Struggles and Successes Implementing Classroom Communication Technology in a College Pre-Calculus Course

Science.gov (United States)

Case, Erin; Pape, Stephen

2013-01-01

This case study documents the struggles and successes encountered by a pre-calculus teacher while using Classroom Connectivity Technology (CCT) daily in her community college mathematics course. CCT refers to a wireless communication system that connects a teacher's computer with an individual student's handheld calculator and has been associated…

Profile of Metacognition of Mathematics Pre-Service Teachers in Understanding the Concept of Integral Calculus with Regard Gender Differences

Science.gov (United States)

Misu, L.; Budayasa, I. K.; Lukito, A.

2018-01-01

This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.

A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.

Science.gov (United States)

BRANT, VINCENT; GERARDI, WILLIAM

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…

Pre-calculus workbook for dummies

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Gilman, Michelle Rose; Neal, Karina

2009-01-01

Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Experimental Design: Utilizing Microsoft Mathematics in Teaching and Learning Calculus

Science.gov (United States)

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

A Note on Discrete Mathematics and Calculus.

Science.gov (United States)

O'Reilly, Thomas J.

1987-01-01

Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)

Pre-college Mathematics *Optional subject

OpenAIRE

ISHIDA, Yukio

2015-01-01

This course is a companion course to Calculus I. It aims to help students with little or no precalculus knowledge to master the basic calculus material in preparation for the more advanced course of Calculus I. This is done by reviewing high school mathematics.

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

Science.gov (United States)

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

Science.gov (United States)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Mathematics Placement Test: Typical Results with Unexpected Outcomes

Science.gov (United States)

Ingalls, Victoria

2011-01-01

Based on the results of a prior case-study analysis of mathematics placement at one university, the mathematics department developed and piloted a mathematics placement test. This article describes the implementation process for a mathematics placement test and further analyzes the test results for the pilot group. As an unexpected result, the…

Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation

OpenAIRE

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

Science.gov (United States)

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

From Calculus to Wavelets: ANew Mathematical Technique

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 4. From Calculus to Wavelets: A New Mathematical Technique Wavelet Analysis Physical Properties. Gerald B Folland. General Article Volume 2 Issue 4 April 1997 pp 25-37 ...

Pre-calculus essentials

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Woodward, Ernest

2012-01-01

REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Pre-Calculus reviews sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents

Teaching and learning of pre-calculus: an insights of educators ...

African Journals Online (AJOL)

The high-failure of Calculus courses has bring dilemma to the educators worldwide. This study has focus on teaching and learning of Pre-Calculus, a fundamental course for higher level Calculus courses. A well-designed questionnaire was distributed to all respondents to find the difficulties faced by both lecturers and ...

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

The Effect of Graphing Calculators on Student Achievement in College Algebra and Pre-Calculus Mathematics Courses

Science.gov (United States)

Hatem, Neil

2010-01-01

This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

Calculus light

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Friedman, Menahem

2011-01-01

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor

Non-Mathematics Students' Reasoning in Calculus Tasks

Science.gov (United States)

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…

THE EFFECTIVENESS OF GUIDED DISCOVERY LEARNING TO TEACH INTEGRAL CALCULUS FOR THE MATHEMATICS STUDENTS OF MATHEMATICS EDUCATION WIDYA DHARMA UNIVERSITY

Directory of Open Access Journals (Sweden)

Yuliana Yuliana

2017-01-01

Full Text Available The objectives of this research are (1 to develop Guided Discovery Learning in integral calculus subject; (2 to identify the effectiveness of Guided Discovery Learning in improving the students’ understanding toward integral calculus subject. This research was quasy experimental research with the students of even semester in Mathematics Education Widya Dharma University as the sample. Cluster Random sampling was conducted to determine control group that was taught using Conventional model and experimental group that was taught using Guided Discovery Learning model. The instruments of this research included pre-test, post-test, and student’s response questionnaire. The data of post-test was analyzed using T-test. The result was H0 was rejected for the level of significance The result of this data analysis found out that Guide Discovery Learning was more effective than Conventional Model. It was supported by the result questionnaire. The result of questionnaire that  more than 75% questionnaire items got 67.65% positive response. It means Guided Discovery Learning can increase students’ interest in joining integral calculus class.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

Science.gov (United States)

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Why good placements matter: Pre-placement and placement risk factors associated with mental health disorders in pre-school children in foster care.

Science.gov (United States)

Hillen, Thomas; Gafson, Leonie

2015-07-01

Pre-school children placed in local authority care show elevated rates of mental health disorders when compared to the general population. This study investigated risk factors for mental health disorders relating to the period prior to entering care and while in care. A representative sample of 43 children in care aged 0-72 months in an inner London borough underwent comprehensive multidimensional assessments. Presence of emotional, behavioural, attachment and adaptive disorders was ascertained. Exposure to two pre-placement risk factors and six placement risk factors was compared between children with and without a disorder. A total of 26 children (60.5%) had at least one mental health disorder. The two pre-placement risk factors, multiple types of maltreatment and entry into care after the age of 6 months, were both significantly associated with mental health disorders. The three placement risk factors of sudden placement moves, multiple placement moves and child-carer alienation showed a significant association with mental health disorders. There was a strong correlation between the number of risk factors and the number of co-morbid mental health disorders per child (r = .67, p school mental health. © The Author(s) 2014.

Intra-mathematical connections made by high school students in performing Calculus tasks

Science.gov (United States)

García-García, Javier; Dolores-Flores, Crisólogo

2018-02-01

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas, concepts, definitions, theorems, procedures, representations and meanings among themselves, with other disciplines or with real life. Task-based interviews were used to collect data and thematic analysis was used to analyze them. Through the analysis of the productions of the 25 participants, we identified 223 intra-mathematical connections. The data allowed us to establish a mathematical connections system which contributes to the understanding of higher concepts, in our case, the Fundamental Theorem of Calculus. We found mathematical connections of the types: different representations, procedural, features, reversibility and meaning as a connection.

Mathematics Underground

Science.gov (United States)

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…

The impact of instructor pedagogy on college calculus students' attitude toward mathematics

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.; Sadler, Samuel M.; Bressoud, David M.

2015-04-01

College calculus teaches students important mathematical concepts and skills. The course also has a substantial impact on students' attitude toward mathematics, affecting their career aspirations and desires to take more mathematics. This national US study of 3103 students at 123 colleges and universities tracks changes in students' attitudes toward mathematics during a 'mainstream' calculus course while controlling for student backgrounds. The attitude measure combines students' self-ratings of their mathematics confidence, interest in, and enjoyment of mathematics. Three major kinds of instructor pedagogy, identified through the factor analysis of 61 student-reported variables, are investigated for impact on student attitude as follows: (1) instructors who employ generally accepted 'good teaching' practices (e.g. clarity in presentation and answering questions, useful homework, fair exams, help outside of class) are found to have the most positive impact, particularly with students who began with a weaker initial attitude. (2) Use of educational 'technology' (e.g. graphing calculators, for demonstrations, in homework), on average, is found to have no impact on attitudes, except when used by graduate student instructors, which negatively affects students' attitudes towards mathematics. (3) 'Ambitious teaching' (e.g. group work, word problems, 'flipped' reading, student explanations of thinking) has a small negative impact on student attitudes, while being a relatively more constructive influence only on students who already enjoyed a positive attitude toward mathematics and in classrooms with a large number of students. This study provides support for efforts to improve calculus teaching through the training of faculty and graduate students to use traditional 'good teaching' practices through professional development workshops and courses. As currently implemented, technology and ambitious pedagogical practices, while no doubt effective in certain classrooms, do

The Hawaii Teleschool: An Evaluation of Distance Learning for Advanced Placement Calculus Instruction in "Paradise."

Science.gov (United States)

Barker, Bruce O.; Bannon, James

This paper describes the Hawaii Interactive Television System (HITS) program and provides an evaluation of the first year of broadcasts for the advanced placement (AP) calculus course. HITS allows two-way video-audio interaction among origination sites, but the configuration used by the Department of Education for its Teleschool program is the…

Assessing Preservice Teachers' Mathematics Cognitive Failures as Related to Mathematics Anxiety and Performance in Undergraduate Calculus

Science.gov (United States)

Awofala, Adeneye O. A.; Odogwu, Helen N.

2017-01-01

The study investigated mathematics cognitive failures as related to mathematics anxiety, gender and performance in calculus among 450 preservice teachers from four public universities in the South West geo-political zone of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

Calculus

CERN Document Server

Spivak, Michael

2006-01-01

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

Discovering the Art of Mathematics: Using String Art to Investigate Calculus

Science.gov (United States)

von Renesse, Christine; Ecke, Volker

2016-01-01

One goal of our Discovering the Art of Mathematics project is to empower students in the liberal arts to become confident creators of art and imaginative creators of mathematics. In this paper, we describe our experience with using string art to guide liberal arts students in exploring ideas of calculus. We provide excerpts from our inquiry-based…

Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

Science.gov (United States)

Dewi, N. R.; Arini, F. Y.

2018-03-01

The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

Intra-Mathematical Connections Made by High School Students in Performing Calculus Tasks

Science.gov (United States)

García-García, Javier; Dolores-Flores, Crisólogo

2018-01-01

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics

Science.gov (United States)

Easey, Michael; Gleeson, Jim

2016-01-01

The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews…

Multivariable calculus with applications

CERN Document Server

Lax, Peter D

2017-01-01

This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...

Formative questioning in computer learning environments: a course for pre-service mathematics teachers

Science.gov (United States)

Akkoç, Hatice

2015-11-01

This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and skills of questioning in CLEs. This study investigates how pre-service mathematics teachers used formative questioning with technological tools such as Geogebra and Graphic Calculus software. Participants are 35 pre-service mathematics teachers. To analyse formative questioning, two types of questions are investigated: mathematical questions and technical questions. Data were collected through lesson plans, teaching notes, interviews and observations. Descriptive statistics of the number of questions in the lesson plans before and after the workshops are presented. Examples of two types of questions are discussed using the theoretical framework. One pre-service teacher was selected and a deeper analysis of the way he used questioning during his three lessons was also investigated. The findings indicated an improvement in using technical questions for formative purposes and that the course provided a guideline in planning and using mathematical and technical questions in CLEs.

Teacher's Guide to Secondary Mathematics.

Science.gov (United States)

Duval County Schools, Jacksonville, FL.

This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

An outline of possible pre-course diagnostics for differential calculus

Directory of Open Access Journals (Sweden)

Aneshkumar Maharaj

2014-07-01

Full Text Available There is a view that many first-year students lack the basic knowledge and skills expected of them to study at university level. We examined the expected work habits and pre-course diagnostics for students who choose to take a course on differential calculus. We focused on the lecturer pre-course expectations of a student in the context of work habits, knowledge and technical skills. In particular, we formulated outcomes and then sample diagnostic questions to test whether the identified learning outcomes on expected work habits and learning are in place. If students are made aware of the expected learning outcomes and if they take the diagnostic test, they should be able to achieve greater success in their studies. The validity of this assumption will be the subject of a future paper which will report on the implementation of the learning outcomes and diagnostic questions that we formulated for pre-course diagnostics in differential calculus.

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

Science.gov (United States)

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

Science.gov (United States)

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

University mathematics teachers' views on the required reasoning in calculus exams

OpenAIRE

Bergqvist, Ewa

2012-01-01

Students often use imitative reasoning, i.e. copy algorithms or recall facts, when solving mathematical tasks. Research show that this type of imitative reasoning might weaken the students' understanding of the underlying mathematical concepts. In a previous study, the author classified tasks from 16 final exams from introductory calculus courses at Swedish universities. The results showed that it was possible to pass 15 of the exams, and solve most of the tasks, using imitative reasoning. Th...

The Effectiveness of Guided Discovery Learning to Teach Integral Calculus for the Mathematics Students of Mathematics Education Widya Dharma University

OpenAIRE

Yuliana, Yuliana; Tasari, Tasari; Wijayanti, Septiana

2017-01-01

The objectives of this research are (1) to develop Guided Discovery Learning in integral calculus subject; (2) to identify the effectiveness of Guided Discovery Learning in improving the students' understanding toward integral calculus subject. This research was quasy experimental research with the students of even semester in Mathematics Education Widya Dharma University as the sample. Cluster Random sampling was conducted to determine control group that was taught using Conventional model a...

Using Student-Made Games to Learn Mathematics

Science.gov (United States)

Gallegos, Irene; Flores, Alfinio

2010-01-01

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

Science.gov (United States)

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

Science.gov (United States)

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

Factors Associated with Success in College Calculus II

Science.gov (United States)

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Instructional Experiences That Align with Conceptual Understanding in the Transition from High School Mathematics to College Calculus

Science.gov (United States)

Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra

2017-01-01

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

Science.gov (United States)

Fields, Chris

2013-08-01

The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

Mathematics a minimal introduction

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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

Bringing Reality into Calculus Classrooms: Mathematizing a Real-life Problem Simulated in a Virtual Environment

Directory of Open Access Journals (Sweden)

Olga V. Shipulina

2013-01-01

Full Text Available The study explores how students, who had completed the AP calculus course, mathematized the optimal navigation real-life problem simulated in the Second Life Virtual Environment. The particular research interest was to investigate whether/how students’ empirical activity in VE influences the way of their mathematizing.

DEVELOPING GUIDED DISCOVERY LEARNING MATERIALS USING MATHEMATICS MOBILE LEARNING APPLICATION AS AN ALTERNATIVE MEDIA FOR THE STUDENTS CALCULUS II

Directory of Open Access Journals (Sweden)

Sunismi .

2015-12-01

Full Text Available Abstract: The development research aims to develop guided-discovery learning materials of Calculus II by implementing Mathematics Mobile Learning (MML. The products to develop are MML media of Calculus II using guided discovery model for students and a guide book for lecturers. The study employed used 4-D development model consisting of define, design, develop, and disseminate. The draft of the learning materials was validated by experts and tried-out to a group of students. The data were analyzed qualitatively and quantitatively by using a descriptive technique and t-test. The findings of the research were appropriate to be used ad teaching media for the students. The students responded positively that the MML media of Calculus II using the guided-discovery model was interestingly structured, easily operated through handphones (all JAVA, android, and blackberry-based handphones to be used as their learning guide anytime. The result of the field testing showed that the guided-discovery learning materials of Calculus II using the Mathematics Mobile Learning (MML application was effective to adopt in learning Calculus II. Keywords: learning materials, guided-discovery, mathematics mobile learning (MML, calculus II PENGEMBANGAN BAHAN AJAR MODEL GUIDED DISCOVERY DENGAN APLIKASI MATHEMATICS MOBILE LEARNING SEBAGAI ALTERNATIF MEDIA PEMBELAJARAN MAHASISWA MATAKULIAH KALKULUS II Abstrak: Penelitian pengembangan ini bertujuan untuk mengembangkan bahan ajar matakuliah Kalkulus II model guided discovery dengan aplikasi Mathematics Mobile Learning (MML. Produk yang dikembangkan berupa media MML Kalkulus II dengan model guided discovery untuk mahasiswa dan buku panduan dosen. Model pengembangan menggunakan 4-D yang meliputi tahap define, design, develop, dan dissemination. Draf bahan ajar divalidasi oleh pakar dan diujicobakan kepada sejumlah mahasiswa. Data dianalisis secara kualitatif dan kuantitatif dengan teknik deskriptif dan uji t. Temuan penelitian

Improving student learning in calculus through applications

Science.gov (United States)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Achievement of course outcome in vector calculus pre-test questions ...

African Journals Online (AJOL)

No Abstract. Keywords: pre-test; course outcome; bloom taxanomy; Rasch measurement model; vector calculus. Full Text: EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians ...

Pre- and Post-Conditions Expressed in Variants of the Modal µ-Calculus

Science.gov (United States)

Tanabe, Yoshinori; Sekizawa, Toshifusa; Yuasa, Yoshifumi; Takahashi, Koichi

Properties of Kripke structures can be expressed by formulas of the modal µ-calculus. Despite its strong expressive power, the validity problem of the modal µ-calculus is decidable, and so are some of its variants enriched by inverse programs, graded modalities, and nominals. In this study, we show that the pre- and post-conditions of transformations of Kripke structures, such as addition/deletion of states and edges, can be expressed using variants of the modal µ-calculus. Combined with decision procedures we have developed for those variants, the properties of sequences of transformations on Kripke structures can be deduced. We show that these techniques can be used to verify the properties of pointer-manipulating programs.

Vector Differential Calculus

OpenAIRE

HITZER, Eckhard MS

2002-01-01

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit.

Directory of Open Access Journals (Sweden)

Jessica Ellis

Full Text Available The substantial gender gap in the science, technology, engineering, and mathematics (STEM workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit.

Science.gov (United States)

Ellis, Jessica; Fosdick, Bailey K; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit

Science.gov (United States)

Ellis, Jessica; Fosdick, Bailey K.; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%. PMID:27410262

Calculus with applications

CERN Document Server

Lax, Peter D

2014-01-01

This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of  functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduc...

Advanced calculus

CERN Document Server

Nickerson, HK; Steenrod, NE

2011-01-01

""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl,

Applications of fractional calculus in physics

CERN Document Server

2000-01-01

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co

Bunny hops: using multiplicities of zeroes in calculus for graphing

Science.gov (United States)

Miller, David; Deshler, Jessica M.; Hansen, Ryan

2016-07-01

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students' pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.

A Study of Pre-Service Elementary Teachers' Mathematical Sophistication in a Reform-Oriented Calculus Course

Science.gov (United States)

Ritter, Carrie Lineberry

2015-01-01

Calls for better preparation of STEM teachers have been prominent in educational communities and among the public for the past several years (e.g. American Association of Colleges for Teacher Education, 2007). Some research suggests one way to improve mathematics instruction is to increase elementary pre-service teachers' "mathematical…

An outline of possible pre-course diagnostics for differential calculus

OpenAIRE

Maharaj, Aneshkumar; Wagh, Vivek

2014-01-01

There is a view that many first-year students lack the basic knowledge and skills expected of them to study at university level. We examined the expected work habits and pre-course diagnostics for students who choose to take a course on differential calculus. We focused on the lecturer pre-course expectations of a student in the context of work habits, knowledge and technical skills. In particular, we formulated outcomes and then sample diagnostic questions to test whether the identified lear...

On the refinement calculus

CERN Document Server

Vickers, Trevor

1992-01-01

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.

Building an Understanding of Functions: A Series of Activities for Pre-Calculus

Science.gov (United States)

Carducci, Olivia M.

2008-01-01

Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

Science.gov (United States)

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

A Comparison of Mathematics Teachers' and Professors' Views on Secondary Preparation for Tertiary Calculus

Science.gov (United States)

Wade, Carol; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra; Watson, Charity

2016-01-01

This article compares the views of teachers and professors about the transition from secondary mathematics to tertiary calculus. Quantitative analysis revealed five categories where teachers and professors differed significantly in the relative frequency of addressing them. Using the rite of passage theory, the separation and incorporation phases…

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

University Students' Problem Posing Abilities and Attitudes towards Mathematics.

Science.gov (United States)

Grundmeier, Todd A.

2002-01-01

Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)

Functional Fractional Calculus

CERN Document Server

Das, Shantanu

2011-01-01

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic

Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

Science.gov (United States)

Haciomeroglu, Guney

2014-01-01

The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…

Calculus, Biology and Medicine: A Case Study in Quantitative Literacy for Science Students

Directory of Open Access Journals (Sweden)

Kim Rheinlander

2011-01-01

Full Text Available This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.

To Math or Not to Math: The Algebra-Calculus Pipeline and Postsecondary Mathematics Remediation

Science.gov (United States)

Showalter, Daniel A.

2017-01-01

This article reports on a study designed to estimate the effect of high school coursetaking in the algebra-calculus pipeline on the likelihood of placing out of postsecondary remedial mathematics. A nonparametric variant of propensity score analysis was used on a nationally representative data set to remove selection bias and test for an effect…

The quantum probability calculus

International Nuclear Information System (INIS)

Jauch, J.M.

1976-01-01

The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)

Advanced calculus a transition to analysis

CERN Document Server

Dence, Thomas P

2010-01-01

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor

Object-Spatial Visualization and Verbal Cognitive Styles, and Their Relation to Cognitive Abilities and Mathematical Performance

Science.gov (United States)

Haciomeroglu, Erhan Selcuk

2016-01-01

The present study investigated the object-spatial visualization and verbal cognitive styles among high school students and related differences in spatial ability, verbal-logical reasoning ability, and mathematical performance of those students. Data were collected from 348 students enrolled in Advanced Placement calculus courses at six high…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

Science.gov (United States)

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

The Vector Space as a Unifying Concept in School Mathematics.

Science.gov (United States)

Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

An evaluation of a pre-scaling gel (SofScale) on the ease of supragingival calculus removal.

Science.gov (United States)

Smith, S R; Foyle, D M; Daniels, J

1994-09-01

SofScale is a pre-scaling gel, containing disodium EDTA and sodium lauryl sulphate, which is claimed to soften calculus and therefore facilitate its removal. 31 subjects were treated in a double blind randomised placebo controlled split mouth study to evaluate this product. Test or placebo gels were applied to the lingual surfaces of the mandibular teeth for 4 min and the time taken to complete the removal of supragingival calculus recorded. The operator recorded on which side the calculus was considered easier to remove and the patient indicated how comfortable the scaling had been. The mean calculus index was 1.99 for the SofScale group and 1.97 for the placebo. The mean time taken to complete scaling was 5.31 min for both groups. Using the Student t-test, there were no statistically significant differences (p > 0.7) between either the calculus index or time taken to complete the scaling between the groups. The operator did not consider SofScale to facilitate calculus removal and patients did not find calculus removal more comfortable when SofScale had been used. There was no increased sensitivity in the SofScale group following scaling. The results of this study do not support the use of SofScale as an adjunct to scaling.

Enhancing Mathematical Communication for Virtual Math Teams

Science.gov (United States)

Stahl, Gerry; Çakir, Murat Perit; Weimar, Stephen; Weusijana, Baba Kofi; Ou, Jimmy Xiantong

2010-01-01

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…

Calculus II For Dummies

CERN Document Server

Zegarelli, Mark

2012-01-01

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

Calculus and analysis in Euclidean space

CERN Document Server

Shurman, Jerry

2016-01-01

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

Science.gov (United States)

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Student Achievement in College Calculus, Louisiana State University 1967-1968.

Science.gov (United States)

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

Science.gov (United States)

Dayal, Hem Chand

2013-01-01

Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

Understanding the calculus

OpenAIRE

Tall, David

1985-01-01

A number of significant changes have have occurred recently that give us a golden opportunity to review the teaching of calculus. The most obvious is the arrival of the microcomputer in the mathematics classroom, allowing graphic demonstrations and individual investigations into the mathematical ideas. But equally potent are new\\ud insights into mathematics and mathematics education that suggest new ways of approaching the subject.\\ud In this article I shall consider some of the difficulties ...

Quantum Variational Calculus

OpenAIRE

Malinowska , Agnieszka B.; Torres , Delfim

2014-01-01

International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...

Visual Thinking and Gender Differences in High School Calculus

Science.gov (United States)

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

AP calculus AB & BC crash course

CERN Document Server

Rosebush, J

2012-01-01

AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our

Three Different Teaching Approaches in Pre-Calculus Bridging Mathematics

Science.gov (United States)

Miller-Reilly, Barbara

2007-01-01

During the past decade three different bridging mathematics courses have been offered at the University of Auckland. A case study approach was used to investigate the effectiveness of these courses: two larger courses and one individual study programme. A different teaching approach, by committed experienced teachers, was used in each course. The…

Calculus and Geometry

Indian Academy of Sciences (India)

IAS Admin

Sphere–Cylinder Theorem, vol- ume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics. (topology), in 2000, from. Panjab University,. Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at.

Interpreting Mathematics Scores on the New Jersey College Basic Skills Placement Test.

Science.gov (United States)

Dass, Jane; Pine, Charles

The New Jersey College Basic Skills Placement Test (NJCBSPT) is designed to measure certain basic language and mathematics skills of students entering New Jersey colleges. The primary purpose of the two mathematics sections is to determine whether students are prepared to begin certain college-level work without a handicap in computation or…

Sex-Related Differences in Mathematical Competencies of Pre-Calculus College Students.

Science.gov (United States)

Stones, Ivan; And Others

1982-01-01

Thirty-eight classes--categorized as College Algebra, Mathematics for Elementary Teachers, and Applied Mathematics-- were selected at four state and six community colleges during the first semester of the 1976-77 school year. Results reinforced the notion there is actually no difference in ability due to sex. (MP)

Backpropagation and ordered derivatives in the time scales calculus.

Science.gov (United States)

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

Science.gov (United States)

Briley, Jason S.

2012-01-01

Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Instructor Use of Tablet PCs in a College Pre-Calculus Course: Implementation & Assessment

Science.gov (United States)

Connelly Stockton, Julianna; Gregory, Peter

2012-01-01

A group of six math instructors used tablet PCs to teach their individual sections of a high enrollment gateway Pre-Calculus course in a diverse urban four-year college. Student performance in the experimental sections were compared to those in 31 other sections in terms of student retention, pass rates, and score on the department-wide…

Hands-On Calculus

Science.gov (United States)

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

The absolute differential calculus calculus of tensors

CERN Document Server

Levi-Cività, Tullio

1926-01-01

Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro

The Relationships among Pre-Service Mathematics Teachers' Beliefs about Mathematics, Mathematics Teaching, and Use of Technology in China

Science.gov (United States)

Yang, Xinrong; Leung, Frederick K. S.

2015-01-01

This paper investigated pre-service mathematics teachers' mathematics beliefs, beliefs about information and communication technology (ICT), and their relationships. 787 pre-service mathematics teachers in China completed a survey questionnaire measuring their beliefs about the nature of mathematics, beliefs about mathematics learning and…

Pre-Service Teachers' Mathematics Self-Efficacy and Mathematics Teaching Self-Efficacy

Science.gov (United States)

Zuya, Habila Elisha; Kwalat, Simon Kevin; Attah, Bala Galle

2016-01-01

Pre-service mathematics teachers' mathematics self-efficacy and mathematics teaching self-efficacy were investigated in this study. The purpose was to determine the confidence levels of their self-efficacy in mathematics and mathematics teaching. Also, the study was aimed at finding whether their mathematics self-efficacy and teaching…

The calculus primer

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Schaaf, William L

2011-01-01

Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different

The Development of an Individualized Instructional Program in Beginning College Mathematics Utilizing Computer Based Resource Units. Final Report.

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Rockhill, Theron D.

Reported is an attempt to develop and evaluate an individualized instructional program in pre-calculus college mathematics. Four computer based resource units were developed in the areas of set theory, relations and function, algebra, trigonometry, and analytic geometry. Objectives were determined by experienced calculus teachers, and…

The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers

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Galante, Dianna

2014-01-01

Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the…

An Introductory Calculus-Based Mechanics Investigation

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Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

Multivariable dynamic calculus on time scales

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Bohner, Martin

2016-01-01

This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.

Noncommutative operational calculus

Directory of Open Access Journals (Sweden)

Henry E. Heatherly

1999-12-01

Full Text Available Oliver Heaviside's operational calculus was placed on a rigorous mathematical basis by Jan Mikusinski, who constructed an algebraic setting for the operational methods. In this paper, we generalize Mikusi'{n}ski's methods to solve linear ordinary differential equations in which the unknown is a matrix- or linear operator-valued function. Because these functions can be zero-divisors and do not necessarily commute, Mikusi'{n}ski's one-dimensional calculus cannot be used. The noncommuative operational calculus developed here,however, is used to solve a wide class of such equations. In addition, we provide new proofs of existence and uniqueness theorems for certain matrix- and operator valued Volterra integral and integro-differential equations. Several examples are given which demonstrate these new methods.

The link between middle school mathematics course placement and achievement.

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Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

Pre-service teachers' mathematical knowledge for teaching basic ...

African Journals Online (AJOL)

This study measured pre-service teachers' mathematical knowledge for teaching (MKT) basic school mathematics. MKT multiple-choice test was administered to 100 pre-service teachers from two colleges of education (located at Mampong in the Ashanti Region of Ghana) to assess their mathematical knowledge for ...

Programming Language Concepts - The Lambda Calculus Approach

NARCIS (Netherlands)

Fokkinga, M.M.; Asveld, P.R.J.; Nijholt, Antinus

1987-01-01

The Lambda Calculus is a formal system, originally intended as a tool in the foundation of mathematics, but mainly used to study the concepts of algorithm and effective computability. Recently, the Lambda Calculus and related systems acquire attention from Computer Science for another reason too:

Constructivized Calculus in College Mathematics

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Lawrence, Barbara Ann

2012-01-01

The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…

Educating about Sustainability while Enhancing Calculus

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Pfaff, Thomas J.

2011-01-01

We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…

Scale development for pre-service mathematics teachers ...

African Journals Online (AJOL)

The purpose of this study is to develop a scale to determine pre-service mathematics teachers' perceptions related to their pedagogical content knowledge. Firstly, a preliminary perception scale of pedagogical content knowledge was constructed and then administered to 112 pre-service mathematics teachers who were ...

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

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Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

The calculus a genetic approach

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Toeplitz, Otto

2007-01-01

When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a

AP calculus AB/BC

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Schwartz, Stu

2013-01-01

All Access for the AP® Calculus AB & BC Exams Book + Web + Mobile Everything you need to prepare for the Advanced Placement® exam, in a study system built around you! There are many different ways to prepare for an Advanced Placement® exam. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge. This book, and the free online tools that come with it, will help you personalize your AP® Cal

The Effectiveness of the North Carolina Early Mathematics Placement Test in Preparing High School Students for College-Level Introductory Mathematics Courses

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Hilgoe, Ellen; Brinkley, Jason; Hattingh, Johannes; Bernhardt, Robert

2016-01-01

Since its establishment in 1996, the North Carolina Early Mathematics Placement Testing (NC EMPT) Program has provided a low stakes reality check of readiness for college-level mathematics to more than 600,000 high school students statewide. The program strives to help reduce the percentage of incoming college freshmen requiring mathematics…

Reading the World with Calculus

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Verzosa, Debbie

2015-01-01

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Projects for calculus the language of change

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Stroyan, Keith D

1999-01-01

Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology

A delivery mode study: The effect of self-paced video learning on first-year college students' achievement in calculus

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Oktaviyanthi, Rina; Herman, Tatang

2016-10-01

In this paper, the effect of two different modes of deliver are proposed. The use of self-paced video learning and conventional learning methods in mathematics are compared. The research design classified as a quasi-experiment. The participants were 80 students in the first-year college and divided into two groups. One group as an experiment class received self-paced video learning method and the other group as a control group taught by conventional learning method. Pre and posttest were employed to measure the students' achievement, while questionnaire and interviews were applied to support the pre and posttest data. Statistical analysis included the independent samples t-test showed differences (p Calculus, such as appropriate learning for both audio and visual of students' characteristics, useful to learn Calculus, assisting students to be more engaging and paying attention in learning, helping students in making the concepts of Calculus are visible, interesting media and motivating students to learn independently.

Semiclassical dynamics and magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Maximilian Stefan

2011-01-01

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Semiclassical dynamics and magnetic Weyl calculus

Energy Technology Data Exchange (ETDEWEB)

Lein, Maximilian Stefan

2011-01-19

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Neutrosophic Precalculus and Neutrosophic Calculus

OpenAIRE

Florentin Smarandache

2015-01-01

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o...

EARLINET Single Calculus Chain - technical - Part 1: Pre-processing of raw lidar data

Science.gov (United States)

D'Amico, Giuseppe; Amodeo, Aldo; Mattis, Ina; Freudenthaler, Volker; Pappalardo, Gelsomina

2016-02-01

In this paper we describe an automatic tool for the pre-processing of aerosol lidar data called ELPP (EARLINET Lidar Pre-Processor). It is one of two calculus modules of the EARLINET Single Calculus Chain (SCC), the automatic tool for the analysis of EARLINET data. ELPP is an open source module that executes instrumental corrections and data handling of the raw lidar signals, making the lidar data ready to be processed by the optical retrieval algorithms. According to the specific lidar configuration, ELPP automatically performs dead-time correction, atmospheric and electronic background subtraction, gluing of lidar signals, and trigger-delay correction. Moreover, the signal-to-noise ratio of the pre-processed signals can be improved by means of configurable time integration of the raw signals and/or spatial smoothing. ELPP delivers the statistical uncertainties of the final products by means of error propagation or Monte Carlo simulations. During the development of ELPP, particular attention has been payed to make the tool flexible enough to handle all lidar configurations currently used within the EARLINET community. Moreover, it has been designed in a modular way to allow an easy extension to lidar configurations not yet implemented. The primary goal of ELPP is to enable the application of quality-assured procedures in the lidar data analysis starting from the raw lidar data. This provides the added value of full traceability of each delivered lidar product. Several tests have been performed to check the proper functioning of ELPP. The whole SCC has been tested with the same synthetic data sets, which were used for the EARLINET algorithm inter-comparison exercise. ELPP has been successfully employed for the automatic near-real-time pre-processing of the raw lidar data measured during several EARLINET inter-comparison campaigns as well as during intense field campaigns.

Improving Student Success in Calculus: A Comparison of Four College Calculus Classes

Science.gov (United States)

Bagley, Spencer Franklin

The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the

Calculus Instructors' and Students' Discourses on the Derivative

Science.gov (United States)

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Improving Calculus II and III through the Redistribution of Topics

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George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

Metaphor Perceptions of Pre-Service Teachers towards Mathematics and Mathematics Education in Preschool Education

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Keles, Oguz; Tas, Isil; Aslan, Durmus

2016-01-01

The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…

FEATURES OF FOREIGN STUDENTS PRE-UNIVERSITY MATHEMATICAL TRAINING

Directory of Open Access Journals (Sweden)

Наталья Александровна Пыхтина

2017-12-01

Full Text Available The aim of improving the international competitiveness of the higher education Russian system at the global level by increasing the number of foreign students leads to the fact, that pre-university training is becoming essential for next years at higher educational programmes.Pre-university mathematical training of international students contributes to the scientific style formation of speech skills, which is so useful in higher educational institute. This article highlights some of the features of foreign students pre-university mathematical training.Design of “Mathematics” course methodical ware for preparatory departments of higher educational institutions is an important element of the educational process. Features of mathematics teaching are shown by the example of such important for foreign students pre-university mathematical training branch of mathematics like the set theory.The article also gives consideration to such aspects of mathematics teaching for foreign students as the inclusion of text mathematical problems in the “Mathematics” course programme for helping to achieve lexical skills and abilities, as well as the organization of individual work of the students with the use of information and communication technologies.The paper refers to the collection of exercises and tasks for the “Mathematics” course for foreign citizens studying at the preparatory departments of higher educational institutions, it additionally gives the themes of the course.

Pre-Service Elementary Teachers' Mathematics Content Knowledge: A Predictor of Sixth Graders' Mathematics Performance

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Shirvani, Hosin

2015-01-01

This study examined the knowledge of mathematics content of elementary pre-service teachers at a sixth grade level. The researcher administered a mathematics test for sixth graders mandated by the Texas Education Agency to pre-service teachers; the same test was given to sixth graders in Texas. The study found that pre-service teachers performed…

Improving University Students' Perception of Mathematics and Mathematics Ability

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Shelly L. Wismath

2015-01-01

Full Text Available Although mathematical and quantitative reasoning skills are an essential part of adult life in our society, many students arrive at post-secondary education without such skills. Taking a standard mathematics course such as calculus may do little to improve those skills. Using a modification of the Tapia & Marsh questionnaire, we surveyed 62 students taking a broad quantitative reasoning course designed to develop quantitative skills, with respect to two broad attitudinal areas: students’ perception of their own ability, confidence and anxiety, and their perception of the value of mathematics in their studies and their lives. Pre- to post-course comparisons were done by both paired t-tests and Wilcoxon signed-rank tests. Our results showed a significant increase in confidence and decrease in anxiety, while perception of the value of mathematics was already high and changed little by the end of the course.

The umbral calculus

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Roman, Steven

2005-01-01

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial

Calculus in physics classes at UFRGS: an exploratory study

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Maria Cecilia Pereira Santarosa

2011-11-01

Full Text Available This study is part f a larger one whose general objective is to investigate and to develop a new strategy for teaching Differential and Integral Calculus I, specifically for physics majors, through a possible integration with the teaching of General and Experimental Physics I. With the specific objective of identifying physics problem-situations that may help in making sense of the mathematical concepts used in Calculus I, and languages and notations that might be used in the teaching of Calculus to favor physics learning, it was investigates, through an ethnographic study, the may mathematics is transposed to classes of General and Experimental Physics I, in classes of physics courses at the Federal University of Rio Grande do Sul (UFRGS. Some findings of this study confirmed those reported in the literature regarding the teaching and learning process in introductory college physics courses. These findings will subsidize the preparation of potentially meaningful instructional materials that will be used in a second stage of the research designed to investigate the learning of declarative and procedural knowledge in basic college physics under an approach that integrates problem-situation in physics and calculus mathematical concepts.

A study of ∇-discrete fractional calculus operator on the radial ...

African Journals Online (AJOL)

The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus. Recently, many scientists have been studying on this eld to provide the development and applicability to various areas of mathematics, physics, engineering and other ...

Multivariable calculus with Matlab with applications to geometry and physics

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Lipsman, Ronald L

2017-01-01

This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical ...

Fractional dynamic calculus and fractional dynamic equations on time scales

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Georgiev, Svetlin G

2018-01-01

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

Coordinating Multiple Representations in a Reform Calculus Textbook

Science.gov (United States)

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2016-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Malliavin Calculus With Applications to Stochastic Partial Differential Equations

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Sanz-Solé, Marta

2005-01-01

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

Elementary calculus an infinitesimal approach

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Keisler, H Jerome

2012-01-01

This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p

Lacroix and the calculus

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Domingues, João Caramalho

2008-01-01

Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a...

A course of higher mathematics

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Smirnov, Vladimir Ivanovich; Lohwater, A J

1964-01-01

A Course of Higher Mathematics, I: Elementary Calculus is a five-volume course of higher mathematics used by mathematicians, physicists, and engineers in the U.S.S.R. This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameter

Using Dynamic Software to Address Common College Calculus Stumbling Blocks

Science.gov (United States)

Seneres, Alice W.; Kerrigan, John A.

2014-01-01

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Finite-dimensional calculus

International Nuclear Information System (INIS)

Feinsilver, Philip; Schott, Rene

2009-01-01

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.

A Cross-National Study of Calculus

Science.gov (United States)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Students attitude towards calculus subject: Bumiputera case-study

Science.gov (United States)

Awang, Noorehan; Ilias, Mohd Rijal; Che Hussain, Wan Siti Esah; Mokhtar, Siti Fairus

2013-04-01

Mathematics has always become the most dislike subject among other subjects in school. Study showed that attitudes of students in science subjects such as mathematics were closely related to how they solve problems, accessing ideas and making a right decision. According to another study on mathematics achievement of eighth grade students in Malaysia, mathematics grades among bumiputera students was lower when compared to other races such as Chinese and Indians. The poor performance was due to their attitude and pre-conceived ideas towards the subject. Therefore, this study was designed todetermine the criteria and subcriteria that were considered important in measuring students' attitude toward mathematics among the bumiputeras. Factor analysis was carried out to identify the groups among criterion. Instrument used to measure mathematics attitude was Test of Mathematics Related Attitude (TOMRA) which measured student attitudes in four criteria: normality of mathematics, attitudes towards mathematics inquiry, adoption of mathematics attitude and enjoyment of mathematics lessons. The target population of this study was all computer science and quantitative science students who enrolled Calculus subject in UiTM Kedah. Findings shows that there are two criteria that influenced students attitude toward mathematics namely normality of mathematics with eleven subcriteria and enjoyment of mathematics with eight subcriteria. From the analysis it shows that the total percentage of variation explained is 35.071% with 0.837 Cronbach's alpha reliability test. The findings will help the lecturers, parents and society to consider what action should be taken to install interest and positive attitude of bumiputera students towards mathematics and thus improve their achievement.

Spatial Skill Profile of Mathematics Pre-Service Teachers

Science.gov (United States)

Putri, R. O. E.

2018-01-01

This study is aimed to investigate the spatial intelligence of mathematics pre-service teachers and find the best instructional strategy that facilitates this aspect. Data were collected from 35 mathematics pre-service teachers. The Purdue Spatial Visualization Test (PSVT) was used to identify the spatial skill of mathematics pre-service teachers. Statistical analysis indicate that more than 50% of the participants possessed spatial skill in intermediate level, whereas the other were in high and low level of spatial skill. The result also shows that there is a positive correlation between spatial skill and mathematics ability, especially in geometrical problem solving. High spatial skill students tend to have better mathematical performance compare to those in two other levels. Furthermore, qualitative analysis reveals that most students have difficulty in manipulating geometrical objects mentally. This problem mostly appears in intermediate and low-level spatial skill students. The observation revealed that 3-D geometrical figures is the best method that can overcome the mentally manipulation problem and develop the spatial visualization. Computer application can also be used to improve students’ spatial skill.

Pre Service Teachers' Usage of Dynamic Mathematics Software

Science.gov (United States)

Bulut, Mehmet; Bulut, Neslihan

2011-01-01

Aim of this study is about mathematics education and dynamic mathematics software. Dynamic mathematics software provides new opportunities for using both computer algebra system and dynamic geometry software. GeoGebra selected as dynamic mathematics software in this research. In this study, it is investigated that what is the usage of pre service…

Examining mathematical discourse to understand in-service teachers’ mathematical activities

Directory of Open Access Journals (Sweden)

Margot Berger

2013-04-01

Full Text Available In this article I use Sfard’s theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus task required students to examine a function at an undefined point and to decide whether a vertical asymptote is associated with this point or not. Using the different characteristics of mathematical discourse, I argue that the words that students use really matter and show how a change in one participant’s use of the term ‘vertical asymptote’ constituted and reflected her learning. I also show how the other participant used imitation in a ritualised routine to get through the task. Furthermore I demonstrate how digital immigrants may resist the use of technology as the generator of legitimate mathematical objects.

Topology, calculus and approximation

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Komornik, Vilmos

2017-01-01

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

Generalized calculus with applications to matter and forces

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Campos, L M B C

2014-01-01

Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: •Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of ...

Pre-service teachers’ challenges in presenting mathematical problems

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Desfitri, R.

2018-01-01

The purpose of this study was to analyzed how pre-service teachers prepare and assigned tasks or assignments in teaching practice situations. This study was also intended to discuss about kind of tasks or assignments they gave to students. Participants of this study were 15 selected pre-service mathematics teachers from mathematics education department who took part on microteaching class as part of teaching preparation program. Based on data obtained, it was occasionally found that there were hidden errors on questions or tasks assigned by pre-service teachers which might lead their students not to be able to reach a logical or correct answer. Although some answers might seem to be true, they were illogical or unfavourable. It is strongly recommended that pre-service teachers be more careful when posing mathematical problems so that students do not misunderstand the problems or the concepts, since both teachers and students were sometimes unaware of errors in problems being worked on.

Tensor Calculus: Unlearning Vector Calculus

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Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

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Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K

2011-01-01

An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with cle

Bridging the Gulf between Formal Calculus and Physical Reasoning.

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Van Der Meer, A.

1980-01-01

Some ways to link calculus instruction with the mathematical models used in physics courses are presented. The activity of modelling is presented as a major tool in synchronizing physics and mathematics instruction in undergraduate engineering programs. (MP)

Brownian motion, martingales, and stochastic calculus

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Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

Mathematical methods for physical and analytical chemistry

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Goodson, David Z

2011-01-01

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical

Dental hygiene faculty calibration in the evaluation of calculus detection.

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Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

A Case Study on Pre-Service Secondary School Mathematics Teachers' Cognitive-Metacognitive Behaviours in Mathematical Modelling Process

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Sagirli, Meryem Özturan

2016-01-01

The aim of the present study is to investigate pre-service secondary mathematics teachers' cognitive-metacognitive behaviours during the mathematical problem-solving process considering class level. The study, in which the case study methodology was employed, was carried out with eight pre-service mathematics teachers, enrolled at a university in…

White noise calculus and Fock space

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Obata, Nobuaki

1994-01-01

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

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Chen, Jing-Hua; Chen, Yi-Chou

2018-01-01

Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied…

Introductory analysis a deeper view of calculus

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Bagby, Richard J

2000-01-01

Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus

Trickle down Mathematics: Adult Pre-Service Elementary Teachers Gain Confidence in Mathematics--Enough to Pass It Along?

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Ashun, Mary Apea; Reinink, John

2009-01-01

Much research (Ma, 1999; Cohen & Leung, 2004; English, 2003) has been done on mathematics education and pre-service teachers with special emphasis on how the mathematics is taught and the psychology of the pre-service teachers. While there is concern among North American mathematicians that mathematics instruction in K-12 grades needs to be…

Discrete calculus methods for counting

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Mariconda, Carlo

2016-01-01

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...

6th Conference on Non-integer Order Calculus and Its Applications

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Łukaniszyn, Marian; Stanisławski, Rafał

2015-01-01

This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in ap...

Improving Student Success in Calculus I Using a Co-Requisite Calculus I Lab

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Vestal, Sharon Schaffer; Brandenburger, Thomas; Furth, Alfred

2015-01-01

This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…

Effect of a pre-brush mounthrinse containing triclosan and a copolymer on calculus formation: a three-month clinical study in Thailand.

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Triratana, T; Kraivaphan, P; Tandhachoon, K; Rustogi, K; Volpe, A R; Petrone, M

1995-01-01

A three-month, double-blind, parallel clinical study was conducted on a population of Thai adults to evaluate the effect of the twice daily use of a commercially available pre-brush mouthrinse on supragingival calculus formation. The mouthrinse test product contained 0.03% triclosan and 0.13% PVM/MA copolymer with the absence of fluoride. The subjects were initially examined for calculus using the Volpe-Manhold procedure. All subjects received an oral prophylaxis and were assigned to the use of either 1) a triclosan-copolymer mouthrinse, or 2) a matching flavored/colored water placebo mouthrinse. Subjects were instructed to rinse twice daily with 10 cc of the assigned mouthrinse for 1 minute, followed by brushing with the provided toothpaste containing fluoride for 45 seconds. After three months of using the assigned mouthrinse, the subjects were reexamined for calculus formation. The results indicated that the subjects using triclosan/copolymer mouthrinse had 23.17% less supragingival calculus than the placebo mouthrinse subjects. This reduction was statistically significant at the 99% or greater (F = 24.35, p<0.001) level of confidence.

Representations in Calculus: Two Contrasting Cases.

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Aspinwall, Leslie; Shaw, Kenneth L.

2002-01-01

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Elective Drama Course in Mathematics Education: An Assessment of Pre-Service Teachers

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Sagirli, Meryem Özturan

2014-01-01

This study aimed to evaluate a newly introduced elective course "Drama in Mathematics Education" into mathematics education curriculum from the viewpoints of pre-service mathematics teachers. A case study was employed in the study. The study group consisted of 37 pre-service mathematics teachers who were enrolled in a Turkish state…

An Intuitive Calculus Book for Engineers Um Livro de Cálculo Intuitivo para Engenheiros

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Gustavo Alexandre de Miranda

2010-06-01

Full Text Available With the purpose of studying the history of calculus teaching and, particularly, the consequences of Calculus Made Easy (1910 in the mathematics education context, this work intends to make an historical analysis to clarify the connections between Silvanus Phillips Thompson (its author and education in the early Twentieth Century, mainly mathematics education. Thompson was concerned about Physics and Radiology,however, at the dawn of the new century, his interests in technical education had also burgeoned. One of his goals was to demystify Calculus, tackling the subject intuitively – Calculus Made Easy. The book did not draw much respect from mathematicians and was acridly criticized. Keywords: Mathematics Education, History of Mathematics Education, Silvanus Phillips Thompson, Calculus Made Easy.Com o intuito de estudar a história do ensino de Cálculo e, mais especificamente, os desdobramentos do livro Calculus Made Easy (1910 no contexto da educação matemática, este trabalho procura fazer uma análise histórica que elucide as relações entre Silvanus Phillips Thompson (autor do livro e a educação do início do século XX, particularmente a educação matemática. Thompson legou muito às áreas da física e da radiologia, porém, com a chegada do novo século, passou a se dedicar intensamente à educação técnica de seus compatriotas ingleses. Um de seus objetivos era desmistificar alguns conceitos do Cálculo, tratando o assunto de maneira intuitiva. Por esse motivo, o livro foi criticado por alguns matemáticos. Palavras-chave: Educação Matemática. História da Educação Matemática. Silvanus Phillips Thompson. Calculus Made Easy.

Geometric calculus according to the Ausdehnungslehre of H. Grassmann

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Peano, Giuseppe

2000-01-01

Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. In Chapter IX, with the innocent-sounding title "Transformations of a linear system," one finds the crown jewel of the book: Peano's axiom system for a vector space, the first-ever presentation of a set of such axioms. The very wording of the axioms (which Peano calls "definitions") has a remarkably modern ring, almost like a modern introduction to linear algebra. Peano also presents the basic calculus of set operation, introducing the notation for 'intersection,' 'union,' and 'element of,' many years before it was accepted. Despite its uniqueness, Calcolo Geometrico has been strangely neglected by histor...

The development and nature of problem-solving among first-semester calculus students

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Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem

Pre-Service Teachers' Mathematics Content Knowledge: Implications for How Mathematics Is Taught in Higher Education

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Lowrie, Tom; Jorgensen, Robyn

2016-01-01

This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is…

Mathematics Anxiety and Beliefs of Turkish Pre-Service Elementary Teachers

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Uysal, Figen; Dede, Yüksel

2016-01-01

The purpose of this study was to investigate the relationship between pre-service elementary teachers' mathematics teaching beliefs and mathematics anxiety. The participants of the study consist of 96 pre-service elementary teachers from a department of primary education in a state university in Turkey during the 2010-2011 spring term. Mathematics…

Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

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Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

Views of Elementary School Pre-Service Teachers About the Use of Educational Mathematics Games in Mathematics Teaching

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Hasan Topçu

2014-08-01

Full Text Available The aim of this study was to reveal the opinions of elementary school pre-service teachers about the usage of educational mathematics games in elementary mathematics teaching. In this study, case study that, one of qualitative research methods, was used. Data were collected by utilizing a semi-structured interview form to these elementary school pre-service teachers and analyzed using by content analysis method. A total of 10 junior pre-service teachers enrolled in undergraduate programs of elementary teaching attended to this research. In conclusion, these pre-service teachers indicated that educational computer games would provide benefits such as making students’ learning more permanent, visualizing concepts, making students love mathematics, learning by entertaining, reinforcing what has been learnt and developing thinking skills. Nevertheless, these elementary school pre-service teachers stated the limitations about educational computer games such as causing addiction and physical damages, being time-consuming, requiring special equipment and software and making class management difficult. Besides, it was revealed that the pre-service teachers demonstrated positive attitudes towards the use of games in courses while that they did not feel themselves competent in terms of application.Key Words:    Educational computer games, mathematics teaching, elementary school pre-service teachers

The Influence of Pre-University Students' Mathematics Test Anxiety and Numerical Anxiety on Mathematics Achievement

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Seng, Ernest Lim Kok

2015-01-01

This study examines the relationship between mathematics test anxiety and numerical anxiety on students' mathematics achievement. 140 pre-university students who studied at one of the institutes of higher learning were being investigated. Gender issue pertaining to mathematics anxieties was being addressed besides investigating the magnitude of…

Calculus of variations and optimal control theory a concise introduction

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Liberzon, Daniel

2011-01-01

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the h...

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

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Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

Science.gov (United States)

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Advanced calculus

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Fitzpatrick, Patrick M

2009-01-01

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclide

One Usage of Geogebra in Enhancing Pre-service Mathematics Teachers’ Content Knowledge

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Karmelita Pjanic

2015-04-01

Full Text Available A wide range of mathematical ideas could be used to develop and justify a formula for calculating the area of trapezoid. Those ideas lead to different strategies for finding out area of trapezoid that we classify in three groups: decomposing, enclosing and transforming strategies. Those strategies should be part of mathematics content knowledge for teaching. In this study we trace a change in structure of mathematics content knowledge of nine pre-service mathematics teachers as a result of using GeoGebra applets that visualize different approaches in finding out the area of trapezoid. We argue that engaging pre-service mathematics teachers to develop and justify formula for calculating the area of trapezoid using GeoGebra applets is a worth task that enhances pre-service mathematics teachers’ content knowledge for teaching. Our experiment confirmed that the use of Geogebra encourage pre-service mathematics teachers to uncover new ideas that lead them towards clearer justifications and easier way of proving formula for area of trapezoid. Keywords: Area of trapezoid, GeoGebra, content knowledge for teaching

Pre-University Students' Errors in Integration of Rational Functions and Implications for Classroom Teaching

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Yee, Ng Kin; Lam, Toh Tin

2008-01-01

This paper reports on students' errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students' weak algebraic concepts and their lack of understanding of the concept of integration. With the students' inability to link…

Calculus

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Jones, Patrick

2014-01-01

Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

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Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Mathematical Investigations for Supporting Pre-Service Primary Teachers Repeating a Mathematics Education Course

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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…

A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

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Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Hermeneutics of differential calculus in eighteenth-century northern Germany.

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Blanco, Mónica

2008-01-01

This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.

On flipping first-semester calculus: a case study

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Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

Space complexity in polynomial calculus

Czech Academy of Sciences Publication Activity Database

Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil

2015-01-01

Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950

A MATLAB companion for multivariable calculus

CERN Document Server

Cooper, Jeffery

2001-01-01

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...

The cost and value of pre-registration clinical placements for Project 2000 students.

Science.gov (United States)

Jones, M L; Akehurst, R

1999-07-01

The research outlined in this article was commissioned by the Sheffield and North Trent College of Nursing and Midwifery to explore the cost implications of pre-registration clinical placements in the context of Project 2000. The authors outline the methodology and findings of an exercise designed to collect relevant cost information which was not readily available. On the basis of these findings, they suggest that: at 1995/1996 pay and prices, clinical placements cost the education provider approximately pound 890 per student per annum; in terms of real resources, the value to service providers of the service contribution made by second- and third-year nursing and midwifery students on ward-based placements outweighs the value of the time spent by qualified staff on their supervision and education. Once the funding assumptions underlying the introduction of Project 2000 have been taken into account, second- and third-year nursing and midwifery students benefit the service provider by on average pound 3.46 for every hour they spend in an unrostered ward-based placement. The service contribution made by students in community-based clinical placements cannot free staff time in the same way as on the wards and, because qualified staff in these areas are generally more highly graded, the value of the time they spend on the supervision and education of students on placement is higher than in ward-based placements. Second- and third-year students therefore appear to cost the service provider on average pound 0.48 for each hour they spend in a community-based placement. It was not possible to determine whether this cost translates into a reduction in patient contacts.

Are Homeschoolers Prepared for College Calculus?

Science.gov (United States)

Wilkens, Christian P.; Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.

2015-01-01

Homeschooling in the United States has grown considerably over the past several decades. This article presents findings from the Factors Influencing College Success in Mathematics (FICSMath) survey, a national study of 10,492 students enrolled in tertiary calculus, including 190 students who reported homeschooling for a majority of their high…

Evaluation of Mathematical Game Design Skills of Pre-Service Classroom Teachers

Science.gov (United States)

Pilten, Pusat; Pilten, Gülhiz; Divrik, Ramazan; Divrik, Fatma

2017-01-01

The purpose of the research is to evaluate the games prepared by pre-service classroom teachers within the scope of "Mathematics Teaching 1" and "Mathematics Teaching 2" courses, which are included in the undergraduate classroom teaching programs in Turkey, and to make predictions on the game design skills of pre-service…

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

Flipping Freshman Mathematics

Science.gov (United States)

Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

2015-01-01

Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

Science.gov (United States)

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Mathematics for the nonmathematician

CERN Document Server

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.

Enhancing Mathematical Communication for Virtual Math Teams

Directory of Open Access Journals (Sweden)

Gerry Stahl

2010-06-01

Full Text Available The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies the online math discourse that takes place during sessions of virtual math teams working on open-ended problem-solving tasks. In particular, it investigates methods of group cognition that are employed by teams in this setting. The VMT environment currently integrates social networking, synchronous text chat, a shared whiteboard for drawing, web browsers and an asynchronous wiki for exchanging findings within the larger community. A simple version of MathML is supported in the whiteboard, chat and wiki for displaying mathematical expressions. The VMT Project is currently integrating the dynamic mathematics application, GeoGebra, into its collaboration environment. This will create a multi-user version of GeoGebra, which can be used in concert with the chat, web browsers, curricular topics and wiki repository.

The Association of Precollege Use of Calculators with Student Performance in College Calculus

Science.gov (United States)

Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

2017-01-01

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

Formalization of the Integral Calculus in the PVS Theorem Prover

Science.gov (United States)

Butler, Ricky W.

2004-01-01

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY

OpenAIRE

Damianus D Samo

2017-01-01

The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...

A Mathematics Software Database Update.

Science.gov (United States)

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Bridging the Vector Calculus Gap

Science.gov (United States)

Dray, Tevian; Manogue, Corinne

2003-05-01

As with Britain and America, mathematicians and physicists are separated from each other by a common language. In a nutshell, mathematics is about functions, but physics is about things. For the last several years, we have led an NSF-supported effort to "bridge the vector calculus gap" between mathematics and physics. The unifying theme we have discovered is to emphasize geometric reasoning, not (just) algebraic computation. In this talk, we will illustrate the language differences between mathematicians and physicists, and how we are trying reconcile them in the classroom. For further information about the project go to: http://www.physics.orst.edu/bridge

Pre-Service Science and Mathematics Teachers' Thoughts about Technology

Science.gov (United States)

Aran, Özge Can; Derman, Ipek; Yagci, Esed

2016-01-01

This study aims to investigate pre-service teachers' opinions about the technology. In this respect, the opinions of pre-service science and mathematics teachers were taken. The study was carried out at a university, located in the capital of Turkey. The data were collected from 20 pre-service teachers in the department of secondary school science…

The Vector Calculus Gap: Mathematics (Does Not Equal) Physics.

Science.gov (United States)

Dray, Tevian; Manogue, Corinne A.

1999-01-01

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

Unisex Math: Narrowing the Gender Gap.

Science.gov (United States)

Tapia, Martha; Marsh, George E., II

This study examined gender differences in attitudes toward mathematics of undergraduate students. The Attitudes Toward Mathematics Instrument (ATMI) was administered to students enrolled in introductory mathematics classes (Pre-Calculus, Calculus, and Business Calculus) at two Southeast universities, one a large state university and the other one…

Fractional calculus in bioengineering, part 3.

Science.gov (United States)

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts

Science.gov (United States)

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris

2011-01-01

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

Science.gov (United States)

Laursen, Sandra L.; Hassi, Marja-Liisa; Hough, Sarah

2016-02-01

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.

The AP Calculus Exam Reading Experience: Implications for Teacher Classroom Practice and Student Comprehension

Science.gov (United States)

Corcoran, Mimi

2017-01-01

This dissertation explores the views and experiences of high school calculus teachers and college mathematics professors on the professional development which occurs at the annual national AP Calculus exam grading. This professional development experience comes in several forms: the exam briefing sessions, the actual reading of the exams, the…

In-service and Pre-service Middle School Mathematics Teachers' Attitudes and Decisions Regarding Teaching Mathematics Using Mobile Phones

Directory of Open Access Journals (Sweden)

Wajeeh M. Daher

2014-10-01

Full Text Available Several researches examined students' mathematics learning using mobile phones, while very few researches examined mathematics teaching using this new educational tool. This research attempts to analyze in-service and pre-service teachers' attitudes and decisions regarding mathematics teaching with mobile phones using activity theory. More specifically, three case studies are analyzed in this research: One concerns an in-service teacher who used mobile phones in her class, the second case study involves a pre-service teacher who collaborated with the in-service teacher to teach mathematics lessons using mobile phones, and the third case study is about 15 pre-service teachers who were observers of the experiment but did not use mobile phones in their teaching. We held one-hour semi-structured interviews with the in-service teacher, with the leading pre-service teacher and with the group of other observer pre-service teachers. This happened three times during the academic year: at the beginning of the experiment, after three months and after it ended. The research findings indicate that different factors have an impact on the attitudes and decisions of the teacher: history of the teacher using technologies in teaching, perceptions of the teacher using technologies in teaching, community’s teacher, rules regulating the use of technologies in teaching mathematics, and division of labor. For example, questions as to who decides which technologies to use in the classroom and who should prepare the learning material for the students. Contradictions were identified in mathematics teachers' activity when utilizing mobile phones in their teaching. These contradictions hinder or slow such utilization. Community, especially its leading members, mediated and helped overcome the activity contradictions that arose throughout the experiment regarding the teaching processes in and/or out of the mathematics classroom.

Analysis of the coupling efficiency of a tapered space receiver with a calculus mathematical model

Science.gov (United States)

Hu, Qinggui; Mu, Yining

2018-03-01

We establish a calculus mathematical model to study the coupling characteristics of tapered optical fibers in a space communications system, and obtained the coupling efficiency equation. Then, using MATLAB software, the solution was calculated. After this, the sample was produced by the mature flame-brush technique. The experiment was then performed, and the results were in accordance with the theoretical analysis. This shows that the theoretical analysis was correct and indicates that a tapered structure could improve its tolerance with misalignment. Project supported by The National Natural Science Foundation of China (grant no. 61275080); 2017 Jilin Province Science and Technology Development Plan-Science and Technology Innovation Fund for Small and Medium Enterprises (20170308029HJ); ‘thirteen five’ science and technology research project of the Department of Education of Jilin 2016 (16JK009).

Pre-service mathematics teachers' attitudes towards learning English: A case study in Yogyakarta

Science.gov (United States)

Setyaningrum, Wahyu

2017-08-01

This study investigated attitudes of pre-service mathematics teachers towards English as one of the subject at the university. It is a qualitative study in which questionnaire and face-to-face interview were employed to collect the data. The participants of this study were sixty students of mathematics education department at one of the university in Yogyakarta. The main research question was concern with how pre-service mathematics teachers perceive the importance of learning English. This study found that most of the participants perceive English as an important language that should be acquired by mathematics teachers. Their beliefs about the importance of English were mostly due to instrumental orientation rather than integrative orientation, such as getting a good job, getting a scholarship and understanding learning sources that are written in English. The data also revealed some obstacles faced by pre-service mathematics teachers in learning English as an additional language for them. The main obstacles were related to the differences between English for mathematics and English in daily life including its vocabulary and structure. Most of the participants argued that several mathematics vocabularies had precise meaning and different from daily English. In addition, they found difficult to understand some sentences used in the paper journal due to its structure. This study therefore, provided an insight into the pre-service mathematics teachers' perception and obstacles when learning English that could be use in improving pre-service teachers' education.

Evaluating the Use of Learning Objects for Improving Calculus Readiness

Science.gov (United States)

Kay, Robin; Kletskin, Ilona

2010-01-01

Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

An Examination of Multiple Intelligence Domains and Learning Styles of Pre-Service Mathematics Teachers: Their Reflections on Mathematics Education

Science.gov (United States)

Ozgen, Kemal; Tataroglu, Berna; Alkan, Huseyin

2011-01-01

The present study aims to identify pre-service mathematics teachers' multiple intelligence domains and learning style profiles, and to establish relationships between them. Employing the survey model, the study was conducted with the participation of 243 pre-service mathematics teachers. The study used the "multiple intelligence domains…

Relationship between mathematical abstraction in learning parallel coordinates concept and performance in learning analytic geometry of pre-service mathematics teachers: an investigation

Science.gov (United States)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2018-05-01

As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.

Applied mathematics

International Nuclear Information System (INIS)

Nedelec, J.C.

1988-01-01

The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr

Mathematics Teachers and ICT: Factors Affecting Pre-Service Use in School Placements

Science.gov (United States)

Bozkurt, Gulay

2016-01-01

This study examines the factors influencing student teachers' use of information and communication technology (ICT) to teach mathematics. Data collection involved questionnaire surveys and individual follow-up semi-structured interviews of student teachers concerning the factors that they felt had hindered or promoted their development in the use…

Exploring the Impact of Reform Mathematics on Entry-Level Pre-Service Primary Teachers Attitudes towards Mathematics

Science.gov (United States)

Leavy, Aisling; Hourigan, Mairead; Carroll, Claire

2017-01-01

This study reports entry-level mathematics attitudes of pre-service primary teachers entering an initial teacher education (ITE) program one decade apart. Attitudes of 360 pre-service primary teachers were compared to 419 pre-service teachers entering the same college of education almost one decade later. The latter experienced reform school…

An operator calculus for surface and volume modeling

Science.gov (United States)

Gordon, W. J.

1984-01-01

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

Formalization of the Integral Calculus in the PVS Theorem Prover

Directory of Open Access Journals (Sweden)

Ricky Wayne Butler

2009-04-01

Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

Pre-Service Secondary Science and Mathematics Teachers' Classroom Management Styles in Turkey

Science.gov (United States)

Yilmaz, Kursad

2009-01-01

The aim of this study is to determine Pre-service secondary science and mathematics teachers' classroom management styles in Turkey. In addition, differences in pre-service secondary science and mathematics teachers' classroom management styles by gender, and field of study were examined. In the study, the survey model was employed. The research…

Introduction to stochastic calculus

CERN Document Server

Karandikar, Rajeeva L

2018-01-01

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...

Changing Pre-Service Elementary Teachers' Beliefs about Mathematical Knowledge

Science.gov (United States)

Stohlmann, Micah; Moore, Tamara; Cramer, Kathleen; Maiorca, Cathrine

2015-01-01

Studies have reported that pre-service teachers often enter teacher preparation programs with beliefs and attitudes not conducive to teaching the subject conceptually. In the USA, the Common Core State Standards for Mathematics have brought a renewed focus on procedural and conceptual understanding. However, many U.S. pre-service teachers have…

Pre-Service Mathematics Teachers' Noticing Skills and Scaffolding Practices

Science.gov (United States)

Kilic, Hulya

2018-01-01

A 14-week course program was designed to investigate pre-service teachers' noticing skills and scaffolding practices. Six pre-service teachers were matched with a pair of sixth grade students to observe and scaffold students' mathematical understanding while they were working on the given tasks. Data was collected through pre-service teachers' own…

Partial differential equations and calculus of variations

CERN Document Server

Leis, Rolf

1988-01-01

This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

Full Lambek Calculus with Contraction is Undecidable

Czech Academy of Sciences Publication Activity Database

Chvalovský, Karel; Horčík, Rostislav

2016-01-01

Roč. 81, č. 2 (2016), s. 524-540 ISSN 0022-4812 R&D Projects: GA ČR GAP202/11/1632 Institutional support: RVO:67985807 Keywords : substructural logic * full Lambek calculus * contraction rule * square-increasing residuated lattice * equational theory * decidability Subject RIV: BA - General Mathematics Impact factor: 0.511, year: 2016

Challenge and Thrill of Pre-College Mathematics

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 5. Challenge and Thrill of Pre-College Mathematics-A Treasure House for Students. A M Vaidya. Book Review Volume 2 Issue 5 May 1997 pp 86-87. Fulltext. Click here to view fulltext PDF. Permanent link:

Using Technology to Promote Mathematical Discourse Concerning Women in Mathematics

Science.gov (United States)

Phy, Lyn

2008-01-01

This paper discusses uses of technology to facilitate mathematical discourse concerning women in mathematics. Such a topic can be introduced in various traditional courses such as algebra, geometry, trigonometry, probability and statistics, or calculus, but it is not included in traditional textbooks. Through the ideas presented here, you can…

CIMAC: A Coordinated Introduction to Calculus and Mechanics

Science.gov (United States)

Fathe, Laurie; Quinn, Jennifer; McDonald, Michael A.

1997-04-01

CIMAC, new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, CIMAC, a new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, the class contains specific content while exploiting the substantial commonality of these subjects. CIMAC also addresses variety of non-content areas, including supplementing basic mathematics and communication skills, accommodating various learning styles, and building student confidence. Specific approaches include class formats; gateway exams; group assignments; emphasis on writing and reading; use of computers and graphing calculators for comprehension, data acquisition, analysis, and modeling; student-led help sessions; and use of the Web http://www.oxy.edu/ departments/math/cimac/ This talk highlights the development of the course and teaching insights and innovations which have arisen from it, and addresses benefits and difficulties of coordinating material and team teaching across disciplinary lines. Finally, it presents data on student success and retention.

Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students

Science.gov (United States)

Muzangwa, Jonatan; Chifamba, Peter

2012-01-01

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

On Flipping First-Semester Calculus: A Case Study

Science.gov (United States)

Petrillo, Joseph

2016-01-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are "flipping" (or inverting) their classrooms. By flipping, we…

Science and Mathematics Teaching Efficacy Beliefs of Pre-School Teachers

Science.gov (United States)

Aydogdu, Bülent; Peker, Murat

2016-01-01

The aim of this research was to examine science and mathematics teaching efficacy beliefs of pre-school teachers in terms of some variables. The sample of the study was comprised of 191 pre-school teachers working in a city in Aegean Region of Turkey. Since it attempted to define self-efficacy beliefs of pre-school teachers toward science and…

Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

Science.gov (United States)

Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

2017-01-01

Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

A course of higher mathematics

CERN Document Server

Smirnov, Vladimir Ivanovich

1964-01-01

A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in

An Investigation of Calculus Learning Using Factorial Modeling.

Science.gov (United States)

Dick, Thomas P.; Balomenos, Richard H.

Structural covariance models that would explain the correlations observed among mathematics achievement and participation measures and related cognitive and affective variables were developed. A sample of college calculus students (N=268; 124 females and 144 males) was administered a battery of cognitive tests (including measures of spatial-visual…

Stochastic calculus an introduction through theory and exercises

CERN Document Server

Baldi, Paolo

2017-01-01

This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical ...

Ancient DNA analysis of dental calculus.

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Weyrich, Laura S; Dobney, Keith; Cooper, Alan

2015-02-01

Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.

Research in collegiate mathematics education IV

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Dubinsky, Ed; Kaput, Jim

2001-01-01

This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume co

Analyzing Mathematics Beliefs of Pre-Service Teachers Using Confirmatory Factor Analysis

Directory of Open Access Journals (Sweden)

Mazlini Adnan

2011-12-01

Full Text Available Mathematics beliefs play an important role in enhancing the quality and the effectiveness of teaching and learning. This study analyzes the mathematics beliefs of 317 pre-service teachers from six Higher Education Institutions (HEIs (Government Public Universities who were randomly selected to participate in this study. Questionnaires consisting of twenty three items were given to the respondents during the data collection process. The validation of the items was done by using confirmatory factor analysis (CFA. In order to obtain a model fit for the measurement model of mathematics beliefs, several fit index tests such as CMINDF, GFI, AGFI, IFI, NFI, CFI, TLI and RMSEA were used. Constructivist beliefs and traditional beliefs were identified as the contributing factors in the model. The analysis also revealed that mathematics beliefs consist of structures of two hidden variables. The correlation between the two variables (constructivist beliefs and traditional beliefs is at a moderate level. Hence, pre-service teachers should be able to recognize their type of mathematics beliefs in order to become effective mathematics teachers.

Enhancing Student Writing and Computer Programming with LATEX and MATLAB in Multivariable Calculus

Science.gov (United States)

Sullivan, Eric; Melvin, Timothy

2016-01-01

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

Introduction to the calculus of variations

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Sagan, Hans

1992-01-01

Excellent text provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares readers for the study of modern optimal control theory. Treatment limited to extensive coverage of single integral problems in one and more unknown functions. Carefully chosen variational problems and over 400 exercises. ""Should find wide acceptance as a text and reference.""-American Mathematical Monthly. 1969 edition. Bibliography.

A Guided Tour of Mathematical Methods - 2nd Edition

Science.gov (United States)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

Discrete Calculus as a Bridge between Scales

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Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

Capsule calculus

CERN Document Server

Ritow, Ira

2003-01-01

This brief introductory text presents the basic principles of calculus from the engineering viewpoint. Excellent either as a refresher or as an introductory course, it focuses on developing familiarity with the basic principles rather than presenting detailed proofs.Topics include differential calculus, in terms of differentiation and elementary differential equations; integral calculus, in simple and multiple integration forms; time calculus; equations of motion and their solution; complex variables; complex algebra; complex functions; complex and operational calculus; and simple and inverse

Shifting Pre-Service Teachers' Beliefs about Mathematics Teaching: The Contextual Situation of a Mathematics Methods Course

Science.gov (United States)

Jao, Limin

2017-01-01

For pre-service teachers (PSTs) who have been exposed to traditional approaches, teacher education courses can be a revelatory experience in their development as educators. This study explores if Canadian upper elementary/lower secondary (grades 4-10) PSTs change their beliefs about mathematics teaching as a result of taking a mathematics methods…

Examining Pre-Service Mathematics Teachers' Conceptual Structures about "Geometry"

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Erdogan, Ahmet

2017-01-01

The aim of this study is to examine pre-service mathematics teachers' conceptual structures about "geometry". Qualitative research methodology has been adopted in the study. The data of the study is obtained from mathematics teacher candidates who have been students at the faculties of education of an Anatolian university in the academic…

A primer on the calculus of variations and optimal control theory

CERN Document Server

Mesterton-Gibbons, Mike

2009-01-01

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical softwa...

MODERN OR TRADITIONAL TEACHING STRATEGY IN LEARNING ENGINEERING MATHEMATICS COURSE

Directory of Open Access Journals (Sweden)

N. RAZALI

2016-11-01

Full Text Available First-year engineering students of the Faculty of Engineering and Built Environment, UKM are in the process of transition in the way they learn mathematics from pre-university level to the undergraduate level. It is essential for good engineers to have the ability to unfold mathematical problems in an efficient way. Thus, this research is done to investigate students preference in learning KKKQ1123 Engineering Mathematics I (Vector Calculus (VC course; either individually or in a team; using modern (e-learning or traditional (cooperative-learning teaching strategy. Questionnaires are given to the first year Chemical and Process Engineering students from academic year 2015/2016 and the results were analysed. Based on the finding, the students believed that the physical educators or teachers play an important role and that they have slightest preference in the traditional teaching strategy to learn engineering mathematics course.

The early period of the calculus of variations

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Freguglia, Paolo

2016-01-01

This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Addi...

Making Implicit Multivariable Calculus Representations Explicit: A Clinical Study

Science.gov (United States)

McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael

2015-01-01

Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…

Mathematical thinking and origami

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Wares, Arsalan

2016-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

Science.gov (United States)

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

Science.gov (United States)

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Mathematical Rigor in Introductory Physics

Science.gov (United States)

Vandyke, Michael; Bassichis, William

2011-10-01

Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

Science.gov (United States)

Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Mathematical logic foundations for information science

CERN Document Server

Li, Wei

2010-01-01

This book presents the basic principles and formal calculus of mathematical logic. It covers core contents, extensions and developments of classical mathematical logic, and it offers formal proofs and concrete examples for all theoretical results.

Secondary School Pre-Service Mathematics Teachers' Content Knowledge of Algebraic Word Problem in Nigeria

Science.gov (United States)

Usman, Ahmed Ibrahim

2015-01-01

Knowledge and understanding of mathematical operations serves as a pre-reequisite for the successful translation of algebraic word problems. This study explored pre-service teachers' ability to recognize mathematical operations as well as use of those capabilities in constructing algebraic expressions, equations, and their solutions. The outcome…

Investigating Classroom Teaching Competencies of Pre Service Elementary Mathematics Teachers

Science.gov (United States)

Gokalp, Murat

2016-01-01

The study has sought answers to two major questions: What is the current situation in Elementary Mathematics Education programs at Faculty of Education in terms of classroom teaching competencies? To what extent do pre service teachers acquire these competencies? The research was conducted on 202 senior pre service teachers studying at the…

An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking

Science.gov (United States)

Yavuz Mumcu, Hayal; Aktürk, Tolga

2017-01-01

The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…

Assessing the Impact of Computer Programming in Understanding Limits and Derivatives in a Secondary Mathematics Classroom

Science.gov (United States)

de Castro, Christopher H.

2011-01-01

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

Calculus

CERN Document Server

Larson, Ron

2014-01-01

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Difficulties First-Year University Mathematics Students Have in Reading Their Mathematics Textbook. Technical Report. No. 2009-1

Science.gov (United States)

Shepherd, Mary D.; Selden, Annie; Selden, John

2009-01-01

This exploratory study examined the experiences and difficulties certain first-year university students displayed in reading new passages from their mathematics textbooks. We interviewed eleven precalculus and calculus students who were considered to be good at mathematics, as indicated by high ACT mathematics scores. These students were also …

Continuation calculus

NARCIS (Netherlands)

Geron, B.; Geuvers, J.H.; de'Liguoro, U.; Saurin, A.

2013-01-01

Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

Science.gov (United States)

Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

2018-04-01

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

Handbook of mathematics

CERN Document Server

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

Electronic Algebra and Calculus Tutor

Directory of Open Access Journals (Sweden)

Larissa Fradkin

2012-06-01

Full Text Available Modern undergraduates join science and engineering courses with poorer mathematical background than most contemporaries of the current faculty had when they were freshers. The problem is very acute in the United Kingdom but more and more countries adopt less resource intensive models of teaching and the problem spreads. University tutors and lecturers spend more and more time covering the basics. However, most of them still rely on traditional methods of delivery which presuppose that learners have a good memory and considerable time to practice, so that they can memorize disjointed facts and discover for themselves various connections between the underlying concepts. These suppositions are particularly unrealistic when dealing with a large number of undergraduates who are ordinary learners with limited mathematics background. The first author has developed a teaching system that allows such adult learners achieve relatively deep learning of mathematics – and remarkably quickly – through a teacher-guided (often called Socratic dialog, which aims at the frequent reinforcement of basic mathematical abstractions through Eulerian sequencing. These ideas have been applied to create a prototype of a Cognitive Mathematics Tutoring System aimed at teaching basic mathematics to University freshers., an electronic Personal Algebra and Calculus Tutor (e- PACT.

A structural equation modeling of executive functions, IQ and mathematical skills in primary students: Differential effects on number production, mental calculus and arithmetical problems.

Science.gov (United States)

Arán Filippetti, Vanessa; Richaud, María Cristina

2017-10-01

Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.

Impact of Calculus Reform in a Liberal Arts Calculus Course.

Science.gov (United States)

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

Science.gov (United States)

Wagner, Elaine Rumsey; Orme, Susan Marla; Turner, Heidi Jean; Yopp, David

2017-01-01

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Multivariate Limits and Continuity: A Survey of Calculus Textbooks.

Science.gov (United States)

Thompson, Thomas M.; Wiggins, Kenneth L.

There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…

Calculus

CERN Document Server

Grossman, Stanley I

1981-01-01

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics

Solving applied mathematical problems with Matlab

CERN Document Server

Xue, Dingyu

2008-01-01

Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

Methods of applied mathematics

CERN Document Server

Hildebrand, Francis B

1992-01-01

This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.

Geometric Calculus -- Engineering Mathematics for the 21st century

OpenAIRE

HITZER, Eckhard MS

2002-01-01

This paper treats important questions at the interface of mathmatics and the engineering science. It starts off with a quick quotation tour through 2300 years of mathmatical history. At the beginning of the 21 century,technology has developed beyond every expectation. But do we also learn and practice an adequately modern form of mathmatics? The papaer argues that this role is very likely to be played by universal geometric calculus. The fundamental geometric product of vectors is introduced....

Operational calculus

CERN Document Server

Boehme, Thomas K

1987-01-01

Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho

The benefits of a 5-day dysphagia intensive placement

OpenAIRE

Cocks, N.; Harding, C.; Pritchard, M.

2014-01-01

Finding practical dysphagia opportunities for students pre-qualification is challenging. Discussions with clinicians led to the development of a new placement model. The placement was just five days and had an accompanying workbook. The current study aimed to evaluate the benefits of the placement. Data were analysed from 40 students who attended an adult dysphagia placement and 13 who attended a paediatric dysphagia placement. Measures included a pre and post self-rating questionnaire, quali...

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

International Nuclear Information System (INIS)

Huang, Chih-Hsien; Hsieh, Wen-Feng; Wu, Jing-Nuo; Cheng, Szu-Cheng; Li, Yen-Yin

2011-01-01

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.

Fractional Calculus in Hydrologic Modeling: A Numerical Perspective

Energy Technology Data Exchange (ETDEWEB)

David A. Benson; Mark M. Meerschaert; Jordan Revielle

2012-01-01

Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.

From Calculus to Wavelets: ANew Mathematical Technique

Indian Academy of Sciences (India)

expansions have many theoretical and practical ..... them into a rigorous mathematical theory. Meyer con- structed an ... engineers for signal processing, Ingrid Daubechies con- ..... and its applications on a somewhat higher mathematical level.

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Fundamentals of calculus

CERN Document Server

Morris, Carla C

2015-01-01

Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions

Using a communication audit to improve communication on clinical placement in pre-registration nursing.

Science.gov (United States)

Hogard, Elaine; Ellis, Roger; Ellis, Jackie; Barker, Chris

2005-02-01

This article describes a novel communication audit conducted with those concerned with the practice placements of pre-registration Nursing students. The study, uniquely, addressed all who were involved in communication concerning placement in what is described as an organisational analysis. The aim of the audit was to identify levels of satisfaction and dissatisfaction with present communication processes and to identify points for improvement. The audit used the Hogard-Barker Communication Audit of Practice a customized version of a well established tool, devised to cover issues relevant to practice placements. A key feature of the tool is the opportunity for participants to identify the amount of communication they are receiving on particular topics and issues against the amount they would like to receive. Participants in the audit included students, assessor mentors, ward managers, clinical facilitators and link tutors. Overall there was considerable dissatisfaction with what was perceived to be the insufficient amount of communication received on a number of topics including allocations, the curriculum, students' learning outcomes and commitments in terms of college work. In addition to identifying points for improvement the audit provides a baseline against which progress can be assessed through a future audit.

Boundary crossing and brokering between disciplines in pre-service mathematics teacher education

Science.gov (United States)

Goos, Merrilyn; Bennison, Anne

2017-12-01

In many countries, pre-service teacher education programs are structured so that mathematics content is taught in the university's mathematics department and mathematics pedagogy in the education department. Such program structures make it difficult to authentically interweave content with pedagogy in ways that acknowledge the roles of both mathematicians and mathematics educators in preparing future teachers. This article reports on a project that deliberately fostered collaboration between mathematicians and mathematics educators in six Australian universities in order to investigate the potential for learning at the boundaries between the two disciplinary communities. Data sources included two rounds of interviews with mathematicians and mathematics educators and annual reports prepared by each participating university over the three years of the project. The study identified interdisciplinary boundary practices that led to integration of content and pedagogy through new courses co-developed and co-taught by mathematicians and mathematics educators, and new approaches to building communities of pre-service teachers. It also developed an evidence-based classification of conditions that enable or hinder sustained collaboration across disciplinary boundaries, together with an empirical grounding for Akkerman and Bakker's conceptualisation of transformation as a mechanism for learning at the boundary between communities. The study additionally highlighted the ambiguous nature of boundaries and implications for brokers who work there to connect disciplinary paradigms.

Calculus for cognitive scientists derivatives, integrals and models

CERN Document Server

Peterson, James K

2016-01-01

This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors – a fact that must always be kept in mind.

A course in advanced calculus

CERN Document Server

Borden, Robert S

1997-01-01

This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as lim

A useful demonstration of calculus in a physics high school laboratory

Science.gov (United States)

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

Calculus refresher

CERN Document Server

Klaf, A A

1956-01-01

This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc

Secondary Schools Curriculum Guide, Mathematics, Grades 10-12. Revised.

Science.gov (United States)

Cranston School Dept., RI.

Behavioral objectives for grades 10 through 12 are specified for plane geometry, algebra, general mathematics, computer mathematics, slide rule mathematics, basic college mathematics, trigonometry, analytic geometry, calculus and probability. Most sections present material in terms of portions of a school year. At least one major objective is…

Line integral on engineering mathematics

Science.gov (United States)

Wiryanto, L. H.

2018-01-01

Definite integral is a basic material in studying mathematics. At the level of calculus, calculating of definite integral is based on fundamental theorem of calculus, related to anti-derivative, as the inverse operation of derivative. At the higher level such as engineering mathematics, the definite integral is used as one of the calculating tools of line integral. the purpose of this is to identify if there is a question related to line integral, we can use definite integral as one of the calculating experience. The conclusion of this research says that the teaching experience in introducing the relation between both integrals through the engineer way of thinking can motivate and improve students in understanding the material.

Setting visual pre-placement testing in a technology manufacturing environment.

Science.gov (United States)

Gowan, Nancy J

2014-01-01

Every day we use our eyes to perform activities of daily living and work. Aging changes as well as health conditions can impact an individual's visual function, making it more difficult to accurately perform work activities. Occupational therapists work closely with optometrists and employers to develop ways to accommodate for these changes so that the employee can continue to perform the work tasks. This manuscript outlines a case study of systematically developing visual demands analyses and pre-placement vision screening assessment protocols for individuals completing quality inspection positions. When the vision screening was completed, it was discovered that over 20% of the employees had visual deficits that were correctable. This screening process yielded improved quality results but also identification of previously undetected visual deficits. Further development of vision screening in the workplace is supported.

Simulating non-prenex cuts in quantified propositional calculus

Czech Academy of Sciences Publication Activity Database

Jeřábek, Emil; Nguyen, P.

2011-01-01

Roč. 57, č. 5 (2011), s. 524-532 ISSN 0942-5616 R&D Projects: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * prenex cuts * quantified propositional calculus Subject RIV: BA - General Mathematics Impact factor: 0.496, year: 2011 http://onlinelibrary.wiley.com/doi/10.1002/malq.201020093/abstract

Engineering mathematics-II

CERN Document Server

Ganesh, A

2009-01-01

About the Book: This book Engineering Mathematics-II is designed as a self-contained, comprehensive classroom text for the second semester B.E. Classes of Visveswaraiah Technological University as per the Revised new Syllabus. The topics included are Differential Calculus, Integral Calculus and Vector Integration, Differential Equations and Laplace Transforms. The book is written in a simple way and is accompanied with explanatory figures. All this make the students enjoy the subject while they learn. Inclusion of selected exercises and problems make the book educational in nature. It shou

A Professional Experience Model for Primary Pre-Service Teachers Specialising in Mathematics

Science.gov (United States)

McMaster, Heather; Cavanagh, Michael

2016-01-01

Many primary pre-service teachers (PSTs) who are enthused by tertiary courses that espouse and model a socio-constructivist approach to teaching mathematics, revert to a traditional approach when they encounter mathematics teaching during professional experience. An intervention was designed to translate the initial pedagogical intent of four…

The role of a posteriori mathematics in physics

Science.gov (United States)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

Einstein's Theory A Rigorous Introduction for the Mathematically Untrained

CERN Document Server

Grøn, Øyvind

2011-01-01

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.  Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and genera...

The Use of Peer Tutoring to Improve the Passing Rates in Mathematics Placement Exams of Engineering Students: A Success Story

Science.gov (United States)

García, Rolando; Morales, Juan C.; Rivera, Gloribel

2014-01-01

This paper describes a highly successful peer tutoring program that has resulted in an improvement in the passing rates of mathematics placement exams from 16% to 42%, on average. Statistical analyses were conducted using a Chi-Squared (?[superscript 2]) test for independence and the results were statistically significant (p-value much less than…

Stochastic calculus and applications

CERN Document Server

Cohen, Samuel N

2015-01-01

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...

Pre-service teachers’ TPACK competencies for spreadsheet integration: insights from a mathematics-specific instructional technology course

NARCIS (Netherlands)

Agyei, D.D.; Voogt, J.M.

2015-01-01

This article explored the impact of strategies applied in a mathematics instructional technology course for developing technology integration competencies, in particular in the use of spreadsheets, in pre-service teachers. In this respect, 104 pre-service mathematics teachers from a teacher training

An Investigation into the Perceptions of Mathematics and Information Literacy Self-Efficacy Levels of Pre-Service Primary Mathematics Teachers

Science.gov (United States)

Dinçer, Bahar; Yilmaz, Süha

2016-01-01

The purpose of this study is to examine the relationship between perceptions of the self-efficacy levels for both mathematics literacy and information literacy in pre-service primary mathematics teachers and the factors on which the relationship depends (variables include gender, class level, hours spent reading books and computer-access…

Fundamentals of scientific mathematics

CERN Document Server

Owen, George E

2003-01-01

Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.

A Glossary for Pre-Calculus

Science.gov (United States)

Arnold, Bruce; Kracht, Brenda; Ross, Judy; Teegarden, Terrie; Tompkins, Maurice

2012-01-01

In the deconstruction of the California state standards for trigonometry, linear algebra and mathematical analysis for the Cal-PASS (California Partnership for Achieving Student Success) Content Standards Deconstruction projects, it became apparent that terms were used for which no definition was given. The San Diego Central Cal-PASS Math…

Predicting Performance in a First Engineering Calculus Course: Implications for Interventions

Science.gov (United States)

Hieb, Jeffrey L.; Lyle, Keith B.; Ralston, Patricia A. S.; Chariker, Julia

2015-01-01

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take "Engineering Analysis I," a calculus-based engineering analysis course. After the…

Cause-effect analysis: improvement of a first year engineering students' calculus teaching model

Science.gov (United States)

van der Hoff, Quay; Harding, Ansie

2017-01-01

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of mathematics, factors that the tertiary sector has no control over. The analysis also indicates the undesirable issues that are at the root of impeding success in the calculus module. Most important is that students are not encouraged to become independent thinkers from an early age. This triggers problems in follow-up courses where students are expected to have learned to deal with the work load and understanding of certain concepts. A new model was designed to lessen the impact of these undesirable issues.

Fractional Dynamics Applications of Fractional Calculus to Dynamics of Particles, Fields and Media

CERN Document Server

Tarasov, Vasily E

2010-01-01

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and...

The Impacts of a Service-Learning Experience on Pre-Service Mathematics Teachers

Science.gov (United States)

Lee, Kyong-Hee; Statham, Anne

2010-01-01

This study examines the benefits that can be achieved by pre-service teachers tutoring mathematics in after school programs. Analysis of student journal entries show enhanced ability to meet National Council of Teachers of Mathematics' (NCTM) process standards and methods of assessment, as well as greater awareness of the need to teach to…

Co-operation Between Science Teachers and Mathematics Teachers. Volumes 1-6.

Science.gov (United States)

Rogerson, Alan, Ed.

This document contains six separate works, titled: (1) Functions and Physics; (2) Links Between Geography and Mathematics; (3) Our Inheritance: Common Ground for the Mathematics and Biology Teacher; (4) Mathematics and Chemistry: The Classroom Interface; (5) Mathematical Modeling; and (6) Mathematical Modeling with Calculus. This series of…

Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

Science.gov (United States)

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

[Clinical analysis of 41 children's urinary calculus and acute renal failure].

Science.gov (United States)

Li, Lu-Ping; Fan, Ying-Zhong; Zhang, Qian; Zhang, Sheng-Li

2013-04-01

To analyze the treatment of acute renal failure caused by irrational drug use. Data of 41 cases of acute renal failure seen from July 2008 to June 2012 in our hospital were reviewed. Bilateral renal parenchymas diffuse echo was found enhanced by ultrasound in all cases. Calculus image was not found by X-ray. All children had medical history of using cephalosporins or others. Alkalinization of urine and antispasmodic treatment were given to all children immediately, 17 children were treated with hemodialysis and 4 children accepted intraureteral cannula placement. In 24 children who accepted alkalinization of urine and antispasmodic treatment micturition could be restored within 24 hours, in 11 children micturition recovered after only one hemodialysis treatment and 2 children gradually restored micturition after hemodialysis twice, 4 children who accepted intraureteral cannula immediately restored micturition. In all children micturition recovered gradually after a week of treatment. Ultrasound examination showed that 39 children's calculus disappeared totally and renal parenchymas echo recovered to normal. The residual calculi with diameter less than 5 mm were found in 2 children, but they had no symptoms. The children received potassium sodium hydrogen citrate granules per os and were discharged from hospital. Ultrasound showed calculus disappeared totally one month later. Irrational drug use can cause children urolithiasis combined with acute renal failure, while renal dysfunction can reverse by drug withdrawal and early alkalinization of urine, antispasmodic treatment, intraureteral cannula or hemodialysis when necessary, most calculus can be expelled after micturition recovered to normal.

Gribov's reggeon calculus: its physical basis and implications

International Nuclear Information System (INIS)

Baker, M.; Ter-Martirosyan, K.A.

1976-01-01

The equations of Gribov's Reggeon calculus and the cutting rules of Abramovskii, Gribov and Kancheli are derived from the assumption that processes involving large virtual masses are damped. The discussion is carried out entirely in the s channel and no use is made of the details of any particular field theory. Both the mathematical development and the physical picture which evolves rest on the assumed multiperipheral origin of Regge behavior. (Auth.)

Students Build Mathematical Theory: Semantic Warrants in Argumentation

Science.gov (United States)

Walter, Janet G.; Barros, Tara

2011-01-01

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

The Characteristic of the Process of Students' Metacognition in Solving Calculus Problems

Science.gov (United States)

Purnomo, Dwi; Nusantara, Toto; Subanji; Rahardjo, Swasono

2017-01-01

This article is the result of research aims to describe the patterns and characteristics of the process of metacognition student of mathematics in solving calculus problems. Description was done by looking at changes in "awareness," "evaluation," and "regulation" as components of metacognition. The changes in…

The Negative Sign and Exponential Expressions: Unveiling Students' Persistent Errors and Misconceptions

Science.gov (United States)

Cangelosi, Richard; Madrid, Silvia; Cooper, Sandra; Olson, Jo; Hartter, Beverly

2013-01-01

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

Propositional Calculus in Coq

OpenAIRE

van Doorn, Floris

2015-01-01

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.

Quantifying the advantages and disadvantages of pre-placement genetic screening.

Science.gov (United States)

Palmer, K T; Poole, J; Rawbone, R G; Coggon, D

2004-05-01

Tests of genotype may enable workers at unusual risk of future ill-health to be identified. Using them to select for employment, however, entails gains and losses to employers and employees. Ensuring a fair balance between the rights and obligations of each group requires a value judgement, but the advantages and disadvantages to interested parties must first be quantified in a meaningful way. The purposes of pre-employment screening are reviewed, and several simple measures relevant to the separate interests of employers and job applicants proposed-number screened to prevent a single adverse outcome; number excluded to prevent a case; expected incidence of the adverse outcome in those excluded; and preventable fraction. The derivation of these measures is illustrated, and the factors that influence them (the prevalence of the prognostic trait, the relative risk that it carries for an adverse outcome, and the overall incidence of disease) are related algebraically and graphically, to aid judgement on the utility of screening under different circumstances. In sensitive areas such as genetic testing the onus should be on the employer to justify plans for pre-placement screening. Several quantitative measures can be used to inform the ethical and economic debate about screening and to evaluate alternative strategies for prevention.

Pre-Service Teachers' TPACK Competencies for Spreadsheet Integration: Insights from a Mathematics-Specific Instructional Technology Course

Science.gov (United States)

Agyei, Douglas D.; Voogt, Joke M.

2015-01-01

This article explored the impact of strategies applied in a mathematics instructional technology course for developing technology integration competencies, in particular in the use of spreadsheets, in pre-service teachers. In this respect, 104 pre-service mathematics teachers from a teacher training programme in Ghana enrolled in the mathematics…

Teaching and Learning Calculus in Secondary Schools with the TI-Nspire

Science.gov (United States)

Parrot, Mary Ann Serdina; Eu, Leong Kwan

2014-01-01

Technology can help develop understanding of abstract mathematical concepts through visualisation and graphic representation. The teaching and learning of calculus can be challenging as it involves abstract and complex ideas. The purpose of this study was to investigate how students and teachers attempt to use TI-Nspire, the latest graphing…

Tuplix Calculus

OpenAIRE

Bergstra, J. A.; Ponse, A.; van der Zwaag, M. B.

2007-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio...

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Mathematics and the physical world

CERN Document Server

Kline, Morris

1981-01-01

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

A bridge to advanced mathematics

CERN Document Server

Sentilles, Dennis

2011-01-01

This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a

Mathematics

International Nuclear Information System (INIS)

Demazure, M.

1988-01-01

The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

Continuation calculus

Directory of Open Access Journals (Sweden)

Bram Geron

2013-09-01

Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.

k-Schur functions and affine Schubert calculus

CERN Document Server

Lam, Thomas; Morse, Jennifer; Schilling, Anne; Shimozono, Mark; Zabrocki, Mike

2014-01-01

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with ...

Mathematical preparedness for tertiary mathematics – a need for ...

African Journals Online (AJOL)

Ongoing action research at the University of Pretoria investigates first-year students' preparedness for a study in calculus. In 2005 first-year engineering students completed a mathematics diagnostic survey at the beginning and end of the year. In this article the results of the 2005 survey are compared with the students' final ...

The Role and Relevance of Mathematics in the Maritime Industry

African Journals Online (AJOL)

kofi.mereku

symmetry in chemistry and physics; Calculus (differential equations) applicable in ... and engineering; and is a branch of applied mathematics. .... The maritime and offshore industries use advanced mathematical methods in the design of ships.

Sixth form pure mathematics

CERN Document Server

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

Placement Model for First-Time Freshmen in Calculus I (Math 131): University of Northern Colorado

Science.gov (United States)

Heiny, Robert L.; Heiny, Erik L.; Raymond, Karen

2017-01-01

Two approaches, Linear Discriminant Analysis, and Logistic Regression are used and compared to predict success or failure for first-time freshmen in the first calculus course at a medium-sized public, 4-year institution prior to Fall registration. The predictor variables are high school GPA, the number, and GPA's of college prep mathematics…

Mathematics Course Placement Using Holistic Measures: Possibilities for Community College Students

Science.gov (United States)

Ngo, Federick; Chi, W. Edward; Park, Elizabeth So Yun

2018-01-01

Background/Context: Most community colleges across the country use a placement test to determine students' readiness for college-level coursework, yet these tests are admittedly imperfect instruments. Researchers have documented significant problems stemming from overreliance on placement testing, including placement error and misdiagnosis of…

Intuitionistic fuzzy calculus

CERN Document Server

Lei, Qian

2017-01-01

This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.

Go Figure: Calculus Students' Use of Figures and Graphs in Technical Report Writing

Directory of Open Access Journals (Sweden)

Thomas J. Pfaff

2011-01-01

Full Text Available Understanding how to read and use graphs to communicate scientific and mathematical information is critical for STEM majors, as well as an important part of quantitative literacy. Our study suggests that first-semester calculus students do not know how to use graphs in a technical report without explicit instruction. Although not a surprising result, it leaves us wondering about when such skills are developed, and if calculus I is a place to start. Our work is now exploring the potential benefit on students' use of graphs by having them formally evaluate other students' reports.

Secondary Mathematics Pre-Service Teachers' Processes of Selection and Integration of Technology

Science.gov (United States)

Uzan, Erol

2017-01-01

This study investigated secondary mathematics pre-service teachers' (PSTs) knowledge of resources in terms of digital technologies, and explored the processes of both selection and integration of technology into their lesson plans. This study employed a case study design. Participants were six secondary mathematics PSTs who enrolled in a methods…

Investigating the Representational Fluency of Pre-Service Mathematics Teachers in a Modelling Process

Science.gov (United States)

Delice, Ali; Kertil, Mahmut

2015-01-01

This article reports the results of a study that investigated pre-service mathematics teachers' modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students' individual and group written responses to the mathematical modelling…

Pre-service teachers' experiences teaching secondary mathematics in English-medium schools in Tanzania

Science.gov (United States)

Kasmer, Lisa

2013-09-01

In order to promote mathematical understanding among English Language Learners (ELLs), it is necessary to modify instructional strategies to effectively communicate mathematical content. This paper discusses the instructional strategies used by four pre-service teachers to teach mathematics to secondary students in English-medium schools in Arusha, Tanzania as a result of the tensions they faced and reflections on their teaching. Strategies such as code switching, attending to sentence structure, non-linguistic representations, and placing the content within a familiar context proved to be beneficial strategies for conveying mathematical ideas.

Early Vector Calculus: A Path through Multivariable Calculus

Science.gov (United States)

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

The Effects of GeoGebra Software on Pre-Service Mathematics Teachers' Attitudes and Views toward Proof and Proving

Science.gov (United States)

Zengin, Yilmaz

2017-01-01

The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used…

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Calculus Limits Involving Infinity: The Role of Students' Informal Dynamic Reasoning

Science.gov (United States)

Jones, Steven R.

2015-01-01

Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus…

Continental Mathematics League.

Science.gov (United States)

Quartararo, Joseph

2002-01-01

This article describes the activities of the Continental Mathematics League, which offers a series of meets for children in grades 3 though 9. In addition, a Calculus League and a Computer Contest are offered. The league allows schools to participate by mail so that rural schools can participate. (CR)

[Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

Science.gov (United States)

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P Calculus Bovis group was higher than combination group (P Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

Investigating Pre-Service Mathematics Teachers' Innovation Awareness and Views Regarding Intelligent Tutoring Systems

Science.gov (United States)

Erdemir, Mustafa; Ingeç, Sebnem Kandil

2016-01-01

The purpose of this study is to identify pre-service primary mathematics teachers' views regarding on Web-based Intelligent Tutoring Systems (WBITS) in relation to its usability and influence on teaching. A survey method was used. The study was conducted with 43 students attending the mathematics teaching program under the department of elementary…

Traditional vs. Innovative Uses of Computers among Mathematics Pre-Service Teachers in Serbia

Science.gov (United States)

Teo, Timothy; Milutinovic, Verica; Zhou, Mingming; Bankovic, Dragic

2017-01-01

This study examined pre-service teachers' intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers' experience with computers and their technological pedagogical content knowledge (TPCK).…

Boolean-Like and Frequentistic Nonstandard Semantics for First-Order Predicate Calculus without Functions

Czech Academy of Sciences Publication Activity Database

Kramosil, Ivan

2001-01-01

Roč. 5, č. 1 (2001), s. 45-57 ISSN 1432-7643 R&D Projects: GA AV ČR IAA1030803 Institutional research plan: AV0Z1030915 Keywords : first-order predicate calculus * standard semantics * Boolean-like semantics * frequentistic semantics * completness theorems Subject RIV: BA - General Mathematics

Ureterolithotripsy for a Ureteral Calculus at the Ureteroureterostomy of a Renal-transplant Recipient.

Science.gov (United States)

Mitsui, Yosuke; Wada, Koichiro; Araki, Motoo; Yoshioka, Takashi; Ariyoshi, Yuichi; Nishimura, Shingo; Kobayashi, Yasuyuki; Sasaki, Katsumi; Watanabe, Toyohiko; Nasu, Yasutomo

2017-10-01

We describe a 40-year-old living-donor renal-transplant recipient who underwent successful ureterolithotripsy. He had been on hemodialysis for >15 years pre-transplant and underwent ureteroureterostomy along with the surgery. One year post-transplant, ultrasound examination demonstrated hydronephrosis, and CT showed a 6-mm ureteral calculus at the ureteroureterostomy site. No pain and no elevated serum creatinine were present. As the ureter was easily accessed, we performed a ureterolithotripsy, which would confirm whether a suture caused the calculus. Despite ureteral tortuosity, laser stone fragmentation succeeded. The calculus was completely removed with an antegrade guidewire. Mild postoperative ureteral stenosis resolved with a temporary ureteral stent without balloon dilation. Ureterolithotripsy is effective even in renal transplant recipients with ureteroureterostomy.

Mathematics and electromagnetism

International Nuclear Information System (INIS)

Rodriguez Danta, M.

2000-01-01

Symbiosis between mathematics and electromagnetism is analyzed in a simple and concise manner by taking a historical perspective. The universal tool character of mathematical models allowed the transfer of models from several branches of physics into the realm of electromagnetism by drawing analogies. The mutual interdependence between covariant formulation and tensor calculus is marked. The paper focuses on the guiding idea of field theory and Maxwell's equations. Likewise, geometrization of interactions in connection with gauge fields is also noted. (Author)

Simplicial lattices in classical and quantum gravity: Mathematical structure and application

International Nuclear Information System (INIS)

LaFave, N.J.

1989-01-01

Geometrodynamics can be understood more clearly in the language of geometry than in the language of differential equations. This is the primary motivation for the development of calculational schemes based on Regge Calculus as an alternative to those schemes based on Ricci Calculus. The author develops the mathematics of simplicial lattices to the same level of sophistication as the mathematics of pseudo-Riemannian geometry for continuum manifolds. This involves the definition of the simplicial analogues of several concepts from differential topology and differential geometry-the concept of a point, tangent spaces, forms, tensors, parallel transport, covariant derivatives, connections, and curvature. These simplicial analogues are used to define the Einstein tensor and the extrinsic curvature on a simplicial geometry. He applies this mathematical formalism to the solution of several outstanding problems in the development of a Regge Calculus based computational scheme for general geometrodynamic problems. This scheme is based on a 3 + 1 splitting of spacetime within the Regge Calculus prescription known as Null-Strut Calculus (NSC). NSC, developed by Warner Miller, describes the foliation of spacetime into spacelike hypersurfaces built of tetrahedra. The outstanding problems discussed include (a) the rigidification of the 3-layered sandwich and the evolution problem; (b) the formulation of initial data; and (c) in inclusion of matter on the lattice. The resulting calculational scheme is applied to two test problems, the Friedmann model and the second-order Doppler effect. Finally, he describes avenues of investigation for NSC in quantum gravity

Teaching Mathematics to Civil Engineers

Science.gov (United States)

Sharp, J. J.; Moore, E.

1977-01-01

This paper outlines a technique for teaching a rigorous course in calculus and differential equations which stresses applicability of the mathematics to problems in civil engineering. The method involves integration of subject matter and team teaching. (SD)

Implementation of Technology in an Elementary Mathematics Lesson: The Experiences of Pre-Service Teachers at One University

Science.gov (United States)

Herron, Julie

2010-01-01

This study examined pre-service teachers' responses to implementing technology into elementary mathematics lessons. Instructional Architect (IA) was the web-base technology used by the pre-service teachers. Four themes emerged from the data: (a) insights into technology, (b) struggles with technology, (c) access to the mathematics and (d) learning…

Summability calculus a comprehensive theory of fractional finite sums

CERN Document Server

Alabdulmohsin, Ibrahim M

2018-01-01

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergr...

Self-Perceptions of Pre-Service Mathematics Teachers Completing a Graduate Diploma of Secondary Education

Science.gov (United States)

Hine, Gregory S. C.

2015-01-01

This qualitative research project explored the self-perceptions of pre-service secondary mathematics teachers completing a Graduate Diploma of Secondary Education. Specifically, the researcher investigated the extent to which teachers perceived their readiness to commence a secondary mathematics teaching position. The project relied principally on…

Gestures and Insight in Advanced Mathematical Thinking

Science.gov (United States)

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

Rare calcium oxalate monohydrate calculus attached to the wall of the renal pelvis.

Science.gov (United States)

Grases, Felix; Costa-Bauza, Antonia; Prieto, Rafael M; Saus, Carlos; Servera, Antonio; García-Miralles, Reyes; Benejam, Joan

2011-04-01

Most renal calculi can be classified using well-established criteria in a manner that reflects both composition and fine structure under specific pathophysiological conditions. However, when a large patient population is considered, rare renal calculi invariably appear, some of which have never been classified; careful study is required to establish stone etiology in such cases. The patient in the present case report formed two types of calculi. One was attached on the wall of the renal pelvis near the ureter and part of the calculus was embedded inside pelvic renal tissue. The calculus developed on an ossified calcification located in the pelvis tissue. Current knowledge on the development of calcification in soft tissues suggests a pre-existing injury as an inducer of its development. A mechanism of calculus formation is proposed. The second stone was a typical jack-stone calculus. © 2011 The Japanese Urological Association.

Research in collegiate mathematics education VI

CERN Document Server

Selden, Annie; Harel, Guershon; Hauk, Shandy

2006-01-01

The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based

Tuplix calculus

NARCIS (Netherlands)

Bergstra, J.A.; Ponse, A.; van der Zwaag, M.B.

2008-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy

Energy Technology Data Exchange (ETDEWEB)

Juan, Hsu-Cheng; Chou, Yii-Her [Kaohsiung Medical University Hospital, Department of Urology, Kaohsiung (China); Lin, Hung-Yu [Kaohsiung Medical University, Graduate Institute of Medicine, Kaohsiung (China); E-Da Hospital/ I-Shou University, Department of Urology, Kaohsiung (China); Yang, Yi-Hsin [Kaohsiung Medical University, Institute of Oral Health Sciences, Kaohsiung (China); Shih, Paul Ming-Chen [Kaohsiung Municipal Hsiao-Kang Hospital, Department of Radiology, Kaohsiung (China); Kaohsiung Medical University, Department of Radiology, Kaohsiung (China); Chuang, Shu-Mien [Yuh-Ing Junior College of Health Care and Management, Kaohsiung (China); Shen, Jung-Tsung [Kaohsiung Municipal Hsiao-Kang Hospital, Department of Urology, Kaohsiung (China); Juan, Yung-Shun [Kaohsiung Medical University Hospital, Department of Urology, Kaohsiung (China); Kaohsiung Medical University, Graduate Institute of Medicine, Kaohsiung (China); Kaohsiung Medical University, Department of Urology, Faculty of Medicine, Kaohsiung (China)

2012-08-15

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. (orig.)

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy

International Nuclear Information System (INIS)

Juan, Hsu-Cheng; Chou, Yii-Her; Lin, Hung-Yu; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-01-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. (orig.)

Calculus problems

CERN Document Server

Baronti, Marco; van der Putten, Robertus; Venturi, Irene

2016-01-01

This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-...

Beliefs and Attitudes about Science and Mathematics in Pre-Service Elementary Teachers, STEM, and Non-STEM Majors in Undergraduate Physics Courses

Science.gov (United States)

Michaluk, Lynnette; Stoiko, Rachel; Stewart, Gay; Stewart, John

2018-04-01

Elementary teachers often hold inaccurate beliefs about the Nature of Science (NoS) and have negative attitudes toward science and mathematics. Using a pre-post design, the current study examined beliefs about the NoS, attitudes toward science and mathematics, and beliefs about the teaching of mathematics and science in a large sample study ( N = 343) of pre-service teachers receiving a curriculum-wide intervention to improve these factors in comparison with Science, Technology, Engineering, and Mathematics (STEM) and non-STEM majors in other physics courses ( N = 6697) who did not receive the intervention, over a 10-year period. Pre-service teachers evidenced initially more negative attitudes about mathematics and science than STEM majors and slightly more positive attitudes than non-STEM majors. Their attitudes toward mathematics and science and beliefs about the NoS were more similar to non-STEM than STEM majors. Pre-service teachers initially evidenced more positive beliefs about the teaching of mathematics and science, and their beliefs even increased slightly over the course of the semester, while these beliefs in other groups remained the same. Beliefs about the NoS and the teaching of mathematics and science were significantly negatively correlated for STEM and non-STEM majors, but were not significantly correlated for pre-service teachers. Beliefs about the NoS and attitudes toward mathematics and science were significantly positively correlated for both pre-service teachers and STEM students pursing the most mathematically demanding STEM majors. Attitudes toward science and mathematics were significantly positively correlated with accurate beliefs about the teaching of mathematics and science for all student groups.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Rémi Léandre. Articles written in Proceedings – Mathematical Sciences. Volume 116 Issue 4 November 2006 pp 507-518 Non-commutative Probability Theory. Malliavin Calculus of Bismut Type without Probability · Rémi Léandre · More Details Abstract Fulltext PDF.

Using Technology (Instead of Calculus) To Derive the Law of Reflection for Parabolic Mirrors from Fermat's Principle of Least Time.

Science.gov (United States)

Helfgott, Michel; Simonsen, Linda M.

1998-01-01

Presents an activity to investigate physico-mathematical concepts and provide mathematics arguments that are very close to a proof with the advent and availability of powerful technology. Demonstrates without using calculus how the law of reflection for parabolas is derived from Fermat's principle of least time. (ASK)

Integrating HIV & AIDS education in pre-service mathematics education for social justice

Directory of Open Access Journals (Sweden)

Linda van Laren

2011-01-01

Full Text Available Since 1999, many South African education policy documents have mandated integration of HIV & AIDS education in learning areas/disciplines. Policy document research has shown that although South African politicians and managers have produced volumes of eloquent and compelling legislation regarding provision for HIV & AIDS education, little of this is translated into action. The impact of HIV & AIDS permeates the social, economic and political arenas in South Africa. Integration of HIV & AIDS education across disciplines can serve as a strategy to further the ideals of social justice. This paper focuses on how integration in the teaching and learning of Mathematics Education provides opportunities to take action for social justice. The inquiry explores the following question: How can the myth that there is 'nothing we can do' about HIV & AIDS, which is linked to social justice issues, be addressed through integration of HIV & AIDS education in Mathematics pre-service teacher education? Drawing on self-study, the work of a Mathematics teacher educator who worked with pre-service teachers to integrate HIV & AIDS education at a higher education institution is described. By considering integration of HIV & AIDS education in Mathematics Education and taking action it is possible to develop strategies which directly relate to social justice.

Tensor calculus, relativity, and cosmology a first course

CERN Document Server

Dalarsson, M

2005-01-01

This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses

Calculus of one variable

CERN Document Server

Grossman, Stanley I

1986-01-01

Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students.

Time scales: from Nabla calculus to Delta calculus and vice versa via duality

OpenAIRE

Caputo, M. Cristina

2009-01-01

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

A professional experience learning community for secondary mathematics: developing pre-service teachers' reflective practice

Science.gov (United States)

Cavanagh, Michael; McMaster, Heather

2015-12-01

This paper reports on the reflective practice of a group of nine secondary mathematics pre-service teachers. The pre-service teachers participated in a year-long, school-based professional experience program which focussed on observing, co-teaching and reflecting on a series of problem-solving lessons in two junior secondary school mathematics classrooms. The study used a mixed methods approach to consider the impact of shared pedagogical conversations on pre-service teachers' written reflections. It also examined whether there were differences in the focus of reflections depending on whether the lesson was taught by an experienced mathematics teacher, or taught by a pair of their peers, or co-taught by themselves with a peer. Results suggest that after participants have observed lessons taught by an experienced teacher and reflected collaboratively on those lessons, they continue to reflect on lessons taught by their peers and on their own lessons when co-teaching, rather than just describe or evaluate them. However, their written reflections across all contexts continued to focus primarily on teacher actions and classroom management rather than on student learning.

DOE Fundamentals Handbook: Mathematics, Volume 1

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

DOE Fundamentals Handbook: Mathematics, Volume 2

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

An Introduction to Business Mathematics

OpenAIRE

Henk van Elst

2015-01-01

These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output matrix model, linear programming, elementary financial mathematics, as well as differential and integral calculus of real-valued functions of one real variable. A special focus...

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

Science.gov (United States)

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

Cross-Cultural Communication in Teacher Education: A Case Study of an Australian Pre-Service Teacher Placement in Liaoning, China

Science.gov (United States)

Jin, Aijing; Cooper, Maxine; Golding, Barry

2016-01-01

This paper presents a case study of the experiences and reflections of four fourth year pre-service teachers from Federation University Australia who completed their three-week teaching placement in Anshan, Liaoning Province, China, in April 2014. The study also explores the perspectives and opinions of both the Chinese mentor teachers and Chinese…

The calculus lifesaver all the tools you need to excel at calculus

CERN Document Server

Banner, Adrian

2009-01-01

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of

Bridging a Cultural Gap

Science.gov (United States)

Leviatan, Talma

2008-01-01

There has been a broad wave of change in tertiary calculus courses in the past decade. However, the much-needed change in tertiary pre-calculus programmes--aimed at bridging the gap between high-school mathematics and tertiary mathematics--is happening at a far slower pace. Following a discussion on the nature of the gap and the objectives of a…

Connecting Mathematics and Literature: An Analysis of Pre-Service Elementary School Teachers' Changing Beliefs and Knowledge

Science.gov (United States)

Wilburne, Jane M.; Napoli, Mary

2008-01-01

The National Council of Teachers of Mathematics calls for students to see relationships and connections with mathematics (2000). This study examined the influences on eight pre-service elementary school teachers' beliefs and knowledge of teaching mathematics through literature. The semester long project involved both the language arts and…

Spontaneous emission near the band edge of a three-dimensional photonic crystal: a fractional calculus approach

International Nuclear Information System (INIS)

Cheng, S-C; Wu, J-N; Tsai, M-R; Hsieh, W-F

2009-01-01

We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.

Investigating a Link between Pre-Calculus Students' Uses of Graphing Calculators and Their Understanding of Mathematical Symbols

Science.gov (United States)

Kenney, Rachael H.

2014-01-01

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

Calculus of variations an introduction to the one-dimensional theory with examples and exercises

CERN Document Server

Kielhöfer, Hansjörg

2018-01-01

This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself.  Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous th...

Engineering-Based Problem Solving Strategies in AP Calculus: An Investigation into High School Student Performance on Related Rate Free-Response Problems

Science.gov (United States)

Thieken, John

2012-01-01

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple…

Mathematics for quantum chemistry

CERN Document Server

Anderson, Jay Martin

2005-01-01

This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.

Applying π-Calculus to Practice

DEFF Research Database (Denmark)

Abendroth, Jorg

2003-01-01

The π-Calculus has been developed to reason about behavioural equivalence. Different notations of equivalence are defined in terms of process interactions, as well as the context of processes. There are various extensions of the π-Calculus, such as the SPI calculus, which has primitives...... modles are instantiated correctly. In this paper we will utilize the to π-Calculus reason about access control policies and mechanism. An equivalence of different policy implementations, as well as access control mechanism will be shown. Finally some experiences regarding the use of π-Calculus...

Mathematical tapas

CERN Document Server

Hiriart-Urruty, Jean-Baptiste

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.

Mathematical analysis fundamentals

CERN Document Server

Bashirov, Agamirza

2014-01-01

The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric o

Exploring Preservice Mathematics Teachers' Perception of the Mathematics Teacher through Communities of Practice

Science.gov (United States)

Akkoç, Hatice; Balkanlioglu, Mehmet Ali; Yesildere-Imre, Sibel

2016-01-01

This research aimed to analyse the induction experiences of preservice mathematics teachers during their school placements through the lens of communities of practice. The main research question was concerned with how preservice mathematics teachers perceive what constitutes the practice of a professional community of mathematics teachers. A…

Calculus Problem Solution And Simulation Using GUI Of Matlab

Directory of Open Access Journals (Sweden)

Syaharuddin

2017-09-01

Full Text Available This research aims to develop the project application in teaching and learning Calculus using Grapichal User Interface GUI of Matlab. The scope of the development result includes 1 PreCalculus 2 Function Limit 3 Derivative and its application and 4 Integral and its application. Every aspect of development is presented according to the standards of material competence learning achievement indicators and solutions or settlement steps on each issue presented. This project application can be used by lecturers and students in universities to improve motivation mastery of material and student learning outcomes in the Calculus course. Development of this project application is done through 4 stages called 4-D namely Define Design Development and Dissemination. Based on the data analysis the results obtained at the validation stage of expert validity level average of 3.575 which means quite valid. Then on a limited trial the average student gave a response of 92.00 which means very good. While in the first field trial the average student gave a response of 89.30 which means very good and in the second field trial the average student gave a responded of 90.15 which means very good. Besides that we also solve computational calculus problems in Edwin J. Purcell Dale Varbergs Book of Volume 1 of Edition 5 of 48 questions that are divided into 64 cases.

A generalized nonlocal vector calculus

Science.gov (United States)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

University Students' Reading of Their First-Year Mathematics Textbooks

Science.gov (United States)

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…

Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

Science.gov (United States)

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

Handbook of mathematical formulas and integrals

CERN Document Server

Jeffrey, Alan

2003-01-01

The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik''s Table of Integrals, Series, and Products and other important reference works.The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation.Key Features: * Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results * Contents selected and organized to suit the needs of students, scientists, and engineers * Contains tables of Laplace and Fourier transfor...

Pre-Service Teacher Training on Game-Enhanced Mathematics Teaching and Learning

Science.gov (United States)

Meletiou-Mavrotheris, Maria; Prodromou, Theodosia

2016-01-01

The paper reports the main insights from a study aimed at equipping a group of pre-service teachers with the knowledge, skills, and practical experience required to effectively integrate educational games within the mathematics curriculum. An instructional intervention based on the Technological Pedagogical and Content Knowledge framework was…

Cause-Effect Analysis: Improvement of a First Year Engineering Students' Calculus Teaching Model

Science.gov (United States)

van der Hoff, Quay; Harding, Ansie

2017-01-01

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of…

Calculus

CERN Document Server

Grossman, Stanley I

1984-01-01

Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro

Calculus of variations

CERN Document Server

Elsgolc, L E; Stark, M

1961-01-01

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency

Connecting Pre-Service Teachers with Contemporary Mathematics Practices: Selecting and Sequencing Students' Work Samples

Science.gov (United States)

Livy, Sharyn; Muir, Tracey; Downton, Ann

2017-01-01

One of the challenges facing teacher educators is providing our pre-service teachers (PSTs) with authentic experiences that cross the boundaries between Initial Teacher Education (ITE) and the classroom. An additional challenge facing the mathematics teacher educator, is addressing and deepening PSTs' mathematical content knowledge (MCK), which…

A Weakest Pre-Expectation Semantics for Mixed-Sign Expectations

OpenAIRE

Kaminski, Benjamin Lucien; Katoen, Joost-Pieter

2017-01-01

We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of \\emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is well-defined as the limit of iteratively applying a functional to a zero-element just as in the traditional weakest pre-expectation calculus, even though a standard least fixed point argument is not applicable in this context. A striking feature of our semantics i...

Approximate calculus of the auto transformers and power transformers capacitances; Calculo aproximado de las capacitancias de autotransformadores y transformadores de potencia

Energy Technology Data Exchange (ETDEWEB)

Carrasco, Gustavo [C.V.G. Electrificacion del Caroni, C.A. (EDELCA), Caracas (Venezuela)]. E-mail: gcarrasco@edelca.com.ve

2001-07-01

This paper develops a mathematical relation for the approximated calculus of the capacitances of the EDELCA power transformers and auto transformers. This mathematical relation is based on the type of transformers construction (Nucleus and shell type), the dielectric properties of the internal insulation material and the electric parameters (Voltage and power)

Latina/o Pre-Service Teachers' Use of Language and Culture while Assisting Children in Mathematics

Science.gov (United States)

Vomvoridi-Ivanovic, Eugenia

2009-01-01

Guided by symbolic interactionism and cultural historical activity theory this study investigated how four bilingual Latina/o pre-service teachers use language (Spanish and English) and culture, defined as social practices, as instructional resources in mathematics. The setting of the study was an after-school bilingual mathematics program, namely…

"Change My Thinking Patterns towards Maths": A Bibliotherapy Workshop for Pre-Service Teachers' Mathematics Anxiety

Science.gov (United States)

Wilson, Sue; Raven, Monica

2014-01-01

In small-group workshops, a joint initiative of the researcher and the student counsellor, primary (elementary) pre-service teachers (PSTs) wrote about critical incidents in their mathematics learning, and shared them with the group. Then, PSTs read extracts about mathematics anxiety (maths anxiety), and wrote and shared their reflections…

The calculus gallery masterpieces from Newton to Lebesgue

CERN Document Server

Dunham, William

2008-01-01

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. ""Students of literat

Foundations of mathematical logic

CERN Document Server

Curry, Haskell B

2010-01-01

Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.

Teachers' Beliefs about Improving Transfer of Algebraic Skills from Mathematics into Physics in Senior Pre-University Education

Science.gov (United States)

Tursucu, Süleyman; Spandaw, Jeroen; Flipse, Steven; de Vries, Marc J.

2017-01-01

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Mathematical foundations of elasticity

CERN Document Server

Marsden, Jerrold E

1994-01-01

This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con

Differential geometry and mathematical physics

CERN Document Server

Rudolph, Gerd

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...

Mathematics for everyman from simple numbers to the calculus

CERN Document Server

Colerus, Egmont

2003-01-01

Many people suffer from an inferiority complex where mathematics is concerned, regarding figures and equations with a fear based on bewilderment and inexperience. This book dispels some of the subject's alarming aspects, starting at the very beginning and assuming no mathematical education.Written in a witty and engaging style, the text contains an illustrative example for every point, as well as absorbing glimpses into mathematical history and philosophy. Topics include the system of tens and other number systems; symbols and commands; first steps in algebra and algebraic notation; common fr

Exact penalty results for mathematical programs with vanishing constraints

Czech Academy of Sciences Publication Activity Database

Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří

2010-01-01

Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/outrata-exact penalty results for mathematical programs with vanishing constraints.pdf

A Mathematics Support Programme for First-Year Engineering Students

Science.gov (United States)

Hillock, Poh Wah; Jennings, Michael; Roberts, Anthony; Scharaschkin, Victor

2013-01-01

This article describes a mathematics support programme at the University of Queensland, targeted at first-year engineering students identified as having a high risk of failing a first-year mathematics course in calculus and linear algebra. It describes how students were identified for the programme and the main features of the programme. The…

Space Mathematics, A Resource for Teachers Outlining Supplementary Space-Related Problems in Mathematics.

Science.gov (United States)

Reynolds, Thomas D.; And Others

This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…

Calculus for dummies

CERN Document Server

Ryan, Mark

2014-01-01

Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s

Modelling the Intention to Use Technology for Teaching Mathematics among Pre-Service Teachers in Serbia

Science.gov (United States)

Teo, Timothy; Milutinovic, Verica

2015-01-01

This study aims to examine the variables that influence Serbian pre-service teachers' intention to use technology to teach mathematics. Using the technology acceptance model (TAM) as the framework, we developed a research model to include subjective norm, knowledge of mathematics, and facilitating conditions as external variables to the TAM. In…

Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

Science.gov (United States)

Aljaberi, Nahil M.; Gheith, Eman

2016-01-01

This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…

Examining Primary Pre-Service Teachers' Difficulties of Mathematics Teaching with the Micro-Teaching Method

Science.gov (United States)

Savas Basturk; Tastepe, Mehtap

2015-01-01

The purpose of the study was to examine primary pre-service teachers' difficulties of the teaching of mathematics with micro-teaching method. The participants of the study were 15 third grade pre-service teachers from the department of primary education in the faculty of education. In this grade which includes four sections, there were…

[Comparative analysis of the efficacy of a playful-narrative program to teach mathematics at pre-school level].

Science.gov (United States)

Gil Llario, M D; Vicent Catalá, Consuelo

2009-02-01

Comparative analysis of the efficacy of a playful-narrative program to teach mathematics at pre-school level. In this paper, the effectiveness of a programme comprising several components that are meant to consolidate mathematical concepts and abilities at the pre-school level is analyzed. The instructional methodology of this programme is compared to other methodologies. One-hundred 5-6 year-old children made up the sample that was distributed in the following conditions: (1) traditional methodology; (2) methodology with perceptual and manipulative components, and (3) methodology with language and playful components. Mathematical competence was assessed with the Mathematical Criterial Pre-school Test and the subtest of quantitative-numeric concepts of BADyG. Participants were evaluated before and after the academic course during which they followed one of these methodologies. The results show that the programme with language and playful components is more effective than the traditional methodology (p<.000) and also more effective than the perceptual and manipulative methodology (p<.000). Implications of the results for instructional practices are analyzed.

A short course in discrete mathematics

CERN Document Server

Bender, Edward A

2004-01-01

What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, seq

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

Science.gov (United States)

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Mathematics for the liberal arts

CERN Document Server

Bindner, Donald; Hemmeter, Joe

2014-01-01

Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...

Investigating Pre-service Mathematics Teachers’ Geometric Problem Solving Process in Dynamic Geometry Environment

Directory of Open Access Journals (Sweden)

Deniz Özen

2013-03-01

Full Text Available The aim of this study is to investigate pre-service elementary mathematics teachers’ open geometric problem solving process in a Dynamic Geometry Environment. With its qualitative inquiry based research design employed, the participants of the study are three pre-service teachers from 4th graders of the Department of Elementary Mathematics Teaching. In this study, clinical interviews, screencaptures of the problem solving process in the Cabri Geomery Environment, and worksheets included 2 open geometry problems have been used to collect the data. It has been investigated that all the participants passed through similar recursive phases as construction, exploration, conjecture, validate, and justification in the problem solving process. It has been thought that this study provide a new point of view to curriculum developers, teachers and researchers

Maxima and Minima Without Calculus.

Science.gov (United States)

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

The Initial Conditions of Fractional Calculus

International Nuclear Information System (INIS)

Trigeassou, J. C.; Maamri, N.

2011-01-01

During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.

Paragrassmann differential calculus

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.V.

1993-01-01

This paper significantly extends and generalizes the paragrassmann calculus previous paper. Explicit general constructions for paragrassmann calculus with one and many vaiables are discussed. A general construction of many-variable differentiation algebras is given. Some particular examples are related to multi-parametric quantum deformation of the harmonic oscillators

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

Science.gov (United States)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

Perspectives of Pre-Service Middle and Secondary Mathematics Teachers on the Use of Webquests in Teaching and Learning Geometry

Science.gov (United States)

Halat, Erdogan

2009-01-01

The aim of this study was to examine the views of pre-service mathematics teachers on the use of webquests in teaching and learning geometry with reference to a theoretical framework developed by Dodge in 1995. For this study the researcher identified four groups containing nineteen pre-service mathematics teachers, which were then assigned to…

[Fluorescence control of dental calculus removal].

Science.gov (United States)

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

Pre-Service Mathematics Teachers’ Problem Solving Processes with Geometer’s Sketchpad: Mirror Problem

OpenAIRE

ÖÇAL, Mehmet Fatih; ŞİMŞEK, Mertkan

2016-01-01

Problem solving skill is the core of mathematics education and its importance cannot be denied. This study specifically examined 56 freshmen pre-service mathematics teachers’ problem solving processes on a specific problem with the help of Geometer’s Sketchpad (GSP). They were grouped into two-person teams to solve a problem called "the mirror problem". They were expected to solve it by means of GSP. According to their works on GSP and related reflections, there appeared two differe...

A Logical Process Calculus

Science.gov (United States)

Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.

Dental Hygiene Faculty Calibration Using Two Accepted Standards for Calculus Detection: A Pilot Study.

Science.gov (United States)

Santiago, Lisa J; Freudenthal, Jacqueline J; Peterson, Teri; Bowen, Denise M

2016-08-01

Faculty calibration studies for calculus detection use two different standards for examiner evaluation, yet the only therapeutic modality that can be used for nonsurgical periodontal treatment is scaling/root debridement or planing. In this study, a pretest-posttest design was used to assess the feasibility of faculty calibration for calculus detection using two accepted standards: that established by the Central Regional Dental Testing Service, Inc. (CRDTS; readily detectible calculus) and the gold standard for scaling/root debridement (root roughness). Four clinical dental hygiene faculty members out of five possible participants at Halifax Community College agreed to participate. The participants explored calculus on the 16 assigned teeth (64 surfaces) of four patients. Calculus detection scores were calculated before and after training. Kappa averages using CRDTS criteria were 0.561 at pretest and 0.631 at posttest. Kappa scores using the scaling/root debridement or planing standard were 0.152 at pretest and 0.271 at posttest. The scores indicated improvement from moderate (Kappa=0.41-0.60) to substantial agreement (Kappa=0.61-0.80) following training using the CRDTS standard. Although this result differed qualitatively and Kappas were significantly different from 0, the differences for pre- to post-Kappas for patient-rater dyads using CRDTS were not statistically significant (p=0.778). There was no difference (p=0.913) in Kappa scores pre- to post-training using the scaling/root debridement standard. Despite the small number of participants in this study, the results indicated that training to improve interrater reliability to substantial agreement was feasible using the CRDTS standard but not using the gold standard. The difference may have been due to greater difficulty in attaining agreement regarding root roughness. Future studies should include multiple training sessions with patients using the same standard for scaling/root debridement used for

Promoting Active Learning in Calculus and General Physics through Interactive and Media-Enhanced Lectures

Directory of Open Access Journals (Sweden)

Guoqing Tang

2004-02-01

Full Text Available In this paper we present an approach of incorporating interactive and media-enhanced lectures to promote active learning in Calculus and General Physics courses. The pedagogical practice of using interactive techniques in lectures to require "heads-on" and "hands-on" learning, and involve students more as active participants than passive receivers is a part of academic curricular reform efforts undertaken currently by the mathematics, physics and chemistry departments at North Carolina A&T State University under the NSF funded project "Talent-21: Gateway for Advancing Science and Mathematics Talents."

A Calculus for Context-Awareness

DEFF Research Database (Denmark)

Zimmer, Pascal

2005-01-01

In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile...... ambients, and a generic multi-agent synchronization mechanism, inspired from the join-calculus. After general ideas and introduction, we review the full calculus' syntax and semantics, as well as some motivating examples, study its expressiveness, and show how the notion of computation itself can be made...

Placement Evaluations and Remedial Education: Are Students Shopping for Bargains?

Science.gov (United States)

Fletcher, Stephen H.

2014-01-01

The purpose of this study is to provide evidence that students may be doing comparison shopping when it comes to community college placement in English and mathematics courses. Comparisons may occur because of the difference in the placement process across campuses and the variation in the levels of developmental education offered. The…

Introduction to mathematical fluid dynamics

CERN Document Server

Meyer, Richard E

2010-01-01

An introduction to the behavior of liquids and gases, this volume provides excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. It is geared toward advanced undergraduate and graduate students of mathematics and general science, and it requires a background in calculus and vector analysis. 1971 edition.

Investigation of Pre-School Teachers' Beliefs about Mathematics Education in Terms of Their Experience and Structure of Their Education

Science.gov (United States)

Karatas, Ilhan; Guven, Bulent; Öztürk, Yasin; Arslan, Selahattin; Gürsöy, Kadir

2017-01-01

The aim of this study was to determine pre-school teachers' beliefs about teaching mathematics to young learners. In this context, we compared preschool teachers' beliefs with mathematical learning, talent-development-age appropriateness for mathematical learning, the nature of mathematics, the curriculum, teacher efficacy, and the teacher's role…

The Incorporation of Micro-Computer Technology into School Mathematics: Some Suggestions for Middle and Senior Mathematics Courses.

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Newton, Bill

1987-01-01

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

The malliavin calculus and related topics

CERN Document Server

Nualart, David

1995-01-01

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions

A descriptive survey investigating pre-registration student nurses' perceptions of clinical skill development in clinical placements.

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Stayt, Louise C; Merriman, Clair

2013-04-01

Clinical skill development is essential to nurse education. Clinical skills are frequently taught in higher education institutions using clinical simulation. It is unclear if clinical skills are subsequently consolidated and developed in clinical placements. The aim of this survey was to evaluate pre-registration student nurses perceptions of the frequency of opportunities to practise, the level of supervision and assessment of, clinical skills in their clinical placements. This was a cross-sectional survey design using an online, self-report questionnaire including a Likert-type scale and open ended comments. Four hundred and twenty one students, from all year groups, from a university in the south of England on a wide variety of clinical placements participated. Participants evaluated the frequency of opportunity to practise, level of supervision and assessment of and feedback on performance of specific clinical skills. Clinical skills evaluated were measurement of vital signs, aseptic non-touch technique, assisting with eating and drinking, and assisting with comfort and hygiene. Data were analysed utilising Statistical Package for the Social Sciences Version 19. The frequency of opportunities to practise skills in clinical placement was variable with some participants reporting that they never had opportunity to practise essential skills. Similarly the level of supervision and assessment was also inconsistent suggesting that participants frequently practised clinical skills unsupervised without being assessed as competent. Inconsistencies in clinical skill development may lead to graduates who are not work ready and as a result, insufficient clinical competence potentially leads to unsafe practice and poor patient care. This calls for stronger partnerships between educators and clinical areas and the prioritisation of mentor preparation and education as well as organisational support in terms of mentor workload planning. Copyright © 2012 Elsevier Ltd. All

Calculus Problem Solving Behavior of Mathematic Education Students

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Rizal, M.; Mansyur, J.

2017-04-01

The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. (2) To give two mathematical problems with different characteristics. The first problem (M1), the statement does not lead to a resolution. The second problem (M2), a statement leads to problem-solving. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data’s credibility by providing equivalent problem contexts and at different times. The results show that the behavioral problem solvers (mathematic education students) who are capable of high mathematic competency (ST). In understanding M1, ST is more likely to pay attention to an image first, read the texts piecemeal and repeatedly, then as a whole and more focus to the sentences that contain equations, numbers or symbols. As a result, not all information can be received well. When understanding the M2, ST can link the information from a problem that is stored in the working memory to the information on the long-term memory. ST makes planning to the solution of M1 and M2 by using a formula based on similar experiences which have been ever received before. Another case when implementing the troubleshooting plans, ST complete the M1 according to the plan, but not all can be resolved correctly. In contrast to the implementation of the solving plan of M2, ST can solve the problem according to plan quickly and correctly. According to the solving result of M1 and M2, ST conducts by reading the job based on an algorithm and reasonability. Furthermore, when SS and SR understand the

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy.

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Juan, Hsu-Cheng; Lin, Hung-Yu; Chou, Yii-Her; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-08-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. • Unenhanced CT is now widely used to assess ureteric calculi. • The same CT protocol can provide measurements of abdominal fat distribution. • Ureteric calculi are usually treated by shock wave lithotripsy (SWL). • Greater intra-abdominal fat stores are generally associated with poorer SWL results.

The Vectorial $\\lambda$-Calculus

OpenAIRE

Arrighi, Pablo; Díaz-Caro, Alejandro; Valiron, Benoît

2013-01-01

We describe a type system for the linear-algebraic $\\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\\lambda$-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed $\\lambda$-calculus is strongly normalising and fea...

Teaching the Calculus

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Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

An Investigation of Pre-Service Science and Mathematics Teachers' Personal Growth Initiative

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Büyükgöze, Hilal

2015-01-01

The current paper primarily aims to investigate pre-service science and mathematics teachers' personal growth initiative levels. The second aim of the study is to examine whether participants' initiative levels differ in relation to their gender, grade, department, perceived academic achievement, and willingness to attend graduate education after…

Adapting the Academic Motivation Scale for Use in Pre-Tertiary Mathematics Classrooms

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Lim, Siew Yee; Chapman, Elaine

2015-01-01

The Academic Motivation Scale (AMS) is a comprehensive and widely used instrument for assessing motivation based on the self-determination theory. Currently, no such comprehensive instrument exists to assess the different domains of motivation (stipulated by the self-determination theory) in mathematics education at the pre-tertiary level (grades…

Generalized vector calculus on convex domain

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Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Dental Calculus Arrest of Dental Caries.

Science.gov (United States)

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

Science.gov (United States)

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

Verified Representations of Landau's "Grundlagen" in the lambda-delta Family and in the Calculus of Constructions

Directory of Open Access Journals (Sweden)

Ferruccio Guidi

2016-01-01

Full Text Available Landau's "Grundlagen der Analysis" formalized in the language Aut-QE, represents an early milestone in computer-checked mathematics and is the only non-trivial development finalized in the languages of the Automath family. Here we discuss an implemented procedure producing a faithful representation of the Grundlagen in the Calculus of Constructions, verified by the proof assistant Coq 8.4.3. The point at issue is distinguishing lambda-abstractions from pi-abstractions where the original text uses Automath unified binders, taking care of the cases in which a binder corresponds to both abstractions at one time. It is a fact that some binders can be disambiguated only by verifying the Grundlagen in a calculus accepting Aut-QE and the Calculus of Constructions. To this end, we rely on lambda-delta version 3, a system that the author is proposing here for the first time.

Latent transition analysis of pre-service teachers' efficacy in mathematics and science

Science.gov (United States)

Ward, Elizabeth Kennedy

This study modeled changes in pre-service teacher efficacy in mathematics and science over the course of the final year of teacher preparation using latent transition analysis (LTA), a longitudinal form of analysis that builds on two modeling traditions (latent class analysis (LCA) and auto-regressive modeling). Data were collected using the STEBI-B, MTEBI-r, and the ABNTMS instruments. The findings suggest that LTA is a viable technique for use in teacher efficacy research. Teacher efficacy is modeled as a construct with two dimensions: personal teaching efficacy (PTE) and outcome expectancy (OE). Findings suggest that the mathematics and science teaching efficacy (PTE) of pre-service teachers is a multi-class phenomena. The analyses revealed a four-class model of PTE at the beginning and end of the final year of teacher training. Results indicate that when pre-service teachers transition between classes, they tend to move from a lower efficacy class into a higher efficacy class. In addition, the findings suggest that time-varying variables (attitudes and beliefs) and time-invariant variables (previous coursework, previous experiences, and teacher perceptions) are statistically significant predictors of efficacy class membership. Further, analyses suggest that the measures used to assess outcome expectancy are not suitable for LCA and LTA procedures.

Teachers’ beliefs about improving transfer of algebraic skills from mathematics into physics in senior pre-university education

NARCIS (Netherlands)

Tursucu, S.; Spandaw, J.G.; Flipse, S.M.; de Vries, M.J.

2017-01-01

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers’ beliefs about improving the transfer of algebraic skills from mathematics into physics. We

Initialized Fractional Calculus

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Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

Basic mathematics for the biological and social sciences

CERN Document Server

Marriott, F H C

2013-01-01

Basic Mathematics for the Biological and Social Sciences deals with the applications of basic mathematics in the biological and social sciences. Mathematical concepts that are discussed in this book include graphical methods, differentiation, trigonometrical or circular functions, limits and convergence, integration, vectors, and differential equations. The exponential function and related functions are also considered. This monograph is comprised of 11 chapters and begins with an overview of basic algebra, followed by an introduction to infinitesimal calculus, scalar and vector quantities, co

The effects of GeoGebra software on pre-service mathematics teachers' attitudes and views toward proof and proving

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Zengin, Yılmaz

2017-11-01

The purpose of this study is to determine the effect of GeoGebra software on pre-service mathematics teachers' attitudes towards proof and proving and to determine pre-service teachers' pre- and post-views regarding proof. The study lasted nine weeks and the participants of the study consisted of 24 pre-service mathematics teachers. The study used the 'Attitude Scale Towards Proof and Proving' and an open-ended questionnaire that were administered before and after the intervention as data collection tools. Paired samples t-test analysis was used for the analysis of quantitative data and content and descriptive analyses were utilized for the analysis of qualitative data. As a result of the data analysis, it was determined that GeoGebra software was an effective tool in increasing pre-service teachers' attitudes towards proof and proving.

The logical foundations of mathematics

CERN Document Server

Hatcher, William S

1981-01-01

The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory.Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and

Space Mathematics: A Resource for Secondary School Teachers

Science.gov (United States)

Kastner, Bernice