Learning Abstract Algebra With Isetl
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Learning Abstract Algebra With Isetl
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Author : Ed Dubinsky
language : de
Publisher: Springer-Verlag
Release Date : 2019-06-12
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-12 with Mathematics categories.
Learning Abstract Algebra With Isetl
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Author : Ed Dubinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 1994
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Education categories.
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are preseted in a lecture.
Learning Abstract Algebra With Isetl
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Author : Ed Dubinsky
language : en
Publisher: Springer
Release Date : 1993-12-14
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-14 with Mathematics categories.
This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers
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Author : Nicholas H. Wasserman
language : en
Publisher: Springer
Release Date : 2018-12-12
Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers written by Nicholas H. Wasserman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Education categories.
Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.
Learning Abstract Algebra With Isetl
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Author : Ed Dubinsky
language : en
Publisher: Springer
Release Date : 2014-09-12
Learning Abstract Algebra With Isetl written by Ed Dubinsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Mathematics categories.
This book is based on the belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities that will establish an experiential base for any future verbal explanations and to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies, as well as on the substantial experience of the authors in teaching Abstract Algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the math-like programming language ISETL; the main tool for reflection is work in teams of two to four students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics. Each topic is first introduced through computer activities, which are then followed by a text section and exercises. The text section is written in an informal, discursive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture.
Apos Theory
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Author : Ilana Arnon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-04
Apos Theory written by Ilana Arnon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-04 with Education categories.
In spite of the fact that APOS Theory has been used extensively in numerous scholarly publications, in the design of textbooks, and in teaching practice, there is no single references that contains all the relevant information about its components, and provides guidance about its application. The goal of this book is to present the main elements of APOS theory. It should be useful for researchers who work with, or would like to learn more about, this theoretical approach, people who are interested in the way which mathematical conceptions are constructed according to this theory, Mathematics Education researchers, graduate students in Mathematics Education, and Mathematics instructors.
Second International Handbook Of Mathematics Education
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Author : Alan Bishop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-02
Second International Handbook Of Mathematics Education written by Alan Bishop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-02 with Education categories.
ALAN 1. BISHOP The first International Handbook on Mathematics Education was published by Kluwer Academic Publishers in 1996. However, most of the writing for that handbook was done in 1995 and generally reflected the main research and development foci prior to 1994. There were four sections, 36 chapters, and some 150 people contributed to the final volume either as author, reviewer, editor, or critical friend. The task was a monumental one, attempting to cover the major research and practice developments in the international field of mathematics education as it appeared to the contributors in 1995. Inevitably there were certain omissions, some developments were only starting to emerge, and some literatures were only sketchy and speculative. However that Handbook has had to be reprinted three times, so it clearly fulfilled a need and I personally hope that it lived up to what I wrote in its Introduction: The Handbook thus attempts not merely to present a description of the international 'state-of-the-field', but also to offer synthetic and reflective overviews on the different directions being taken by the field, on the gaps existing in our present knowledge, on the current problems being faced, and on the future possibilities for development. (Bishop et aI. , 1996) Since that time there has been even more activity in our field, and now seems a good time to take stock again, to reflect on what has happened since 1995, and to create a second Handbook with the same overall goals.
Learning Discrete Mathematics With Isetl
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Author : Nancy Baxter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Learning Discrete Mathematics With Isetl written by Nancy Baxter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The title of this book, Learning Discrete Mathematics with ISETL raises two issues. We have chosen the word "Learning" rather than "Teaching" because we think that what the student does in order to learn is much more important than what the professor does in order to teach. Academia is filled with outstanding mathematics teachers: excellent expositors, good organizers, hard workers, men and women who have a deep understanding of Mathematics and its applications. Yet, when it comes to ideas in Mathe matics, our students do not seem to be learning. It may be that something more is needed and we have tried to construct a book that might provide a different kind of help to the student in acquiring some of the fundamental concepts of Mathematics. In a number of ways we have made choices that seem to us to be the best for learning, even if they don't always completely agree with standard teaching practice. A second issue concerns students' writing programs. ISETL is a pro gramming language and by the phrase "with ISETL" in the title, we mean that our intention is for students to write code, think about what they have written, predict its results, and run their programs to check their predic tions. There is a trade-off here. On the one hand, it can be argued that students' active involvement with constructing Mathematics for themselves and solving problems is essential to understanding concepts.
The Teaching And Learning Of Mathematics At University Level
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Author : Derek Holton
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
The Teaching And Learning Of Mathematics At University Level written by Derek Holton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Education categories.
This book is the final report of the ICMI study on the Teaching and Learning of Mathematics at University Level. As such it is one of a number of such studies that ICMI has commissioned. The other Study Volumes cover assessment in mathematics education, gender equity, research in mathematics education, the teaching of geometry, and history in mathematics education. All ofthese Study Volumes represent a statement of the state of the art in their respective areas. We hope that this is also the case for the current Study Volume. The current study on university level mathematics was commissioned for essentially four reasons. First, universities world-wide are accepting a much larger and more diverse group of students than has been the case. Consequently, universities have begun to adopt a role more like that of the school system and less like the elite institutions of the past. As a result the educational and pedagogical issues facing universities have changed. Second, although university student numbers have increased significantly, there has not been a corresponding increase in the number of mathematics majors. Hence mathematics departments have to be more aware of their students’ needs in order to retain the students they have and to attract future students. As part of this awareness, departments of mathematics have to take the teaching and learning of mathematics more seriously than perhaps they have in the past.
How To Teach Mathematics
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Author : Steven G. Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-07
How To Teach Mathematics written by Steven G. Krantz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-07 with Education categories.
This third edition is a lively and provocative tract on how to teach mathematics in today's new world of online learning tools and innovative teaching devices. The author guides the reader through the joys and pitfalls of interacting with modern undergraduates--telling you very explicitly what to do and what not to do. This third edition has been streamlined from the second edition, but still includes the nuts and bolts of good teaching, discussing material related to new developments in teaching methodology and technique, as well as adding an entire new chapter on online teaching methods.