Bass’ latest book is a conceptual contribution to mathematics education.
Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics and Mathematics Education at U-M and member of the National Academy of Sciences and of the National Academy of Education, has published The Mathematical Neighborhoods of School Mathematics. Bass’ intention is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but—most importantly—its interconnections and overall coherence, a perspective not easily available from the school curriculum. This aim entailed assembling a variety of substantial mathematical domains that do not typically cohabit the same volume. The book begins with an in-depth treatment of topics in the school curriculum, often with novel approaches and connections. A unifying thread is the group theoretic study of addition and multiplication in the various number systems of school mathematics. The exposition is mathematically rigorous, including proofs of many fundamental theorems not otherwise easily available in mathematically accessible form.
The Mathematical Neighborhoods of School Mathematics is intended to be a conceptual contribution to mathematics education. Bass hopes it will be a valuable resource in professional development of mathematics teachers, and in mathematical enrichment programs, for both students and teachers. In this regard, many of the chapters are relatively self-contained. Bass says it could also serve as a text for undergraduate mathematics majors with an interest in teaching. In particular, Chapter 11 presents novel instructional designs for problem-solving activities meant to cultivate “connection-oriented mathematical thinking.”
Bass published The Mathematical Neighborhoods of School Mathematics with the assistance of Jason Brasel, a former high school mathematics teacher, who is a mathematics educator and researcher in secondary mathematics for TeachingWorks.