Mathematics Matters In Education: Essays In Honor Of Roger E. Howe (advances In Stem Education)

"This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange."--Page 4 of cover Front Matter ....Pages i-viii Front Matter ....Pages 1-1 “Mathematics Matters in Education” to Roger E. Howe and to All: An Introduction (Yeping Li, W. James Lewis, James J. Madden)....Pages 3-7 About Roger E. Howe and His Contributions to Mathematics Education (Yeping Li, W. James Lewis)....Pages 9-18 Cultural Knowledge for Teaching Mathematics (Roger E. Howe)....Pages 19-39 Front Matter ....Pages 41-41 The Content Knowledge Mathematics Teachers Need (Hung-Hsi Wu)....Pages 43-91 Knowing Ratio and Proportion for Teaching (James J. Madden)....Pages 93-115 How Future Teachers Reasoned with Variable Parts and Strip Diagrams to Develop Equations for Proportional Relationships and Lines (Sybilla Beckmann, Torrey K. Kulow)....Pages 117-148 Giving Reason and Giving Purpose (Yvonne Lai, Mary Alice Carlson, Ruth M. Heaton)....Pages 149-171 Who Are the Experts? (John Ewing)....Pages 173-181 Front Matter ....Pages 183-183 Building on Howe’s Three Pillars in Kindergarten to Grade 6 Classrooms (Karen C. Fuson)....Pages 185-207 Is the Real Number Line Something to Be Built or Occupied? (Hyman Bass)....Pages 209-218 What Content Knowledge Should We Expect in Mathematics Education? (Richard Askey)....Pages 219-231 Approaching Euclidean Geometry Through Transformations (Zalman Usiskin)....Pages 233-244 Curricular Coherence in Mathematics (Al Cuoco, William McCallum)....Pages 245-256 Front Matter ....Pages 257-257 Attracting and Supporting Mathematicians for the Mathematical Education of Teachers (Amy Cohen)....Pages 259-275 The Contributions of Mathematics Faculty to K-12 Education: A Department Chair’s Perspective (Solomon Friedberg)....Pages 277-285 Supporting Education and Outreach in a Research Mathematics Department (Jerry Dwyer, Lawrence Schovanec)....Pages 287-299 Back Matter ....Pages 301-303