity of research has examined the utility of curriculum-based measurement (CBM) for data-based decision making at the secondary level. As schools move to multitiered systems of service delivery, it is conceivable that multiple screening measures will be used that address various academic subject areas. The value of including different CBM indices measures is not well understood. The purpose of this study was to (a) examine the relationship among a variety of reading, writing, and mathematics CBM indices administered to 249 seventh-grade students; (b) investigate amount and patterns of growth; and (c) examine predictive validity to a high-stakes state test using latent factor analysis and multiple indicator growth models. Results indicated strong correspondence among CBM types for fall static scores but weak relationships among slopes. Different patterns of growth were yielded for CBM writing than for CBM reading and mathematics. Findings from this study suggested that although reading, mathematics, and writing CBM were independently and moderately related to both English Language Arts and Math test scores, reading was the strongest predictor when all 3 CBM constructs were considered jointly.
Trinajstić, Nenad; Gutman, Ivan
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Alexander, Serena; Poggo, Tammy
Features the complete set of answers to the exercises in Mathematics Year 5, to save you time marking work and enable you to identify areas requiring further attention. The book includes diagrams and workings where necessary, to ensure pupils understand how to present their answers. Also available from Galore Park www.galorepark.co.uk :. - Mathematics Year 5. - Mathematics Year 6. - 11+ Maths Practice Exercises. - 11+ Maths Revision Guide. - 10-Minute Maths Tests Workbook Age 8-10. - 10-Minute Maths Tests Workbook Age 9-11. - Mental Arithmetic Workbook Age 8-10. - Mental Arithmetic Workbook Ag
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
Sørensen, John Aasted
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
9 July 2012 - Academy of Sciences Malaysia (ASM), Chairman, Mathematical and Physical Sciences Discipline Group M. Yahaya FASc and his delegation visiting the LHC superconducting magnet test hall with Technology Department G. De Rijk.
9 July 2012 - Academy of Sciences Malaysia (ASM), Chairman, Mathematical and Physical Sciences Discipline Group M. Yahaya FASc and his delegation visiting the LHC superconducting magnet test hall with Technology Department G. De Rijk.
How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life. From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson’s Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises. Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to und...
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Full Text Available The purpose of the study is to explore the content and significance of the Gifted Education Database (GED, a Korean information service system for gifted education. The GED functions as: 1 an information management system and 2 a teacher recommendation system. The information management system collects and provides data in terms of statistics on institutions, teachers, and students, teaching and learning materials, and notifications. The teacher recommendation system helps teachers to recommend students through an on-line system. It also assists in the student selection process by providing users a step-by-step interface specifically designed for each stage. Overall, as a comprehensive collective information system in gifted education, the GED supports policy making on providing appropriate educational experiences for the outstanding individuals, particularly those with disadvantaged socio-cultural background by providing reliable data at the national level. At the user level, it increases data accessibility and provides customized services for people concerned with gifted education. As a result, the GED connects information and people and is a driving force for national growth. Key Words: gifted education, database for gifted, Korean Information System Öz Bu çalışmanın amacı Kore’de üstün yetenekliler eğitimi bilgi servisi olan Üstün Yetenekliler Veri Tabanını (GED açıklayarak önemini ortaya koymaktır. GED’in iki işlevi vardır; 1 bilgi yönetim sistemi ve 2 öğretmen öneri sistemi. Bilgi yönetim sistemi olarak kurumlar, öğretmenler, öğrenciler, öğrenme ve öğretme materyalleri hakkında bilgiler ve duyurular toplanarak istatistikler halinde sunulur. Öğ- retmen öneri sistemi, online bir sistemle öğ- retmenlerin öğrencileri aday göstermelerine yardımcı olur. Ayrıca sistem, öğrenci seçme sürecinde kullanıcılara her aşama için özel olarak tasarlanmış bir ara-yüz ile adım adım yard
Rotbard, G.; La Rana, G.; Vergnes, M.; Berrier, G.; Kalifa, J.; Guilbaut, G.; Tamisier, R.
The 70 Ge, 72 Ge, 74 Ge, 76 Ge(d, 3 He) 69 Ga, 71 Ga, 73 Ga, 75 Ga reactions have been studied at 26 MeV with 15 keV resolution (F.W.H.M), using the Orsay MP tandem accelerator and a split pole magnetic spectrometer. The spectroscopic factors are determined for 15 levels in 69 Ga and 11 levels in each of the 3 other Ga isotopes. Level schemes are proposed for the practically unknown 73 Ga and 75 Ga. Very simple model wave functions previously proposed for Ge nuclei are seen to reproduce quite well the measured occupation numbers for the proton orbitals. Anomalies in these occupation numbers are observed between Z=31 and 32 and between N=40 and 42, this last one corresponding to the structural transition observed recently in a comparison of the (p,t) and (t,p) reactions. These anomalies could be related to changes in the nuclear shape
Aigner, Martin; Spain, Philip G
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Jothi, A Lenin
Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
The purpose of this study was to examine Addis Ababa secondary school mathematics teachers’ attitude in teaching mathematics. 148 mathematics teachers were selected using cluster sampling from Addis Ababa administration region. The study used survey method of data collection and it includes both quantitative and qualitative research methods. From the independent t-test, ANOVA, tukey test and regression analysis, some of the results obtained were: the majority of the secondary school mathemati...
Kleene, Stephen Cole
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Batchelder, William H
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Sørensen, John Aasted
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
Murray, James D
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Parshall, Karen Hunger
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle
Logan, J David
Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat
This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud
Karakoc Alatli, Betul; Ayan, Cansu; Polat Demir, Betul; Uzun, Gulcin
Problem Statement: Student achievement is considered an indicator of the quality of education, and achievement tests are applied to assess student achievement. International tests are adapted into different languages and cultures with the aim of assessing student achievement on an international level and comparing the achievements of different…
Berriaud, C.; Cebe, E.; Livolant, M.; Buland, P.
Two series of horizontal tests have been performed at Saclay on the shaking table VESUVE: sinusoidal test and time history response. Sinusoidal tests have shown the strongly nonlinear dynamic behavior of the core. The resonant frequency of the core is dependent on the level of the excitation. These phenomena have been explained by a computer code, which is a lumped mass nonlinear model. El Centro time history displacement at the level of PCRV was reproduced on the shaking table. The analytical model was applied to this excitation and good comparison was obtained for forces and velocities [fr
Virdi, Surinder; Virdi, Narinder Kaur
Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...
Eck, Christof; Knabner, Peter
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim
Sørensen, John Aasted
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
Sørensen, John Aasted
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
Full Text Available This study aims to determine students’ decision making strategy to answer TIMSS science reasoning test in cognitive reasoning domain. This research is quantitative descriptive research. The result shows that students tend to use compensatory strategy for decision making in solving multiple-choice questions and use rational category to answer essay questions. The result shows that more than half of students have been able to answer the questions TIMSS science tests correctly.
Earn College Credit with REA's Test Prep for CLEP* College Mathematics Everything you need to pass the exam and get the college credit you deserve.CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs. Our test prep for CLEP* College Mathematics and the free online tools that come with it, allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your lea
Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem  and of the Poincare Conjecture  have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Bennett, Randy Elliot; Braswell, James; Oranje, Andreas; Sandene, Brent; Kaplan, Bruce; Yan, Fred
This article describes selected results from the Math Online (MOL) study, one of three field investigations sponsored by the National Center for Education Statistics (NCES) to explore the use of new technology in NAEP. Of particular interest in the MOL study was the comparability of scores from paper- and computer-based tests. A nationally…
Sireci, Stephen G.; Hauger, Jeffrey B.; Wells, Craig S.; Shea, Christine; Zenisky, April L.
The National Assessment Governing Board used a new method to set achievement level standards on the 2005 Grade 12 NAEP Math test. In this article, we summarize our independent evaluation of the process used to set these standards. The evaluation data included observations of the standard-setting meeting, observations of advisory committee meetings…
Belsom, C. G. H.; Elton, L. R. B.
Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)
Bergstrom, Haley C; Housh, Terry J; Zuniga, Jorge M; Traylor, Daniel A; Lewis, Robert W; Camic, Clayton L; Schmidt, Richard J; Johnson, Glen O
Estimates of critical power (CP) and anaerobic work capacity (AWC) from the power output vs. time relationship have been derived from various mathematical models. The purpose of this study was to examine estimates of CP and AWC from the multiple work bout, 2- and 3-parameter models, and those from the 3-minute all-out CP (CP3min) test. Nine college-aged subjects performed a maximal incremental test to determine the peak oxygen consumption rate and the gas exchange threshold. On separate days, each subject completed 4 randomly ordered constant power output rides to exhaustion to estimate CP and AWC from 5 regression models (2 linear, 2 nonlinear, and 1 exponential). During the final visit, CP and AWC were estimated from the CP3min test. The nonlinear 3-parameter (Nonlinear-3) model produced the lowest estimate of CP. The exponential (EXP) model and the CP3min test were not statistically different and produced the highest estimates of CP. Critical power estimated from the Nonlinear-3 model was 14% less than those from the EXP model and the CP3min test and 4-6% less than those from the linear models. Furthermore, the Nonlinear-3 and nonlinear 2-parameter (Nonlinear-2) models produced significantly greater estimates of AWC than did the linear models and CP3min. The current findings suggested that the Nonlinear-3 model may provide estimates of CP and AWC that more accurately reflect the asymptote of the power output vs. time relationship, the demarcation of the heavy and severe exercise intensity domains, and anaerobic capabilities than will the linear models and CP3min test.
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Tyler, John H.; Murnane, Richard J.; Willett, John B.
As part of standards-based educational reform efforts, more than 40 states will soon require students to achieve passing scores on standardized exams in order to obtain a high school diploma. Currently, many states are struggling with the design of their examination systems, debating such questions as which subjects should be tested, what should…
This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...
This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...
Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim
Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci
Charlton, Bruce G
Crick and Watson gave complementary advice to the aspiring scientist based on the insight that to do your best work you need to make your greatest possible effort. Crick made the positive suggestion to work on the subject which most deeply interests you, the thing about which you spontaneously gossip - Crick termed this 'the gossip test'. Watson made the negative suggestion of avoiding topics and activities that bore you - which I have termed 'the boredom principle'. This is good advice because science is tough and the easy things have already been done. Solving the harder problems that remain requires a lot of effort. But in modern biomedical science individual effort does not necessarily correlate with career success as measured by salary, status, job security, etc. This is because Crick and Watson are talking about revolutionary science - using Thomas Kuhn's distinction between paradigm-shifting 'revolutionary' science and incremental 'normal' science. There are two main problems with pursuing a career in revolutionary science. The first is that revolutionary science is intrinsically riskier than normal science, the second that even revolutionary success in a scientific backwater may be less career-enhancing than mundane work in a trendy field. So, if you pick your scientific problem using the gossip test and the boredom principle, you might also be committing career suicide. This may explain why so few people follow Crick and Watson's advice. The best hope for future biomedical science is that it will evolve towards a greater convergence between individual effort and career success.
Lo, Bruce W. N.
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Elkjær, Lars Skou; Bech, Bodil Hammer; Sun, Yuelian
by Statistics Denmark on April 15, 2016. All children born alive in Denmark between 1997 and 2006 (n = 656 496) were identified. From this cohort, children who did not participate in the national tests, with presumed coding errors in gestational age and children missing information on their mother's educational......Importance: Valproate sodium is used for the treatment of epilepsy and other neuropsychiatric disorders in women of childbearing potential. However, there are concerns about impaired cognitive development in children who have been exposed to valproate during pregnancy. Objective: To estimate...... the association between long-term school performance and prenatal exposure to valproate and a number of other antiepileptic drugs (AEDs). Design, Setting, and Participants: In a prospective, population-based cohort study conducted from August 1, 2015, to May 31, 2017, data used in the study were provided...
Gatewood, B. E.
The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.
The workshop on mathematical cosmology was devoted to four topics of current interest. This report contains a brief discussion of the historical background of each topic and a concise summary of the content of each talk. The topics were; the observational cosmology program, the cosmological perturbation program, isotropic singularities, and the evolution of Bianchi cosmologies. (author)
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.
Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on t...
Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.
Kent, Kimberly Penn
The primary purpose of this study was to determine if there was a difference between self-contained and departmentalized classroom organization on the Kentucky Core Content Test (KCCT) in reading and mathematics for students in fourth and fifth grade. A secondary purpose of this study was to consider how these organizational structures affect the…
Overwhelming evidence shows that domestic violence is a very serious problem affecting women in the United States. Black et al. (2010) report that approximately 34 million women in the United States, or approximately 30%, have experienced some form of violence including rape, physical, violence, and/or stalking in their lifetimes. Twenty-two…
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Driessche, Pauline; Wu, Jianhong
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...
The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr
Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.
Full Text Available This study was conducted to determine the effect of Realistic Mathematics Education Approach on mathematics achievement and student attitudes towards mathematics. This study also sought determine the relationship between student achievement and attitudes towards mathematics. This study used a quasi-experimental design conducted on 61 high school students at SMA Unggul Sigli. Students were divided into two groups, the treatment group $(n = 30$ namely, the Realistic Mathematics Approach group (PMR and the control group $(n = 31$ namely, the traditional group. This study was conducted for six weeks. The instruments used in this study were the achievement test and the attitudes towards mathematics questionnaires. Data were analyzed using SPSS. To determine the difference in mean achievement and attitudes between the two groups, data were analyzed using one-way ANOVA test. The result showed significant differences between the Realistic Mathematics Approach and the traditional approach in terms of achievement. The study showed no significant difference between the Realistic Mathematics Approach and the traditional approach in term of attitudes towards mathematics. It can be concluded that the use of realistic mathematics education approach enhanced students' mathematics achievement, but not attitudes towards mathematics. The Realistic Mathematics Education Approach encourage students to participate actively in the teaching and learning of mathematics. Thus, Realistic Mathematics Education Approach is an appropriate methods to improve the quality of teaching and learning process.
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Dostal, Hannah M.; Robinson, Richard
Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…
Bednarz, Nadine; Proulx, Jérôme
Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…
A discriminant analysis was conducted to investigate how an essay, a mathematics/science type of essay, a college scholastic ability test, and grade point average affect acceptance to a pre-med course at a Korean medical school. Subjects included 122 and 385 applicants for, respectively, early and regular admission to a medical school in Korea. The early admission examination was conducted in October 2007, and the regular admission examination was conducted in January 2008. The analysis of early admission data revealed significant F values for the mathematics/science type of essay (51.64; Pgrade point average (10.66; P=0.0014). The analysis of regular admission data revealed the following F values: 28.81 (Pgrade point average, 27.47 (P<0.0001) for college scholastic ability test, 10.67 (P=0.0012) for the essay, and 216.74 (P<0.0001) for the mathematics/science type of essay. Since the mathematics/science type of essay had a strong effect on acceptance, an emphasis on this requirement and exclusion of other kinds of essays would be effective in subsequent entrance examinations for this premed course.
Dragalin, A G
This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.
Shelly L. Wismath
Full Text Available Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done by both paired t-tests and Wilcoxon signed-rank tests. Our results showed a significant increase in confidence and decrease in anxiety, while perception of the value of mathematics was already high and changed little by the end of the course.
This study concerns the use of e-learning in the educational system shedding the light on its advantages and disadvantages, and analyzing its applicability either partially or totally. From mathematical perspectives, theories are developed to test the courses tendency to online transformation. This leads to a new trend of learning, the offline-online-offline learning (fnf-learning), it merges e-learning mode with the traditional orientation of education. The derivation of the new trend is bas...
Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas
To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....
The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.
Ansari, B. I.; Wahyu, N.
This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.
Tooke, D. James
Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)
In a local middle school, students were not meeting standards on the state mathematics tests. The purpose of this qualitative study was to explore mathematics teachers' perspectives on effective mathematics instruction vis-a-vis the principles of the National Council of Teachers of Mathematics (NCTM). Within this framework, the 6 principles in the…
Tran, Dung; Dougherty, Barbara J.
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Harwell, Michael; Moreno, Mario; Post, Thomas
This study examined the relationship between the American College Testing (ACT) college mathematics readiness standard and college mathematics achievement using a sample of students who met or exceeded the minimum 3 years high school mathematics coursework recommended by ACT. According to ACT, a student who scores 22 or higher on the ACT…
A discriminant analysis was conducted to investigate how an essay, a mathematics/science type of essay, a college scholastic ability test, and grade point average affect acceptance to a pre-med course at a Korean medical school. Subjects included 122 and 385 applicants for, respectively, early and regular admission to a medical school in Korea. The early admission examination was conducted in October 2007, and the regular admission examination was conducted in January 2008. The analysis of ea...
Ajogbeje Oke James
Full Text Available The urge to excel or perform maximally in mathematics varies from individual to individual because achievement motivation is often developed or learnt during socialization and learning experiences. The study examined the relationship between College of Education students’ achievement motivation and mathematics achievement, correlation coefficient between mathematics anxiety and college students’ achievement motivation as well as mathematics anxiety and mathematics achievement. The sample, 268 College of Education students offering mathematics as one of their subject combination, was selected using purposive sampling techniques. Three research instruments namely: Mathematics Anxiety Scale (MAS, Achievement Motivation Scale (AMS and Mathematics Achievement Test (MAT were used to collect data for the study. Data collected for the study were analyzed using correlational analysis and ANOVA. The results showed that a significantly low negative correlation coefficient existed between mathematics anxiety and mathematics achievement. There is a negative and significant correlation coefficient between mathematics anxiety and achievement motivation. Similarly, a positive and significant correlation coefficient also exists between achievement motivation and mathematics achievement. Based on the findings of the study, it was recommended that mathematics teachers should adopt activity based strategies and conducive learning environment in order to reduce college students’ anxieties in mathematics learning.
* Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...
Chicago Board of Education, IL. Dept. of Curriculum.
The curriculum guide for mathematics instruction in the bilingual education program of the Chicago public schools is designed to assist teachers in the instruction of limited-English-speaking students in their native language. The guide outlines, for each of two levels, lessons on absolute and relative values of numbers, whole number operations,…
Chicago Board of Education, IL. Dept. of Curriculum.
The introductory level curriculum guide for bilingual education for Spanish-speaking children in the Chicago public schools is divided into four difficulty levels and is designed to facilitate acquisition of mathematical concepts by presenting them in the children's native language. At each level, the concepts covered include the meaning of…
van der Flier, H.; Thijs, G.D.; Zaaiman, H.
The identification of students with the potential to succeed in mathematics- and science-based study despite previous educational disadvantage is a critical issue currently facing many South African higher education institutions. The possible use of school-leaving examination (Matric) results and/or
Bonello, Mary Rose; Camilleri, Silvana
'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)
Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc
Wong, Chun Wa
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above
Owens, Kay; Paraides, Patricia; Jannok Nutti, Ylva; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul
As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological perspective that particularly noted the role of Elders and the place of the child in the family. However, there was also the issue of curriculum and mathematics education to be addressed. It was recognised that a colonised curriculum reduces the vision of what might be the potential for Indigenous mathematics education. This paper reports on the sharing that developed between our local community and some researchers and teachers from Sweden, Papua New Guinea and New Zealand. It has implications for recognising the impact of testing regimes, the teaching space, understanding the ways children learn, the curriculum, and teacher education. As a result of these discussions, a critical pedagogy that considers culture and place is presented as an ecocultural perspective on mathematics education. This perspective was seen as critical for the curriculum and learning experiences of Indigenous children.
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Nordin, Sayed Kushairi Sayed; Samat, Khairul Fadzli; Sultan, Al Amin Mohamed; Halim, Bushra Abdul; Ismail, Siti Fatimah; Mafazi, Nurul Wirdah
Mathematics is an essential and fundamental tool used by engineers to analyse and solve problems in their field. Due to this, most engineering education programs involve a concentration of study in mathematics courses whereby engineering students have to take mathematics courses such as numerical methods, differential equations and calculus in the first two years and continue to do so until the completion of the sequence. However, the students struggled and had difficulties in learning courses that require mathematical abilities. Hence, this study presents the factors that caused mathematics anxiety among engineering students using Abbreviated Mathematics Anxiety Rating Scale (AMARS) through 95 students of Universiti Teknikal Malaysia Melaka (UTeM). From 25 items in AMARS, principal component analysis (PCA) suggested that there are four mathematics anxiety factors, namely experiences of learning mathematics, cognitive skills, mathematics evaluation anxiety and students' perception on mathematics. Minitab 16 software was used to analyse the nonparametric statistics. Kruskal-Wallis Test indicated that there is a significant difference in the experience of learning mathematics and mathematics evaluation anxiety among races. The Chi-Square Test of Independence revealed that the experience of learning mathematics, cognitive skills and mathematics evaluation anxiety depend on the results of their SPM additional mathematics. Based on this study, it is recommended to address the anxiety problems among engineering students at the early stage of studying in the university. Thus, lecturers should play their part by ensuring a positive classroom environment which encourages students to study mathematics without fear.
Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.
Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi
Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.
The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…
Hansen, Vagn Lundsgaard
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
Hansen, Vagn Lundsgaard
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
Mumcu, Hayal Yavuz
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss
Danylov, Iu V; Motkov, K V; Shevchenko, T I
The morphometric estimation of parenchyma and stroma condition included the determination of 29 parameters in testicles at 27 persons. The mathematical model of morphogenesis of testicles was created by Bayes' method. The method of differential diagnosis of testicles tissues' changes conditioned by the influence of the Chernobyl factor and/or unfavorable terms of the work in underground coal mines have been worked out. Its practical use provides exactness and reliability of the diagnosis (not less than 95%), independence from the level of the qualification and personal experience of the doctor, allows us to unify, optimize and individualize the diagnostic algorithms, answer the requirements of evidential medicine.
Ely, Jane Alice
The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Full Text Available The purpose of this study was to determine the influence of CBT and PBT national examination in terms of students’ cognitive readiness and anxiety facing mathematics national examination in DIY province, the influence of major in terms of students’ cognitive readiness and anxiety facing mathematics national examination in DIY Province, and the interaction between national examination and major. This research was descriptive explorative and the method was ex-post facto. The population was all of natural and social science high school students in grade XII in DIY province. The number of sample used was 654 students The results showed that there was influence of national examination in terms of students’ cognitive readiness and anxiety facing national examination. CBT and PBT national examination did not influence the cognitive readiness facing national examination, CBT and PBT national examination influence in national examinations in terms of students’ anxiety facing national examination. The average score of the students’ anxiety facing CBT national exam was greater than that of the students’ anxiety facing PBT national examination. There was no effect caused by differences in majoring in terms of cognitive readiness and national examination math anxiety; and there was no interaction between the different types of national examinations and majors.
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
The field tested construction industry-related mathematics unit is intended to familiarize seventh grade students with various facets of the construction industry, including the various occupations available and the mathematical abilities and other skills and training necessary to pursue an occupation in the industry. The final set of activities…
This study examined the knowledge of mathematics content of elementary pre-service teachers at a sixth grade level. The researcher administered a mathematics test for sixth graders mandated by the Texas Education Agency to pre-service teachers; the same test was given to sixth graders in Texas. The study found that pre-service teachers performed…
This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.
This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
"[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...
Johansen, Mikkel Willum; Misfeldt, Morten
This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical...... cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new...... in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding....
Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.
.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...
Full Text Available Objectives: One of the issues that have consistently been the concern for the health affair specialists and cure and massive social governors in health fields is the rate of disorders prevalence, diseases and the related subjects to epidemiology. Purpose of this study was to estimate the prevalence of mathematic disability amongst primary schools of Karaj. Methods: Totally 432 students were selected with multi-stage sampling method. Participants completed Raven test, Frostig Visual-Perception test and Wepman Auditory discrimination test, Rutter behavioral questionnaire and Iran Key-math test. In order to diagnosis mathematic disability, inter criterion was normal quotient intelligence and out criteria were to have one of visual perception, auditory and behavioral problems. The participants whose total standard scores in Iran Key-math test were one standard deviation below the mean were selected as a mathematical disability (MD. Results: The mathematic disability prevalence in primary students was estimated 0.46%. In addition, proportion of mathematic disability prevalence was not function of gender or grade. Discussion: The findings demonstrated that the prevalence of mathematic disability is much less than the previous researches. A possible explanation was that inappropriate screening co morbid disorders with the mathematic disability. The theoretical implications of findings are discussed in detail.
Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional
Roberts, A. M.
The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Several episodes in the relation between Mathematics and Quantum Mechanics are discussed; and the emphasis is put in the existence of multiple and sometimes unexpected connections between ideas originating in Mathematics and in Quantum Physics. The question of the unresasonable effectiveness of Mathematics in Physics is also presented in the same light. (Author) 3 refs
Grootenboer, Peter; Edwards-Groves, Christine
In this paper we argue that mathematics teaching can be conceptualised as a form of praxis. Viewing mathematics teaching as praxis foregrounds the moral nature of teaching and the educational practices that are developed in response to the educational needs in particular sites. The case for praxis in mathematics education is then made by drawing…
Martin, Tami S.; Speer, William R.
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Coomes, Jacqueline; Lee, Hyung Sook
Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…
Turner, Vanshelle E.
Learning mathematics is problematic for most primary school age children because mathematics is rote and the memorization of steps rather than an approach to seeing relationships that builds inquiry and understanding. Therefore, the traditional "algorithmic" way of teaching mathematics has not fully prepared students to be critical…
Pre-Mathematical Logic Languages Metalanguage Syntax Semantics Tautologies Witnesses Theories Proofs Argot Strategies Examples Mathematics ZFC Sets Maps Relations Operations Integers Induction Rationals Combinatorics Sequences Reals Topology Imaginaries Residues p-adics Groups Orders Vectors Matrices Determinants Polynomials Congruences Lines Conics Cubics Limits Series Trigonometry Integrality Reciprocity Calculus Metamodels Categories Functors Objectives Mathematical Logic Models Incompleteness Bibliography Index
The study of mathematics, with other ''gendered'' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers.
Focus and Scope. MATHEMATICS CONNECTION aims at providing a forum to promote the development of Mathematics Education in Ghana. Articles that seek to enhance the teaching and/or learning of mathematics at all levels of the educational system are welcome ...
Principal Contact. Dr. Kofi Mereku Executive Editor Department of Mathematics Education, UCE Mathematical Association of Ghana, C/o Department of Mathematics Education University College of Education of Winneba P. O. Box 25, Winneba, Ghana Phone: +233244961318. Email: firstname.lastname@example.org ...
In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…
Utah State Office of Education, 2011
Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…
Thomas, Jan; Muchatuta, Michelle; Wood, Leigh
This article investigates enrolment trends in mathematical sciences in Australian universities. Data has been difficult to extract and the coding for mathematical disciplines has made investigation challenging. We show that the number of mathematics major undergraduates in Australia is steadily declining though the number studying…
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…
Amidon, Joel C.
What happens when the problem of inequitable access to mathematics is addressed by agape (pronounced agapa) or attending to the relationships students develop with mathematics? To respond to this question, this paper offers a description of the journey towards teaching mathematics as agape. First, I organized examples of equity pedagogy around the…
Author Affiliations. K B Athreya1 2 M G Nadkarni3. Department of Mathematics Iowa State University, Ames, Iowa; I M I, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India. Department of Mathematics, University of Mumbai Kalina, Mumbai, 400098, India.
Rebollo, M A; Rodríguez, A L
To discuss our concern for some aspects of mathematics learning disorders related to the nomenclature employed and their diagnosis; these aspects refer to the term 'dyscalculia' and to its diagnosis (especially syndromatic diagnosis). We also intend to propose a classification that could help to define the terminology. Lastly we are going to consider the different aspects of diagnosis and to determine which of them are indispensable in the diagnosis of primary and secondary disorders. As far as the nomenclature is concerned, we refer to the term 'dyscalculia'. The origins of the term are analysed along with the reasons why it should not be used in children with difficulties in learning mathematics. We propose a classification and denominations for the different types that should undoubtedly be discussed. With respect to the diagnosis, several problems related to the syndromatic diagnosis are considered, since in our country there are no standardised tests with which to study performance in arithmetic and geometry. This means that criterion reference tests are conducted to try to establish current and potential performance. At this stage of the diagnosis pedagogical and psychological studies must be conducted. The important factors with regard to the topographical and aetiological diagnoses are prior knowledge, results from the studies that have been carried out and findings from imaging studies. The importance of a genetic study must be defined in the aetiological diagnosis. We propose a nomenclature to replace the term 'dyscalculia'. Standardised tests are needed for the diagnosis. The need to establish current and potential performance is hierarchized. With regard to the topographical diagnosis, we highlight the need for more information about geometry, and in aetiological studies the analyses must be conducted with greater numbers of children.
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.
This study measured pre-service teachers' mathematical knowledge for teaching (MKT) basic school mathematics. MKT multiple-choice test was administered to 100 pre-service teachers from two colleges of education (located at Mampong in the Ashanti Region of Ghana) to assess their mathematical knowledge for ...
Hutton, B M
This study explores the effectiveness of a revision programme in nursing mathematics for student nurses. Students who took the revision programme achieved a marked improvement in test results, although some still scored low in written tests. When interviewed, the students reported that they had difficulty applying written work in the classroom to actual calculations in the workplace. They found that only by 'doing' mathematics did the theory make sense. The author recommends that students should be encouraged to maximise the opportunities to practise mathematics in the clinical setting.
Crossley, J N; Brickhill, CJ; Stillwell, JC
Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg
Balakrishnan, V K
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Mortimer, Robert G
Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit
Goodstein, R L
Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people
Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems.A highly involving book which encourages the reader to enter into the spirit of mathematical ex
Gabbay, Dov M; Woods, John
One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat
Jourdain, Philip E B
Anyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author p
Bell, Eric Temple
""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from
More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led
Martin, B R
Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...
Valero, Paola; Hoyles, Celia; Skovsmose, Ole
What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed - theoretical and practical - and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge.
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
Herman, Russell L
Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions
Enns, Richard H
Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is use...
of regular high school instruction. The GED test battery contains five testsz writing skills, social studies, science, reading skills, and mathematics ...expanded apprentice train- ing program for airmen and seamen might, ceteris paribus, bring the GENDET attrition rate closer to acceptable lvels . 13 ] KN
Bidrag med en kortfattet, introducerende, perspektiverende og begrebsafklarende fremstilling af begrebet test i det pædagogiske univers.......Bidrag med en kortfattet, introducerende, perspektiverende og begrebsafklarende fremstilling af begrebet test i det pædagogiske univers....
A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...
Nash, Jr, John Forbes
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
This paper considers idea generation during the mathematical writing process. Two contrasting explanations of the creative potential in connection to writing is presented; writing as a process of setting and obtaining rhetorical goals and writing as a process of discovery. These views...... are then related to two empirically found categories of functions that writing serves researchers in the field of mathematics, concluding that both views contributes to understanding the creative potential in relation to mathematical writing....
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
We claim that important considerations have been overlooked in designinginteractive mathematics educational software in the past.In particular,most previous work has concentrated on how to make use ofpre-existing software in mathematics education, rather than firstasking the more...... fundamentalquestion of which requirements mathematics education puts on software, and thendesigning software to fulfil these requirements.We present a working prototype system which takes a script defining an interactivemathematicaldocument and then provides a reader with an interactive realization of thatdocument....
Misfeldt, Morten; Ejsing-Duun, Stine
In this paper we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....
Højgaard, Tomas; Jankvist, Uffe Thomas
The paper argues for a three-dimensional course design structure for future mathematics teacher educators. More precisely we describe the design and implementation of a course basing itself on: the two mathematical competencies of modelling and problem tackling, this being the first dimension......; the two mathematical topics of differential equations and stochastics, this being the second dimension; and finally a third dimension the purpose of which is to deepen the two others by means of a didactical perspective....
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Full Text Available Modern Internet technologies open new possibilities in wide spectrum of traditional methods used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay at their schools or universities and try to solve as many mathematical problems as possible and then submit their solutions through Internet. Simple Internet technologies supply audio and video connection between participants and organizers.
Malasari, P. N.; Herman, T.; Jupri, A.
The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.
Full Text Available The problem in this research is to know how the process of developing mathematics physics instructional book based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting documents (semester learning activity plan, lesson plan and mathematical problem-solving test to improve students' mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach book was better than the students who use the regular book.
House, Peggy A.
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for t
Jesseph, Douglas M
In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r
Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi
Resnikoff, Howard L
Space flight, computers, lasers, and information technology ― these are but a few examples of the spectacular growth, development, and far-reaching applications of mathematics. But what of the field's past? Upon which intellectual milestones were the foundations of modern mathematics constructed? How has our comprehension of the physical universe, language, and the nature of thought itself been influenced and informed by the developments of mathematics through the ages?This lucid presentation examines how mathematics shaped and was shaped by the course of human events. In a format suited to co
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.
Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...
Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.
Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut
Ma, Xin; McIntyre, Laureen J.
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Cai, Jinfa; Ding, Meixia
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Jett, Christopher C.
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Lee, H.C.; Couture, M.; Douglas, S.; Leivo, H.P.
The Workshop on Applied Mathematics was held at the Cockcroft Centre, Deep River, Ontario, 1992 February 7-8. The purpose of the workshop was to provide a forum for applied mathematicians to survey the use and to discuss the future of applied mathematics at AECL Research. There were 57 participants at the workshop A total of eight 30-minute and 25 15-minute talks were presented describing mathematical techniques used in the whole range of activities at AECL Research, from numerical simulation of fluid flow through eddy current testing to quantum algebra and accelerator physics
Lee, H C; Couture, M; Douglas, S; Leivo, H P
The Workshop on Applied Mathematics was held at the Cockcroft Centre, Deep River, Ontario, 1992 February 7-8. The purpose of the workshop was to provide a forum for applied mathematicians to survey the use and to discuss the future of applied mathematics at AECL Research. There were 57 participants at the workshop A total of eight 30-minute and 25 15-minute talks were presented describing mathematical techniques used in the whole range of activities at AECL Research, from numerical simulation of fluid flow through eddy current testing to quantum algebra and accelerator physics.
Caro-Vega, Yanink; del Rio, Carlos; Lima, Viviane Dias; Lopez-Cervantes, Malaquias; Crabtree-Ramirez, Brenda; Bautista-Arredondo, Sergio; Colchero, M Arantxa; Sierra-Madero, Juan
To estimate the impact of late ART initiation on HIV transmission among men who have sex with men (MSM) in Mexico. An HIV transmission model was built to estimate the number of infections transmitted by HIV-infected men who have sex with men (MSM-HIV+) MSM-HIV+ in the short and long term. Sexual risk behavior data were estimated from a nationwide study of MSM. CD4+ counts at ART initiation from a representative national cohort were used to estimate time since infection. Number of MSM-HIV+ on treatment and suppressed were estimated from surveillance and government reports. Status quo scenario (SQ), and scenarios of early ART initiation and increased HIV testing were modeled. We estimated 14239 new HIV infections per year from MSM-HIV+ in Mexico. In SQ, MSM take an average 7.4 years since infection to initiate treatment with a median CD4+ count of 148 cells/mm3(25th-75th percentiles 52-266). In SQ, 68% of MSM-HIV+ are not aware of their HIV status and transmit 78% of new infections. Increasing the CD4+ count at ART initiation to 350 cells/mm3 shortened the time since infection to 2.8 years. Increasing HIV testing to cover 80% of undiagnosed MSM resulted in a reduction of 70% in new infections in 20 years. Initiating ART at 500 cells/mm3 and increasing HIV testing the reduction would be of 75% in 20 years. A substantial number of new HIV infections in Mexico are transmitted by undiagnosed and untreated MSM-HIV+. An aggressive increase in HIV testing coverage and initiating ART at a CD4 count of 500 cells/mm3 in this population would significantly benefit individuals and decrease the number of new HIV infections in Mexico.
Assessment of math learning by the Early Mathematical Competence Test Spanish version. Estimación del aprendizaje matemático mediante la versión española del Test de Evaluación Matemática Temprana de Utrecht
José I. Navarro
Full Text Available The Early Mathematical Competence Test (EMTC assesses mathematical knowledge for kindergarden and primary school children. The test has 3 versions, of 40 items each and measures eight aspects of mathematical competence: Concepts of comparison; Classification; Correspondence; Seriation; Using counting words, forwards and backwards; Structures counting; Resultative counting; and General knowledge of numbers. Each subtest has five questions and a total score of 40 points. The main aim of this study was the standardization of EMTC for a Spanish population, following the international reliability and validation statistical rules. The test was administered to 1053 participants aged 4 to 7 (539 male and 514 female from 14 schools. The EMTC provides a Mathematical Competence index, has a standard prediction value, and validation and reliability scores were significant.
Key words: Early math, cognition, assessment, number sense, kindergarden, primary school.
El Test de Evaluación Matemática Temprana está orientado a medir el nivel de competencia matemática temprana. Se ha desarrollado para de educación infantil y 1º y 2º de primaria. Dispone de tres versiones paralelas, de 40 ítems cada una. Consta de 8 tareas, divididas en grupos de 5: Comparación, clasificación, correspondencia, seriación, conteo verbal, conteo estructurado, conteo resultante y conocimiento general de los números. Tiene una puntuación máxima de 40 puntos (uno por cada ítem correcto. El objetivo fundamental de este estudio consistió en adaptar el test a la población española con todas las garantías de validez y fiabilidad, que permita tener un instrumento para detectar posibles problemas en el aprendizaje de las matemáticas en los inicios de la escolaridad. El TEMT se ha baremado con una muestra de 1.053 niños/as pertenecientes a 14 colegios. 539 eran varones y 514 mujeres. Nos da un índice cuantitativo del nivel de competencia matem
Sead Rešić; Eldina Atić
In this research, the application of contemporary teaching aids in Mathematics teaching in elementary school was analyzed from the aspect of teachers, students and parents. The application of contemporary teaching aids in Mathematics teaching was analyzed through a sample of 100 students, and attitudes about the aids were examined from the points of view of students, teachers and parents. In this research, descriptive method, questionnaire and test were used. Results of the resear...
Moreno-García, Elena; García-Santillán, Arturo; Molchanova, Violetta S.; Larracilla-Salazar, Némesis
In the educational field, anxiety towards mathematics has been a recurrent theme that has been intensified with the results of the PISA test of 2012 and 2015. Since students who are anxious about mathematics tend to avoid any area related to mathematics, it leads to a decrease in the number of professionals in mathematics. However, this construct…
These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...
Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++.......Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++....
Hansen, Vagn Lundsgaard; Gray, Jeremy
Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....
Full Text Available The objective of mathematics education is not only preparingmathematicians but making well-informed citizens. This is a broad generalterms for objective of the teaching of mathematics. And, this might beimplemented as “accurate thorough knowledge” or “original logicalthinking”. So, teaching mathematics is not the conversation andtransmission of mathematical knowledge, but on the aim of preparing wellinformedcitizens trained in independent, critical thinking.By the mathematics, sciences become simple, clearer, and easier to bedeveloped. The mathematics is often applied for solving any problem ofother field of sciences, either in the physics such as astronomy, chemistry,technique; or social sciences such as economy, demography, and assurance.Those all need an analysis reading ability.Mathematical skill, therefore, relates strongly with the analysisreading ability in the human intellectual structure. This study is about therelationship between them. And, result of the study shows us as below:Both Mathematical skill and analysis reading ability possess the “high type”of thinking operation. Both also involve the same content of the abstractintelligent, i.e. symbolic and semantic contents. Last but not least, both alsouse the same product of thinking, i.e. units, classes, relations, and systems.Both can be transformed and have an implication.
Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications
The paper discusses the question “What is mathematics?” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected - almost essentially determined, indeed - by the dynamics of the specific social, mostly professional...
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
Items 1 - 9 of 9 ... Archives: Mathematics Connection. Journal Home > Archives: Mathematics Connection. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register · Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives. 1 - 9 of 9 Items. 2011 ...
This volume contains the proceedings of the 3rd Nordic Research Conference on Special Needs Education in Mathematics, which took place in Rebild organised by Aalborg University in November 23-25, 2005. The theme of the conference was Mathematics Education and Inclusion. The conference theme...
In both China and the West, mathematics is closely connected with literature. The maths thought implied in Chinese and western literature is worth our study, and the maths thought in the field of literature is also appear in aesthetics and philoso-phy, so literature, mathematics, aesthetics and philosophy become a network of interconnected.
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Outlines mathematical topics of use to college geography students identifies teaching methods for mathematical techniques in geography at the University of Leeds; and discusses problem of providing students with a framework for synthesizing all content of geography education. For journal availability, see SO 506 593. (Author/AV)
give a better and more correct idea of modern mathematics than whole volumes of the. Bourbaki ... The de-geometrisation of mathematical education and the divorce from physics sever these ties. ... is their traditional national trait. I do not ...
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Grassl, Richard M.; Mingus, Tabitha T. Y.
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…
The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…
Hoyles, Celia; Woodhouse, Geoffrey
At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.
Blomhøj, Morten; Jensen, Tomas Højgaard
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...
Lenz, Daniel; Savinien, Jean
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomolog...
O. N. Krakhmalev
Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.
For two weeks in August, 1975 more than 140 mathematicians and other scientists gathered at the Universite de Sherbrooke. The occasion was the 15th Biennial Seminar of the Canadian Mathematical Congress, entitled Mathematics and the Life Sciences. Participants in this inter disciplinary gathering included researchers and graduate students in mathematics, seven different areas of biological science, physics, chemistry and medical science. Geographically, those present came from the United States and the United Kingdom as well as from academic departments and government agencies scattered across Canada. In choosing this particular interdisciplinary topic the programme committee had two chief objectives. These were to promote Canadian research in mathematical problems of the life sciences, and to encourage co-operation and exchanges between mathematical scientists" biologists and medical re searchers. To accomplish these objective the committee assembled a stim ulating programme of lectures and talks. Six ...
Bates, Alan B.; Latham, Nancy; Kim, Jin-ah
This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…
Hebert, Michael A.; Powell, Sarah R.
Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…
Milošević Nikoleta M.
Full Text Available Findings presented herein are a part of a large international study of primary school final grade student achievement in mathematics and science (TIMSS 2003. Studies were also conducted on the degree of correlation between student family socioeconomic status, mathematical self-concept and achievement in mathematics. Pilot studies, whose findings are discussed comprised 112 seventh-grade students. "Family socioeconomic status" was defined by variables such as the number of family members, economically disadvantaged/affluent home, and parental educational status. "Mathematical self-concept" was defined as one of the more narrow domains of academic self-concept. "Achievement in mathematics" was measured by the test assessing two dimensions of knowledge of mathematics: content and cognitive skills. The analyses of partial correlations indicate that the most significant predictors of achievement in mathematics test are as follows mathematical self-concept, mother’s educational status and some indicators of family socioeconomic status (access to the Internet, number of household members, number of books available at home. Concerning the correlation found between family characteristics and mathematical self-concept and achievement in mathematics, the developers of current changes in mathematics teaching should not disregard the findings of this study.
Connor, Carol McDonald; Mazzocco, Michèle M M; Kurz, Terri; Crowe, Elizabeth C; Tighe, Elizabeth L; Wood, Taffeta S; Morrison, Frederick J
Accumulating evidence suggests that assessment-informed personalized instruction, tailored to students' individual skills and abilities, is more effective than more one-size-fits-all approaches. In this study, we evaluate the efficacy of Individualizing Student Instruction in Mathematics (ISI-Math) compared to Reading (ISI-Reading) where classrooms were randomly assigned to ISI-Math or ISI-Reading. The literature on child characteristics X instruction or skill X treatment interaction effects point to the complexities of tailoring instruction for individual students who present with constellations of skills. Second graders received mathematics instruction in small flexible learning groups based on their assessed learning needs. Results of the study (n=32 teachers, 370 students) revealed significant treatment effects on standardized mathematics assessments. With effect sizes (d) of 0.41-0.60, we show that we can significantly improve 2nd graders' mathematics achievement, including for children living in poverty, by using assessment data to individualize the mathematics instruction they receive. The instructional regime, ISI-Math, was implemented by regular classroom teachers and it led to about a 4-month achievement advantage on standardized mathematics tests when compared to students in control classrooms. These results were realized within one school year. Moreover, treatment effects were the same regardless of school-level poverty and students' gender, initial mathematics or vocabulary scores. Copyright © 2017 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.
Wieschenberg, Agnes Arvai
A discussion of mathematics anxiety and learned helplessness in mathematics focuses on student failure and avoidance in college mathematics learning. It explores possible causes and suggests classroom activities to foster students' interest and success. (MSE)
Indarti, D.; Mardiyana; Pramudya, I.
The aim of this research is to find out the effect of learning model toward mathematics achievement. This research is quasi-experimental research. The population of research is all VII grade students of Karanganyar regency in the academic year of 2016/2017. The sample of this research was taken using stratified cluster random sampling technique. Data collection was done based on mathematics achievement test. The data analysis technique used one-way ANOVA following the normality test with liliefors method and homogeneity test with Bartlett method. The results of this research is the mathematics learning using Group Investigation learning model with scientific approach produces the better mathematics learning achievement than learning with conventional model on material of quadrilateral. Group Investigation learning model with scientific approach can be used by the teachers in mathematics learning, especially in the material of quadrilateral, which is can improve the mathematics achievement.
This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.
Caponera, Elisa; Sestito, Paolo; Russo, Paolo M.
The aim of this study was to evaluate the influence of students' reading literacy, measured by the PIRLS (Progress in International Reading Literacy Study) test, on their performance in the TIMSS (Trends in International Mathematics and Science Study) mathematics and science tests. The data on 4,125 Italian students from 199 schools were analyzed:…
Adeneye Olarewaju Awofala
Full Text Available The study investigated educational values of mathematics in relation to gender and attitudes toward mathematics among 480 Nigerian preservice mathematics teachers from four universities in Southwest, Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were analysed using the descriptive statistics of frequency, percentage, mean, and standard deviation and inferential statistics of independent samples t-test, Pearson moment correlation, and multiple regression analysis. Findings revealed that preservice mathematics teachers showed high level of educational value of mathematics. There were significant possible correlations among preservice mathematics teachers’ practical value, aesthetic value, cultural value, social value, moral value, disciplinary value, recreational value, and attitudes toward mathematics. While gender differences in some dimensions of educational value of mathematics (practical value, disciplinary value, social value, and cultural value are no longer important and are declining there are subtle gender differences in attitudes toward mathematics and educational values of mathematics in this study. In addition, 73.7% of the variance in preservice teachers’ attitudes toward mathematics was accounted for by the eight predictor variables (gender, practical or utilitarian value, disciplinary value, cultural value, social value, moral value, aesthetic value and recreational value taken together. Based on this baseline study, it was thus, recommended that future studies in Nigeria should investigate the educational value of mathematics of in-service teachers with varied ethnicity and socio-economic background so as to generalise the results of this study.
Marr, M Jackson
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.
Belolipetskiy, A.A.; Lalinina, E.A.; Panina, L.V.
; Layering stage optimization (computation and experiments): First step requires (a) choosing an optimal temperature of target input into the layering channel, (b) analyzing the 'liquid-vapor' interface behavior at different cooling rates, and (c) computation of the FST layering time; A preliminary concept of the FST-layering module for HiPER-class targets (including the interface unit for target-and-sabot assembly) is presented. The results of the mock-ups testing are discussed, namely: (a) FST layering channels (LC) of different geometry have been created and the time of target residence inside LC has been measured for 2 mm diameter targets of different weight and material, including a HiPER-class surrogate target. This allows determining the requirements on the LC manufacturing. (b) Mock-up of target positioning device has been constructed and tested. It was found that the device ensures a comprehensive look at the target for the time less than 1 sec. Acknowledgements. This work supported by the International Science and Technology Center (ISTC) under contract No. 3927 (partner of the project is Science and Technology Facilities Council (STFC), UK).
The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship between these sciences has been reinforced repeatedly in history. In the early 20th century, for example, astronomer Arthur Eddington used photographic evidence from a 1919 solar eclipse to verify Einstein's mathematical theory of relativity. This study was conducted in 5 undergraduate mathematics classes over the course of 2 years. An introductory course in ordinary differential equations, taught in Spring Semester 2013, involved 4 students. A similar course in Spring Semester 2014 involved 6 students, a Summer Semester 2014 Calculus II course involved 2 students, and a Summer 2015 Astronomy course involved 8 students. The students were asked to use Kepler's astronomical evidence to deduce mathematical laws normally encountered on an undergraduate level. They were also asked to examine the elementary mathematical aspects involved in a theoretical trajectory to the planet Neptune. The summer astronomy class was asked to draw mathematical conclusions about large numbers from the recent discoveries concerning the dwarf planet Pluto. The evidence consists primarily of videotaped PowerPoint presentations conducted by the students in both differential equations classes, along with interviews and tests given in all the classes. All presentations were transcribed and examined to determine the effect of astronomy as a generator of student understanding of mathematics. An analysis of the data indicated two findings: definite student interest in a subject previously unknown to most of them and a desire to make the mathematical connection to celestial phenomena.
This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its te
Designed to support both teachers and university-based tutors in mentoring pre-service and newly qualified mathematics teachers at both primary and secondary levels, Mentoring Mathematics Teachers offers straightforward practical advice that is based on practice, underpinned by research, and geared specifically towards this challenging subject area.Developed by members of The Association of Mathematics Education Teachers, the authors draw upon the most up-to-date research and theory to provide evidence-based practical guidance. Themes covered include:
In India and in so many other countries, the science students are generally separated into two main streams: one opting mathematical sciences, the other studying biological sciences. As a result, medicos and biologists have no adequate knowledge of mathematical sciences. It causes a great drawback to them in order to be perfect and updated in their profession, due to the tremendous application of mathematics in bio-sciences, now-a-days. The main aim of this article is to emphasize on the need of the time to produce the mathematico-biologists in abundance for the better service of mankind. (author)
Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.
A practical introduction to the core mathematics principles required at higher engineering levelJohn Bird's approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses. Now in
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Tikhonov, A N
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested
Dobrushin, R L; Shubin, M A; Vershik, Anatoly M
This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The te
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
Achieve the best possible standard with this bestselling book of traditional practice and guidance - now in colour!. First Aid in Mathematics provides all the help and support needed for learning and practising Mathematics. It offers comprehensive coverage of core mathematical topics in clear and accessible language. It is suitable for both native English speakers and students of English as a second language and can be used in class, or as a reference and revision book. - Develops a strong basis of understanding with core topics covered in clear and accessible language. - Improves student's ab
Hollingdale, S. H
Fascinating and highly readable, this book recounts the history of mathematics as revealed in the lives and writings of the most distinguished practitioners of the art: Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Hamilton, Einstein, and many more. Author Stuart Hollingdale introduces and explains the roles of these gifted and often colorful figures in the development of mathematics as well as the ways in which their work relates to mathematics as a whole.Although the emphasis in this absorbing survey is primarily biographical, Hollingdale also discusses major historic
McGregor, C M; Stothers, W W
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differe
Bailey, David H.; Borwein, Jonathan M.
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Palinussa, Anderson L.
This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…
Tabla de Especificaciones e Instructivo sobre Elaboracion de Pruebas Objetivas en la Ensenanza Primaria, para las asignaturas de Estudios Sociales, Idioma Espanol, Matematicas y Ciencias Naturales (Specification Tables and Instructions for the Construction of Objective Tests in the Primary Grades in Social Studies, Spanish, Mathematics, and Natural Sciences).
Ministerio de Educacion, Guatemala City (Guatemala). Direccion de Bienestar Estudiantil y Educacion Especial.
This booklet presents specification tables illustrating the relative importance given to topics on tests within a particular subject area. The general subject areas are social studies, Spanish, mathematics, and natural sciences. Tables are provided for final exams in each of these areas for several primary grades, illustrating the importance of…
Frederico B de Sousa
Full Text Available The aim of this study was to test the possibility of the concomitant formation of calculus deposits and caries from in situ dentin caries model for short time periods. Six volunteers wore palatal removal appliances with four polished dentin specimens protected from intra-oral mechanical forces for up to 14 days. Each volunteer applied a 50% sucrose solution (four times a day on the specimens and performed a daily mouthwash with 0.05% NaF. Samples were removed after 2, 5, 9 and 14 days in situ. Demineralization was analyzed by stereomicroscopy and SEM (secondary electrons and backscattered electrons modes and calculus was analyzed by energy dispersive spectroscopy and fluorescence spectroscopy. Seventeen samples, at least one sample from each volunteer, presented dental calculus on both carious and non-carious ones, detected in all time intervals. Ca/P ratios of dental calculus ranged from 1.1 to 1.7. Some large calculus deposits on carious surfaces were confirmed by fluorescence. In conclusion, concomitant caries and calculus formation can be found in dentin caries formed in situ. This has important repercussions on the study of surface phenomena on the interface between hard dental tissues and dental plaque.
Fuchs, Dmitry; Fuchs, Dmitry
The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.
Kool, Marjolein; Keijzer, Ronald
A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathema...
Full Text Available In the process of reaching a medium income country, science, mathematics and technology have become an emphasis of Ethiopia. But, currently, students' interest to study mathematics and ability in mathematics is declining. This study therefore aimed to investigate the prevalence of mathematics anxiety and its effect on students' current mathematics achievement. Additionally, by grounding on the literature, some strategies supposed to reduce the negative effects of math anxiety were identified for practice. The study was conducted on five randomly selected public secondary schools of East Shoa Zone in Oromia region. Math anxiety was measured using a validated instrument called Math Anxiety Rating Scale (MARS, whereas students' current mathematics achievement was measured using achievement test. Structural model was developed to examine causal relationship of the variables treated in the study. The finding revealed that there was a significant negative relationship between mathematics anxiety and achievement. There was also a statistically significant gender difference in mathematics anxiety and current math achievement, with effect size small and typical respectively. Based on the findings of the study, imperative implication for practice and future research were made.
Bindner, Donald; Hemmeter, Joe
Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Louise M. Saija
Full Text Available Salah satu standar yang diberikan oleh National Council of Teachers of Mathematics (NCTM adalah disposisi matematik. Disposisi bukan sekedar merujuk pada sikap tetapi suatu kecenderungan untuk berpikir dan bersikap dalam cara yang positif. Penelitian ini bertujuan untuk menganalisa disposisi matematik dan hubungannya dengan hasil belajar matematika siswa-siswa sekolah menengah atas (SMA. Sampel pada penelitian ini adalah 149 siswa SMA di Bandung. Analisa statistik didasarkan pada korelasi peringkat Spearman dan uji-t. Ditemukan bahwa secara rata-rata, disposisi matematik dari siswa-siswa SMA dikategorikan rendah. Selanjutnya, terdapat korelasi positif dan signifikan antara disposisi matematik dan hasil belajar matematika siswa-siswa SMA, walaupun nilai koefisien korelasinya tidak tinggi. Suatu observasi juga dilakukan untuk menganalisa hubungan ini, dan didapati bahwa walaupun beberapa siswa memiliki disposisi matematik yang baik, kadang kala mereka tidak dapat menyelesaikan ujian dengan baik, karena padatnya kurikulum, dan juga aktifitas sosial mereka, yang membuat hasil belajar matematika mereka lebih rendah. Temuan lainnya adalah bahwa siswa-siswa SMA memerlukan guru-guru matematika dengan lebih banyak strategi mengajar agar mereka dapat memiliki disposisi matematik yang lebih baik. Kata Kunci: Disposisi Matematik, Hasil Belajar Matematika One of the evaluation standards given by the National Council of Teachers of Mathematics (NCTM was mathematical disposition. Disposition refers not simply to attitudes but to a tendency to think and to act in positive ways. This study aimed to analyze the mathematical disposition and its correlation with mathematics achievement of senior high school (SMA students. A total of 149 SMA students in Bandung were procured as samples. Statistical analysis was based on the Spearman rank correlation and on the t-test. The findings showed that at average, the mathematical disposition of the SMA
Fasni, N.; Turmudi, T.; Kusnandi, K.
This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Tyagi, Tarun Kumar
This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…
Kaya, Defne; Aydin, Hasan
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...
Neto, Joao Pedro
User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.
This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems. All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication The variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/
at Department of Mathematics, Berhampur University, Berhampur 760007, Orissa ... Applications are invited. from University/College teachers and Researchers interested in ... Pre-requisites: A basic knowledge of analysis, topology, differential ...
Arfken, George B
This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted
Wickerhauser, Mladen Victor
Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and s...
This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt
Effective procedures for mathematical tasks in many fields: resolving linear independence, finding null spaces and factors of matrices; differentiating vectors and matrices by chain rule, many more. Techniques illustrated in examples. 1,300 problems. 1978 edition.
Mortimer, Robert G
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...
The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...
Farlow, Stanley J
Students and puzzle enthusiasts will get plenty of enjoyment plus some painless mathematical instruction from 28 conundrums, including The Curve That Shook the World, Space Travel in a Wineglass, and Through Cantor's Looking Glass.
Owen, George E
Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.
This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions
Manin, Yu I
A bird's eye view of mathematics ; physical quantities, dimensions and constants : the source of numbers in physics ; a drop of milk : observer, observation, observable and unobservable ; space-time as a physical system ; action and symmetry.
Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.
particularly to the mathematics decision viz., that of how to optimally combine making, otherwise known as operations evaluations of several experts on nonquan-. --------~-------- ... a short account of how the ratings of sports- persons are arrived ...
Howson, D P
Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma
Rodriguez Danta, M.
Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)
Giles, R; Stark, M; Ulam, S
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn
Landauer, C.; Bellman, K.L.
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
De Finetti, Bruno
Preface by B. de Finetti.- G.Th. Guilbaud: Les equilibres dans les modeles economiques.-H.W. Kuhn: Locational problems and mathematical programming.- M. Morishima: The multi-sectoral theory of economic growth.- B. Martos, J. Kornai: Experiments in Hungary with industry-wide and economy wide programming.- A. Prekopa: Probability distribution problems concerning stochastic programming problems.- R. Frisch: General principles and mathematical techniques of macroeconomic programming.
The extraordinary quantitative achievements of contemporary science often hide their qualitative dimension. In mathematics, the understanding of fundamental theoretical phenomena we have got today goes much beyond that achieved in previous periods. This also holds when it comes to the theorisation of mathematical practice.Philosophically, these changes remain largely to be properly analyzed. The present article will address this issue from the point of view of Bachelard's epistemology.
Today mathematical competitions are very popular with primary and secondary school students and there are many countries all around the world where they are regularly organised. There are several rounds and a lot of students are included, especially at the beginning rounds. The best students from the previous round have the right to continue on the higher level of competition. The final level for the secondary school student competitors is the International Mathematical Olympiad (IMO). The te...
Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo
Ligomenides, Panos A.
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presen...
Boyer, Carl B
"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...
Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)
The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)
Pedroso de Lima, J.J.
The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)
Pontrjagin, Lev Semenovič
Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge ometry in the plane and 3-dimensional space. Refin...
Shepley, Richard A.
The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State...
Mathematics teaching in Denmark was recently recommended better organized in sequences with clear mathematical pedagogical goals and a focus on mathematical points. In this paper I define a mathematical point and inform on coding of transcripts in a video based Danish research study on grade 8 te...
Anhalt, Cynthia Oropesa; Cortez, Ricardo
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
BÉLA ILLÉS; GABRIELLA BOGNÁR
Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’ performance at the end of each semester for these courses. Our goal is to overview a few questions on mathematics as a core subject of engineering.
Cunningham, R. S.; Smith, David A.
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Koopman, L.; Brouwer, N.; Heck, A.; Buma, W.J.
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the
This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…
Duval County Schools, Jacksonville, FL.
This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…
Kenney, Margaret J.
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Handayani, I.; Januar, R. L.; Purwanto, S. E.
This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.
Full Text Available The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.
Information literacy is mostly seen from the perspective of library science or information and communication technology. Taking another point of view, this study was aimed to explore students’ information literacy from the perspective of mathematical literacy. For this purpose, a test addressing Programme for International Student Assessment (PISA) mathematics tasks were administered to 381 eighth and ninth graders from nine junior high schools in the Province of Yogyakarta. PISA mathematics ...
This book enables teachers to effectively meet the needs of their most able mathematicians. Using a tried and tested set of principles developed and used by The Able Children's Education Unit at Brunel University, the author demonstrates how to: identify high mathematical ability in a pupil, plan suitably challenging activities and teach them most effectively within the existing National Numeracy framework, make the most of the classroom resources available, including ICT and external agencies, implement strategies for differentiation, illustrated with real-life classroom examples. Ac
Mrs. Manju Devi*
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistrystudents in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialistsof the chemistry-related fields (physicists, mathematicians, biologists, etc.) intothe world of the chemical applications.Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others we
Morris, Carla C
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Janke, Steven J
A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap
Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.
Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900
Wang, J.; Hansen, P.K.; Christensen, S.; Qi, G.Z.
This article discusses the structure of weed reproduction incorporating the application of a mathematical model. This mathematical methodology enables the construction, testing and application of distribution models for the analysis of the structure of weed reproduction and weed ecology. The
Ali İhsan BORAN
Full Text Available The purpose of this study is to investigate relationship of mathematics Olympiad (analysis-algebra and geometry scores of gifted students with IQ scores (verbal, performance and general and mathematics achievement scores of the gifted students. Study group of the study included 64 gifted students (27 girls and 37 boys who took courses from one Science and Art Center. Data of study involved scores of the participants on mathematics Olympiad exam, WISC-R test and school mathematics achievement. For analysis of the data Pearson correlation analysis, Spearman correlation analysis, independent groups’ t-test and Mann Whitney U test were utilized. The findings showed that there was no significant relationship between the Olympiad scores on analysis-algebra and geometry and IQ scores (general, performance and verbal. But the Olympiad scores on analysis-algebra and geometry factors were significantly related to school mathematics achievement. Comparing IQ scores of highest and lowest scorer groups on the Olympiad scores showed that there were no significant differences between IQ scores (general, performance and verbal of the groups. However school mathematics scores of the participants significantly differed in terms of groups determined based on analysis-algebra and geometry scores.
Hsu, Pao-sheng; Pollatsek, Harriet
Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...
Gaber, David; Schlimm, Dirk
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. © 2015 John Wiley & Sons, Ltd.
Hadley, Kristin M.; Dorward, Jim
Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...
Szpiro, George G
Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author
This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.
Schmidt, Maria Christina Secher
This article investigates possible links between inclusion, students, for whom mathematics is extensively difficult, and classroom leadership through a case study on teaching strategies and student participation in four classrooms at two different primary schools in Denmark. Three sets of results...... are presented: 1) descriptions of the teachers’ classroom leadership to include all their students in the learning community, 2) the learning community produced by stated and practiced rules for teaching and learning behavior, 3) the classroom behavior of students who experience difficulties with mathematics....... The findings suggest that the teachers’ pedagogical choices and actions support an active learning environment for students in diverse learning needs, and that the teachers practise dimensions of inclusive classroom leadership that are known to be successful for teaching mathematics to all students. Despite...
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...
Roe, John; Jamshidi, Sara
Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...
Yamagishi, Michel Eduardo Beleza
This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.
Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. Great attention was paid to ensuring fast access to the information, and each carefully reviewed article includes a glossary of terms and a guide to further reading. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic Methods - Analytic Methods - Fourier and Other Mathematical Transforms - Fractal Geometry - Geometrical Methods - Green's Functions - Group Theory - Mathematical Modeling - Monte Carlo Methods - Numerical Methods - Perturbation Methods - Quantum Computation - Quantum Logic - Special Functions - Stochastic Processes - Symmetries and Conservation Laws - Topology - Variational Methods. (orig.)
Some teachers of biochemistry think it positively beneficial for students to struggle with difficult mathematics. I do not number myself among these people, although I have derived much personal pleasure from the study of mathematics and from applying it to problems that interest me in biochemistry. On the contrary, I think that students choose courses in biochemistry out of interest in biochemistry and that they should not be encumbered with more mathematics than is absolutely required for a proper understanding of biochemistry. This of course includes physical chemistry, because a biochemist ignorant of physical chemistry is no biochemist. I have been guided by these beliefs in writing this book. I have laid heavy emphasis on those topics, such as the use of logarithms, that play an important role in biochemistry and often cause problems in teaching; I have ignored others, such as trigonometry, that one can manage without. The proper treatment of statistics has been more difficult to decide. Although it cle...
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Volume 100, which is the final volume of the LNBM series serves to commemorate the acievements in two decades of this influential collection of books in mathematical biology. The contributions, by the leading mathematical biologists, survey the state of the art in the subject, and offer speculative, philosophical and critical analyses of the key issues confronting the field. The papers address fundamental issues in cell and molecular biology, organismal biology, evolutionary biology, population ecology, community and ecosystem ecology, and applied biology, plus the explicit and implicit mathematical challenges. Cross-cuttting issues involve the problem of variation among units in nonlinear systems, and the related problems of the interactions among phenomena across scales of space, time and organizational complexity.