Connecting Abstract Algebra To Secondary Mathematics For Secondary Mathematics Teachers

Author : Nicholas H. Wasserman
Publisher : Springer
Page : 461 pages
File Size : 43,8 Mb
Release : 2018-12-12
Category : Education
ISBN : 9783319992143

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Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers by Nicholas H. Wasserman Pdf

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 : Olympia Nicodemi,Melissa A. Sutherland,Gary W. Towsley
Publisher : Pearson
Page : 0 pages
File Size : 43,8 Mb
Release : 2007
Category : Algebra, Abstract
ISBN : 0131019635

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An Introduction to Abstract Algebra by Olympia Nicodemi,Melissa A. Sutherland,Gary W. Towsley Pdf

This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities. Includes "To the Teacher" sections that Draw connections from the number theory or abstract algebra under consideration to secondary mathematics. Provides historical context with "From the Past" sections in each chapter. Features "Worksheets" that outline the framework of a topic in most chapters. A useful reference for mathematics teachers who need to brush up on their abstract algebra skills. An Introduction to Abstract Algebra with Notes to the Future Teacher, 1/E Olympia Nicodemi Melissa A Sutherland Gary W Towsley

Author : Nicholas H. Wasserman,Timothy Fukawa-Connelly,Keith Weber,Juan Pablo Mejía Ramos,Stephen Abbott
Publisher : Springer Nature
Page : 226 pages
File Size : 44,6 Mb
Release : 2022-01-03
Category : Education
ISBN : 9783030891985

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Understanding Analysis and its Connections to Secondary Mathematics Teaching by Nicholas H. Wasserman,Timothy Fukawa-Connelly,Keith Weber,Juan Pablo Mejía Ramos,Stephen Abbott Pdf

Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book. The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.

Author : Richard Grassl
Publisher : Independently Published
Page : 0 pages
File Size : 55,9 Mb
Release : 2022-04-04
Category : Electronic
ISBN : 9798441684613

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Some Abstract Algebra by Richard Grassl Pdf

This primer is designed to provide an adequate introduction to the essentials of abstract algebra and to some related number theory. A problem solving approach has been taken -- there are over 150 problems -- so be prepared for minimal text material to read. Very little background in abstract algebra is needed for a course based on this primer. The content and methodology has been implemented successfully for well over a decade with in-service secondary teachers seeking licensure or an MA degree in teaching mathematics. The oft-quoted maxim, "You learn mathematics by doing mathematics" is embraced.

Author : Tony Gardiner
Publisher : Open Book Publishers
Page : 334 pages
File Size : 41,6 Mb
Release : 2016-02-08
Category : Mathematics
ISBN : 9781783741403

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Teaching Mathematics at Secondary Level by Tony Gardiner Pdf

Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.

Author : Babette M. Benken
Publisher : IAP
Page : 490 pages
File Size : 41,9 Mb
Release : 2024-02-01
Category : Mathematics
ISBN : 9798887305431

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The AMTE Handbook of Mathematics Teacher Education by Babette M. Benken Pdf

This new volume of The Association of Mathematics Teacher Educators (AMTE) Professional Book Series is a critical and timely resource that paves the way and guides the future of mathematics teacher education. The collection of work in this AMTE Handbook of Mathematics Teacher Education reflects on research and what we know about how best to prepare and support both mathematics teachers and mathematics teacher educators and presents what is happening in the field. Examples included in the 22 chapters highlight how we are preparing teachers across multiple contexts (e.g., within district, in content courses for the major) and grade ranges (K-20+) and all chapters highlight relevant connections to the AMTE Standards for Preparing Teachers of Mathematics. Most importantly, this volume explores what we do not yet fully understand and where we are going. In essence, it considers how we can move the field forward. The 95 contributing authors range from graduate students to those who have served as leaders in the field in multiple ways for many years. Authors include K-12 teachers, school administrators, district leaders, graduate students, higher education faculty, and professional development facilitators.

Author : Zalman Usiskin
Publisher : Prentice Hall
Page : 616 pages
File Size : 46,8 Mb
Release : 2003
Category : Education
ISBN : UVA:X004662628

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Mathematics for High School Teachers by Zalman Usiskin Pdf

For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.

Author : Marilyn E. Strutchens,Rongjin Huang,Leticia Losano,Despina Potari,Márcia Cristina de Costa Trindade Cyrino,João Pedro da Ponte,Rose Mary Zbiek
Publisher : Springer
Page : 58 pages
File Size : 41,6 Mb
Release : 2016-10-22
Category : Education
ISBN : 9783319389653

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The Mathematics Education of Prospective Secondary Teachers Around the World by Marilyn E. Strutchens,Rongjin Huang,Leticia Losano,Despina Potari,Márcia Cristina de Costa Trindade Cyrino,João Pedro da Ponte,Rose Mary Zbiek Pdf

This volume shares and discusses significant new trends and developments in research and practices related to various aspects of preparing prospective secondary mathematics teachers from 2005–2015. It provides both an overview of the current state-of-the-art and outstanding recent research reports from an international perspective. The authors completed a thorough review of the literature by examining major journals in the field of mathematics education, and other journals related to teacher education and technology. The systematic review includes four major themes: field experiences; technologies, tools and resources; teachers' knowledge; and teachers' professional identities. Each of them is presented regarding theoretical perspectives, methodologies, and major findings. Then the authors discuss what is known in the field and what we still need to know related to the major topics.

Author : Jerry A. McIntosh
Publisher : Prentice Hall
Page : 284 pages
File Size : 46,7 Mb
Release : 1971
Category : Mathematics
ISBN : UCAL:B4342394

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Perspectives on Secondary Mathematics Education by Jerry A. McIntosh Pdf

Author : M. Kathleen Heid,Patricia S. Wilson,Glendon W. Blume
Publisher : IAP
Page : 471 pages
File Size : 42,5 Mb
Release : 2015-12-01
Category : Education
ISBN : 9781681231150

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Mathematical Understanding for Secondary Teaching by M. Kathleen Heid,Patricia S. Wilson,Glendon W. Blume Pdf

A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level. The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use—each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice. Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations—examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers.

Author : Roza Leikin
Publisher : Springer Nature
Page : 580 pages
File Size : 46,8 Mb
Release : 2023-03-17
Category : Education
ISBN : 9783031188688

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Mathematical Challenges For All by Roza Leikin Pdf

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students’ mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students’ mathematical potential, quality mathematical instruction results from matching the level of mathematical challenge to different students’ potential. Thus, effective integration of mathematical challenge in the instructional process is strongly connected to the equity principle of mathematics education. In the three sections in this volume readers can find diverse views on mathematical challenges in curriculum and instructional design, kinds and variation of mathematically challenging tasks and collections of mathematical problems. Evidence-based analysis is interwoven with theoretical positions expressed by the authors of the chapters. Cognitive, social and affective characteristics of challenging mathematical activities are observed and analyzed. The volume opens new avenues of research in mathematics education, and pose multiple questions about mathematical instruction rich in mathematical challenge for all. The authors invite readers to explore and enjoy mathematical challenges at different levels.

Author : Marilyn Paula Carlson,Chris Rasmussen
Publisher : MAA
Page : 340 pages
File Size : 42,8 Mb
Release : 2008
Category : Mathematics
ISBN : 0883851830

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Making the Connection by Marilyn Paula Carlson,Chris Rasmussen Pdf

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.

Author : Robert Q. Berry III,Basil M. Conway IV,Brian R. Lawler,John W. Staley
Publisher : Corwin Press
Page : 328 pages
File Size : 48,5 Mb
Release : 2020-03-09
Category : Education
ISBN : 9781071806463

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High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice by Robert Q. Berry III,Basil M. Conway IV,Brian R. Lawler,John W. Staley Pdf

Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.

Author : Yeping Li,Rongjin Huang
Publisher : BRILL
Page : 314 pages
File Size : 52,7 Mb
Release : 2018-05-16
Category : Education
ISBN : 9789463512367

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How Chinese Acquire and Improve Mathematics Knowledge for Teaching by Yeping Li,Rongjin Huang Pdf

How Chinese Acquire and Improve Mathematics Knowledge for Teaching takes a unique approach to present new research that views knowledge acquisition and improvement as part of teachers’ life-long professional learning process in China.

Author : Alan Sultan,Alice F. Artzt
Publisher : Routledge
Page : 761 pages
File Size : 54,5 Mb
Release : 2010-09-13
Category : Education
ISBN : 9781135157838

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The Mathematics that Every Secondary Math Teacher Needs to Know by Alan Sultan,Alice F. Artzt Pdf

What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.