The Mathematical Neighborhoods of School
Mathematics visits regions beyond, but proximal to and accessible
from school mathematics. Its aim 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. 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. It could also serve as a text for undergraduate
mathematics majors with an interest in teaching. The exceptional
Chapter 11 presents some novel instructional designs for
problem-solving activities meant to cultivate “connection-oriented
mathematical thinking.”
Hyman Bass is the Samuel Eilenberg Distinguished University
Professor of Mathematics and Mathematics Education at the University
of Michigan. He is a member of the National Academy of Sciences and of
the National Academy of Education.
Jason Brasel, a former high school mathematics teacher, is a
mathematics educator and researcher in secondary mathematics, who
works at TeachingWorks, University of Michigan.
Readership
Pre-service and in-service secondary teachers (and
faculty who teach them) interested in expanding their knowledge of
the deeper mathematics underlying what they teach.