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\input zb-matheduc
\iteman{ZMATH 2014a.00807}
\itemau{Brown, Stephen I.}
\itemti{Insights into mathematical thought. Excursions with distributivity.}
\itemso{Reston, VA: National Council of Teachers of Mathematics (NCTM) (ISBN 978-0-87353-712-4/pbk). 111~p. (2013).}
\itemab
Publisher's description: The distributive principle is one of the most important and widely used concepts in mathematics. Though interlaced with other mathematical concepts, it provides a spotlight on major educational and mathematical themes. It is a significant tool in seeking ways of relating algebraic and geometric thinking and of expanding their very different potential to formulate generalizations. Stephen Brown, through his research, writings, and practice in the classroom, has discovered the deep and powerful educational and mathematical implications of applying the distributive principle as a way to encourage students to relate mathematics to the ``real world," to seek connections beyond science and mathematics, and to include literature and language as ways of expanding their mathematical thinking. This extraordinary collection of essays, each of which uses the distributive principle to shed light on a different aspect of mathematical thought, encourages readers to find new ways of understanding the significance and limitations of a subject that is usually presented as purely logical and not often connected with how the mind works in other domains. Using the distributive property as a vantage point, the essays cast a wide net. For example, in one essay the connections between algebraic and geometric variations of the property are developed in the context of presenting enticing problems. Though prime numbers are part of the curriculum (in such diverse topics as the infinitude of primes, the unique factorization of composites into a product of primes, and the ability to reduce all fractions to ``lowest terms"), in focusing on the distributive property, the author expands on the concept of prime numbers in ways that point out the deep significance of concepts that are often prematurely taken for granted. A truly innovative and unique approach to an important concept, this book provides readers with a new perspective on mathematical thought. The book will inspire both teachers of mathematics of all levels and readers interested in mathematics to incorporate aspects of thinking and feeling that are rarely included in mathematical activities.
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\itemcc{M10 C30 D40}
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