Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers

✍ Scribed by Nicholas H. Wasserman

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 465
• Series: Research in Mathematics Education
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xxiii
Exploring Advanced Mathematics Courses and Content for Secondary Mathematics Teachers (Nicholas H. Wasserman)....Pages 1-15
Front Matter ....Pages 17-17
Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level (Kathleen Melhuish, Joshua Fagan)....Pages 19-45
Monster-Barring as a Catalyst for Bridging Secondary Algebra to Abstract Algebra (John Paul Cook)....Pages 47-70
What Kind of Opportunities Do Abstract Algebra Courses Provide for Strengthening Future Teachers’ Mathematical Knowledge for Teaching? (Sean Larsen, Erin Glover, Anna Marie Bergman, John Caughman)....Pages 71-84
Front Matter ....Pages 85-85
Excavating School Mathematics (William McCallum)....Pages 87-101
Foreshadowing Ideas in Abstract Algebra: Reflections from the Secondary School Mathematics Curriculum Improvement Study (J. Philip Smith)....Pages 103-124
Understanding School Mathematics in Terms of Linear Measure and Discrete Real Additive Groups (Hyman Bass)....Pages 125-147
Abstract Algebra and Secondary School Mathematics Connections as Discussed by Mathematicians and Mathematics Educators (Ashley L. Suominen)....Pages 149-173
Making Mathematical Connections Between Abstract Algebra and Secondary Mathematics Explicit: Implications for Curriculum, Research, and Faculty Professional Development (James A. Mendoza Álvarez, Diana White)....Pages 175-185
Front Matter ....Pages 187-187
Making Connections from the Secondary Classroom to the Abstract Algebra Course: A Mathematical Activity Approach (Rose Mary Zbiek, M. Kathleen Heid)....Pages 189-209
Learning Mathematical Practices to Connect Abstract Algebra to High School Algebra (Erin E. Baldinger)....Pages 211-239
From Equations to Structures: Modes of Relevance of Abstract Algebra to School Mathematics as Viewed by Teacher Educators and Teachers (Josephine Shamash, Marita Barabash, Ruhama Even)....Pages 241-262
Using Geometric Habits of Mind to Connect Geometry from a Transformation Perspective to Graph Transformations and Abstract Algebra (Yvonne Lai, Allan Donsig)....Pages 263-289
Developing a Structural Perspective and Its Role in Connecting School Algebra and Abstract Algebra: A Factorization Example (Younhee Lee, M. Kathleen Heid)....Pages 291-318
Building a Coherent Research Program that Links Abstract Algebra to Secondary Mathematics Pedagogy via Disciplinary Practices (James Cummings, Elise Lockwood, Keith Weber)....Pages 319-331
Front Matter ....Pages 333-333
Exploring an Instructional Model for Designing Modules for Secondary Mathematics Teachers in an Abstract Algebra Course (Nicholas H. Wasserman, Patrick Galarza)....Pages 335-361
Groups to the Rescue: Responding to Situations of Contingency (Rina Zazkis, Ofer Marmur)....Pages 363-381
Some Applications of Abstract Algebra to High School Teaching: Task Design and Polynomial Interpolation (Al Cuoco)....Pages 383-401
Impact of Abstract Algebra on Teachers’ Understanding of and Approaches to Instruction in Solving Equations (Eileen Murray, Erin E. Baldinger)....Pages 403-429
Blue Skies Above the Horizon (Ami M. Mamolo, Peter D. Taylor)....Pages 431-450
Back Matter ....Pages 451-461

✦ Subjects

Education; Mathematics Education; Learning and Instruction