Download or read book The Evolution of Student Understanding of the Concept of Derivative written by Michelle J. Zandieh and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This research seeks to answer the question, "What does it mean for a student to understand the concept of derivative?" A structured way to describe an individual student's understanding of derivative is developed and applied to analyzing the evolution of that understanding for each of nine high school seniors during their year-long calculus course. The methodology is a multiple case study. Interviews, including both task-based and open-ended questions, are the primary instruments for collecting data on each student's understanding. Other data collected include tests, written questions, and classroom observations. Several theoretical frameworks contribute to the research: concept image (Tall, Vinner, and Dreyfus), process-object (Sfard; Dubinsky and colleagues), and notions of multiple representations for function, limit, and derivative. I describe the concept of derivative as three layers of process-objects: the ratio or difference quotient, the limit, and the function layers. Each layer may be observed in multiple contexts: graphical (slope), verbal description (rate of change), kinematic (e.g. velocity or acceleration), and symbolic (the symbolic difference quotient definition of derivative). A description of the connections between the various aspects of the concept of derivative comes from the work of Fischbein on paradigmatic, analogic, and diagrammatic models and the work of Lakoff on metaphor and metonymy. The major theoretical result of the dissertation is the development of a structured way of describing the concept of derivative including a diagrammatic methodology for displaying which aspects of the derivative concept a student has demonstrated. This methodology may be applied to other studies and other concepts. The major result of this study of nine students is the realization that the layers and representations of the concept of derivative do not appear to be hierarchical in that none of the nine students learn the aspects in the same order.
Download or read book Holomorphic Vector Fields on Compact K hler Manifolds written by Yoz_ Matsushima and published by American Mathematical Soc.. This book was released on 1971-12-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Teaching and Learning of Calculus written by David Bressoud and published by Springer. This book was released on 2016-06-14 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.
Download or read book Research in Collegiate Mathematics Education IV written by Ed Dubinsky and published by American Mathematical Soc.. This book was released on 2000 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning. This series is published in cooperation with the Mathematical Association of America.
Download or read book Research in Collegiate Mathematics Education III written by James J. Kaput and published by American Mathematical Soc.. This book was released on 1998 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.
Download or read book A Historian Looks Back written by Judith V. Grabiner and published by MAA. This book was released on 2010-10-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inspiring collection of a historian's work on the history of mathematics.
Download or read book MAA Notes written by and published by . This book was released on 1983 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Dialogue on Explanation written by C. Mantzavinos and published by Springer. This book was released on 2019-01-01 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a panorama of the philosophical theory of explanation. Written as a philosophical dialogue between two interlocutors, Philip and a student, it presents a defense of the position of explanatory pluralism. The fictional dialogue takes place on Cape Sounion, near Athens, where the two interlocutors are enjoying the view over the Aegean Sea. An initial exchange of arguments leads to a dialogue unfolding the development of the contemporary philosophical theory of explanation. The second part of the dialogue is devoted to an exchange of arguments on explanatory pluralism as a novel approach to the philosophical theory of explanation. The two also discuss historical cases as well as the ways of achieving explanatory progress in science. We are all philosophers and we develop our own philosophy by exchanging views and arguments. The dialogue form is and should remain the principal form of philosophizing, since ideas do not merely exist – they develop. This is certainly the case in real-world philosophical interaction, and as this book aptly demonstrates, it can also be the case in written philosophical exposition.
Download or read book The Teaching and Learning of Mathematics at University Level written by Derek Holton and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a text that contains the latest in thinking and the best in practice. It provides a state-of-the-art statement on tertiary teaching from a multi-perspective standpoint. No previous book has attempted to take such a wide view of the topic. The book will be of special interest to academic mathematicians, mathematics educators, and educational researchers. It arose from the ICMI Study into the teaching and learning of mathematics at university level (initiated at the conference in Singapore, 1998).
Download or read book Calculus Reordered written by David M. Bressoud and published by Princeton University Press. This book was released on 2021-05-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
Download or read book Changing Calculus written by Susan L. Ganter and published by Mathematical Association of America (MAA). This book was released on 2001 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Third International Conference on Computing Mathematics and Statistics iCMS2017 written by Liew-Kee Kor and published by Springer. This book was released on 2019-03-27 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a product of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017) to be held in Langkawi in November 2017. It is divided into four sections according to the thrust areas: Computer Science, Mathematics, Statistics, and Multidisciplinary Applications. All sections sought to confront current issues that society faces today. The book brings collectively quantitative, as well as qualitative, research methods that are also suitable for future research undertakings. Researchers in Computer Science, Mathematics and Statistics can use this book as a sourcebook to enrich their research works.
Download or read book Research and Development in University Mathematics Education written by Viviane Durand-Guerrier and published by Routledge. This book was released on 2021-04-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last thirty years or so, the need to address the challenges of teaching and learning mathematics at university level has become increasingly appreciated by university mathematics teachers, and beyond, by educational institutions around the world. Indeed, mathematics is both a condition and an obstacle to success for students in many educational programmes vital to the 21st century knowledge society, for example in pure and applied mathematics, engineering, natural sciences, technology, economics, finance, management and so on. This breadth of impact of mathematics implies the urgency of developing research in university mathematics education, and of sharing results of this research widely. This book provides a bespoke opportunity for an international audience of researchers in didactics of mathematics, mathematicians and any teacher or researcher with an interest in this area to be informed about state-of-the-art developments and to heed future research agendas. This book emerged from the activities of the research project INDRUM (acronym for International Network for Didactic Research in University Mathematics), which aims to contribute to the development of research in didactics of mathematics at all levels of tertiary education, with a particular concern for the development of early-career researchers in the field and for dialogue with university mathematicians. The aim of the book is to provide a deep synthesis of the research field as it appears through two INDRUM conferences organised in 2016 and 2018. It is an original contribution which highlights key research perspectives, addresses seminal theoretical and methodological issues and reports substantial results concerning the teaching and learning of mathematics at university level, including the teaching and learning of specific topics in advanced mathematics across a wide range of university programmes.
Download or read book The Development of Multiplicative Reasoning in the Learning of Mathematics written by Guershon Harel and published by SUNY Press. This book was released on 1994-01-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.
Download or read book Mathematical Modelling written by C Haines and published by Elsevier. This book was released on 2007-08-01 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research
Download or read book Comparison of Mathematics and Physics Education II written by Frederik Dilling and published by Springer Nature. This book was released on 2022-07-01 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interdisciplinary teaching is considered as one of the main goals of education worldwide. At the same time, it poses an immense challenge to teachers who have been trained in only one of the combines subjects. This is true even for closely related disciplines such as mathematics and physics. In this volume, practice-oriented educational comparisons are made across various topics that are highly relevant in both subjects. Furthermore, practical examples are presented in the form of lesson plans in which exemplary implementation in class is presented, considering both educational perspectives.
Download or read book The Learning and Development of Mathematics Teacher Educators written by Merrilyn Goos and published by Springer Nature. This book was released on 2021-04-07 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in mathematics teacher education as a distinctive field of inquiry has grown substantially over the past 10-15 years. Within this field there is emerging interest in how mathematics teacher educators (MTEs) themselves learn and develop. Until recently there were few published studies on this topic, and the processes by which mathematics teacher educators learn, and the forms of knowledge they require for effective practice, had not been systematically investigated. However, researchers in mathematics education are now beginning to investigate the development of MTE expertise and associated issues. This volume draws on the latest research and thinking in this area is therefore timely to stimulate future development and directions. It will survey the emerging field of inquiry in mathematics education, combining the work of established scholars with perspectives of newcomers to the field, with the aim of influencing development of the field, invite cross-cultural comparisons in becoming a mathematics teacher educator by highlighting issues in the development of MTEs in different countries, and examine the roles of both mathematics educators and mathematicians in preparing future teachers of mathematics. The primary audience will be university-based mathematics teacher educators and MTE researchers, and postgraduate research students who are seeking academic careers as MTEs. Additional interest may come from teacher educators in disciplines other than mathematics, and education policy makers responsible for accreditation and quality control of initial teacher education programs.
