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Traditionally the approach to teaching arithmetic at the primary level has been based upon algorithms. Changes are underway that provide opportunities for children to develop more effective mental strategies. This study focuses on these changed methods.
This book is written for parents and other interested parties so that they can understand the great debate taking place in many states in this country about how to teach basic math. The debate centers around the standards written by the National Council of Teachers of Mathematics (NCTM), which call for a radically different approach to mathematics education. Because the issues are so heated between the NCTM-oriented curricula and traditional curricula (the curricula that NCTM-oriented replaced), the term Math Wars was coined to describe them. Parents are concerned about their children's math learning. Teachers are concerned about math teaching. When parents see what children are bringing home under the new curriculum, it is clear that their children are not working on the same mathematics that parents remember from the time when they were in school. But, the problem goes beyond grades K-12. Post-secondary mathematics courses are the fear of many students. The standards created by the NCTM do not necessarily prepare students for success, either on SATs or in college. Besides lack of knowledge about mathematics education, many parents have an additional problem in that they feel they lack knowledge in mathematics itself. This is very intimidating; thus it is difficult for parents to do anything about the confusing state of mathematics education. This book provides some answers.
Mathematical Connections is about some of the topics that form the foundations for high school mathematics. It focuses on a closely knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics--topics that have fallen out of fashion and that deserve to be resurrected. While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.
Stanford mathematician and NPR Math Guy Keith Devlin explains why, fun aside, video games are the ideal medium to teach middle-school math. Aimed primarily at teachers and education researchers, but also of interest to game developers who want to produce videogames for mathematics education, Mathematics Education for a New Era: Video Games as a Med