Friday, June 20, 2008

A Few More Gleanings: Dispelling Myths

Here are more snippets from the
Math Coach, A Parent's Guide to Helping Children Succeed in Math, responding to several "myths" being promoted by the "new math" proponents:

"Concrete and abstract ideas are not separated in the brain, but lie on a continuum. So the implied mental leap necessary to cross from concrete ideas to abstract ones is fictitious." (written in response to "new math" supporters' claim that children under twelve years of age are not capable of learning abstract concepts and operations)

"Object-oriented activities are very useful for young children who are just getting a grasp of the concepts of number, addition, and subtraction. But kids get a grip on such abstractions quickly, and they rapidly outgrow the need to manipulate beads and lay rods end to end every time they are asked to add and subtract. Once children are ready to start doing math on paper, such activities are a tedious waste of time." (responding to the overuse of exercises that involve manipulating objects to teach arithmetic)

"Age is not an important factor; knowledge is." (responding to the myth that the brains of middle school students are too immature to learn algebra, and elementary students have limited ability to understand story problems because they have trouble understanding the meaning of addition or subtraction)

"Over the past two decades, cognitive psychology researchers have repeatedly shown that problem-solving methods and other higher order thinking skills can be used effectively only when a person has a large body of knowledge on which the thinking skills can operate." (responding to the big push to teach students general problem-solving methods)

Dr. Wickelgren points out that these general methods are not really beneficial because they are replacing math facts and specific problem solving skills.

"Creativity is an outgrowth of learning, and a lot of it. . . the more a person knows about a subject, the more creative he or she can be in it. . . A student's ability to be creative in any area of knowledge increases with his or her knowledge of that area. . . Thus, a desire to enhance creativity should not move a curriculum away from the math basics -- but closer to them." (responding to the idea that developing creativity frees a child to let his/her thoughts blossom and thus allows him/her to gain more knowledge)

. . . . . . . .

In response to a comment by Concerned, I need to make clear that Dr. Wickelgren's book is not only about identifying "new math" teaching. The book is divided into two parts.

Part 1 covers such topics as Setting Goals for Your Child, Evaluating Schools, Strategies for Excellence. In Part 2, he covers such topics as Teaching Tips for Parents, Basic Arithmetic, Basic Story Problems, Fractions, and Algebra.