Re-review...Did You Read This Book...Highly Recommended?
Interesting mathematics books abound. Unfortunately, I am not talking about the texts we give our students.
Alberto Martinez' Negative Math: How Mathematical Rules Can be Positively Bent Princeton University Press, 2006) is a recent book that should be read by mathematics teachers...and it should indirectly affect how students interact with their texts and the included mathematics.
Negative Math reflects on many interesting questions and statements made in mathematics classrooms. For example, consider the common statement of "minus times a minus is a positive," a claim that students memorize but rarely understand at any level. Martinez suggests that we should suppose that "minus times a minus is a minus"...and then creatively investigate what our mathematical world (e.g. high school algebra) would look like then. His observations and conclusions are both fun and revealing, producing new curves not akin to coordinate geometry.
In other chapters, the book deals with other negative number situations (e.g. what if -1 > 0) and other "impossible" numbers. The latter nomenclature reflects episodes in the history of mathematics, when mathematicians disallowed negative numbers as allowable solutions of algebraic equations.
One of Martinez' goals is to ducument that the "mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong." One implication is that students need to know this history as it revelas much about the development of mathematics as a human construction. Another implication is that as teachers we tend to present concepts and rules as being obvious and certain, when the opposite is the case.
And, yes there is some connection between the spoon on the cover, the book's title, and the book's message. As a hint in a nutshell, think "Uri Geller."
Note: This review is repeated from December 15, 2005.....You still have time to read it!