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Author: Allen C. Hibbard
Publisher: Mathematical Association of America (MAA)
Published: 2002
Total Pages: 174
ISBN-13:
DOWNLOAD EBOOKDownload or read book Innovations in Teaching Abstract Algebra written by Allen C. Hibbard and published by Mathematical Association of America (MAA). This book was released on 2002 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Stephen Lovett
Publisher: CRC Press
Published: 2022-07-05
Total Pages: 570
ISBN-13: 1000605442
DOWNLOAD EBOOKWhen a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?" Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, −, ×, and ÷) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties. This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas. This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research. The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.
Download or read book Abstract Algebra written by Stephen Lovett and published by CRC Press. This book was released on 2022-07-05 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?" Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, −, ×, and ÷) on real numbers. Abstract algebra studies properties of operations without specifying what types of number or object we work with. Any theorem established in the abstract context holds not only for real numbers but for every possible algebraic structure that has operations with the stated properties. This textbook intends to serve as a first course in abstract algebra. The selection of topics serves both of the common trends in such a course: a balanced introduction to groups, rings, and fields; or a course that primarily emphasizes group theory. The writing style is student-centered, conscientiously motivating definitions and offering many illustrative examples. Various sections or sometimes just examples or exercises introduce applications to geometry, number theory, cryptography and many other areas. This book offers a unique feature in the lists of projects at the end of each section. the author does not view projects as just something extra or cute, but rather an opportunity for a student to work on and demonstrate their potential for open-ended investigation. The projects ideas come in two flavors: investigative or expository. The investigative projects briefly present a topic and posed open-ended questions that invite the student to explore the topic, asking and to trying to answer their own questions. Expository projects invite the student to explore a topic with algebraic content or pertain to a particular mathematician’s work through responsible research. The exercises challenge the student to prove new results using the theorems presented in the text. The student then becomes an active participant in the development of the field.
Author: Kaye Stacey
Publisher: Springer Science & Business Media
Published: 2006-04-11
Total Pages: 382
ISBN-13: 1402081316
DOWNLOAD EBOOKKaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist discussion and action at the international‚ national‚ regional‚ and institutional levels. The ICMI Study running from 2000 to 2004 was on The Future of the Teaching and Learning of Algebra‚ and its Study Conference was held at The University of Melbourne‚ Australia fromDecember to 2001. It was the first study held in the Southern Hemisphere. There are several reasons why the future of the teaching and learning of algebra was a timely focus at the beginning of the twenty first century. The strong research base developed over recent decades enabled us to take stock of what has been achieved and also to look forward to what should be done and what might be achieved in the future. In addition‚ trends evident over recent years have intensified. Those particularly affecting school mathematics are the “massification” of education—continuing in some countries whilst beginning in others—and the advance of technology.
Download or read book The Future of the Teaching and Learning of Algebra written by Kaye Stacey and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist discussion and action at the international‚ national‚ regional‚ and institutional levels. The ICMI Study running from 2000 to 2004 was on The Future of the Teaching and Learning of Algebra‚ and its Study Conference was held at The University of Melbourne‚ Australia fromDecember to 2001. It was the first study held in the Southern Hemisphere. There are several reasons why the future of the teaching and learning of algebra was a timely focus at the beginning of the twenty first century. The strong research base developed over recent decades enabled us to take stock of what has been achieved and also to look forward to what should be done and what might be achieved in the future. In addition‚ trends evident over recent years have intensified. Those particularly affecting school mathematics are the “massification” of education—continuing in some countries whilst beginning in others—and the advance of technology.
Author: Joan B. Garfield
Publisher: Mathematical Association of America (MAA)
Published: 2005
Total Pages: 176
ISBN-13:
DOWNLOAD EBOOK"This is a book of stories about teaching statistics. These stories are told by fourteen different instructors of innovative statistics courses, who demonstrate that learning statistics can be a positive, meaningful, and even exciting experience. Despite the prevailing opinion that statistics courses are dull and difficult for students, these stories paint quite a different picture. In the classes of the instructors whose stories fill this book, students are engaged in learning, are empowered to do statistics, and appreciate the instructional methods of their teachers. The instructors profiled in this book are inspiring, dedicated teachers who have devoted considerable effort to creating courses and materials that enable students to successfully learn statistics. Each chapter begins by describing how the author became a teacher of statistics, then provides details about the courses they currently teach, describing their teaching method, textbook, types of student assessments, and uses of technology. One typical class is described in detail, to provide a snapshot of what each person's teaching looks like. The writers then tell the story of the process they went through in developing an innovative course, and conclude their chapters with a discussion of their future plans for course revision or development. As you read these stories, you will learn about some great activities, some helpful technological tools and some innovative assessment methods. By reading these stories, teachers of statistics will understand and be motivated to try different ways to implement reform recommendations, so that these recommendations may continue to lead to a variety of new materials, activities, and teaching approaches. I hope that teachers of statistics may be inspired by these stories and feel encouraged to try new methods, leave behind more traditional approaches to teaching statistics, and carefully examine the effect of their teaching on student learning." -- Publisher.
Download or read book Innovations in Teaching Statistics written by Joan B. Garfield and published by Mathematical Association of America (MAA). This book was released on 2005 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a book of stories about teaching statistics. These stories are told by fourteen different instructors of innovative statistics courses, who demonstrate that learning statistics can be a positive, meaningful, and even exciting experience. Despite the prevailing opinion that statistics courses are dull and difficult for students, these stories paint quite a different picture. In the classes of the instructors whose stories fill this book, students are engaged in learning, are empowered to do statistics, and appreciate the instructional methods of their teachers. The instructors profiled in this book are inspiring, dedicated teachers who have devoted considerable effort to creating courses and materials that enable students to successfully learn statistics. Each chapter begins by describing how the author became a teacher of statistics, then provides details about the courses they currently teach, describing their teaching method, textbook, types of student assessments, and uses of technology. One typical class is described in detail, to provide a snapshot of what each person's teaching looks like. The writers then tell the story of the process they went through in developing an innovative course, and conclude their chapters with a discussion of their future plans for course revision or development. As you read these stories, you will learn about some great activities, some helpful technological tools and some innovative assessment methods. By reading these stories, teachers of statistics will understand and be motivated to try different ways to implement reform recommendations, so that these recommendations may continue to lead to a variety of new materials, activities, and teaching approaches. I hope that teachers of statistics may be inspired by these stories and feel encouraged to try new methods, leave behind more traditional approaches to teaching statistics, and carefully examine the effect of their teaching on student learning." -- Publisher.
Author: Meni Tsitouridou
Publisher: Springer
Published: 2019-05-28
Total Pages: 634
ISBN-13: 3030209547
DOWNLOAD EBOOKThis book constitutes the thoroughly refereed post-conference proceedings of the First International Conference on Technology and Innovation in Learning, Teaching and Education, TECH-EDU 2018, held in Thessaloniki, Greece, on June 20-22, 2018. The 30 revised full papers along with 18 short papers presented were carefully reviewed and selected from 80 submissions.The papers are organized in topical sections on new technologies and teaching approaches to promote the strategies of self and co-regulation learning (new-TECH to SCRL); eLearning 2.0: trends, challenges and innovative perspectives; building critical thinking in higher education: meeting the challenge; digital tools in S and T learning; exploratory potentialities of emerging technologies in education; learning technologies; digital technologies and instructional design; big data in education and learning analytics.
Download or read book Technology and Innovation in Learning, Teaching and Education written by Meni Tsitouridou and published by Springer. This book was released on 2019-05-28 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the First International Conference on Technology and Innovation in Learning, Teaching and Education, TECH-EDU 2018, held in Thessaloniki, Greece, on June 20-22, 2018. The 30 revised full papers along with 18 short papers presented were carefully reviewed and selected from 80 submissions.The papers are organized in topical sections on new technologies and teaching approaches to promote the strategies of self and co-regulation learning (new-TECH to SCRL); eLearning 2.0: trends, challenges and innovative perspectives; building critical thinking in higher education: meeting the challenge; digital tools in S and T learning; exploratory potentialities of emerging technologies in education; learning technologies; digital technologies and instructional design; big data in education and learning analytics.
Author: Charles Arthur Coppin
Publisher: MAA
Published: 2009
Total Pages: 262
ISBN-13: 9780883851852
DOWNLOAD EBOOKThe Moore method is a type of instruction used in advanced mathematics courses that moves away from a teacher-oriented experience to a learner-centered one. This book gives an overview of the Moore Method as practiced by the four authors. The authors outline six principles they all have as goals : elevating students from recipients to creators of knowledge; letting students discover the power of their minds; believing every student can and will do mathematics; allowing students to discover, present and debate mathematics; carefully matching problems and materials to the students; and having the material cover a significant body of knowledge. Topics include establishing a classroom culture, grading methods, materials development and more. Appendices include sample tests, notes and diaries of individual courses.
Download or read book The Moore Method written by Charles Arthur Coppin and published by MAA. This book was released on 2009 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Moore method is a type of instruction used in advanced mathematics courses that moves away from a teacher-oriented experience to a learner-centered one. This book gives an overview of the Moore Method as practiced by the four authors. The authors outline six principles they all have as goals : elevating students from recipients to creators of knowledge; letting students discover the power of their minds; believing every student can and will do mathematics; allowing students to discover, present and debate mathematics; carefully matching problems and materials to the students; and having the material cover a significant body of knowledge. Topics include establishing a classroom culture, grading methods, materials development and more. Appendices include sample tests, notes and diaries of individual courses.
Author: Mohammad-Hossain Ahmadi
Publisher: University Press of America
Published: 2002
Total Pages: 194
ISBN-13: 9780761823254
DOWNLOAD EBOOKProfessional mathematicians from the US and Britain address practical aspects of innovative ideas in teaching mathematics, but shy away from either theoretical or historical perspectives on any particular pedagogical approaches. They set out the pros and cons of implementing creative instructional styles in order to share their insights with teachers at all educational levels. Annotation copyrighted by Book News, Inc., Portland, OR.
Download or read book Readings in Innovative Ideas in Teaching Collegiate Mathematics written by Mohammad-Hossain Ahmadi and published by University Press of America. This book was released on 2002 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professional mathematicians from the US and Britain address practical aspects of innovative ideas in teaching mathematics, but shy away from either theoretical or historical perspectives on any particular pedagogical approaches. They set out the pros and cons of implementing creative instructional styles in order to share their insights with teachers at all educational levels. Annotation copyrighted by Book News, Inc., Portland, OR.
Author: Amy Shell-Gellasch
Publisher: MAA
Published: 2007
Total Pages: 191
ISBN-13: 0883851822
DOWNLOAD EBOOKIn an increasingly electronic society, these exercises are designed to help school and collegiate educators use historical devices of mathematics to balance the digital side of mathematics.
Download or read book Hands on History written by Amy Shell-Gellasch and published by MAA. This book was released on 2007 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an increasingly electronic society, these exercises are designed to help school and collegiate educators use historical devices of mathematics to balance the digital side of mathematics.
Author: Nicholas H. Wasserman
Publisher: Springer
Published: 2018-12-12
Total Pages: 461
ISBN-13: 3319992147
DOWNLOAD EBOOKSecondary 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.
Download or read book Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers written by Nicholas H. Wasserman and published by Springer. This book was released on 2018-12-12 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author: Marilyn Paula Carlson
Publisher: MAA
Published: 2008
Total Pages: 340
ISBN-13: 9780883851838
DOWNLOAD EBOOKThe chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
Download or read book Making the Connection written by Marilyn Paula Carlson and published by MAA. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
