Polly, Drew; McGee, Jennifer R.; Sullivan, Christie
2010-01-01
While technology has potential to improve the teaching and learning of mathematics, research indicates that teachers struggle in their efforts to implement technology-rich mathematical tasks in their classrooms. Effective technology integration in mathematics requires teachers to be able to apply their classroom knowledge related to mathematics…
Technology-Rich Mathematics Instruction
Thach, Kim J.; Norman, Kimberly A.
2008-01-01
This article uses one of the authors' classroom experiences to explore how teachers can create technology-rich learning environments that support upper elementary students' mathematical understanding of algebra and number and operations. They describe a unit that presents a common financial problem (the use of credit cards) to engage sixth graders…
Reflections on a Technology-Rich Mathematics Classroom
Hodges, Thomas E.; Conner, Elizabeth
2011-01-01
Integrating technology into the mathematics classroom means more than just new teaching tools--it is an opportunity to redefine what it means to teach and learn mathematics. Yet deciding when a particular form of technology may be appropriate for a specific mathematics topic can be difficult. Such decisions center on what is commonly being…
Pre-Service Mathematics Teachers' Use of Multiple Representations in Technology-Rich Environments
Ozmantar, Mehmet Faith; Akkoc, Hatice; Bingolbali, Erhan; Demir, Servet; Ergene, Berna
2010-01-01
In this paper, we examine the development of pre-service mathematics teachers' use of multiple representations during teaching in technology-rich environments. The pre-service teachers took part in a preparation program aimed at integration of technology into teaching mathematics. The program was designed on the basis of Technological Pedagogical…
Mathematics for Gifted Students in an Arts- and Technology-Rich Setting
Gadanidis, George; Hughes, Janette; Cordy, Michelle
2011-01-01
In this paper we report on a study of a short-term mathematics program for grade 7-8 gifted students that integrated open-ended mathematics tasks with the arts (poetry and drama) and with technology. The program was offered partially online and partially in a classroom setting. The study sought to investigate (a) students' perceptions of their…
Putting Mathematical Tasks into Context
Nagle, Courtney R.; Styers, Jodie L.
2015-01-01
Although many factors affect students' mathematical activity during a lesson, the teacher's selection and implementation of tasks is arguably the most influential in determining the level of student engagement. Mathematical tasks are intended to focus students' attention on a particular mathematical concept and it is the careful developing and…
What Makes a Mathematical Task Interesting?
Nyman, Rimma
2016-01-01
The study addresses the question of what makes a mathematical task interesting to the 9th year students. Semi-structured interviews were carried out with 15 students of purposive selection of the 9th year. The students were asked to recall a task they found interesting and engaging during the past three years. An analysis of the tasks was made…
Developing Mathematization with Physics Invention Tasks
Brahmia, Suzanne; Kanim, Stephen E
2016-01-01
Experts in physics develop and communicate ideas through mathematization, the mental practice of translating between the physical world and the symbolic world. Research in mathematics education and physics education has shown that introductory college physics students often struggle with the idiosyncratic ways that familiar mathematics is used in physics. Additional work has shown that invention tasks have promise as an instructional approach for helping students use math flexibly and generatively in science and in statistics. In this paper we describe our physics invention tasks,* classroom activities designed to support construction of quantitative physics concepts and relationships and to prepare students to better understand the reasoning introduced in subsequent formal instruction. We share results from a preliminary study of the impact of physics invention tasks in a reformed introductory calculus-based physics course. The reformed course, taught by one of the authors and designed specifically for mathe...
The Role of Tasks in Developing Communities of Mathematical Inquiry.
Peressini, Dominic; Knuth, Eric
2000-01-01
Examines the nature of mathematically rich tasks and varied ways in which students respond to these tasks. Explores approaches for using such tasks to foster inquiry that engages children in mathematical practice. (Contains 16 references.) (ASK)
Research on Mathematics Teachers as Partners in Task Design
Jones, Keith; Pepin, Birgit
2016-01-01
Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the "design" of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to…
When Mathematics and Statistics Collide in Assessment Tasks
Bargagliotti, Anna; Groth, Randall
2016-01-01
Because the disciplines of mathematics and statistics are naturally intertwined, designing assessment questions that disentangle mathematical and statistical reasoning can be challenging. We explore the writing statistics assessment tasks that take into consideration potential mathematical reasoning they may inadvertently activate.
A Worthwhile Mathematical Task for Students and Their Teachers
Chamberlin, Michelle T.; Zawojewski, Judith
2006-01-01
Worthwhile mathematical tasks not only prompt students to learn mathematics, they also prompt teachers to learn and improve their teaching in their own mathematics classrooms. When teachers use worthwhile tasks, they have to learn "what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask…
Seegers, Gerard; van Putten, Cornelis M; de Brabander, Cornelis J
2002-09-01
In earlier studies, it has been found that students' domain-specific cognitions and personal learning goals (goal orientation) influence task-specific appraisals of actual learning tasks. The relations between domain-specific and task-specific variables have been specified in the model of adaptive learning. In this study, additional influences, i.e., perceived task outcome on a former occasion and variations in task demands, were investigated. The purpose of this study was to identify personality and situational variables that mediate students' attitude when confronted with a mathematics task. Students worked on a mathematics task in two subsequent sessions. Effects of perceived task outcome at the first session on students' attitude at the second session were investigated. In addition, we investigated how differences in task demands influenced students' attitude. Variations in task demands were provoked by different conditions in task-instruction. In one condition, students were told that the result on the test would add to their mark on mathematics. This outcome orienting condition was contrasted with a task-orienting condition where students were told that the results on the test would not be used to give individual grades. Participants were sixth grade students (N = 345; aged 11-12 years) from 14 primary schools. Multivariate and univariate analyses of (co)variance were applied to the data. Independent variables were goal orientation, task demands, and perceived task outcome, with task-specific variables (estimated competence for the task, task attraction, task relevance, and willingness to invest effort) as the dependent variables. The results showed that previous perceived task outcome had a substantial impact on students' attitude. Additional but smaller effects were found for variation in task demands. Furthermore, effects of previous perceived task outcome and task demands were related to goal orientation. The resulting pattern confirmed that, in general
Middle School Teachers' Views and Approaches to Implement Mathematical Tasks
Yesildere-Imre, Sibel; Basturk-Sahin, Burcu Nur
2016-01-01
This research examines middle school mathematics teachers' views regarding implementation of mathematical tasks and their enactments. We compare their views on tasks and their implementation, and determine the causes of difference between the two using qualitative research methods. We interview sixteen middle school mathematics teachers based on…
Akayuure, Peter; Apawu, Jones
2014-01-01
The study was designed to engage prospective mathematics teachers in creating web learning modules. The aim was to examine the mathematical task and perceived pedagogical usability of the modules for mathematics instructions in Ghana. The study took place at University of Education, Winneba. A class of 172 prospective mathematics teachers working in design groups were involved in the study. Data were collected using Mathematical Task Usability Scale and Pedagogical Usability Rubrics. The resu...
Designing Prediction Tasks in a Mathematics Software Environment
Brunström, Mats; Fahlgren, Maria
2015-01-01
There is a recognised need in mathematics teaching for new kinds of tasks which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study…
Tasks that May Occasion Mathematical Creativity: Teachers' Choices
Levenson, Esther
2013-01-01
Promoting mathematical creativity is one of the aims of mathematics education. This study investigates the tasks teachers chose when their aim was to occasion mathematical creativity in the classroom. Five cases are described in depth, and general trends found among these cases as well as in additional data are discussed. Findings indicated that…
Learners' Approaches to Solving Mathematical Tasks: Does Specialisation Matter?
Machaba, France; Mwakapenda, Willy
2016-01-01
This article emerged from an analysis of learners' responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by…
Akayuure, Peter; Apawu, Jones
2015-01-01
The study was designed to engage prospective mathematics teachers in creating web learning modules. The aim was to examine the mathematical task and perceived pedagogical usability of the modules for mathematics instructions in Ghana. The study took place at University of Education, Winneba. Classes of 172 prospective mathematics teachers working…
Students' Reasoning in Mathematics Textbook Task-Solving
Sidenvall, Johan; Lithner, Johan; Jäder, Jonas
2015-01-01
This study reports on an analysis of students' textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such…
Supporting Teachers in Structuring Mathematics Lessons Involving Challenging Tasks
Sullivan, Peter; Askew, Mike; Cheeseman, Jill; Clarke, Doug; Mornane, Angela; Roche, Anne; Walker, Nadia
2015-01-01
The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers…
GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT
Directory of Open Access Journals (Sweden)
V. A. Testov
2014-01-01
Full Text Available The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Imagining Mathematics Teaching via Scripting Tasks
Zazkis, Rina; Sinclair, Nathalie
2013-01-01
We discuss an innovative task used in teacher education--Lesson Play--that involves presenting a lesson in the form of an interaction between a teacher and students. We describe the motivation for the development of this task and, through specific examples, describe the iterative design process in which the task was refined and improved. We…
Biza, Irene; Nardi, Elena; Joel, Gareth
2015-01-01
In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees' considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the…
Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis
Hamburg, Maryanna P.
2009-01-01
This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…
Non-Mathematics Students' Reasoning in Calculus Tasks
Jukic Matic, Ljerka
2015-01-01
This paper investigates the reasoning of first year non-mathematics students in non-routine calculus tasks. The students in this study were accustomed to imitative reasoning from their primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, non-routine tasks were implemented as an explicit part of…
Professional Development for Mathematics Teachers: Using Task Design and Analysis
Lee, Hea-Jin; Özgün-Koca, S. Asli
2016-01-01
This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…
Supporting Teachers Developing Mathematical Tasks with Digital Technology
Ratnayake, Iresha; Oates, Greg; Thomas, Mike
2016-01-01
A crucial step towards improving the conceptual use of digital technology (DT) in the mathematics classroom is to increase teacher involvement in the development of tasks. Hence, this research considers some teacher factors that might influence DT algebra task development and implementation in secondary schools. We observed and assisted one group…
Mathematical Knowledge for Teaching and Task Unfolding: An Exploratory Study
Charalambous, Charalambos Y.
2010-01-01
Although teachers' knowledge is thought to contribute to the selection and implementation of mathematical tasks, empirical evidence supporting this claim is scarce. To investigate this relationship and understand its nature, this exploratory study examines the unfolding of tasks in a series of lessons led by 2 elementary school teachers who…
Chamberlin, Scott A.; Powers, Robert A.
2013-01-01
The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…
Gibney, Janette
2014-01-01
This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that…
Children's mathematical performance: five cognitive tasks across five grades.
Moore, Alex M; Ashcraft, Mark H
2015-07-01
Children in elementary school, along with college adults, were tested on a battery of basic mathematical tasks, including digit naming, number comparison, dot enumeration, and simple addition or subtraction. Beyond cataloguing performance to these standard tasks in Grades 1 to 5, we also examined relationships among the tasks, including previously reported results on a number line estimation task. Accuracy and latency improved across grades for all tasks, and classic interaction patterns were found, for example, a speed-up of subitizing and counting, increasingly shallow slopes in number comparison, and progressive speeding of responses especially to larger addition and subtraction problems. Surprisingly, digit naming was faster than subitizing at all ages, arguing against a pre-attentive processing explanation for subitizing. Estimation accuracy and speed were strong predictors of children's addition and subtraction performance. Children who gave exponential responses on the number line estimation task were slower at counting in the dot enumeration task and had longer latencies on addition and subtraction problems. The results provided further support for the importance of estimation as an indicator of children's current and future mathematical expertise.
Fredenberg, Michael Duane
The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the
Koichu, Boris; Zaslavsky, Orit; Dolev, Lea
2016-01-01
The goal of the study presented in this article was to examine how variations in task design may affect mathematics teachers' learning experiences. The study focuses on sorting tasks, i.e., learning tasks that require grouping a given set of mathematical items, in as many ways as possible, according to different criteria suggested by the learners.…
Richardson, Miles; Hunt, Thomas E; Richardson, Cassandra
2014-12-01
This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7-8, 10-11, and 13-14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability.
Choosing High-Yield Tasks for the Mathematical Development of Practicing Secondary Teachers
Epperson, James A. Mendoza; Rhoads, Kathryn
2015-01-01
Many mathematics teacher educators encounter the challenge of creating or choosing mathematical tasks that evoke important mathematical insights and connections yet remain firmly grounded in school mathematics. This challenge increases substantially when trying to meet the needs of practicing secondary mathematics teachers pursuing graduate work…
Martin, Christie; Polly, Drew; McGee, Jen; Wang, Chuang; Lambert, Richard; Pugalee, David
2015-01-01
This study examined the mathematical discourse of elementary school teachers and their students while participating in a year-long professional development project focused on implementing reform-based mathematics curriculum. The teacher participants included 12 teachers, two from each grade level from Kindergarten through Grade 5. Field notes were…
Peled, Irit
2007-01-01
This article discusses the design of tasks for teacher education. It focuses on tasks that are used in a university course for pre-service secondary school mathematics teachers. Special attention is given to tasks that use analogical thinking in their construction or implementation. These tasks are categorized by type of teacher education goal and…
Uses and goals of mathematical tasks : an experiment with pre-service teachers
Gomes, Alexandra
2011-01-01
Mathematical tasks can be used in teacher education for several purposes: to introduce mathematical ideas, to enhance mathematical understanding or to explore issues related to the pedagogy of mathematics, among others. In this paper we will describe a model to examine the use of mathematical tasks, in teacher education, proposed by Liljedahl, Chernoff and Zazkis (2007) and based on this model we will describe an experiment that went on with pre-service teachers. They were g...
[Influence of music on a decision of mathematical logic tasks].
Pavlygina, R A; Karamysheva, N N; Sakharov, D S; Davydov, V I
2012-01-01
Accompaniment of a decision of mathematical logical tasks by music (different style and power) influenced on the time of the decision. Classical music 35 and 65 dB and roc-music 65 and 85 dB decreased the time of the decision. More powerful classical music (85 dB) did not effect like that. The decision without the musical accompaniment led to increasing of coherent values especially in beta1, beta2, gamma frequency ranges in EEG of occipital cortex. The intrahemispheric and the interhemispheric coherences of frontal EEG increased and EEG asymmetry (in a number of Coh-connections in left and right hemispheres) arose during the tasks decision accompanied by music. Application of classical music 35 and 65 dB caused left-side asymmetry in EEG. Using of more powerful classical or rock music led to prevalence of quantity of Coh-connections in a right hemisphere.
Snapshots of mathematics teacher noticing during task design
Choy, Ban Heng
2016-09-01
Designing a mathematically worthwhile task is critical for promoting students' reasoning. To improve task design skills, teachers often engage in collaborative lesson planning activities such as lesson study. However, to learn from the process of lesson study, it is important for teachers to notice productively the concepts, students' confusion and the design of the task. But what researchers mean by productive noticing varies. In this article, I present the FOCUS Framework which highlights two characteristics of productive noticing: having an explicit focus for noticing and focusing noticing through pedagogical reasoning. Using these two characteristics, I develop snapshots of noticing as a representation of practice to present a fine-grained analysis of teacher noticing. Through vignettes of teachers discussing the design of a task to teach fractions, I illustrate how two teachers' noticing can be analysed and represented using snapshots of noticing. To conclude, I highlight what snapshots of noticing tell us about a teacher's noticing and suggest ways to use these snapshots in future studies of noticing.
Jamieson, Thad Spencer
2015-01-01
The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…
A Highly Capable Year 6 Student's Response to a Challenging Mathematical Task
Livy, Sharyn; Holmes, Marilyn; Ingram, Naomi; Linsell, Chris; Sullivan, Peter
2016-01-01
Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…
The Relation between Types of Assessment Tasks and the Mathematical Reasoning Students Use
Boesen, Jesper; Lithner, Johan; Palm, Torulf
2010-01-01
The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did…
Maciejewski, Wes; Merchant, Sandra
2016-04-01
Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students' academic outcomes. This study takes a cross-sectional look at the approaches to learning used by students from courses across all four years of undergraduate mathematics and analyses how these relate to the students' grades. We find that deep learning correlates with grade in the first year and not in the upper years. Surficial learning has no correlation with grades in the first year and a strong negative correlation with grades in the upper years. Using Bloom's taxonomy, we argue that the nature of the tasks given to students is fundamentally different in lower and upper year courses. We find that first-year courses emphasize tasks that require only low-level cognitive processes. Upper year courses require higher level processes but, surprisingly, have a simultaneous greater emphasis on recall and understanding. These observations explain the differences in correlations between approaches to learning and course grades. We conclude with some concerns about the disconnect between first year and upper year mathematics courses and the effect this may have on students.
Oktiningrum, Wuli; Zulkardi; Hartono, Yusuf
2016-01-01
The aim of this research is produce a set of PISA-like mathematics task with Indonesia natural and cultural heritage as context which are valid, practical, to assess students' mathematics literacy. This is design research using type of development research with formative evaluation. A total of 20 students of SMP Negeri 1 Palembang. Beside, 10…
Mahanin, Hajah Umisuzimah Haji; Shahrill, Masitah; Tan, Abby; Mahadi, Mar Aswandi
2017-01-01
This study investigated the use of interdisciplinary learning activity task to construct students' knowledge in Mathematics, specifically on the topic of scale drawing application. The learning activity task involved more than one academic discipline, which is Mathematics, English Language, Art, Geography and integrating the Brunei Darussalam…
Designing Tasks to Promote and Assess Mathematical Transfer in Primary School Children
Clark, Julie; Page, Shaileigh; Thornton, Steve
2013-01-01
This study aims to design learning situations and tasks that promote and assess the capacity of primary school children to transfer mathematical knowledge to new contexts. We discuss previous studies investigating mathematical transfer, and particularly the strengths and limitations of tasks used to assess transfer in these studies. We describe…
Lowrie, Tom; Diezmann, Carmel M.; Logan, Tracy
2012-01-01
Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students' mathematics understandings. Through an iterative design, the investigation described the sense making of 11-12-year-olds as they…
Gender and Performance in Mathematical Tasks: Does the Context Make a Difference?
Zohar, Anat; Gershikov, Anna
2008-01-01
This study investigates how the context of mathematical tasks affects the performance of young children (ages 5-11). Subjects were 523 children from age 5 to 11. Three contexts of mathematical tasks (stereotypically boys' contexts, stereotypically girls' contexts and neutral contexts) are examined in three age groups (young, medium, and old).…
Gender and Performance in Mathematical Tasks: Does the Context Make a Difference?
Zohar, Anat; Gershikov, Anna
2008-01-01
This study investigates how the context of mathematical tasks affects the performance of young children (ages 5-11). Subjects were 523 children from age 5 to 11. Three contexts of mathematical tasks (stereotypically boys' contexts, stereotypically girls' contexts and neutral contexts) are examined in three age groups (young, medium, and old).…
Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle
Antonijevic, Radovan
2016-01-01
In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…
Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Exploring Ava's Developing Sense for Tasks That May Occasion Mathematical Creativity
Levenson, Esther
2015-01-01
This study explores the relationship between participating in a graduate course aimed at enhancing teachers' theoretical and practical knowledge of mathematical creativity and one teacher's changing perspectives regarding mathematical creativity and tasks that may occasion mathematical creativity. Results indicated that perceptions of…
Exploring Ava's Developing Sense for Tasks That May Occasion Mathematical Creativity
Levenson, Esther
2015-01-01
This study explores the relationship between participating in a graduate course aimed at enhancing teachers' theoretical and practical knowledge of mathematical creativity and one teacher's changing perspectives regarding mathematical creativity and tasks that may occasion mathematical creativity. Results indicated that perceptions of…
Stylianides, Andreas J.; Stylianides, Gabriel J.
2008-01-01
Mathematical tasks embedded in real-life contexts have received increased attention by educators, in part due to the considerable levels of student engagement often triggered by their motivational features. Nevertheless, it is often challenging for teachers to implement high-level (i.e., cognitively demanding), real-life tasks in ways that exploit…
Second-Graders' Mathematical Practices for Solving Fraction Tasks
Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Tucker, Stephen I.
2014-01-01
Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…
Tasks and activities to enhance technological Pedagogical Mathematical Content Knowledge of teachers
Powell, Arthur B.
2016-01-01
From a sociocultural perspective, we examine activities generated by genres of tasks to understand how the tasks shape teachers knowledge of technology and mathematical content for teaching. The tasks and activities come from a professional development project that engages the cyberlearning system, Virtual Math Teams with GeoGebra. Working in teams, teachers enhance their understanding of dynamic geometry and how to engage in productive mathematical discussion. We theorize and discuss princip...
Directory of Open Access Journals (Sweden)
John Monaghan
2007-07-01
Full Text Available This article considers one class of high school students as they worked on a task given to them by a company director of a haulage firm. The article provides details of students’ transformation of the given task into a subtly different task. It is argued that this transformation is interrelated with students’ understandings of mathematics, of technology and of the real world and students’ emerging goals. It is argued that the students did not address the company director’s task. Educational implications with regard to student engagement with realistic tasks are considered.
Entering into dialogue about the mathematical value of contextual mathematising tasks
Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng
2017-06-01
Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for three classroom stakeholders: (1) students, who wish to reflect on and enhance their mathematical learning; (2) teachers, who wish to integrate contextual mathematising tasks into their teaching practice and (3) researchers, who seek rich tasks for generating observable instances of mathematical thinking and learning. We anticipate that these reports and the underlying theoretical framework for creating them will contribute to greater awareness of and appreciation for the mathematical value of contextual mathematising tasks in learning, teaching and research.
Studying Mathematics Teacher Education: Analysing the Process of Task Variation on Learning
Bragg, Leicha A.
2015-01-01
Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in…
Directory of Open Access Journals (Sweden)
Wuli Oktiningrum
2016-01-01
Full Text Available The aim of this research is produce a set of PISA-like mathematics task with Indonesia natural and cultural heritage as context which are valid, practical, to assess students’ mathematics literacy. This is design research using type of development research with formative evaluation. A total of 20 students of SMP Negeri 1 Palembang. Beside, 10 experts were involved in this research to assess the feasibility of prototyping in terms of content, context and language. Walk through, documentation, questionnaire, test result, and interviews are way to collect the data. This research produced a PISA-like math task is as many 12 category of content, context, and process valid, practical and has potential effect. The validity came empirical evaluation of validation and reliability testing during small group. From the field test, we conclude that the tasks also potentially effect to the students’ mathematical literacy in activating the indicators of each Fundamental Mathematical Capabilities.Keywords: development research, PISA task, mathematics literacy, fundamental mathematical capabilities DOI: http://dx.doi.org/10.22342/jme.7.1.2812.1-8
Teachers enacting a technology-rich curriculum for emergent literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2011-01-01
Cviko, A., McKenney, S., & Voogt, J. (2012). Teachers enacting a technology-rich curriculum for emergent literacy. Educational Technology Research and Development, 60(1), 31-54. doi:10.1007/s11423-011-9208-3
Toward a mathematical formalism of performance, task difficulty, and activation
Samaras, George M.
1988-01-01
The rudiments of a mathematical formalism for handling operational, physiological, and psychological concepts are developed for use by the man-machine system design engineer. The formalism provides a framework for developing a structured, systematic approach to the interface design problem, using existing mathematical tools, and simplifying the problem of telling a machine how to measure and use performance.
Jupri, Al
2017-04-01
In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.
Zaslavsky, Orit
2010-01-01
This book offers a unifed approach to tasks used in the education of secondary mathematics teachers, based on broad goals such as adaptability, identifying similarities, productive disposition, overcoming barriers, micro simulations, choosing tools, and more.
Construction of Tasks in Order to Develop and Promote Classroom Communication in Mathematics
Olteanu, Lucian
2015-01-01
In this article, the focus is on task construction and the importance of this process to develop and promote classroom communication in mathematics. The students' tests, examination of students' mathematical work, the teachers' lesson plans, and reports of the lessons' instructions are the basic data for this article. The analysis indicated that…
USING TASK LIKE PISA’S PROBLEM TO SUPPORT STUDENT’S CREATIVITY IN MATHEMATICS
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Rita Novita
2016-01-01
Full Text Available Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also In mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize. Doing so causes many children’s natural curiosity and enthusiasm for mathematics to disappear as they get older, creating a tremendous problem for mathematics educators who are trying to instil these very qualities. In order to investigate the increase in awareness of elementary school students’ creativity in solving mathematics’ problems by using task like PISA’s Question, a qualitative research emphasizing on holistic description was conducted. We used a formative evaluation type of development research as a mean to develop mathematical tasks like PISA’s question that have potential effect to support students’ creativity in mathematics. Ten elementary school students of grade 6 in Palembang were involved in this research. They judged the task given for them is very challenging and provokes their curiosity. The result showed that task like PISA’s question can encourage students to more creatively in mathematics.
The Effect of Mathematical Games on On-Task Behaviours in the Primary Classroom
Bragg, Leicha A.
2012-01-01
A challenge for primary classroom teachers is to maintain students' engagement with learning tasks while catering for their diverse needs, capabilities and interests. Multiple pedagogical approaches are employed to promote on-task behaviours in the mathematics classroom. There is a general assumption by educators that games ignite children's…
Lacan, Subjectivity and the Task of Mathematics Education Research
Brown, Tony
2008-01-01
This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud's psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan's subjectivity…
Spatial Reasoning Influences Students' Performance on Mathematics Tasks
Lowrie, Tom; Logan, Tracy; Ramful, Ajay
2016-01-01
Although the psychological literature has demonstrated that spatial reasoning and mathematics performance are correlated, there is scant research on these relationships in the middle years. The current study examined the commonalities and differences in students' performance on instruments that measured three spatial reasoning constructs and two…
Lacan, Subjectivity and the Task of Mathematics Education Research
Brown, Tony
2008-01-01
This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud's psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan's subjectivity…
The mathematical model of the task of compiling the time-table
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О.Є. Литвиненко
2004-01-01
Full Text Available The mathematical model of the task of compiling the time-table in High-school has been carried out. It has been showed, that the task may be reduced to canonical form of extrimal combinatorial tasks with unlinear structure after identical transformations. The algorithm of the task’s decision for realizing the scheme of the directed sorting of variants is indicated.
The mathematical model of the task of compiling the time-table
Литвиненко, О. Є.; Г.С. Краліна; О.П. Стьопушкіна
2004-01-01
The mathematical model of the task of compiling the time-table in High-school has been carried out. It has been showed, that the task may be reduced to canonical form of extrimal combinatorial tasks with unlinear structure after identical transformations. The algorithm of the task’s decision for realizing the scheme of the directed sorting of variants is indicated.
Development of a Framework to Characterise the Openness of Mathematical Tasks
Yeo, Joseph B. W.
2017-01-01
Educators usually mean different constructs when they speak of open tasks: some may refer to pure-mathematics investigative tasks while others may have authentic real-life tasks in mind; some may think of the answer being open while others may refer to an open method. On the other hand, some educators use different terms, e.g. open and open-ended,…
Collaer, Marcia L; Hill, Erica M
2006-01-01
Visuospatial performance, assessed with the new, group-administered Judgment of Line Angle and Position test (JLAP-13), varied with sex and mathematical competence in a group of adolescents. The JLAP-13, a low-level perceptual task, was modeled after a neuropsychological task dependent upon functioning of the posterior region of the right hemisphere [Benton et al, 1994 Contributions to Neuropsychological Assessment: A Clinical Manual (New York: Oxford University Press)]. High-school boys (N = 52) performed better than girls (N = 62), with a large effect for sex (d = 1.11). Performance increased with mathematical competence, but the sex difference did not vary significantly across different levels of mathematics coursework. On the basis of earlier work, it was predicted that male, but not female, performance in line judgment would decline with disruptions to task geometry (page frame), and that the sex difference would disappear with disruptions to geometry. These predictions were supported by a number of univariate and sex-specific analyses, although an omnibus repeated-measures analysis did not detect the predicted interaction, most likely owing to limitations in power. Thus, there is partial support for the notion that attentional predispositions or strategies may contribute to visuospatial sex differences, with males more likely than females to attend to, and rely upon, internal or external representations of task geometry. Additional support for this hypothesis may require development of new measures or experimental manipulations with more powerful geometrical disruptions.
Hsu, Hui-Yu; Silver, Edward A.
2014-01-01
We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…
Time-on-task, technology and mathematics achievement.
Louw, Johann; Muller, Johan; Tredoux, Colin
2008-02-01
Information and communication technologies hold much promise for use in education in developing countries. This study reports on an evaluation conducted on the introduction of computers in the delivery of the mathematics curriculum in one of the provinces of South Africa. Although the request was for an outcome evaluation very early in the implementation of the program, it was tailored in such a way as to fulfill a more formative role. Despite substantial variability in implementation, and in most cases with very weak exposure of the learners to the intervention, sufficient evidence emerged to indicate that this mode of curriculum delivery may be effective. Improvement in mathematics performance was related to a range of variables: some concerned classroom teaching practices, some referred to social differences between the learners, and some to the specific intervention. The strongest of these predictors in the sample was the strength of the intervention: the more time learners spent on using the software to study mathematics, the more improvement they showed from 1 year to the next in their performance in the subject.
Unique Signal mathematical analysis task group FY03 status report.
Energy Technology Data Exchange (ETDEWEB)
Baty, Roy Stuart (Los Alamos National Laboratory, Los Alamos, NM); Johnston, Anna Marie; Hart, Elizabeth (Utah State University, Logan, UT); White, Allan (NASA, Langley Research Center, Hampton, VA); Cooper, James Arlin
2003-12-01
The Unique Signal is a key constituent of Enhanced Nuclear Detonation Safety (ENDS). Although the Unique Signal approach is well prescribed and mathematically assured, there are numerous unsolved mathematical problems that could help assess the risk of deviations from the ideal approach. Some of the mathematics-based results shown in this report are: 1. The risk that two patterns with poor characteristics (easily generated by inadvertent processes) could be combined through exclusive-or mixing to generate an actual Unique Signal pattern has been investigated and found to be minimal (not significant when compared to the incompatibility metric of actual Unique Signal patterns used in nuclear weapons). 2. The risk of generating actual Unique Signal patterns with linear feedback shift registers is minimal, but the patterns in use are not as invulnerable to inadvertent generation by dependent processes as previously thought. 3. New methods of testing pair-wise incompatibility threats have resulted in no significant problems found for the set of Unique Signal patterns currently used. Any new patterns introduced would have to be carefully assessed for compatibility with existing patterns, since some new patterns under consideration were found to be deficient when associated with other patterns in use. 4. Markov models were shown to correspond to some of the engineered properties of Unique Signal sequences. This gives new support for the original design objectives. 5. Potential dependence among events (caused by a variety of communication protocols) has been studied. New evidence has been derived of the risk associated with combined communication of multiple events, and of the improvement in abnormal-environment safety that can be achieved through separate-event communication.
Digital literacy and problem solving in technology-rich environments
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Vesna Dolničar
2015-07-01
Full Text Available Rapid development and progress, as well as the growing presence of information and communications technologies dictate the need for more highly developed digital skills in individuals. The paper focuses on the concepts of digital skills and problem solving in technology-rich environments. It examines these on the basis of empirical data obtained in the international study PIAAC. The introductory part presents an overview of the literature and the results of previous research in the field of measurement of digital skills, and data on the use of information society services among the EU Member States. The second part of the article refers to the results obtained in the study PIAAC. The results, confirmed by the results of other studies, showed the impact of age and education level on the problem solving in technology-rich environments. Article concludes with suggestions for improving the current state of integration of all population groups in training programs in the field of digital skills.
A Daunting Task for Pre-Service Mathematics Teachers: Developing Students' Mathematical Thinking
Tataroglu Tasdan, Berna; Erduran, Ayten; Çelik, Adem
2015-01-01
The purpose of this study was to examine pre-service teachers' teaching practice in terms of providing suitable conditions for developing students' mathematical thinking in the frame of the Advancing Children's Thinking framework. In the study, Advancing Children's Thinking framework developed by Fraivillig et al. was adopted as theoretical…
Task Design for Ways of Working: Making Distinctions in Teaching and Learning Mathematics
Coles, Alf; Brown, Laurinda
2016-01-01
A problem identified in the literature around task design is the persistence of a gap between teacher intention and student activity. We show how principles designed around the making of distinctions and having an explicit language of mathematical thinking can eliminate the "gap" by guiding teacher planning, teacher actions in the…
Teacher Actions That Encourage Students to Persist in Solving Challenging Mathematical Tasks
Ingram, Naomi; Linsell, Chris; Holmes, Marilyn; Livy, Sharyn; Sullivan, Peter
2016-01-01
As part of a project exploring the use of challenging mathematical tasks, data from New Zealand teachers and their students were analysed to explore teachers' actions that encouraged students to persist. Rather than rescuing the students when they needed help, the teachers' actions included arranging for and encouraging students to work…
An Approach to the Design of Mathematical Task Sequences: Conceptual Learning as Abstraction
Simon, Martin A.
2016-01-01
This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…
Difficulties in solving context-based PISA mathematics tasks : An analysis of students' errors
Wijaya, Ariyadi; van den Heuvel-Panhuizen, Marja; Doorman, Michiel; Robitzsch, Alexander
2014-01-01
The intention of this study was to clarify students' difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA math
Wilhelm, Anne Garrison
2014-01-01
This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…
Polly, Drew
2016-01-01
This study explored the relationship between technology use, tasks, and questions posed during mathematics lessons in three elementary school classrooms. Teachers were observed between 21 to 30 times per classroom during the year. Data was recorded about the types of technologies, mathematical tasks, and questions observed. Chi-square tests for…
Sherman, Milan
2011-01-01
This study investigates the role of digital cognitive technologies in supporting students' mathematical thinking while engaging with instructional tasks. Specifically, the study sought to better understand how the use of technology is related to the cognitive demand of tasks. Data were collected in four secondary mathematics classrooms via…
Polly, Drew; Neale, Henry; Pugalee, David K.
2014-01-01
This study examined how a task-focused, year-long mathematics professional development program influenced elementary school teachers' knowledge, beliefs, and practices. Participants completed 84 h of professional development over 13 months that were focused on exploring, modifying and implementing cognitively-demanding mathematical tasks.…
Laina, Vasiliki; Monaghan, John
2014-01-01
This paper reports on two students' work on geometry tasks in a dynamic geometry system. It augments prior work on students' instrumental geneses via a consideration of emergent goals that arise in students' work. It offers a way to interpret students' (working with new software) awareness of what software can and cannot do and students'…
Mathematics anxiety reduces default mode network deactivation in response to numerical tasks
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Belinda ePletzer
2015-04-01
Full Text Available Mathematics anxiety is negatively related to mathematics performance, thereby threatening the professional success. Preoccupation with the emotional content of the stimuli may consume working memory resources, which may be reflected in decreased deactivation of areas associated with the default mode network (DMN activated during self-referential and emotional processing. The common problem is that math anxiety is usually associated with poor math performance, so that any group differences are difficult to interpret.Here we compared the BOLD-response of 18 participants with high (HMAs and 18 participants with low mathematics anxiety (LMAs matched for their mathematical performance to two numerical tasks (number comparison, number bisection. During both tasks, we found stronger deactivation within the DMN in LMAs compared to HMAs, while BOLD-response in task-related activation areas did not differ between HMAs and LMAs. The difference in DMN deactivation between the HMA and LMA group was more pronounced in stimuli with additional requirement on inhibitory functions, but did not differ between number magnitude processing and arithmetic fact retrieval.
Mathematics anxiety reduces default mode network deactivation in response to numerical tasks.
Pletzer, Belinda; Kronbichler, Martin; Nuerk, Hans-Christoph; Kerschbaum, Hubert H
2015-01-01
Mathematics anxiety is negatively related to mathematics performance, thereby threatening the professional success. Preoccupation with the emotional content of the stimuli may consume working memory resources, which may be reflected in decreased deactivation of areas associated with the default mode network (DMN) activated during self-referential and emotional processing. The common problem is that math anxiety is usually associated with poor math performance, so that any group differences are difficult to interpret. Here we compared the BOLD-response of 18 participants with high (HMAs) and 18 participants with low mathematics anxiety (LMAs) matched for their mathematical performance to two numerical tasks (number comparison, number bisection). During both tasks, we found stronger deactivation within the DMN in LMAs compared to HMAs, while BOLD-response in task-related activation areas did not differ between HMAs and LMAs. The difference in DMN deactivation between the HMA and LMA group was more pronounced in stimuli with additional requirement on inhibitory functions, but did not differ between number magnitude processing and arithmetic fact retrieval.
A mathematical modeling proposal for a Multiple Tasks Periodic Capacitated Arc Routing Problem
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Cleverson Gonçalves dos Santos
2015-12-01
Full Text Available The countless accidents and incidents occurred at dams at the last years, propelled the development of politics related with dams safety. One of the strategies is related to the plan for instrumentation and monitoring of dams. The monitoring demands from the technical team the reading of the auscultation data, in order to periodically monitor the dam. The monitoring plan of the dam can be modeled as a problem of mathematical program of the periodical capacitated arcs routing program (PCARP. The PCARP is considered as a generalization of the classic problem of routing in capacitated arcs (CARP due to two characteristics: 1 Planning period larger than a time unity, as that vehicle make several travels and; 2 frequency of associated visits to the arcs to be serviced over the planning horizon. For the dam's monitoring problem studied in this work, the frequent visits, along the time horizon, it is not associated to the arc, but to the instrument with which is intended to collect the data. Shows a new problem of Multiple tasks Periodic Capacitated Arc Routing Problem and its elaboration as an exact mathematical model. The new main characteristics presented are: multiple tasks to be performed on each edge or edges; different frequencies to accomplish each of the tasks; heterogeneous fleet; and flexibility for more than one vehicle passing through the same edge at the same day. The mathematical model was implemented and examples were generated randomly for the proposed model's validation.
Open-ended Tasks in the Promotion of Classroom Communication in Mathematics
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Floriano VISEU
2012-03-01
Full Text Available Mathematics programmes in basic education are currently undergoing reform in Portugal. This paper sets out to see how teachers are putting the new guidelines for the teaching of mathematics intopractice, with particular emphasis on maths communication in the classroom. To achieve this, an experiment in teaching the topic 'Sequences and Regularities' with open-ended tasks, using a qualitative and interpretative approach, is reported. Data were collected during two class observations, from two interviews and by analysing the activities of the students. An exploratory task was chosen in the first lesson and a investigative one in the second. One month separated the two lessons, and during this time the teacher read and discussed texts on mathematics communication. Observation of the first lesson showed that the communication in the classroom was mostly focused on the teacher, which provided little student-student and student-class interaction. In the second observed lesson, the teacher changed the attention she paid to what each student said and did, encouraging the students to ask each other and encouraged student-class and the student-student communication.
An approach to the design of mathematical task sequences: Conceptual learning as abstraction
Directory of Open Access Journals (Sweden)
Martin A. Simon
2016-06-01
Full Text Available This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from approaches in which learning to solve the problem posed is the intended learning. The paper illustrates the approach through data from a teaching experiment on division of fractions.
Cranfield, Corvell
2013-01-01
The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and…
Venville, Grady; Rennie, Léonie; Wallace, John
2004-04-01
This article reports on students'' decision making processes and sources of knowledge in an integrated teaching and learning setting. The study was conducted in a Year 9 classroom as students undertook a 10-week solar-powered boat project and were exposed to related concepts from science, technology and mathematics. Data collection involved detailed case studies of three pairs of students, interviews, classroom observation and analysis of the artefacts and portfolios produced by the students. Students were found to access knowledge from a variety of sources, including teacher''s notes from formal instruction, informal interactions with the teacher, observation of and interaction with other students, as well as sources outside the classroom. However, the utility of the knowledge sources was influenced by the nature of the task. When students were performing open-ended tasks, they drew on a wider variety of knowledge sources than when they were performing less open tasks. Moreover, subject discipline-based sources often were not as helpful in solving open tasks. The study leads to several important implications for designing teaching and learning in integrated curriculum settings.
Teachers as co-designers of technology-rich learning activities for emergent literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2016-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning outc
Teachers as co-designers of technology-rich learning activities for early literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning outco
Teachers as Co-Designers of Technology-Rich Learning Activities for Early Literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning outcomes. A case-study method was used to investigate:…
Teachers as co-designers of technology-rich learning activities for early literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning outco
Teachers as co-designers of technology-rich learning activities for emergent literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2016-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning outc
Teachers as co-designers of technology-rich learning activities for early literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning
Teachers as co-designers of technology-rich learning activities for emergent literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2016-01-01
Although kindergarten teachers often struggle with implementing technology, they are rarely involved in co-designing technology-rich learning activities. This study involved teachers in the co-design of technology-rich learning activities and sought to explore implementation and pupil learning
Roll paper pilot. [mathematical model for predicting pilot rating of aircraft in roll task
Naylor, F. R.; Dillow, J. D.; Hannen, R. A.
1973-01-01
A mathematical model for predicting the pilot rating of an aircraft in a roll task is described. The model includes: (1) the lateral-directional aircraft equations of motion; (2) a stochastic gust model; (3) a pilot model with two free parameters; and (4) a pilot rating expression that is a function of rms roll angle and the pilot lead time constant. The pilot gain and lead time constant are selected to minimize the pilot rating expression. The pilot parameters are then adjusted to provide a 20% stability margin and the adjusted pilot parameters are used to compute a roll paper pilot rating of the aircraft/gust configuration. The roll paper pilot rating was computed for 25 aircraft/gust configurations. A range of actual ratings from 2 to 9 were encountered and the roll paper pilot ratings agree quite well with the actual ratings. In addition there is good correlation between predicted and measured rms roll angle.
Guberman, Raisa; Leikin, Roza
2013-01-01
The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…
Lai, Mun Yee; Murray, Sara
2015-01-01
Most studies of students' understanding of decimals have been conducted within Western cultural settings. The broad aim of the present research was to gain insight into Chinese Hong Kong grade 6 students' general performance on a variety of decimals tasks. More specifically, the study aimed to explore students' mathematical reasoning for their use…
Group Work in a Technology-Rich Environment
Penner, Nikolai; Schulze, Mathias
2010-01-01
This paper addresses several components of successful language-learning methodologies--group work, task-based instruction, and wireless computer technologies--and examines how the interplay of these three was perceived by students in a second-year university foreign-language course. The technology component of our learning design plays a central…
Group Work in a Technology-Rich Environment
Penner, Nikolai; Schulze, Mathias
2010-01-01
This paper addresses several components of successful language-learning methodologies--group work, task-based instruction, and wireless computer technologies--and examines how the interplay of these three was perceived by students in a second-year university foreign-language course. The technology component of our learning design plays a central…
Pertl, Marie-Theres; Zamarian, Laura; Delazer, Margarete
2017-08-01
In this study, we assessed to what extent reasoning improves performance in decision making under risk in a laboratory gambling task (Game of Dice Task-Double, GDT-D). We also investigated to what degree individuals with above average mathematical competence decide better than those with average mathematical competence. Eighty-five participants performed the GDT-D and several numerical tasks. Forty-two individuals were asked to calculate the probabilities and the outcomes associated with the different options of the GDT-D before performing it. The other 43 individuals performed the GDT-D at the beginning of the test session. Both reasoning and mathematical competence had a positive effect on decision making. Different measures of mathematical competence correlated with advantageous performance in decision making. Results suggest that decision making under explicit risk conditions improves when individuals are encouraged to reflect about the contingencies of a decision situation. Interventions based on numerical reasoning may also be useful for patients with difficulties in decision making.
Zandvliet, D B; Straker, L M
2001-07-15
This paper reports on a study of environments in emerging Internet classrooms. At issue for this study is to what extent these 'technological classrooms' are providing a positive learning environment for students. To investigate this issue, this study involved an evaluation of the physical and psychosocial environments in computerized school settings through a combination of questionnaires and inventories that were later cross-referenced to case studies on a subset of these classrooms. Data were obtained from a series of physical evaluations of 43 settings in 24 school locations in British Columbia, Canada and Western Australia. Evaluations consisted of detailed inventories of the physical environment using the Computerised Classroom Environment Inventory (CCEI): an instrument developed specifically for this study. Data on psychosocial aspects of the environment were obtained with the What is Happening in this Class? (WIHIC) questionnaire administered to 1404 high school students making routine use of these computerized classrooms. Potential deficiencies in the physical environment of these locations included problems with individual workspaces, lighting and air quality, whereas deficiencies in the psychosocial environment were confined to the dimension of Autonomy. Further analysis of these classroom environment data indicated that student Autonomy and Task orientation were independently associated with students' Satisfaction with learning and that many physical (e.g. lighting and workspace dimensions) and psychosocial factors (e.g. students' perceptions of Co-operation and Collaboration) were also associated. The results provide a descriptive account of the learning environment in 'technology-rich' classrooms and, further, indicate that ergonomic guidelines used in the implementation of IT in classrooms may have a positive influence on the learning environment.
Understanding Graphicacy: Students' Making Sense of Graphics in Mathematics Assessment Tasks
Lowrie, Tom; Diezmann, Carmel M.; Logan, Tracy
2011-01-01
The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed:…
Using Task Like PISA's Problem to Support Students' Creativity in Mathematics
Novita, Rita; Putra, Mulia
2016-01-01
Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also in mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom…
Teachers' Perceptions of Factors Affecting the Educational Use of ICT in Technology-Rich Classrooms
Badia, Antoni; Meneses, Julio; Sigales, Carles
2013-01-01
Introduction: The purpose of this study is to identify the main factors that influence teachers' decision-making regarding the educational use of ICT (Information and Communication Technologies) in technology-rich classrooms. Method: We collected data from 278 teachers in Catalonia (Spain) working in eight primary and secondary education schools…
The Influence of Technology-Rich Early Childhood Field Experiences on Preservice Teachers
Lux, Nicholas; Lux, Christine
2015-01-01
Despite a comprehensive body of research on field experiences in teacher education, technology-rich early field experiences in early childhood environments is one particular area of inquiry lacking substantive current research. Therefore, this study was conducted to better understand how preservice teachers' perceptions of global concepts related…
Teachers' Perceptions of Factors Affecting the Educational Use of ICT in Technology-Rich Classrooms
Badia, Antoni; Meneses, Julio; Sigales, Carles
2013-01-01
Introduction: The purpose of this study is to identify the main factors that influence teachers' decision-making regarding the educational use of ICT (Information and Communication Technologies) in technology-rich classrooms. Method: We collected data from 278 teachers in Catalonia (Spain) working in eight primary and secondary education schools…
The Design of Technology-Rich Learning Environments as Metacognitive Tools in History Education
Poitras, Eric; Lajoie, Susanne; Hong, Yuan-Jin
2012-01-01
Research has shown that learners do not always engage in appropriate metacognitive and self-regulatory processes while learning complex historical topics. However, little research exists to guide the design of technology-rich learning environments as metacognitive tools in history education. In order to address this issue, we designed a…
Teacher roles in designing technology-rich learning activities for early literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
The present study aims to provide insight into the value of different teacher roles in designing and implementing technology-rich learning activities for early literacy. Three cases, each with a different teacher role (executor-only, re-designer, co-designer) were examined. In the executor-only
Building on Authentic Learning for Pre-Service Teachers in a Technology-Rich Environment
Latham, Gloria; Carr, Nicky
2015-01-01
The article "Authentic learning for pre-service teachers in a technology-rich environment" (Latham & Carr, 2012) appeared in the "Journal of Learning Design," Volume 5, Issue 1 in 2012. Since writing this paper three years ago, the authors reflect upon and brainstorm what they describe here as a radically revised approach.…
VET Workers' Problem-Solving Skills in Technology-Rich Environments: European Approach
Hämäläinen, Raija; Cincinnato, Sebastiano; Malin, Antero; De Wever, Bram
2014-01-01
The European workplace is challenging VET adults' problem-solving skills in technology-rich environments (TREs). So far, no international large-scale assessment data has been available for VET. The PIAAC data comprise the most comprehensive source of information on adults' skills to date. The present study (N = 50 369) focuses on gaining insight…
Teachers conversations during design of technology rich curriculum activities for early literacy
Boschman, Ferry; McKenney, Susan; Voogt, Joke
2014-01-01
Boschman, F., McKenney, S. & Voogt (2013). Teachers conversations during design of technology rich curriculum activities for early literacy. Paper presentation at the European Association for Practitioner Research on Improving Learning (EAPRIL) Annual Conference. November 27-29, Biel/Bienne, Switzer
Teacher roles in designing technology-rich learning activities for early literacy
Cviko, Amina; McKenney, Susan; Voogt, Joke
2015-01-01
The present study aims to provide insight into the value of different teacher roles in designing and implementing technology-rich learning activities for early literacy. Three cases, each with a different teacher role (executor-only, re-designer, co-designer) were examined. In the executor-only role
Rousselle, Laurence; Noël, Marie-Pascale
2008-01-01
The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the proposed and the correct answer was manipulated. Both typically achieving groups were sensitive to answer plausibility on simple problems, were faster at rejecting extremely incorrect results than at accepting correct answers on complex addition problems, and showed a reduction of the complexity effect on implausible problems, attesting to the use of approximate calculation. Conversely, children with mathematics disabilities were unaffected by answer plausibility on simple addition problems, processed implausible and correct sums with equal speed on complex problems, and exhibited a smaller reduction of the complexity effect on implausible problems. They also made more errors on implausible problems. Different hypotheses are discussed to account for these results.
Eringen, A Cemal
2013-01-01
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
Cai, Jinfa, And Others
1996-01-01
Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…
Assessment of a Problem Posing Task in a Jamaican Grade Four Mathematics Classroom
Munroe, Kayan Lloyd
2016-01-01
This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer…
The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning
Sullivan, Peter; Davidson, Aylie
2014-01-01
The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…
Stein, Sherman K
2010-01-01
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 Value of Emoticons in Investigating Student Emotions Related to Mathematics Task Negotiation
D'Agostin, Fabio
2014-01-01
"Emoticons" are simple face icons expressing common feelings such as happiness, interest and boredom and are popularly used in electronic communication. Emoticons were utilised in this study as experience sampling devices. Year 10 students selected emoticons to indicate their emotional states at set intervals during classroom tasks.…
Energy Technology Data Exchange (ETDEWEB)
Brinkmann, A. [Univ. Muenster (Germany). Inst. fuer Didaktik der Mathematik und Informatik; Brinkmann, K. [FH Trier (Germany). Fachbereich Umweltplanung/Umwelttechnik, Automatisierungstechnik und Energiesystemtechnik, Umwelt-Campus Birkenfeld
2008-07-01
Aim of this paper is to present the result of a work, which began in the year 2000 (12. Internationales Sonnenforum in Freiburg), to provide a collection of mathematical problems concerning future energy issues for mathematical classrooms. Now, since the year 2005, a complete book is available for schools in Germany at Franzbecker, a well known publisher for educational purposes. One of the most effective methods to achieve a sustainable change of our momentary existing power supply system to a system mainly based on renewable energy conversion is the education of our children. Especially the young generation would be more conflicted with the environmental consequences of the extensive usage of fossil fuels. For our children it is indispensable to become familiar with renewable energies, because the decentralised character of this future kind of energy supply requires surely more personal effort of everyone. In comparison to the parental education, the public schools give the possibility of a successful and especially easier controllable contribution to this theme. This can even be done advantageously for classroom teaching, as realistic and attractive contents have a particular motivating effect on students. In addition to that, a contribution to interdisciplinary teaching would be given, which is a significant educational method, demanded by school curricula. (orig.)
Johannsen, G.; Rouse, W. B.
1978-01-01
A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.
Technology-rich inquiry science in urban classrooms: What are the barriers to inquiry pedagogy?
Butler Songer, Nancy; Lee, Hee-Sun; Kam, Rosalind
2002-02-01
What are the barriers to technology-rich inquiry pedagogy in urban science classrooms, and what kinds of programs and support structures allow these barriers to be overcome? Research on the pedagogical practices within urban classrooms suggests that as a result of many constraints, many urban teachers' practices emphasize directive, controlling teaching, that is, the pedagogy of poverty (Haberman, [1991]), rather than the facilitation of students' ownership and control over their learning, as advocated in inquiry science. On balance, research programs that advocate standards-based or inquiry teaching pedagogies demonstrate strong learning outcomes by urban students. This study tracked classroom research on a technology-rich inquiry weather program with six urban science teachers. The teachers implemented this program in coordination with a district-wide middle school science reform. Results indicated that despite many challenges in the first year of implementation, students in all 19 classrooms of this program demonstrated significant content and inquiry gains. In addition, case study data comprised of twice-weekly classroom observations and interviews with the six teachers suggest support structures that were both conducive and challenging to inquiry pedagogy. Our work has extended previous studies on urban science pedagogy and practices as it has begun to articulate what role the technological component plays either in contributing to the challenges we experienced or in helping urban science classrooms to realize inquiry science and other positive learning values. Although these data outline results after only the first year of systemic reform, we suggest that they begin to build evidence for the role of technology-rich inquiry programs in combating the pedagogy of poverty in urban science classrooms.
Tirosh, Dina; Tsamir, Pessia; Levenson, Esther; Tabach, Michal; Barkai, Ruthi
2013-01-01
This article reports on young children's self-efficacy beliefs and their corresponding performance of mathematical and nonmathematical tasks typically encountered in kindergarten. Participants included 132 kindergarten children aged 5-6 years old. Among the participants, 69 children were identified by the social welfare department as being abused…
Tirosh, Dina; Tsamir, Pessia; Levenson, Esther; Tabach, Michal; Barkai, Ruthi
2013-01-01
This article reports on young children's self-efficacy beliefs and their corresponding performance of mathematical and nonmathematical tasks typically encountered in kindergarten. Participants included 132 kindergarten children aged 5-6 years old. Among the participants, 69 children were identified by the social welfare department as being abused…
Desco, Manuel; Navas-Sanchez, Francisco J; Sanchez-González, Javier; Reig, Santiago; Robles, Olalla; Franco, Carolina; Guzmán-De-Villoria, Juan A; García-Barreno, Pedro; Arango, Celso
2011-07-01
The main goal of this study was to investigate the neural substrates of fluid reasoning and visuospatial working memory in adolescents with precocious mathematical ability. The study population comprised two groups of adolescents: 13 math-gifted adolescents and 14 controls with average mathematical skills. Patterns of activation specific to reasoning tasks in math-gifted subjects were examined using functional magnetic resonance images acquired while the subjects were performing Raven's Advanced Progressive Matrices (RAPM) and the Tower of London (TOL) tasks. During the tasks, both groups showed significant activations in the frontoparietal network. In the math-gifted group, clusters of activation were always bilateral and more regions were recruited, especially in the right hemisphere. In the TOL task, math-gifted adolescents showed significant hyper-activations relative to controls in the precuneus, superior occipital lobe (BA 19), and medial temporal lobe (BA 39). The maximum differences between the groups were detected during RAPM tasks at the highest level of difficulty, where math-gifted subjects showed significant activations relative to controls in the right inferior parietal lobule (BA 40), anterior cingulated gyrus (BA 32), and frontal (BA 9, and BA 6) areas. Our results support the hypothesis that greater ability for complex mathematical reasoning may be related to more bilateral patterns of activation and that increased activation in the parietal and frontal regions of math-gifted adolescents is associated with enhanced skills in visuospatial processing and logical reasoning.
Designs for Teaching and Learning in Technology-Rich Learning Environments
Directory of Open Access Journals (Sweden)
Andreas Lund
2011-10-01
Full Text Available In this paper we argue that the notion of design is conducive to analyzing and developing learning and teaching in technology rich environments. Our argument is inspired by Cultural Historical Activity Theory (CHAT. From a CHAT perspective we briefly discuss the term design, especially in connection with the advent of digital networks, increased complexity of learning environments, and Web 2.0 applications. We also draw on the German/Nordic concept of didactics as well as the Russian/Vygotskyan concept of obuchenie, often understood to possess the dialectical relationship between learning and teaching, in order to refine our notion of design. Finally, we discuss two empirical cases from our design perspective.
基于数学任务情境的乐高机器人课程初探%Lego Robotics Course Based on Mathematical Task Situation
Institute of Scientific and Technical Information of China (English)
邱雅番
2012-01-01
随着机器人教育在我国基础教育的不断探索与实践，机器人走进了中小学的课堂，走进了不同的学科。笔者通过研读小学数学教材，以新课程标准为依据，将数学与机器人教学结合，设计出基于数学任务情境下的机器人课程，旨在让学生通过机器人制作与任务完成，形成数学学习的积极性和主动性。对一线从事机器人教育的教师具有一定的参考价值和实践指导意义。%Robotics education in basic education in China continues to explore and practice, the robot into the primary and secondary school classroom, into the different disciplines. Through the study of elementary school mathematics textbooks, the new curriculum standards based on the combination of mathematics and robot teaching robotics curriculum design based on the context of mathematical tasks, designed to allow students to be completed by robot production and tasks, the formation of mathematics learning enthusiasm and initiative. First-line robot education teachers with a certain reference value and practical significance.
Thomas, Michael K.; Barab, Sasha A.; Tuzun, Hakan
2009-01-01
This study examined the tensions surrounding the implementation of a technology-rich educational innovation called Quest Atlantis (QA) in a local public elementary school. Three qualitative case studies of three classrooms implementing the innovation and a subsequent cross-case analysis were undertaken to illuminate: 1) the reasons why teachers…
Teachers' Perceptions of Factors Affecting the Educational Use of ICT in Technology-Rich Classrooms
Badia, Antoni; Meneses, Julio; Sigales, Carles
2013-01-01
Introduction: The purpose of this study is to identify the main factors that influence teachers' decision-making regarding the educational use of ICT (Information and Communication Technologies) in technology-rich classrooms. Method: We collected data from 278 teachers in Catalonia (Spain) working in eight primary and secondary education…
VET workers’ problem-solving skills in technology-rich environments: European approach
Directory of Open Access Journals (Sweden)
Raija Hämäläinen
2014-08-01
Full Text Available The European workplace is challenging VET adults’ problem-solving skills in technology-rich environments (TREs. So far, no international large-scale assessment data has been available for VET. The PIAAC data comprise the most comprehensive source of information on adults’ skills to date. The present study (N=50 369 focuses on gaining insight into the problem-solving skills in TREs of adults with a VET background. When examining the similarities and differences in VET adults’ problem-solving skills in TREs across 11 European countries, two main trends can be observed. First, our results show that only a minority of VET adults perform at a high level. Second, there seems to be substantial variation between countries with respect to the proportion of VET adults that can be identified as “at-risk” or “weak” performers. For the future, our findings indicate the variations that can be used as a starting point to identify beneficial VET approaches.
浅谈高职高等数学的任务驱动教学法%Talking about Task-driven Pedagogy in Vocational College Advanced Mathematics
Institute of Scientific and Technical Information of China (English)
何玉华; 汪洋
2014-01-01
Most of the existing vocational mathematics teaching is"teaching"fixed"learning"teaching mode, teaching stat-us and teaching effectiveness worrying. The basic characteristics of task-driven teaching are task-oriented line, teacher-led and student-centered"three for one"pedagogy. This paper talks about the applications of vocational teaching task-driven tea-ching method in vocational advanced mathematics teaching.%现行高职数学教学大多是以“教”定“学”的教学模式，教学现状和教学效果堪忧。而任务驱动教学的基本特征是：以任务为主线、教师为主导和学生为主体的“三为一体”的教学法。本文浅谈任务驱动教学法在高职高数教学的应用。
On the Task-based Teaching Method in Mathematics%任务型教学法在数学教学中的应用研究
Institute of Scientific and Technical Information of China (English)
许丽华
2012-01-01
目前,在中学数学教学中,任务型教学法被广泛采用,它的宗旨是通过设置以＂目标为导向,以学习者为中心＂的课堂活动,让学生在各种活动中通过目标语进行沟通交流,最后通过分工合作的形式完成相应的＂任务＂。结合任务型教学法的特点和原则,论述了该教学法在中学数学教学中的有效应用,并针对当前很多＂学困生＂对数学学习兴趣不高,成绩不理想的现状,提出了让＂学困生＂在日常生活中体味数学学习的任务型教学方法,以培养＂学困生＂数学学习兴趣,提高其学习积极性和主动性,真正实现快乐学习。%Now the task-based teaching is widely used in teaching Mathematics in middle-school whose purpose is to communicate with each other through target language and finish their own tasks through cooperation.The features of their activities are target-centered and student-centered.The paper discusses the effective application in teaching Mathematics with its features,and puts forward the task-based teaching in teaching ＂poor students＂ mathematics to motivate their interests and realize happy studying.
2005-12-14
Vol.41, No.2, April, 1940. 20.Koopman B.O. The bases of probability – Bulletin of the American Mathematical Society , 46 (1940). 21.Koopman B.O...correspond to computer models. Corrected 08.08.02 by Ivakin Y.A. and Vasilev V.V. 13. 06.11.02 CP. Multilanguage
基于任务驱动的离散数学实验教学研究%Researches on Task-based Experimental Teaching of Discrete Mathematics
Institute of Scientific and Technical Information of China (English)
马艳芳; 陈亮
2015-01-01
离散数学是计算机专业的一门必修课程，在学生综合素质培养和逻辑思维能力培养方面发挥重要作用。本文分析离散数学的教学现状，阐述在离散数学教学中增加实验教学的必要性。根据离散数学的内容体系，利用任务驱动教学法，建立和完善离散数学课程实验教学环节。%Discrete mathematics is a compulsory curriculum for computer science,and it is very important to cultivate the ability of logic inference and comprehensive quality of college students. In this study ,we will analyse the current situation of discrete mathematical teaching,and necessity of the experiment teaching. Ac⁃cording to the contents of discrete mathematics,the design of experiment teaching will be established based on task-driven method of teaching.
Application of"Task-driven Method"in Advanced Mathematics Teaching%"任务驱动法"在高等数学教学中的应用
Institute of Scientific and Technical Information of China (English)
孙丽东
2015-01-01
高职教育的背景是大职业教育观,面对的学生群体是职高生、中专生乃至落榜生.这类学生因前期所接受的教育程度及水平的不同,呈现出高职阶段的数学基础良莠不齐.生动的课程讲授将有效地改变这一现状,同时这对老师也提出了更高的要求."任务驱动法"就是这样一个方法,把枯燥的知识点化作亟待解决的任务,在教学中穿插多种教学模式,变被动学习为主动探知,以期体验解决问题的成就感.同时有利于学生建构数学思想,塑造数学理念,产生为后续专业学科的学习提供有效基础的效应.%Vocational education background is the big concept of vocational education, student groups face a vocational school students, secondary school students and even get the job. These students vary accepted the early education level and level, showing the mathematical basis of good and bad higher stage. Vivid courses are taught will effectively change the status quo, and this teacher is also a higher demand."Task-driven method"is one such method, a dull knowledge turned into urgent task, interspersed with a variety of teaching mode in teaching, change from passive learning to active ascertain, in order to experience the problem of accomplishment. While facilitating students to construct mathematical thinking, mathematical modeling concepts, produce a valid basis for subsequent professional disciplines of learning effect.
Jackson, Kara J.; Shahan, Emily C.; Gibbons, Lynsey K.; Cobb, Paul A.
2012-01-01
Mathematics lessons can take a variety of formats. In this article, the authors discuss lessons organized around complex mathematical tasks. These lessons usually unfold in three phases. First, the task is introduced to students. Second, students work on solving the task. Third, the teacher "orchestrates" a concluding whole-class discussion in…
Cates, Gary L.; Erkfritz, Karyn N.
2007-01-01
The current study investigated the discreet task completion hypothesis presented by C. H. Skinner (2002) by investigating how the rate of interspersing affects performance on and preferences for academic assignments. Specifically, 70 sixth-, seventh-, and eighth-grade students were presented with four assignment pairs of multiplication problems.…
Christiansen, Iben Maj
1997-01-01
The negotiation of meaning presupposes a taken-to-be-shared understanding of a situation. Uses an example to illustrate how negotiation of meaning and task may be linked in ways inappropriate to the learning of modeling and critical reflections. Contains 16 references. (Author/ASK)
Directory of Open Access Journals (Sweden)
Ana Lucía Alfaro Arce
2014-06-01
Full Text Available "MATEM" is a university outreach project. Among its objectives is to improve the mathematics education at the high school level and to accomplish it public universities work together with high school´s teachers and students. The study´s aim was to research various aspects of MATEM Project to order to evaluate its development and consider recommendations for making decisions. This paper summarizes the perceptions of high school students enrolled during 2012 in courses Precalculus and Calculus, moreover the opinion of mathematics teachers. The main results were that MATEM is an academic activity attractive for math teachers and student population from different regions of the country, although sometimes are not available the necessary conditions to develop it in their respective institutions, to have passed a university course, get more practice for the standard test at the end of high school, increase their math skills and prepare for college courses were the aspects that motivate students to enroll in the project, however the development of reasoning skills and abilities were more frequently pointed by respondents.
Lee, Taek-Soo; Frey, Eric C; Tsui, Benjamin M W
2015-04-07
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of (99m)Tc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman's rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.
2015-04-01
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
Baghdadi, Golnaz; Towhidkhah, Farzad; Rostami, Reza
2017-07-01
Discovering factors influencing the speed and accuracy of responses in tasks such as "Go/No-Go" is one of issues which have been raised in neurocognitive studies. Mathematical models are considered as tools to identify and to study decision making procedure from different aspects. In this paper, a mathematical model has been presented to show several factors can alter the output of decision making procedure before execution in a "Go/No-Go" task. The dynamic of this model has two stable fixed points, each of them corresponds to the "Press" and "Not-press" responses. This model that focuses on the fronto-striatal-thalamic direct and indirect pathways, receives planned decisions from frontal cortex and sends a regulated output to motor cortex for execution. The state-space analysis showed that several factors could affect the regulation procedure such as the input strength, noise value, initial condition, and the values of involved neurotransmitters. Some probable analytical reasons that may lead to changes in decision-execution regulation have been suggested as well. Bifurcation diagram analysis demonstrates that an optimal interaction between these factors can compensate the weaknesses of some others. It is predicted that abnormalities of response control in different brain disorders such as attention deficit hyperactivity disorder may be resolved by providing treatment techniques that target the regulation of the interaction. The model also suggests a possible justification to show why so many studies insist on the important role of dopamine in some brain disorders. Copyright © 2017 Elsevier Ltd. All rights reserved.
Woolley, Norman N; Jarvis, Yvonne
2007-01-01
The acquisition of a range of diverse clinical skills is a central feature of the pre-registration nursing curriculum. Prior to exposure to clinical practice, it is essential that learners have the opportunity to practise and develop such skills in a safe and controlled environment under the direction and supervision of clinical experts. However, the competing demands of the HE nursing curriculum coupled with an increased number of learners have resulted in a reduced emphasis on traditional apprenticeship learning. This paper presents an alternative model for clinical skills teaching that draws upon the principles of cognitive apprenticeship [Collins, A., Brown, J.S., Newman, S., 1989. Cognitive Apprenticeship: teaching the crafts of reading, writing and mathematics. In: Resnick, L.B. (Ed.) Knowing. Learning and Instruction: Essays in Honor of Robert Glaser. Lawrence Erlbaum Associates, New Jersey, pp. 453-494] and situated cognition within a technologically rich and authentic learning environment. It will show how high quality DVD materials illustrating clinical skills performed by expert practitioners have been produced and used in conjunction with CCTV and digital recording technologies to support learning within a pedagogic framework appropriate to skills acquisition. It is argued that this model not only better prepares the student for the time they will spend in the practice setting, but also lays the foundation for the development of a clinically competent practitioner with the requisite physical and cognitive skills who is fit for purpose [UKCC, 1999. Fitness for Practice: The UKCC Commission for Nursing and Midwifery Education. United Kingdom Central Council for Nursing Midwifery and Health Visiting, London].
Fraser, Virginia; Garofalo, Joe
2015-01-01
The purpose of this study was to describe how and why novice mathematics teachers incorporated technology-generated representations in their instruction. The participants in the study were graduates of a technology-rich mathematics teacher educator program. The teachers were interviewed at the beginning and end of the study concerning their…
Park, Subok; Badal, Andreu; Young, Stefano; Myers, Kyle J.
2012-03-01
For a rigorous x-ray imaging system optimization and evaluation, the need for exploring a large space of many different system parameters is immense. However, due to the high dimensionality of the problem, it is often infeasible to evaluate many system parameters in a laboratory setting. Therefore, it is useful to utilize computer simulation tools and analytical methods to narrow down to a much smaller space of system parameters and then validate the chosen optimal parameters by laboratory measurements. One great advantage of using the simulation and analytical methods is that the impact of various sources of variability on the system's diagnostic performance can be studied separately and collectively. Previously, we have demonstrated how to separate and analyze noise sources using covariance decomposition in a task-based approach to the assessment of digital breast tomosynthesis (DBT) systems in the absence of x-ray scatter and detector blur.1, 2 In this work, we analytically extend the previous work to include x-ray scatter and detector blur. With use of computer simulation, we also investigate the use of the convolution method for approximating the scatter images of structured phantoms in comparison to those computed via Monte Carlo. The extended method is comprehensive and can be used both for exploring a large parameter space in simulation and for validating optimal parameters, chosen from a simulation study, with laboratory measurements.
Trajectories of Mathematics and Technology Education Pointing to Engineering Design
Daugherty, Jenny L.; Reese, George C.; Merrill, Chris
2010-01-01
A brief examination and comparison of mathematics and technology education provides the background for a discussion of integration. In particular, members of each field have responded to the increasing pressures to better prepare students for the technologically rich, globally competitive future. Approaches based within each discipline are varied…
2016-01-01
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.
Bennett, Randy Elliot; Persky, Hilary; Weiss, Andrew R.; Jenkins, Frank
2007-01-01
The Problem Solving in Technology-Rich Environments (TRE) study was designed to demonstrate and explore innovative use of computers for developing, administering, scoring, and analyzing the results of National Assessment of Educational Progress (NAEP) assessments. Two scenarios (Search and Simulation) were created for measuring problem solving…
Institute of Scientific and Technical Information of China (English)
彭庆英
2012-01-01
针对高职数学教学中存在的问题,提出了在高职数学教学中使用任务驱动教学法的必要性,讨论了在高职数学教学中实施任务驱动教学法的策略。使用了任务驱动教学法后的教学得到了很明显的效果。%According to the problems of the higher vocational mathematics teaching,it raised the need of using the task-driven teaching methods in higher vocational mathematics teaching,discussed its implementation strategy.We got obvious effect after the application of task-driven teaching methods.
Institute of Scientific and Technical Information of China (English)
刘崇华; 何远奎
2014-01-01
本文分析了数学建模竞赛的特点及数学建模教学培训的现状和要求，为了培养学生的学习技能和创新能力，在数学建模竞赛培训中采用了任务驱动教学法，加深了认识，提高了运用能力，取得了良好的效果。%This paper analyzed the characteristics of mathematical modeling contest, as well as the current situation and require-ments of mathematical modeling training. In order to develop stu-dents' learning skills and innovative ability, the task-driven ap-proach was adopted in the training of mathematical modeling contest, and it has deepened students' understanding, enhanced their ability to use, and achieved good results.
论任务驱动法在高职数学教学中的作用%On the Role of Task-driven Method in Higher Vocational Mathematics Teaching
Institute of Scientific and Technical Information of China (English)
张永湘
2014-01-01
数学的知识已被广泛应用于社会上的各行各业。除了在企事业单位中需要数学知识之外，诸如经济学研究，航天事业的研究等各个研究领域都需要数学知识。数学是高职院校的基础课程，而数学教学的方法也有很多，任务驱动法就是其中的一种。%Knowledge of mathematics has been widely used in all walks of life in society. In addition to mathematical knowl-edge in enterprises outside, a lot of research, aerospace industry economics research various research fields are required mathematical knowledge. Mathematics is the foundation courses in higher vocational colleges, and there are many methods of teaching mathematics, task-driven method is one of them.
Barriteau Phaire, Candace
2013-01-01
The teaching and learning of mathematics has been the subject of debate for over 30 years and the most recent reform efforts are in response to concerns regarding the mathematical competence of students in the United States (Ball, Hill, & Bass, 2005; Battista, 1994; Cavanagh, 2008). Standards-based Instructional Materials (SBIM) allows…
McDonald, Scott Powell
New understandings about how people learn and constructivist pedagogy pose challenges for teachers. Science teachers face an additional challenge of developing inquiry-based pedagogy to foster complex reasoning skills. Theory provides only fuzzy guidance as to how constructivist or inquiry pedagogy can be accomplished in a wide variety of contexts and local constraints. This study contributes to the understanding of the development of constructivist, inquiry-based pedagogy by addressing the question: How do teachers interpret and enact a technology-rich, inquiry fostering science curricula for fifth grade students' biodiversity learning? This research is a case study of two teachers chosen as critical contrasting cases and represent differences across multiple criteria including: urban I suburban, teaching philosophy, and content preparation. The two fifth grade teachers each enacted BioKIDS: Kids' Inquiry in Diverse Species, an eight week curriculum focused on biodiversity. BioKIDS incorporates multiple learning technologies to support student learning including handheld computer software designed to help students collect field data, and a web-based resource for data on local animal species. The results of this study indicate there are tensions teachers must struggle with when setting goals during enactment of inquiry science curricula. They must find a balance between an emphasis on authentic learning and authentic science, and between natural history and natural science. Authentic learning focuses on students' interests and lives; Authentic science focuses on students working with the tools and processes of science. Natural history focuses on the foundational skills in science of observation and classification. Natural science focuses on analytical science drawing on data to develop claims about the world. These two key tensions in teachers' goal setting were critical in defining and understanding differences in how teachers interpreted a curriculum to meet
Institute of Scientific and Technical Information of China (English)
曹亮
2016-01-01
Among all courses of technician colleges, mathematics is the most fundamental one and also the basic course for the learning of other disciplines, while mathematical ability and knowledge is one of the basic skills that students should possess. Therefore, the learning process of mathematics course will direct-ly influence the cultivation effect of students' occupational ability. This paper will first analyze the current situation of mathematics classroom teaching in technician colleges, then explore the basic connotation of task-driven teaching method, and finally focus on the cases of the practical application of task-driven teaching method in mathematics teaching of technician colleges.%在技工学校的所有课程中,数学是最为基础的课程,同时也是学习其他学科的基础课程,而数学能力及知识是学生必备的基础技能之一.因此,数学课程的学习进展得顺利与否,会对学生的职业能力培养的效果产生直接的影响.本文将先分析技工学校数学课堂教学的现状,再介绍任务驱动教学法的基本内涵,最后重点探讨在技工学校数学教学中任务驱动教学法实际应用的案例.
Institute of Scientific and Technical Information of China (English)
李娟
2014-01-01
Task-driven teaching approach is to divide the teach-ing content into several tasks which are used to drive students' autonomous learning in classroom teaching. By this approach, textbook knowledge is embodied in concrete tasks, which is more easily accepted by students. Based on specific teaching cases, this paper explores the procedure and implementation program of applying task-driven teaching mode in secondary vocational mathematics teaching, and summarizes task-driven teaching ap-proach.%在课堂教学中，将教学内容划分为若干个任务，以任务为中心，通过任务驱动学生自主学习，这叫做任务驱动教学法。任务驱动教学法是将书本知识隐含到具体的任务中，使学生更易于接受。本文以具体的教学案例探讨了在中职数学教学中采用任务驱动教学模式进行教学的步骤和实施方案，并对任务驱动教学法进行了总结。
Mathematics for operations research
1994-01-01
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.
Directory of Open Access Journals (Sweden)
Dina Aleksandrovna Kirillova
2015-12-01
Full Text Available The modern reform of the Russian higher education involves the implementation of competence-based approach, the main idea of which is the practical orientation of education. Mathematics is a universal language of description, modeling and studies of phenomena and processes of different nature. Therefore creating the fund of assessment tools for mathematical disciplines based on the applied problems is actual. The case method is the most appropriate mean of monitoring the learning outcomes, it is aimed at bridging the gap between theory and practice.The aim of the research is the development of methodical materials for the creating the fund of assessment tools that are based on the case-study for the mathematical analisis for direction «Applied Mathematics and Computer Science». The aim follows from the contradiction between the need for the introduction of case-method in the educational process in high school and the lack of study of the theoretical foundations of using of this method as applied to mathematical disciplines, insufficient theoretical basis and the description of the process of creating case-problems for use their in the monitoring of the learning outcomes.
Stallings, L. Lynn
2007-01-01
This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
Wells, Jay Norman
The study was concerned with the effect of dual-media instructional instruments (film and programed text) on learning the method of mathematical induction by college freshmen. One group read the programed text at intervening times during the film showing; one group read the text before and after the showing; and a third group viewed the movie…
Institute of Scientific and Technical Information of China (English)
石彤菊
2012-01-01
Visualizing design of mathematical experiment for task assignments problem is studied in this paper. For task assignments problem with as well as without constraints, the study completed the design of algorithm by making use of Microsoft visual J++6.0 as experimental development platform. Java language and applet embeded in Web page are employed to realize the development of visualization. The software can display the optimal task assignments and the satisfaction rate according to the user's input. The developed system can provide a study platform with functions of visualization and interaction for user to study the task assignments problem.%研究了各种任务分派问题算法,对一般任务分派和有约束任务分配的求解方法进行算法设计,以Microsoft Visual J++ 6.0作为实验开发平台,采用Java语言及Applet嵌入网页技术,实现了网上任务分派问题数学实验的可视化.用户可由可视化界面,输入任意任务分配问题,得到最佳的分配结果及满意率.为学生学习掌握相关知识,提供了具有可视化和交互性功能的学习使用平台
Mathematical Giftedness: A Creative Scenario
Sharma, Yogesh
2013-01-01
Identification and development of giftedness is a major task of mathematics teachers worldwide. An early identification of gifted children in mathematics can have a number of benefits, like, providing opportunities for the nourishment of their talent, saving them from burnout, and proper utilisation of mathematical talent in future. As creativity…
Cheema, Jehanzeb R.; Skultety, Lisa S.
2017-01-01
Subject-specific self-efficacy is a measure of confidence in one's own ability to complete tasks related to that subject. This confidence does not necessarily reflect actual ability in the subject and can be an over- or underestimate of true ability. We use nationally representative samples of 15-year-old students from the US to measure the degree…
DEFF Research Database (Denmark)
Westphael, Henning; Mogensen, Arne
2013-01-01
In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students.......In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students....
Launching a Discourse-Rich Mathematics Lesson
Trocki, Aaron; Taylor, Christine; Starling, Tina; Sztajn, Paola; Heck, Daniel
2014-01-01
The idea of elementary school students working together on mathematical tasks is not new, but recent attention to creating purposeful discourse in mathematics classrooms prompts teachers to revisit discourse-promoting strategies for mathematics lessons. The Common Core's Standards for Mathematical Practice (CCSSI 2010) encourage teachers to…
Teaching Middle-Grades Mathematics through Financial Literacy
Crawford-Ferre, Heather Glynn; Wiest, Lynda R.; Vega, Stephanie
2016-01-01
Because financial literacy is an important skill for middle-grades students, this article suggests numerous personal financial literacy tasks for use in the mathematics classroom. Also provided are specifics for implementing one of these tasks to address mathematical content.
Characterizing Students' Understandings of Mathematical Proof.
Knuth, Eric J.; Elliott, Rebekah L.
1998-01-01
Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)
Wilhelm, Jennifer Anne
This case study examined what student content understanding could occur in an inner city Industrial Electronics classroom located at Tree High School where project-based instruction, enhanced with technology, was implemented for the first time. Students participated in a project implementation unit involving sound waves and trigonometric reasoning. The unit was designed to foster common content learning (via benchmark lessons) by all students in the class, and to help students gain a deeper conceptual understanding of a sub-set of the larger content unit (via group project research). The objective goal of the implementation design unit was to have students gain conceptual understanding of sound waves, such as what actually waves in a wave, how waves interfere with one another, and what affects the speed of a wave. This design unit also intended for students to develop trigonometric reasoning associated with sinusoidal curves and superposition of sinusoidal waves. Project criteria within this design included implementation features, such as the need for the student to have a driving research question and focus, the need for benchmark lessons to help foster and scaffold content knowledge and understanding, and the need for project milestones to complete throughout the implementation unit to allow students the time for feedback and revision. The Industrial Electronics class at Tree High School consisted of nine students who met daily during double class periods giving 100 minutes of class time per day. The class teacher had been teaching for 18 years (mathematics, physics, and computer science). He had a background in engineering and experience teaching at the college level. Benchmark activities during implementation were used to scaffold fundamental ideas and terminology needed to investigate characteristics of sound and waves. Students participating in benchmark activities analyzed motion and musical waveforms using probeware, and explored wave phenomena using waves
Luther, Kenneth H.
2012-01-01
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…
Luther, Kenneth H.
2012-01-01
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…
Baston, Chiara; Contin, Manuela; Calandra Buonaura, Giovanna; Cortelli, Pietro; Ursino, Mauro
2016-01-01
Malfunctions in the neural circuitry of the basal ganglia (BG), induced by alterations in the dopaminergic system, are responsible for an array of motor disorders and milder cognitive issues in Parkinson's disease (PD). Recently Baston and Ursino (2015a) presented a new neuroscience mathematical model aimed at exploring the role of basal ganglia in action selection. The model is biologically inspired and reproduces the main BG structures and pathways, modeling explicitly both the dopaminergic and the cholinergic system. The present work aims at interfacing this neurocomputational model with a compartmental model of levodopa, to propose a general model of medicated Parkinson's disease. Levodopa effect on the striatum was simulated with a two-compartment model of pharmacokinetics in plasma joined with a motor effect compartment. The latter is characterized by the levodopa removal rate and by a sigmoidal relationship (Hill law) between concentration and effect. The main parameters of this relationship are saturation, steepness, and the half-maximum concentration. The effect of levodopa is then summed to a term representing the endogenous dopamine effect, and is used as an external input for the neurocomputation model; this allows both the temporal aspects of medication and the individual patient characteristics to be simulated. The frequency of alternate tapping is then used as the outcome of the whole model, to simulate effective clinical scores. Pharmacokinetic-pharmacodynamic modeling was preliminary performed on data of six patients with Parkinson's disease (both "stable" and "wearing-off" responders) after levodopa standardized oral dosing over 4 h. Results show that the model is able to reproduce the temporal profiles of levodopa in plasma and the finger tapping frequency in all patients, discriminating between different patterns of levodopa motor response. The more influential parameters are the Hill coefficient, related with the slope of the effect sigmoidal
Sigmundsson, H; Polman, R C J; Lorås, H
2013-08-01
Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning.
Mathematical Footprints Discovering Mathematics Everywhere
Pappas, Theoni
1999-01-01
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
Tasks for tests and A-levels using CAS
2012-01-01
Tasks for different years of the secondary level II are presented on the basis of long lasting experience with computer-assisted mathematics instruction. They include applications of mathematical skills as well as the testing of theoretical knowledge. Finally relevant A-levels tasks are presented that integrate different mathematical contents into every day connections from economy, medical science, sports asf.
Mathematical Reasoning in Teachers' Presentations
Bergqvist, Tomas; Lithner, Johan
2012-01-01
This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers' ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on…
Mathematical Reasoning in Teachers' Presentations
Bergqvist, Tomas; Lithner, Johan
2012-01-01
This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers' ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on…
Andreescu, Titu; Tetiva, Marian
2017-01-01
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...
Reed, Nat
2011-01-01
For grades 6-8, our State Standards-based combined resource meets the algebraic concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are opportunities for problem-solving, patterning, algebraic graphing, equations and determining averages. The combined task & drill sheets
Reed, Nat
2011-01-01
For grades 3-5, our State Standards-based combined resource meets the algebraic concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are opportunities for problem-solving, patterning, algebraic graphing, equations and determining averages. The combined task & drill sheets
Exploring Open-Ended Tasks as Teacher Learning
Sullivan, Peter; Griffioen, Mel; Gray, Hayley; Powers, Chris
2009-01-01
The Task Types and Mathematics Learning project is investigating the opportunities and constraints that teachers experience when using particular types of mathematics tasks. Some assumptions underlying this aspect of the project are: (1) that teachers seeking a balanced curriculum choose to use a mix of types of tasks; (2) open-ended questions…
Selecting and Sequencing Mathematics Tasks: Seeking Mathematical Knowledge for Teaching
Galant, Jaamia
2013-01-01
In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two…
African Journals Online (AJOL)
Open Access DOWNLOAD FULL TEXT ... In the transmission culture of teaching and learning, mathematics is seen as a body of knowledge and ... Keyword: algebraic thinking, discussion in mathematics classroom, teaching approaches ...
Welch, Anita G.; Cakir, Mustafa; Peterson, Claudette M.; Ray, Chris M.
2012-04-01
Background . Studies exploring the relationship between students' achievement and the quality of the classroom learning environments have shown that there is a strong relationship between these two concepts. Learning environment instruments are constantly being revised and updated, including for use in different cultures, which requires continued validation efforts. Purpose The purpose of this study was to establish cross-cultural reliability and validity of the Technology-Rich Outcomes-Focused Learning Environment Inventory (TROFLEI) in both Turkey and the USA. Sample Approximately 980 students attending grades 9-12 in Turkey and 130 students attending grades 9-12 in the USA participated in the study. Design and method Scale reliability analyses and confirmatory factor analysis (CFA) were performed separately for Turkish and US participants for both actual and preferred responses to each scale to confirm the structure of the TROFLEI across these two distinct samples. Results Cronbach's alpha reliability coefficients, ranging from α = 0.820 to 0.931 for Turkish participants and from α = 0.778 to 0.939 for US participants, indicated that all scales have satisfactory internal consistency for both samples. Confirmatory factor analyses resulted in evidence of adequate model fit across both samples for both actual and preferred responses, with the root mean square error of approximation ranging from 0.052 to 0.057 and the comparative fit index ranging from 0.920 to 0.982. Conclusions This study provides initial evidence that the TROFLEI is valid for use in both the Turkish and US high-school populations (grades 9-12). However, the psychometric properties should be examined further with different populations, such as middle-school students (grades 6-8).
Directory of Open Access Journals (Sweden)
陳敏瑜 Min-Yu Chen
2013-09-01
Full Text Available 本研究使用國際數學與科學成就趨勢調查（Trends in International Mathematics and Science Study, TIMSS）2007年臺灣八年級學生的資料，以期望價值理論為架構，先進行能力信念與價值相關構面及題項的信度與效度分析，接續探討這些構面對數學成就之影響，並以多群組結構方程模型分析男、女生模型之差異。研究發現，數學能力信念、實用與內在價值三構面及其對應的題項都有良好的信度與效度，三構面中以能力信念的預測力最高，能解釋數學成就約三成六的變異量。男、女生模型在因素負荷量、題項截距、路徑係數及因素變異數／共變異數上皆具跨性別不變性，不過，在構面平均數上，男生的數學能力信念、實用與內在價值的平均數都顯著較女生高，且以在能力信念的差異最大。最後依據結果提出實務應用及未來研究上的建議。 Based on expectancy-value theory, we applied trends in mathematics and science study (TIMSS data to investigate the reliability and validity of items relating to ability beliefs and task values, examine their effects on mathematical achievements, and test gender invariance in the proposed models by using multiple-group structural equation modeling. The results supported a three-factor solution reflecting ability beliefs, utility values, and intrinsic values. These factors and corresponding items all possessed strong reliability and validity. Among the three factors, ability beliefs exerted the strongest effect on mathematical achievements, explaining 36% of the variance of mathematical achievements. Gender invariance evidence was exhibited in the factor loadings, item intercepts, path coefficients, and factor variance/covariance. However, comparisons of latent factor means suggested that boys had significantly high mean scores regarding ability beliefs, utility values, and intrinsic values. Finally
The Effect of Mathematics Self-Efficacy on Anxiety of Teaching Mathematics
Directory of Open Access Journals (Sweden)
Alattin URAL
2015-04-01
Full Text Available The aim of the study is to investigate the effect of mathematics self-efficacy belief on anxiety of teaching mathematics. The participants of the study consist of 42 mathematics teacher candidates in the Department of Mathematics Education, Faculty of Education. The scale of mathematics self-efficacy, developed by Umay (2001, and the scale of mathematics teaching anxiety, developed by Peker (2006, was enrolled as measurement tools. Pearson correlation was used for the correlation between teacher candidates’ average points from the both scales. The results revealed that there was a significant and negative correlation mathematics self-efficacy beliefs and anxiety of teaching mathematics. This result means that the students’ mathematics teaching anxiety decreases as their mathematics self-efficacy beliefs increase. On the other hand, it was seen that mathematics self-efficacy belief explains 35% of the variance in teaching mathematics anxiety. Besides, it was determined that mathematics teacher candidates’ mathematics teaching anxiety was at low level, and mathematics efficacy beliefs are at high level. Mathematics self-efficacy refers to the belief or perception that one is capable of organizing and executing the actions necessary to succeed at a given mathematical task. For this aim, their knowledge and abilities relating mathematical concepts and also their confidences about their mathematical abilities must be enhanced.
Kilpatrick, Jeremy
2014-01-01
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…
Kilpatrick, Jeremy
2014-01-01
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…
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
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
Directory of Open Access Journals (Sweden)
Yinghui Lai
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
2015-01-01
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.
Pontrjagin, Lev Semenovič
1984-01-01
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...
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
What Software to Use in the Teaching of Mathematical Subjects?
Berežný, Štefan
2015-01-01
We can consider two basic views, when using mathematical software in the teaching of mathematical subjects. First: How to learn to use specific software for the specific tasks, e. g., software Statistica for the subjects of Applied statistics, probability and mathematical statistics, or financial mathematics. Second: How to learn to use the…
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
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...
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
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...... 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...... 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...
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
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…
Primary Mathematics Trainee Teacher Confidence and Its Relationship to Mathematical Knowledge
Norton, Stephen J.
2017-01-01
The purpose of this paper is to examine trainee primary school teachers' confidence in their mathematical content knowledge (MCK) and confidence to teach specific primary mathematics concepts (mathematics pedagogical content knowledge --MPCK) which was correlated to their actual MCK on specific tasks. For this correlational study survey and test…
Stöltzner, Michael
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.
Wragg, Regina E.
This dissertation presents my explorations in both molecular biology and science education research. In study one, we determined the ADIPOQ and ADIPORI genotypes of 364 White and 148 Black BrCa patients and used dominant model univariate logistic regression analyses to determine individual SNP and haplotype associations with tumor or patient characteristics in a case-case comparison. We found twelve associations between individual SNPs and patient or tumor characteristics that impact BrCa prognosis. For example, the ADIPOQ rs1501299 C allele was associated with ER+ tumors (OR=4.73, p=0.001) among White women >50 years of age at their time of diagnosis. Also, the A allele was more frequent in the Black patient population among whom more aggressive subtypes are common. Similarly, the ADIPORI rs12733285 T allele was associated with both PR+ and ER+ tumors. (OR=2.18 p=0.001; OR=1.88 p=0.019, respectively). Our data suggest that several polymorphisms individually or as specific ADIPOQ and ADIPOR1 haplotypes are associated with tumor characteristics that impact prognosis in BrCa patients. Thus, genotyping additional groups of patients for these SNPs could offer insight into the involvement of adiponectin signaling allele variance in BrCa outcomes. In our second study, we examined 1) how teachers' beliefs about themselves and their students influence the fidelity of implementation of their enactment of a technology-rich curriculum, and 2) how professional development support during the enactment leads to changes in teacher beliefs. From the analysis of two teachers' experiences through interviews, surveys, journal entries, and video recordings of their enactments, several different themes were identified. For example, teachers' beliefs regarding students' ability to learn using the curriculum influenced the fidelity of implementation and student learning. These observations led to the development of a model of professional development that would promote faithful
Jothi, A Lenin
2009-01-01
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
Aigner, Martin; Spain, Philip G
2010-01-01
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
Pappas, Theoni
1997-01-01
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
2013-01-01
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.
Directory of Open Access Journals (Sweden)
A. Fiol-Zulueta
2009-05-01
Full Text Available El problema de la obtención de secuencias de trabajo en las actividades productivas consiste en ladeterminación de una posible combinación, deseablemente la mejor, de opciones de secuencias detrabajo para cada uno de los elementos que conforman la entidad productiva y por todas ellas, apartir de la elaboración previa de secuencias evaluadas considerando un determinado indicador deeficiencia. En el trabajo se propone un modelo matemático para el caso de un taller de flujo híbridocon tiempos de procesamiento dependientes de la secuencia y de las máquinas, y suimplementación utilizando una meta heurística, con el propósito de ayudar a la toma de decisionescon vistas a mejorar los instrumentos utilizados para lograr la conciliación de las secuencias detrabajo en los talleres de producción, debido a la necesidad de elevar los indicadores de eficienciade dichos talleres.Palabras claves: secuencias de producción en talleres de maquinado, taller de flujo, meta heurística,optimización bajo criterios múltiples.____________________________________________________________________________AbstractThe problem of obtaining work sequences in the productive activities consists on the determinationof a possible combination, desirably the best, of work sequences for each one of the elements ofthe productive entity and for all them starting from the previous elaboration of evaluatedsequences considering a certain efficiency indicator. In the work a mathematical model, for thecase of a hybrid flow shop with times depending of the sequence prosecution and of the machinescharacteristics, and it implementation using a metaheurístic procedure are proposed, with thepurpose of aiding the decisions making process with a view of improving the tools used to achievethe work sequences conciliation of the production shops, due to the necessity of raising theefficiency indicators of these workshops.Key words: work sequences in mechanical industry workshops, flow
Promoting Reasoning through the Magic V Task
Bragg, Leicha A.; Widjaja, Wanty; Loong, Esther Yook-Kin; Vale, Colleen; Herbert, Sandra
2015-01-01
Reasoning in mathematics plays a critical role in developing mathematical understandings. In this article, Bragg, Loong, Widjaja, Vale & Herbert explore an adaptation of the Magic V Task and how it was used in several classrooms to promote and develop reasoning skills.
Promoting Reasoning through the Magic V Task
Bragg, Leicha A.; Widjaja, Wanty; Loong, Esther Yook-Kin; Vale, Colleen; Herbert, Sandra
2015-01-01
Reasoning in mathematics plays a critical role in developing mathematical understandings. In this article, Bragg, Loong, Widjaja, Vale & Herbert explore an adaptation of the Magic V Task and how it was used in several classrooms to promote and develop reasoning skills.
Experimental Mathematics and Mathematical Physics
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
A Population of Assessment Tasks
Daro, Phil; Burkhardt, Hugh
2012-01-01
We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."
A Population of Assessment Tasks
Daro, Phil; Burkhardt, Hugh
2012-01-01
We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."
Kleene, Stephen Cole
2002-01-01
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.
Kodaira, Kunihiko
1996-01-01
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.
Parshall, Karen Hunger
2002-01-01
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...
Murray, James D
1993-01-01
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...
Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection
Wu, Su-Chiao; Lin, Fou-Lai
2016-01-01
A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…
How to Feel about and Learn Mathematics: Therapeutic Intervention and Attentiveness
Namukasa, Immaculate; Gadanidis, George; Cordy, Michelle
2009-01-01
In mathematics teacher education, tasks that centre on doing mathematics are used for a variety of purposes, including learning new mathematics. In our research, we focus on doing mathematics as a therapeutic intervention. Many pre-service teachers in our program narrate impoverished mathematics experiences. We engage pre-service elementary school…
Logan, J David
2013-01-01
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
Handley, Bill
2012-01-01
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
Geroch, Robert
1985-01-01
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
Towards New Documentation Systems for Mathematics Teachers?
Gueudet, Ghislaine; Trouche, Luc
2009-01-01
We study in this article mathematics teachers' "documentation work": looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers' professional activity and professional development. We introduce a distinction between…
Directory of Open Access Journals (Sweden)
Fotini Dina
2009-10-01
mathematics and performance on mathematical tasks were also measured along with metacognitive experiences and emotions, such as interest, and liking of the tasks. Hierarchical cluster analysis revealed 8 distinct student profiles with only some of them involving achievement goal orientations. A series of MANOVAS revealed significant effects of profile and treatment on task performance, on metacognitive experiences and emotions, as well as a significant interaction of profile with treatment in the case of effort ratings.
Key words: Achievement goal orientations, students’ profiles, feedback, metacognitive experiences, interest.
Hougardy, Stefan
2016-01-01
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.
Menzel, Donald H
2003-01-01
Useful treatment of classical mechanics, electromagnetic theory, and relativity includes explanations of function theory, vectors, matrices, dyadics, tensors, partial differential equations, other advanced mathematical techniques. Nearly 200 problems with answers.
Eck, Christof; Knabner, Peter
2017-01-01
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.
Sneyd, James
2009-01-01
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. ...
Yvon, Bernard R.; Walo, Trudy J.
1975-01-01
A large doll can be used to illustrate many mathematical concepts to young children. Examples of the concepts introduced with the doll include one-to-one correspondence (buttons with buttonholes) and relative sizes. (SD)
African Journals Online (AJOL)
posed' with respect to connections are intended to open up possibilities for thinking ... knowledge in the teaching and learning of mathematics, it is essential to take .... two and three dimensions using various approaches in geometry and trigo-.
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Puzzles of purely logical nature are distinguished from most mathematical puzzles,in that thought rather than memory, that is,native mental ingenuity rather than a store of acquired information, is the key to their solution.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
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...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
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...
Pestman, Wiebe R
2009-01-01
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.
Institute of Scientific and Technical Information of China (English)
2005-01-01
<正>20051134 Chen Aibing (Faculty of Land Resource Engineering, Kunming University of Science and Technology) Kunming, Yunnan 650093, China); Qin Dexian MathematicEconomical Model of No. 5 Orebody in Gejiu Tin Mine, Yunnan Province (Acta Mineralogica Sinica, ISSN 1000 - 4734, CN 52 -1045/P, 24(2), 2004, p. 171-175, 5 illus. , 5 tables, 7 refs. ) Key words: tin deposits, mathematical models, Yunnan Province
Berman, Elizabeth
1979-01-01
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
Brain correlates of mathematical competence in processing mathematical representations
Directory of Open Access Journals (Sweden)
Roland H. Grabner
2011-11-01
Full Text Available The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging (fMRI study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left angular gyrus activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left angular gyrus activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.
Technology, Mathematics and Activity Theory
Lerman, Stephen
2013-01-01
This article describes 11 papers in which the authors report their research on technology as enhancement in the teaching and learning of mathematics, in the context of the application of activity theory for design and/or analysis. There is considerable diversity across the papers in how the authors have interpreted their task and in particular how…
The Language of Mathematics Utilizing Math in Practice
Baber, Robert L
2011-01-01
A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process-not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and i
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron
2016-01-01
Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…
Philosophy of Mathematics, Mathematics Education and Philosophy of Mathematics Education.
Zheng, Yuxin
1994-01-01
Uses the modern development of mathematics education in the United States as background for the analysis of the influence of mathematics philosophy on mathematics education. Discusses the problem of how to develop the subject of philosophy of mathematics education, regarded as an impetus from mathematics education, to the further development of…
Mathematical Reasoning Requirements in Swedish Upper Secondary Level Assessments
Palm, Torulf; Boesen, Jesper; Lithner, Johan
2011-01-01
We investigate the mathematical reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new reasoning and to consider the intrinsic mathematical properties involved…
Robotic Toys as a Catalyst for Mathematical Problem Solving
Highfield, Kate
2010-01-01
Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…
Construct Validation and a More Parsimonious Mathematics Beliefs Scales.
Capraro, Mary Margaret
Teacher beliefs are instrumental in defining teacher pedagogical and content tasks and for processing information relevant to those tasks. In this study, a Likert-type instrument, Mathematics Beliefs Scales (E. Fennema, T. Carpenter, and M. Loef, 1990), was used to measure the mathematical beliefs of teachers. This instrument was designed with…
Investigating Mathematics through Digital Media: Cognitive Visual Perturbations
Calder, Nigel
2011-01-01
How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…
Mathematical Reasoning Requirements in Swedish National Physics Tests
Johansson, Helena
2016-01-01
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…
Investigating Mathematics through Digital Media: Cognitive Visual Perturbations
Calder, Nigel
2011-01-01
How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…
Jost, Jürgen
2015-01-01
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...
Rubin, Andrew
2014-01-01
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...
Vivaldi, Franco
2014-01-01
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...
Hiriart-Urruty, Jean-Baptiste
2016-01-01
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.
Cahill, Kevin
2013-01-01
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.
Novikasari, Ifada; Darhim, Didi Suryadi
2015-01-01
This study explored the characteristics of pre-service primary teachers (PSTs) influenced by mathematical belief and mathematical knowledge for teaching (MKT) PSTs'. A qualitative approach was used to investigate the levels of PSTs on mathematical belief and MKT. The two research instruments used in this study were an interview-based task and a…
Novikasari, Ifada; Darhim, Didi Suryadi
2015-01-01
This study explored the characteristics of pre-service primary teachers (PSTs) influenced by mathematical belief and mathematical knowledge for teaching (MKT) PSTs'. A qualitative approach was used to investigate the levels of PSTs on mathematical belief and MKT. The two research instruments used in this study were an interview-based task and a…
Quotable Quotes in Mathematics
Lo, Bruce W. N.
1983-01-01
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)
Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim
2011-01-01
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
Najman, Laurent
2013-01-01
Mathematical Morphology allows for the analysis and processing of geometrical structures using techniques based on the fields of set theory, lattice theory, topology, and random functions. It is the basis of morphological image processing, and finds applications in fields including digital image processing (DSP), as well as areas for graphs, surface meshes, solids, and other spatial structures. This book presents an up-to-date treatment of mathematical morphology, based on the three pillars that made it an important field of theoretical work and practical application: a solid theoretical foun
Green, George
2005-01-01
An almost entirely self-taught mathematical genius, George Green (1793 -1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.The first paper, ""An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,"" which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as desig
Number & operations task & drill sheets
Reed, Nat
2011-01-01
For grades 6-8, our State Standards-based combined resource meets the number & operations concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are problems involving place value, fractions, addition, subtraction and using money. The combined task & drill sheets offer spac
Directory of Open Access Journals (Sweden)
Julie Ann eJordan
2015-03-01
Full Text Available Linguistic influences in mathematics have previously been explored through subtyping methodology and by taking advantage of the componential nature of mathematics and variations in language requirements that exist across tasks. The present longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5-7 years. Initially, 256 children were screened for mathematics and reading difficulties using standardised measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the MD (n=26, MDRD (n=32, reading difficulty (RD, n=22 and typically achieving (TA, n=35 subtypes. These children were tested at four time points, separated by six monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypes could have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
Bailey, Judy
2014-01-01
Preparing to become an effective primary school mathematics teacher is a challenging and complex task; and is influenced by one's past experiences, personal knowledge of, and beliefs and attitudes towards mathematics. This paper examines the experiences of a small group of pre-service teachers who did not pass their first year mathematics…
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
Fujita, Shinsaku
2015-01-01
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.
Weaver, Nik
2001-01-01
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 ...
The language of mathematics telling mathematical tales
Barton, Bill
2008-01-01
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.
Directory of Open Access Journals (Sweden)
Bashirah Ibrahim
2017-10-01
Full Text Available We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.
Enabling collaboration on semiformal mathematical knowledge by semantic web integration
Lange, C
2011-01-01
Mathematics is becoming increasingly collaborative, but software does not sufficiently support that: Social Web applications do not currently make mathematical knowledge accessible to automated agents that have a deeper understanding of mathematical structures. Such agents exist but focus on individual research tasks, such as authoring, publishing, peer-review, or verification, instead of complex collaboration workflows. This work effectively enables their integration by bridging the document-oriented perspective of mathematical authoring and publishing, and the network perspective of threaded
Sierpinska, Anna
1994-01-01
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.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......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...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Capozziello, Salvatore; Faraoni, Valerio
In this chapter we discuss certain mathematical tools which are used extensively in the following chapters. Some of these concepts and methods are part of the standard baggage taught in undergraduate and graduate courses, while others enter the tool-box of more advanced researchers. These mathematical methods are very useful in formulating ETGs and in finding analytical solutions.We begin by studying conformal transformations, which allow for different representations of scalar-tensor and f(R) theories of gravity, in addition to being useful in GR. We continue by discussing variational principles in GR, which are the basis for presenting ETGs in the following chapters. We close the chapter with a discussion of Noether symmetries, which are used elsewhere in this book to obtain analytical solutions.
Driessche, Pauline; Wu, Jianhong
2008-01-01
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...
Energy Technology Data Exchange (ETDEWEB)
Robinson, H.P.; Potter, Elinor
1971-03-01
This collection of mathematical data consists of two tables of decimal constants arranged according to size rather than function, a third table of integers from 1 to 1000, giving some of their properties, and a fourth table listing some infinite series arranged according to increasing size of the coefficients of the terms. The decimal values of Tables I and II are given to 20 D.
Institute of Scientific and Technical Information of China (English)
2007-01-01
<正>20070721 Dong Yaosong (National Key La-boratory of Geological Process and Mineral resources, Institute of Mathematical Geology and Remote Sensing, China University of Geosciences, Wuhan 430074, China); Yang Yanchen Mutual Compensation of Nerval Net and Characteristic Analysis in Mineral Resources Exploration (Mineral Resources and Geology, ISSN1001-5663, CN45-1174/TD, 20(1), 2006, p.1-6, 3 illus., 6 tables, 5 refs.) Key words: prospecting and exploration of mineral, neural network systems
Kharuddin, Azrul Fazwan; Ismail, Noor Azina
2017-01-01
Integrating technology in the mathematics curriculum has become a necessary task for curriculum developers as well as mathematics practitioners across the world and time. In general research studies seeking a better understanding of how best to integrate mathematics analysis tools with mathematics subject matter normally observe mathematics…
Ngware, Moses W.; Ciera, James; Musyoka, Peter K.; Oketch, Moses
2015-01-01
This paper examines the contribution of quality mathematics teaching to student achievement gains. Quality of mathematics teaching is assessed through teacher demonstration of the five strands of mathematical proficiency, the level of cognitive task demands, and teacher mathematical knowledge. Data is based on 1907 grade 6 students who sat for the…
Causal Bayes Model of Mathematical Competence in Kindergarten
Directory of Open Access Journals (Sweden)
Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
Teachers' Mathematics as Mathematics-at-Work
Bednarz, Nadine; Proulx, Jérôme
2017-01-01
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…
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
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…
Designing rich sets of tasks for undergraduate calculus courses
2011-01-01
Research has shown that the types of tasks assigned to students affect their learning. Studies have found that many mathematical tasks created for second and third level students promote instrumental rather than relational understanding, and imitative rather than creative reasoning. In this paper, we describe some frameworks that aim to guide teachers when writing tasks. From these frameworks a set of task types that are deemed appropriate for undergraduate students, and that foster mathem...
DEFF Research Database (Denmark)
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....
ICFHR 2016 CROHME: Competition on Recognition of Online Handwritten Mathematical Expressions
Mouchère, Harold; Viard-Gaudin, Christian; Zanibbi, Richard; Garain, Utpal
2016-01-01
International audience; This paper presents an overview of the 5th Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME). As in previous years, the main task is formula recognition from handwritten strokes (Task 1). Additional tasks include classification of isolated symbols (Task 2a), classification of isolated valid and invalid symbols (Task 2b), a new task on parsing formula structure from valid handwritten symbols (Task 3), and parsing expressions with matrice...
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
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…
Cognitive correlates of performance in advanced mathematics.
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-03-01
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.
Mathematical and information maintenance of biometric systems
Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.
2016-04-01
This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.
Jordan, Julie A; Wylie, Judith; Mulhern, Gerry
2015-01-01
Linguistic influences in mathematics have previously been explored through subtyping methodology and by taking advantage of the componential nature of mathematics and variations in language requirements that exist across tasks. The present longitudinal investigation aimed to examine the language requirements of mathematical tasks in young children aged 5-7 years. Initially, 256 children were screened for mathematics and reading difficulties (RDs) using standardized measures. Those scoring at or below the 35th percentile on either dimension were classified as having difficulty. From this screening, 115 children were allocated to each of the mathematical difficulty (MD; n = 26), MDRD (n = 32), RD (n = 22) and typically achieving (n = 35) subtypes. These children were tested at four time points, separated by 6 monthly intervals, on a battery of seven mathematical tasks. Growth curve analysis indicated that, in contrast to previous research on older children, young children with MD and MDRD had very similar patterns of development on all mathematical tasks. Overall, the subtype comparisons suggested that language played only a minor mediating role in most tasks, and this was secondary in importance to non-verbal skills. Correlational evidence suggested that children from the different subtypes could have been using different mixes of verbal and non-verbal strategies to solve the mathematical problems.
Partial Derivative Games in Thermodynamics: A Cognitive Task Analysis
Kustusch, Mary Bridget; Roundy, David; Dray, Tevian; Manogue, Corinne A.
2014-01-01
Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task…
Devising Principles of Design for Numeracy Tasks
Geiger, Vince; Forgasz, Helen; Goos, Merrilyn; Bennison, Anne
2014-01-01
Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics--in this case, the subject of English. We explore the nature of potential…
Foster, Colin
2013-07-01
In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the expense of more independent engagement with richer, multifaceted tasks risks devaluing the subject and failing to give learners an authentic and enjoyable experience of being a mathematician. Thus, there is a pressing need for mathematical tasks which embed the practice of essential techniques within a richer, exploratory and investigative context. Such tasks can be justified to school management or to more traditional mathematics teachers as vital practice of important skills; at the same time, they give scope to progressive teachers who wish to work in more exploratory ways. This paper draws on the notion of a musical étude to develop a powerful and versatile approach in which these apparently contradictory aspects of teaching mathematics can be harmoniously combined. I illustrate the tactic in three central areas of the high-school mathematics curriculum: plotting Cartesian coordinates, solving linear equations and performing enlargements. In each case, extensive practice of important procedures takes place alongside more thoughtful and mathematically creative activity.
Figures of thought mathematics and mathematical texts
Reed, David
2003-01-01
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.
A mathematical model of the distillation units with heat pump
Directory of Open Access Journals (Sweden)
A. V. Zhuchkov
2013-01-01
Full Text Available Efficient hardware design of the rectification process and reduce energy costs for their implementation is an urgent task. The mathematical description of the alcohol distillation process using a heat pump was obtained in this study.
Introducing philosophy of mathematics
Friend, Michele
2014-01-01
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
Mathematics Education Computer Software and Mathematics Teachers.
Ozgun-Koca, S. Asli
2000-01-01
Presents results from a study that uses questionnaires to ask mathematics teachers' (N=64) opinions about mathematics education computer software. Indicates that respondents overwhelmingly favored discovery and remediation as the purpose of using software in mathematics classrooms. Teachers believed that real world situations and multiple…
Mathematical Story: A Metaphor for Mathematics Curriculum
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving
E Siswono, T. Y.; Kohar, A. W.; Hartono, S.
2017-02-01
This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.
Technology Rich Biology Labs: Effects of Misconceptions.
Kuech, Robert; Zogg, Gregory; Zeeman, Stephan; Johnson, Mark
This paper describes a study conducted on the lab sections of the general biology course for non-science majors at the University of New England, and reports findings of student misconceptions about photosynthesis and the mass/carbon uptake during plant growth. The current study placed high technology analytic tools in the hands of introductory…
Technology-Rich Schools Up Close
Levin, Barbara B.; Schrum, Lynne
2013-01-01
This article observes that schools that use technology well have key commonalities, including a project-based curriculum and supportive, distributed leadership. The authors' research into tech-rich schools revealed that schools used three strategies to integrate technology successfully. They did so by establishing the vision and culture,…
Technology-Rich Schools Up Close
Levin, Barbara B.; Schrum, Lynne
2013-01-01
This article observes that schools that use technology well have key commonalities, including a project-based curriculum and supportive, distributed leadership. The authors' research into tech-rich schools revealed that schools used three strategies to integrate technology successfully. They did so by establishing the vision and culture,…
Institute of Scientific and Technical Information of China (English)
2010-01-01
<正>20102798 Gao Shengxiang(School of Resource and Earth Science,China University of Mining and Technology,Xuzhou 221008,China);Ye Rongzhang Establishment of Complex Geological Body FLAC3D Model by Using MATLAB Interface Program(Coal Geology & Exploration,ISSN1001-1986,CN61-1155/P,37(5),2009,p.51-53,5 illus.,4 refs.,with English abstract)Key words:FLAC3D,computer programs20102799 Li Xiuzhen(Key Laboratory of Mountain Hazards and Surface Processes,Chinese Academy of Sciences,Chengdu 610041,China);Wang Chenghua Potential Landslide Identification Model Based on Fisher Discrimination Analysis Method and Its Application(The Chinese Journal of Geological Hazard and Control,ISSN1003-8035,CN11-2825/P,20(4),2009,p.23-26,40,2 tables,11 refs.)Key words:mathematical models,landslidesAiming at ancient(old)landslides,four kinds of discrimination indexes which included nine secondary indexes for potential landslides,such as landform character,slip surface character,landslide body structure and recent activities characters,were presented.Then according to Fisher Discrimination theory,Fisher Discrimination model for the potential landslides was built.The re
University Students' Reading of Their First-Year Mathematics Textbooks
Shepherd, Mary D.; Selden, Annie; Selden, John
2012-01-01
This article reports the observed behaviors and difficulties that 11 precalculus and calculus students exhibited in reading new passages from their mathematics textbooks. To gauge the "effectiveness" of these students' reading, we asked them to attempt straightforward mathematical tasks, based directly on what they had just read. The…
Unpacking the Nature of Discourse in Mathematics Classrooms.
Knuth, Eric; Peressini, Dominic
2001-01-01
Describes a framework for examining mathematical discourse and shows how to apply this framework to appreciate the complex relationship between discourse and understanding in mathematics. Focuses on the role of discourse and the different types that emerge as students solve a particular task. (KHR)
Clock Reading: An Underestimated Topic in Children with Mathematics Difficulties
Burny, Elise; Valcke, Martin; Desoete, Annemie
2012-01-01
Recent studies have shown that children with mathematics difficulties (MD) have weaknesses in multiple areas of mathematics. Andersson, for example, recently found that children with MD perform significantly worse than other children on clock reading tasks. The present study builds on this recent finding and aims at a more profound understanding…
University Students' Reading of Their First-Year Mathematics Textbooks
Shepherd, Mary D.; Selden, Annie; Selden, John
2012-01-01
This article reports the observed behaviors and difficulties that 11 precalculus and calculus students exhibited in reading new passages from their mathematics textbooks. To gauge the "effectiveness" of these students' reading, we asked them to attempt straightforward mathematical tasks, based directly on what they had just read. The…
Kwiatkowski-Egizio, Erica
2013-01-01
The two research questions that guided this study were: (1) How do preservice teachers develop mathematical knowledge for teaching during a coordinated math methods course and field experience? and (2) What types of portfolio tasks lend themselves to documenting mathematical knowledge in teaching? Six, female, elementary (K-8) teacher candidates…
Occupational Mathematics; Scientific Notation. Report No. 16-S. Final Report.
Rahmlow, Harold F.; And Others
This programed mathematics textbook (Volume I) is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also…
Passive stability and active control in a rhythmic task
Wei, Kunlin; Dijkstra, Tjeerd M. H.; Sternad, Dagmar
2007-01-01
Rhythmically bouncing a ball with a racket is a task that affords passively stable solutions as demonstrated by stability analyses of a mathematical model of the task. Passive stability implies that no active control is needed as errors die out without requiring corrective actions. Empirical results
Trude Nilsen; Carl Angell; Liv Sissel Grønmo
2013-01-01
As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal) on the application of mathematics in physics education compared with the research related to the c...
Students' Difficulties with Proof by Mathematical Induction.
Baker, John Douglas
The cognitive difficulties encountered by 40 high school and 13 college students beginning to learn the proof technique of mathematical induction were investigated. Students provided data in the form of proof-writing and proof-analysis tasks followed by interviews to clarify their written responses. Both groups of students had significant…
Students as Mathematics Consultants
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
2005-01-01
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....
DEFF Research Database (Denmark)
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....
Transforming Primary Mathematics
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Mathematical Epistemologies at Work.
Noss, Richard
2002-01-01
Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…
Mastering mathematics geometry & measures
Various
2014-01-01
Deliver outstanding lessons that build fluency, problem-solving and mathematical reasoning skills to enable sustained progress at Key Stage 3, in preparation for GCSE. Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics . Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or exte
Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron
2016-01-01
Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that involves the construction of an equilateral triangle is used to present and discuss multiple solution approaches that rely on a variety of concepts and ways of reasoning. To this end, the use of a Dynamic Geometry System (GeoGebra) became instrumental in constructing and exploring dynamic models of the task. These model explorations provided a means to generate novel mathematical results.
International Conference on Mathematics and Computing
Giri, Debasis; Saxena, P; Srivastava, P
2014-01-01
This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing p...
Using Student Reasoning in Mathematics Instruction
Marrongelle, Karen
2010-03-01
Using student thinking and understanding as a basis for the development of mathematical ideas in the classroom is a challenging and often overwhelming task. In this session, I will report on two instructional tools, generative alternatives and record-of/tool-for mathematics and physics teachers can use to build on students' thinking and reasoning to develop mathematical concepts and processes. The instructional tools are rooted in the theory of Realistic Mathematics Education. Examples are drawn from a first course in undergraduate differential equations. The examples will illustrate ways in which a teacher can navigate the all-telling -- all-discovery continuum through the use of the generative alternative and record-of/tool-for tools.
Silver, Edward A.; Stein, Mary Kay
1996-01-01
Examines critical features of the QUASAR Project, a mathematics instruction program oriented toward helping students develop a meaningful understanding of mathematical ideas through challenging mathematical tasks, and discusses findings regarding the positive impact it has had on students. Challenges and obstacles in implementing the project are…
Vos, Francisca; Roorda, Gerrit
2016-01-01
When students engage in rich mathematical modelling tasks, they have to handle real-world contexts and mathematics in chorus. This is not easy. In this chapter, contexts and mathematics are perceived as complementary, which means they can be integrated. Based on four types of approaches to modelling
Assessing Students' Theories of Success in Mathematics: Individual and Classroom Differences.
Nicholls, John G.; And Others
1990-01-01
Assessed were second grade students to determine whether their beliefs about causes of success in mathematics were related to their personal goals in mathematics. One class that experienced mathematics instruction consistent with a constructivist view rated higher than traditional classes on Task Orientation, attempting to gain understanding.…
Trinter, Christine P.; Brighton, Catherine M.; Moon, Tonya R.
2015-01-01
Primary grade students enter the mathematics classroom with a range of differences including students' mathematical readiness, mathematical conceptions, interests, and learning profiles. Addressing the learning needs of students is not a trivial task, but accounting for these needs is essential for supporting students as they continually work…
Lein, Amy E.; Jitendra, Asha K.; Starosta, Kristin M.; Dupuis, Danielle N.; Hughes-Reid, Cheyenne L.; Star, Jon R.
2016-01-01
In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…
About the Code of Practice of the European Mathematical Society
DEFF Research Database (Denmark)
Jensen, Arne
2013-01-01
The Executive Committee of the European Mathematical Society created an Ethics Committee in the Spring of 2010. The first task of the Committee was to prepare a Code of Practice. This task was completed in the Spring of 2012 and went into effect on 1 November 2012. Arne Jensen, author...
Musing on the Use of Dynamic Software and Mathematics Epistemology
Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron; Espinosa-Perez, Hugo
2007-01-01
Different computational tools may offer teachers and students distinct opportunities in representing, exploring and solving mathematical tasks. In this context, we illustrate that the use of dynamic software (Cabri Geometry) helped high school teachers to think of and represent a particular task dynamically. In this process, the teachers had the…
About the Code of Practice of the European Mathematical Society
DEFF Research Database (Denmark)
Jensen, Arne
2013-01-01
The Executive Committee of the European Mathematical Society created an Ethics Committee in the Spring of 2010. The first task of the Committee was to prepare a Code of Practice. This task was completed in the Spring of 2012 and went into effect on 1 November 2012. Arne Jensen, author...... of this article, is Chair of the EMS Ethics Committee...
Mathematics without boundaries surveys in pure mathematics
Pardalos, Panos
2014-01-01
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.
Schleicher, Dierk
2011-01-01
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
Seedhouse, Paul
2005-01-01
The article examines "task" as research construct as predominantly conceived in terms of task-as-workplan in the task-based learning/second language acquisition literature. It is suggested that "task" has weak construct validity and ontology in an overwhelmingly quantitative paradigm because the construct has a "split personality."…
Mathematics for Language, Language for Mathematics
Prochazkova, Lenka Tejkalova
2013-01-01
The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…
Journal of applied mathematics
National Research Council Canada - National Science Library
2001-01-01
"[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...
Semiotic Scaffolding in Mathematics
DEFF Research Database (Denmark)
Johansen, Mikkel Willum; Misfeldt, Morten
2015-01-01
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....
Mathematical and statistical analysis
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Mathematical knowledge in teaching
Rowland, Tim
2011-01-01
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.
Developing My Mathematics Identity
Gonzalez, Lidia
2016-01-01
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.
Mathematics for the nonmathematician
Kline, Morris
1967-01-01
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.
Developing My Mathematics Identity
Gonzalez, Lidia
2016-01-01
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.
Aberdein, Andrew
2014-01-01
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.
Directory of Open Access Journals (Sweden)
Devine Amy
2012-07-01
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
2012-07-09
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
Draper, Franklin Gno
This study was focused on what students remembered about five middle school science tasks when they were juniors and seniors in high school. Descriptions of the five tasks were reconstructed from available artifacts and teachers' records, notes and recollections. Three of the five tasks were "authentic" in the sense that students were asked to duplicate the decisions practitioners make in the adult world. The other two tasks were more typical school tasks involving note taking and preparation for a quiz. All five tasks, however, involved use of computers. Students were interviewed to examine what and how well they recalled the tasks and what forms or patterns of recall existed. Analysis of their responses indicated that different kinds of tasks produced different levels of recall. Authentically situated tasks were remembered much better than routine school tasks. Further, authentic tasks centered on design elements were recalled better than those for which design was not as pivotal. Patterns of recall indicated that participants most often recalled the decisions they made, the scenarios of the authentically situated tasks, the consequences of their tasks and the social contexts of the classroom. Task events, in other words, appeared to form a framework upon which students constructed stories of the tasks. The more salient the events, the richer the story, the deeper and more detailed the recall of the task. Thus, authentic tasks appeared to lend themselves to creating stories better than regular school tasks and therefore such tasks were recalled better. Implications of these patterns of recall are discussed with respect to issues of school learning and assessment.
Modern mathematics made simple
Murphy, Patrick
1982-01-01
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
Mastering mathematics statistics & probability
Various
2014-01-01
Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics. Mastering Mathematics Student Books and eBooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or extension steps they need in order to progress, through easy to follow progression charts. - Clear explanations of the tools needed for the chapter followed by questions that develop fluen
Various
2014-01-01
Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics. Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or extension steps they need in order to progress, through easy to follow progression charts. - Clear explanations of the tools needed for the chapter followed by questions tha
Students' Mathematical Noticing
Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan
2013-01-01
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…
Henson, R.; Stumbles, A.
1977-01-01
The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)
Modern Versus Traditional Mathematics
Roberts, A. M.
1974-01-01
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)
Mathematics a minimal introduction
Buium, Alexandru
2013-01-01
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
Mendick, Heather
2006-01-01
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.
Buchman, Aaron; Zimmerman, Robert
This outline for Eleventh Year Mathematics in New York adheres closely to the recommendations of The Commission of Mathematics of the College Entrance Examination Board and thus presents a unified development of certain aspects of algebra, trigonometry, and analytic geometry. Its aim is both as a terminal course in mathematics and as a solid…
Defining Mathematical Giftedness
Parish, Linda
2014-01-01
This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…
Saludes, Jordi; 10.4204/EPTCS.79.6
2012-01-01
This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals. We also present two prototype services and comment on possible future applications in the area of artificial mathematics assistants.
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. Copyright © 2015. Published by Elsevier Ltd.
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
Mathematics, Programming, and STEM
Yeh, Andy; Chandra, Vinesh
2015-01-01
Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…
Walshaw, Margaret
2014-01-01
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…
Translations toward Connected Mathematics
Applebaum, Mark; Leikin, Roza
2010-01-01
The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…
Alkharusi, Hussain
2016-01-01
Introduction: Students are daily exposed to a variety of assessment tasks in the classroom. It has long been recognized that students' perceptions of the assessment tasks may influence student academic achievement. The present study aimed at predicting academic achievement in mathematics from perceptions of the assessment tasks after controlling…
Alkharusi, Hussain
2016-01-01
Introduction: Students are daily exposed to a variety of assessment tasks in the classroom. It has long been recognized that students' perceptions of the assessment tasks may influence student academic achievement. The present study aimed at predicting academic achievement in mathematics from perceptions of the assessment tasks after controlling…
Kokkos? Task DAG Capabilities.
Energy Technology Data Exchange (ETDEWEB)
Edwards, Harold C.; Ibanez, Daniel Alejandro
2017-09-01
This report documents the ASC/ATDM Kokkos deliverable "Production Portable Dy- namic Task DAG Capability." This capability enables applications to create and execute a dynamic task DAG ; a collection of heterogeneous computational tasks with a directed acyclic graph (DAG) of "execute after" dependencies where tasks and their dependencies are dynamically created and destroyed as tasks execute. The Kokkos task scheduler executes the dynamic task DAG on the target execution resource; e.g. a multicore CPU, a manycore CPU such as Intel's Knights Landing (KNL), or an NVIDIA GPU. Several major technical challenges had to be addressed during development of Kokkos' Task DAG capability: (1) portability to a GPU with it's simplified hardware and micro- runtime, (2) thread-scalable memory allocation and deallocation from a bounded pool of memory, (3) thread-scalable scheduler for dynamic task DAG, (4) usability by applications.
TWO CRITICISMS AGAINST MATHEMATICAL REALISM
National Research Council Canada - National Science Library
Seungbae Park
2017-01-01
Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says...
Competence with fractions predicts gains in mathematics achievement.
Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C
2012-11-01
Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.
Jourdain, Philip E B
2007-01-01
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
Crossley, J N; Brickhill, CJ; Stillwell, JC
2010-01-01
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
Mathematics for physical chemistry
Mortimer, Robert G
2013-01-01
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
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
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
Mathematics for the imagination
Higgins, Peter
2002-01-01
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
The development of mathematics
Bell, E T
1992-01-01
""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
Fundamental concepts of mathematics
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
Dantzig, Tobias
2006-01-01
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
Gabbay, Dov M; Woods, John
2009-01-01
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
Clustering of maintenance tasks for the danish railway system
DEFF Research Database (Denmark)
Mohammad Pour, Shahrzad; Benlic, Una
2017-01-01
standards. In this paper, we present a mathematical model for allocation of maintenance tasks to maintenance team members, which is a variant of the Generalized Assignment Problem. The aim is to optimise the following three criteria: (i) the total distance travelled from depots to tasks, (ii) the maximal...... distance between any maintenance task and its allocated crew member, and (iii) the imbalance in workload among crew members. As test cases, we use a set of instances that simulate the distribution of tasks in the Jutland peninsula, the largest region of Denmark....
Simple assembly line balancing problem under task deterioration
Directory of Open Access Journals (Sweden)
M. Emrani Noushabadi
2011-01-01
Full Text Available This paper introduces the effect of task deterioration in simple assembly line balancing problem. In many realistic assembly lines, a deterioration task is considered when a task is started earlier than the assigned time since the station time is constant and the earliness of the task does not reduce the cycle time. This phenomenon is known as deteriorating tasks. Therefore, we seek an optimal assignment and schedule of tasks in workstations, in order to minimize the number of stations for a given cycle time, which is known as SALBP-1. For this purpose, a mathematical model is proposed. Since the pure SALBP-1 is proved to be NP-hard and considering task deterioration complicates problem further, we propose a genetic algorithm for solving such problem. Several well-known test problems are solved to study the performance of the proposed approach.
Martin, B R
2015-01-01
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 ...
Leifer, M S
2015-01-01
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientif...
Meaning in mathematics education
Valero, Paola; Hoyles, Celia; Skovsmose, Ole
2005-01-01
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.
DEFF Research Database (Denmark)
Sørensen, Torben; Hansen, Poul Erik
1998-01-01
Description of the compulsary project tasks to be carried out as a part of DTU course 72238 Robotics......Description of the compulsary project tasks to be carried out as a part of DTU course 72238 Robotics...
Thanheiser, Eva; Olanoff, Dana; Hillen, Amy; Feldman, Ziv; Tobias, Jennifer M.; Welder, Rachael M.
2016-01-01
Mathematical task design has been a central focus of the mathematics education research community over the last few years. In this study, six university teacher educators from six different US institutions formed a community of practice to explore key aspects of task design (planning, implementing, reflecting, and modifying) in the context of…
The History of Mathematics and Mathematical Education
Grattan-Guinness, I.
1977-01-01
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)
Dominguez-Martinez, S.
2009-01-01
An important task of a manager is to motivate her subordinates. One way in which a manager can give incentives to junior employees is through the assignment of tasks. How a manager allocates tasks in an organization, provides information to the junior employees about his ability. Without coaching fr
Lee, Kerry; Ng, Swee Fong; Pe, Madeline Lee; Ang, Su Yin; Hasshim, Muhammad Nabil Azhar Mohd; Bull, Rebecca
2012-01-01
Background: Exposure to mathematical pattern tasks is often deemed important for developing children's algebraic thinking skills. Yet, there is a dearth of evidence on the cognitive underpinnings of pattern tasks and how early competencies on these tasks are related to later development. Aims: We examined the domain-specific and domain-general…
Does Inquiry Based Learning Affect Students' Beliefs and Attitudes towards Mathematics?
McGregor, Darren
2014-01-01
Ill-structured tasks presented in an inquiry learning environment have the potential to affect students' beliefs and attitudes towards mathematics. This empirical research followed a Design Experiment approach to explore how aspects of using ill-structured tasks may have affected students' beliefs and attitudes. Results showed this task type and…
Teaching Formal Methods and Discrete Mathematics
Directory of Open Access Journals (Sweden)
Mathieu Jaume
2014-04-01
Full Text Available Despite significant advancements in the conception of (formal integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help during the development cycle is essential but we think that education of computer scientists and software engineers is also an important challenge to take up. Indeed, we believe that formal methods courses do not appear sufficiently early in compter science curricula and thus are not widely used and perceived as a valid professional skill. In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop- ment within FoCaLiZe. We also believe that this could considerably benefit the learning of discrete mathematics.
Purpura, David J; Logan, Jessica A R
2015-12-01
Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability. Participants included 114 children who were assessed in the fall and spring of preschool on a battery of academic and cognitive tasks. Children were 3.12 to 5.26 years old (M = 4.18, SD = .58) and 53.6% were girls. Both mixed-effect and quantile regressions were conducted. The mixed-effect regressions indicated that mathematical language, but not the ANS, nor other cognitive domains, predicted mathematics performance. However, the quantile regression analyses revealed a more nuanced relation among domains. Specifically, it was found that mathematical language and the ANS predicted mathematical performance at different points on the ability continuum. These dual nonlinear relations indicate that different mechanisms may enhance mathematical acquisition dependent on children's developmental abilities.
Mathematical Education in the Network Environment
Directory of Open Access Journals (Sweden)
V. A. Testov
2013-01-01
Full Text Available The transition to the new educational paradigm in mathematical education is associated with the widespread introduction of information and communication technologies in education. The traditional teaching forms, methods, means and content do not seem to correspond with the new paradigm and need the theoretical reconsideration. In author’s opinion, it should be based on the post-non-classical methodology incorporating the synergetic world outlook and soft modeling ideas. The modern educational environment and network space provide the vast opportunities for self-study and self-education. However, the data perception tends to become nonlinear; and the task of the school, in this case, is to provide the nonlinear systemization of educational information through self-organized systems. The Author argues that the problem solving should remain the main activity in mathematics teaching, especially for the students of mathematical profile; the projecting activity should not dominate and prevail over the problem solving.
Mathematical Education in the Network Environment
Directory of Open Access Journals (Sweden)
V. A. Testov
2015-02-01
Full Text Available The transition to the new educational paradigm in mathematical education is associated with the widespread introduction of information and communication technologies in education. The traditional teaching forms, methods, means and content do not seem to correspond with the new paradigm and need the theoretical reconsideration. In author’s opinion, it should be based on the post-non-classical methodology incorporating the synergetic world outlook and soft modeling ideas. The modern educational environment and network space provide the vast opportunities for self-study and self-education. However, the data perception tends to become nonlinear; and the task of the school, in this case, is to provide the nonlinear systemization of educational information through self-organized systems. The Author argues that the problem solving should remain the main activity in mathematics teaching, especially for the students of mathematical profile; the projecting activity should not dominate and prevail over the problem solving.
Secondary School Mathematics Teachers' Attitude in Teaching Mathematics
Directory of Open Access Journals (Sweden)
Mulugeta Atnafu
2014-02-01
Full Text Available 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 mathematics teachers do not possess positive attitude in teaching mathematics; the most challenge area that affect the attitude in teaching mathematics was motivation in teaching mathematics; no significant differences in all variables with respect to sex and service year; the medium age of mathematics teachers were found to have significantly the most successful in teaching mathematics than young and old mathematics teachers; the master mathematics teachers were found to have significantly the highest and the diploma mathematics teachers were found to have the least attitude, confidence and anxiety of teaching mathematics;the relatively high salary of the mathematics teachers were found to have significantly the highest attitude in teaching mathematics and the average salary of the mathematics teachers were found to have significantly the highest anxiety in teaching mathematics. All the variables sex, age, education, service year and salary of the mathematics teachers were significantly contributing to the equation for predicting mathematics teachers’ attitude and only education was significantly contributing to the equation for predicting mathematics teachers’ attitude in teaching mathematics.
Directory of Open Access Journals (Sweden)
Trude Nilsen
2013-10-01
Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.
Thompson, Carla J.; Davis, Sandra B.
2014-06-01
The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics classroom observational data and student achievement data, and (b) to examine the impact of providing periodic classroom observational data feedback to teachers using a Relational-Feedback-Intervention (RFI) Database Model. This observational research effort focused on an empirical examination of student engagement levels in time spent on specific learning activities observed in primary mathematics classrooms as predictors of student competency outcomes in mathematics. Data were collected from more than 2,000 primary classroom observations in 17 primary schools during 2009-2011 and from standardised end-of-year tests for mathematics achievement. Results revealed predictive relationships among several types of teaching and learning tasks with student achievement. Specifically, the use of mathematics concepts, technology and hands-on materials in primary mathematics classrooms was found to produce substantive predictors of increased student mathematics achievement. Additional findings supported the use of periodic classroom observation data reporting as a positive influence on teachers' decisions in determining instructional tasks for inclusion in primary mathematics classrooms. Study results indicate classroom observational research involving a RFI Database Model is a productive tool for improving teaching and learning in primary mathematics classrooms.
Comparison of Mathematics and Humanitarian Sciences Students’ Metacognitive Strategies
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Gholam Hossein Javanmard
2014-09-01
Full Text Available Abstract The purpose of this study was to compare the differences of using meta-cognitive strategies in high school students who study in the fields of mathematics and humanities. For do this, 140 high school students were selected randomly. The Swanson’s Meta-cognition Strategies Test was administrated for sample groups. The acquired means for two regroups were compared with t-test for two independent groups’ method. Results indicated that two groups were meaningfully differed from each other (sig=0.01 in using meta-cognitive strategies, and mean of students in mathematics field were high. Also there was a meaningful difference in task component between two groups (sig=0.002, and the mean of students in mathematics field was higher than from students in humanities field in this component. The high school students in mathematics field use more metacognitive strategies, especially task component, than the students in humanities field.
Mathematical Sciences Institute Workshop
Scott, Philip
1990-01-01
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
2016-01-01
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...
International Mathematical Internet Olympiad
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Alexander Domoshnitsky
2012-10-01
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.
Interactive Mathematics Textbooks
DEFF Research Database (Denmark)
Sinclair, Robert
1999-01-01
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....
Advances in mathematical economics
Maruyama, Toru
2016-01-01
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.
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
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.
Educating mathematics teacher educators
DEFF Research Database (Denmark)
Højgaard, Tomas; Jankvist, Uffe Thomas
2014-01-01
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....
Advances in mathematical economics
Maruyama, Toru
2015-01-01
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.
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
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.
Advances in mathematical economics
Maruyama, Toru
2017-01-01
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.
Hwang, Jiwon; Riccomini, Paul J.
2016-01-01
Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…
Mathematical reasoning in Elementary School and Higher Education
Joana Mata-Pereira; Ana Henriques; João Pedro da Ponte
2012-01-01
This paper analyzes the reasoning processes in mathematical tasks of two students in the 9th year of elementary school and two students in the second year of college. It also focuses the representation and meaningfulness, given their close relation with the mathematical reasoning. Results presented are based on two qualitative and interpretive studies which resort to several data sources. These results show that mastering of the algebraic language by the students in the 9th year is still insu...
Clock reading: an underestimated topic in children with mathematics difficulties
2012-01-01
Recent studies have shown that children with mathematics difficulties (MD) have weaknesses in multiple areas of mathematics. Andersson (2008), for example, recently found that children with MD perform significantly worse than other children on clock reading tasks. The present study builds on this recent finding and aims at a more profound understanding of the difficulties that children with MD experience with telling time. Therefore, clock reading abilities of 154 children with MD were compar...
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
Jett, Christopher C.
2014-01-01
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…
Mathematics for Teaching: A Form of Applied Mathematics
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
Jett, Christopher C.
2014-01-01
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…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
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…
On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers
Cai, Jinfa; Ding, Meixia
2017-01-01
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…
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
Ma, Xin; McIntyre, Laureen J.
2005-01-01
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…
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Task decomposition is a kind of powerful technique increasingly being used within industry as a pathway for achieving product's developing success. In this paper, topology's concept in modern mathematics is used for task decomposition technique's deduction in product developing process. It puts forward the views of resolvability, measurability and connectivity of tasks and their practical principles. Combined with an example of developing the typical mechanical product, it explains the implementing method of task decomposition in Concurrent Engineering (CE).
Adaptation of educational tasks for children with autism spectrum disorders
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Khaustov A.V.
2016-06-01
Full Text Available The second part of the article describes variations of adapted learning tasks of different levels for children with autism spectrum disorders who study in second grade according to adapted basic educational programs. The article presents examples of tasks for mathematics, Russian language, literary reading and environmental studies. The materials were developed and tested in the Center for psychological, medical and social help for children and adolescents of Moscow State University of Psychology and Education.
Kuipers, L
1969-01-01
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
2011-01-01
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.
Teaching secondary mathematics
Rock, David
2013-01-01
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
2015-01-01
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
Plumpton, C
1968-01-01
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
O'Briain, Dara
2014-01-01
Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of
Mathematics, Mathematicians, and Desire
Roodal Persad, Veda
2014-01-01
This thesis is about mapping the landscape of engagement with mathematics, including elucidating aspects of who we are, as human beings, when we do mathematics and of what mathematics calls us to do if we are to engage with it. Using the concept of desire in the psychoanalytic theory of Jacques Lacan and the forms of desire as elucidated by the Lacanian theorist, Mark Bracher, I seek to find out what the mathematical encounter takes (the demands and costs) and what it gives (the offers and re...
Plofker, Kim
2009-01-01
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
Mathematical fallacies and paradoxes
Bunch, Bryan
1982-01-01
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.
Winkler, Peter
2007-01-01
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
Nelwan, Michel; Kroesbergen, Evelyn H.
2016-01-01
The goal of this randomized controlled trial was to investigate whether Jungle Memory working memory training (JM) affects performance on working memory tasks, performance in mathematics and gains made on a mathematics training (MT) in school aged children between 9-12 years old (N = 64) with both d
Rajotte, Thomas; Marcotte, Christine; Bureau-Levasseur, Lisa
2016-01-01
In recent decades, the dropout rate in Abitibi-Témiscamingue is a worrying phenomenon. An analysis of ministerial examination results identifies that students in Abitibi-Témiscamingue have specific difficulties with mathematical problem solving tasks. Among the activities that develop those skills, the daily routines in mathematics seem to be a…
Proof and knowledge in mathematics
Detlefsen, Michael
2005-01-01
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,
Remedial Mathematics for Quantum Chemistry
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
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 mathematics problem, a remedial mathematics…
Wang, Li; Sun, Yuhua; Zhou, Xinlin
2016-01-01
Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants’ performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement. PMID:28066291
SOME TYPES OF METASUBJECT RESULTS WHEN TEACHING MATHEMATICS
Directory of Open Access Journals (Sweden)
V. A. Testov
2016-01-01
Full Text Available The aim of the study is to allocate in the content of teaching mathematics those elements, those kinds of mathematical cognitive activities that are metasubject character, which are the basis for the formation of cognitive learning activities, as a means to study not only of mathematical objects, but some objects of other sciences.Methods. Research is based on a system-structural and activity-based approaches; literature analysis, theoretical research and experimental work.Results. Among of metasubject results of studying mathematics, the following types of mathematical schemes of thinking are identified: logical, algorithmic, combinatory, figurative-geometrical, stochastic. The characteristic is given; the specifics of each type of mathematical structures of thinking are described. The main means of the formation of such schemes is the decision of the respective types of non-standard tasks.Scientific novelty. The author gives a theoretical justification of the role of mathematical thinking schemes as metasubject results of training and points out funds for their formation in educational activity.Practical significance. The perspective directions of accents change in the content of training of mathematics directed on increase in training of a role of mathematical schemes of thinking as bases of formation of universal informative cognitive actions are emphasized.
Mathematical literacy skills of students' in term of gender differences
Lailiyah, Siti
2017-08-01
Good mathematical literacy skills will hopefully help maximize the tasks and role of the prospective teacher in activities. Mathematical literacy focus on students' ability to analyze, justify, and communicate ideas effectively, formulate, solve and interpret mathematical problems in a variety of forms and situations. The purpose of this study is to describe the mathematical literacy skills of the prospective teacher in term of gender differences. This research used a qualitative approach with a case study. Subjects of this study were taken from two male students and two female students of the mathematics education prospective teacher who have followed Community Service Program (CSP) in literacy. Data were collected through methods think a loud and interviews. Four prospective teachers were asked to fill mathematical literacy test and video taken during solving this test. Students are required to convey loud what he was thinking when solving problems. After students get the solution, researchers grouped the students' answers and results think aloud. Furthermore, the data are grouped and analyzed according to indicators of mathematical literacy skills. Male students have good of each indicator in mathematical literacy skills (the first indicator to the sixth indicator). Female students have good of mathematical literacy skills (the first indicator, the second indicator, the third indicator, the fourth indicator and the sixth indicator), except for the fifth indicators that are enough.
The mathematics companion mathematical methods for physicists and engineers
Fischer-Cripps, Anthony C
2014-01-01
Part 1 Essential Mathematics: Basic mathematics. Differentiation. Integration. Exponentials and logarithms. Hyperbolic functions. Infinite series. Part 2 Advance Mathematics: Ordinary differential equations. Laplace transforms. Vector analysis. Partial derivatives. Multiple integrals. Fourier series. Special functions. Partial differential equations.
Mathematical knowledge: a case study in empirical philosophy of mathematics
Löwe, B.; Müller, T.; Wilhelmus, E.; Van Kerkhove, B.; De Vuyst, J.; Van Bendegem, J.P.
2010-01-01
In this paper, we present a paradigm for the philosopher of mathematics who takes mathematical practice seriously: Empirical Philosophy of Mathematics. In this philosophical paradigm, we use empirical methods (from sociology, psychology, cognitive science, didactics) to evaluate empirical questions
Knots and surfaces a guide to discovering mathematics
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequi
Dialogue in mathematics classrooms: Beyond question-and- answer methods
Directory of Open Access Journals (Sweden)
Karin Brodie
2007-10-01
Full Text Available This paper explores different kinds of interaction observed in South African mathematics classrooms in order to unpack the notion of participation in mathematics learning. It argues that conventional question-and-answer methods do not promote the kind of interaction that the new South African curriculum calls for. It presents more appropriate kinds of interactions, where teachers maintain high task demands, respond to genuine learner questions and support conversations among learners. The paper argues that combinations of different kinds of interaction are most likely to support learner participation and mathematical thinking in classrooms.
2nd International Conference on Mathematics and Computing
Chowdhury, Dipanwita; Giri, Debasis
2015-01-01
This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in com...
Working memory resources in young children with mathematical difficulties.
Kyttälä, Minna; Aunio, Pirjo; Hautamäki, Jarkko
2010-02-01
Working memory (WM) (Baddeley, 1986, 1997) is argued to be one of the most important cognitive resources underlying mathematical competence (Geary, 2004). Research has established close links between WM deficits and mathematical difficulties. This study investigated the possible deficits in WM, language and fluid intelligence that seem to characterize 4- to 6-year-old children with poor early mathematical skills before formal mathematics education. Children with early mathematical difficulties showed poor performance in both verbal and visuospatial WM tasks as well as on language tests and a fluid intelligence test indicating a thoroughly lower cognitive base. Poor WM performance was not moderated by fluid intelligence, but the extent of WM deficits was related to language skills. The educational implications are discussed.
Mathematics and culture in Micronesia
Directory of Open Access Journals (Sweden)
A. J. (Sandy Dawson
2015-07-01
Full Text Available Wheatley and Frieze‟s book, Walk Out Walk On, provides the conceptual framework for an examination of Project MACIMISE, a National Science Foundation funded project that focused on the languages and cultural practices of nine Pacific islands and the state of Hawai„i. MACIMISE, pronounced as if spelled „maximize‟, is a 5-year Project. The Project‟s task is the development of elementary school mathematics curriculum units sensitive to local mathematical thought and experience. There were twenty-one participants (who call themselves the Macimisers in the Project. The participants were educated in ethnographic and anthropological research strategies to enable them to retrieve/uncover cultural practices extant in the communities where they lived. This academics work was accomplished partially via distance learning when the participants were registered in advanced degree programs at the University of Hawai„i—Mānoa. In this paper, the Project is analyzed in terms of the concepts (scaling across, start anywhere—follow it everywhere, intervention to friendship, the art of hosting and the use of circle advanced by Wheatley and Frieze.
Maciejewski, Wes; Merchant, Sandra
2016-01-01
Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students' academic outcomes. This study takes a…
Developing Mathematical Vocabulary.
Monroe, Eula Ewing; Orme, Michelle P.
2002-01-01
This article discusses the importance of mathematical vocabulary, difficulties students encounter in learning this vocabulary, and some instructional strategies. Two general methods for teaching vocabulary are discussed: context and explicit vocabulary instruction. The methods are summarized as they apply to mathematical vocabulary instruction and…
Mathematical Graphic Organizers
Zollman, Alan
2009-01-01
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…
DEFF Research Database (Denmark)
Sinclair, Robert
1998-01-01
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++....
Institute of Scientific and Technical Information of China (English)
田琳
2016-01-01
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.
DEFF Research Database (Denmark)
Winsløw, Carl
2015-01-01
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...
Teaching Mathematical Induction I.
Dubinsky, Ed
1986-01-01
A novel approach to teaching mathematical induction was used, based on a Piagetian theory of learning abstract mathematical concepts in which the learner uses reflective abstraction to construct new schemas out of old ones. Computer experiences are used to induce students to make the appropriate reflective abstractions. (MNS)
Building Mathematics Vocabulary
Kovarik, Madeline
2010-01-01
Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…
Oldfield, Christine
1996-01-01
Describes aspects of learning the language of mathematics including vocabulary and grammar, the origins of the vocabulary, the pronunciation problem, and translation of English phrases and sentences into mathematical language accompanied by conceptual understanding of the process being described. Gives suggestions for teachers in class and…
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
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)
DEFF Research Database (Denmark)
Sinclair, Robert
1998-01-01
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++....
DEFF Research Database (Denmark)
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....
Mathematics across the Curriculum.
Kleiman, Glenn M.
1991-01-01
Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…
DEFF Research Database (Denmark)
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....
Mathematics Teaching and Inclusion
DEFF Research Database (Denmark)
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...
Mathematics Education in Argentina
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
Teaching Mathematical Modelling.
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Experimenting with Mathematical Biology
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
Dyslexia, Dyspraxia and Mathematics.
Yeo, Dorian
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…
Mathematics Education in Argentina
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
Educating mathematics teacher educators
DEFF Research Database (Denmark)
Højgaard, Tomas; Jankvist, Uffe Thomas
2014-01-01
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...
Mathematics: Content and Pedagogy
Ediger, Marlow
2009-01-01
The debate has gone on for some time in terms of which is more salient for the teacher to be well versed in, mathematical content versus methods and approaches in teaching. Both are salient. They cannot be separated from each other. The mathematics teacher must indeed have broad, in-depth knowledge of subject matter as well as in teaching and…
Astronomy and Mathematics Education
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.
This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…
Elementary Mathematics Leaders
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
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…
Haigh, John
2016-01-01
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...
Rethinking the mathematics curriculum
Hoyles, Celia; Woodhouse, Geoffrey
1998-01-01
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.
Canadian Mathematical Congress
1977-01-01
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 ...
Mathematics of aperiodic order
Lenz, Daniel; Savinien, Jean
2015-01-01
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...
African Americans in mathematics
1997-01-01
This volume contains research and expository papers by African-American mathematicians on issues related to their involvement in the mathematical sciences. Little is known, taught, or written about African-American mathematicians. Information is lacking on their past and present contributions and on the qualitative and quantitative nature of their existence in and distribution throughout mathematics. This lack of information leads to a number of questions that have to date remained unanswered. This volume provides details and pointers to help answer some of these questions. Features: Research articles by distinguished African-American mathematicians. Accomplishments of African-American researchers in the mathematical sciences. Articles that explore issues important to the African-American community and to the mathematics community as a whole. Inspiration for African-American students who wish to pursue advancement in the mathematical sciences.
Advanced engineering mathematics
Jeffrey, Alan
2001-01-01
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...
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
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....
Hebert, Michael A.; Powell, Sarah R.
2016-01-01
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…
Directory of Open Access Journals (Sweden)
Erovenko V. A.
2014-01-01
Full Text Available The article examines the current state of the mathematical education of the students-philosophers that depends on language of the humanitarian mathematics, evidence of its statements and methodological problem of the cognition of the mathematical facts. One of important tasks of philosophy of mathematical education consists in motivation of the need for training mathematics of students-philosophers. The main criterion of the usefulness of mathematics for philosophers is revealed in the ways of justification of its truth and completeness of reasoning of mathematical statements. This reflects the attractiveness of mathematical knowledge for philosophers that is characterized by the fact that the truth is revealed along with a proof in mathematics. One of the main so-called “acupuncture points” of mathematical education of philosophers, as the author believes, is the language of modern mathematics. In General, the linguistic aspect is very important in modern science. The second “acupuncture point” of mathematical education of philosophers is the level of evidence claims. Third, according to the author, is responsible for knowledge of mathematical truths, is involved in not only our existence, but also transcendental knowledge. In the context of philosophy of the future of modern civilization, mathematics is indispensable as a necessary element of scientific and philosophical picture of the world. To support the conclusions the author draws a broad philosophical and scientific context.
Positioning during Group Work on a Novel Task in Algebra II
DeJarnette, Anna F.; González, Gloriana
2015-01-01
Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We…
Wilkie, Karina J.
2016-01-01
Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…
Using Visualization to Generalize on Quadratic Patterning Tasks
Kirwan, J. Vince
2017-01-01
Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…
Directory of Open Access Journals (Sweden)
Camilla Gilmore
Full Text Available Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate.
Gilmore, Camilla; Attridge, Nina; Clayton, Sarah; Cragg, Lucy; Johnson, Samantha; Marlow, Neil; Simms, Victoria; Inglis, Matthew
2013-01-01
Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate.
Johnson, Keith
2000-01-01
Describes a research project that is concerned with the design procedures followed by those engaged in designing pedagogic tasks for use in classrooms. Focuses on the part of the project that involves actual observation of designers in the process of developing one specific task for class use. Findings are presented under three headers: control…
Philosophical dimensions in mathematics education
Francois, Karen
2007-01-01
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.
Xenofontos, Constantinos; Papadopoulos, Christos,
2015-01-01
International audience; In this paper, we examine the ways the history of mathematics is integrated in the national textbooks of Cyprus and Greece. Our data-driven analyses suggest that the references identified can be clustered in four categories: (a) biographical references about mathematicians or historical references regarding the origins of a mathematical concept, (b) references to the history of a mathematical method or formula containing a solution or proof, (c) mathematical tasks of p...
Supporting complex search tasks
DEFF Research Database (Denmark)
Gäde, Maria; Hall, Mark; Huurdeman, Hugo
2015-01-01
There is broad consensus in the field of IR that search is complex in many use cases and applications, both on the Web and in domain specific collections, and both professionally and in our daily life. Yet our understanding of complex search tasks, in comparison to simple look up tasks, is fragme......There is broad consensus in the field of IR that search is complex in many use cases and applications, both on the Web and in domain specific collections, and both professionally and in our daily life. Yet our understanding of complex search tasks, in comparison to simple look up tasks......, and recommendations, and supporting exploratory search to sensemaking and analytics, UI and UX design pose an overconstrained challenge. How do we know that our approach is any good? Supporting complex search task requires new collaborations across the whole field of IR, and the proposed workshop will bring together...
Supporting complex search tasks
DEFF Research Database (Denmark)
Gäde, Maria; Hall, Mark; Huurdeman, Hugo;
2015-01-01
There is broad consensus in the field of IR that search is complex in many use cases and applications, both on the Web and in domain specific collections, and both professionally and in our daily life. Yet our understanding of complex search tasks, in comparison to simple look up tasks......, is fragmented at best. The workshop addressed the many open research questions: What are the obvious use cases and applications of complex search? What are essential features of work tasks and search tasks to take into account? And how do these evolve over time? With a multitude of information, varying from...... introductory to specialized, and from authoritative to speculative or opinionated, when to show what sources of information? How does the information seeking process evolve and what are relevant differences between different stages? With complex task and search process management, blending searching, browsing...
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"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.
Task-baseret kommunikativ sprogundervisning
DEFF Research Database (Denmark)
Pedersen, Michael Svendsen
2015-01-01
Definition af task-baseret sprogundervisning, kriterier for task. Forskning i Second Language Acquisition med brug af task, tilrettelæggelse af task-baseret kommunikativ undervisning. Begrænsninger i og perspektiver for videreudvikling af task-baseret sprogundervising-......Definition af task-baseret sprogundervisning, kriterier for task. Forskning i Second Language Acquisition med brug af task, tilrettelæggelse af task-baseret kommunikativ undervisning. Begrænsninger i og perspektiver for videreudvikling af task-baseret sprogundervising-...
The Greatest Mathematical Discovery?
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
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.
Fundamentals of university mathematics
McGregor, C M; Stothers, W W
2010-01-01
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
Hollingdale, Stuart
2011-01-01
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
Alexander, Serena; Poggo, Tammy
2014-01-01
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
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
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.
Higher engineering mathematics
John Bird
2014-01-01
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
Equations of mathematical physics
Tikhonov, A N
2011-01-01
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
Logic in elementary mathematics
Exner, Robert M
2011-01-01
This applications-related introductory treatment explores facets of modern symbolic logic useful in the exposition of elementary mathematics. The authors convey the material in a manner accessible to those trained in standard elementary mathematics but lacking any formal background in logic. Topics include the statement calculus, proof and demonstration, abstract mathematical systems, and the restricted predicate calculus. The final chapter draws upon the methods of logical reasoning covered in previous chapters to develop solutions of linear and quadratic equations, definitions of order and
Mathematization in introductory physics
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
Learning Mathematics through Programming
DEFF Research Database (Denmark)
Misfeldt, Morten; Ejsing-Duun, Stine
2015-01-01
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...... as producers of knowledge and artifacts, (2) support abstraction and encapsulation, and (3) promote thinking in algorithms. Programming is a topic that has recently gained interest in primary and lower secondary education levels in various countries, and hence a specific analysis of the potentials in relation...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....
Troelstra, AS
1988-01-01
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