The Myth of Ability: Nurturing Mathematical Talent in Every Child.

THE MYTH OF ABILITY: Nurturing Mathematical Talent in Every Child. John Mighton. Walker & Company, 2004. 216 pp. $14.00. Like reading, math is universally accepted as one of the core academic subjects. Both are taught from the earliest grades, are regularly included in high-stakes assessments, and are understood to be the future gateway to new learning opportunities. The current trend in education is to make children and students happy in their studies, so as to prevent "math anxiety." My experience is that children and students are happiest when they truly understand the principal concepts of mathematics, not when we make believe that they do. Mighton believes that while many teachers are good at math, they may find it hard to isolate or describe steps and often blame students for their own failures as teachers. He notes that math manuals are intended for teachers and contain almost no discussion of how to guide a student, step by step, to understand and problem-solve. He also believes that a teacher who expects a student to fail is almost certain to produce a failure.

Six units from The JUMP Method Manual are included in this book. The manual assumes that young children are capable of understanding advanced mathematics, but it does not ask students who have fallen behind to struggle with open-ended problems without guidance. Mighton shares several stories of dramatic improvements in mathematical abilities, particularly with remedial students. New concepts and operations are introduced through extremely mechanical steps that a student cannot fail to grasp. While the steps are simple, the goal is not to produce students who can do math only by rote, but rather students who can solve problems requiring careful reasoning and systematic search. Mighton is convinced that all children, except possibly those who are severely disabled, can be led to think mathematically.

JUMP (Junior Undiscovered Math Prodigies) started with a series of fortunate events. Mighton came across two books that determined how he taught math for the next 20 years. The stories awoke in him a sense of wonder and helped him recall how much mathematics they had behind the storyboard. One story was science fiction from the local library and the other was a thick psychology book on giftedness in children. As he read the books, he learned that the "mental process of a great scientist and mathematician were of an order entirely different from those of an ordinary person." As this belief sank in, he began to find math more difficult.

The year after he finished graduate studies, he read a book of letters by the poet Sylvia Plath. She wrote sonnets and sestinas, memorized the thesaurus, and read mythology. Ten years later, Mighton emulated her style of writing, and taught himself to write. At 28, he worked in a center as a math tutor. One of his first students was close to failing Grade 8 math. He had been told by his teacher that he wasn't bright enough to do well in math. Mighton began his work with this student without making any judgment about his ability; he proved to be an ideal student who worked hard. In Grade 13, the same student did so well in the Sir Isaac Newton physics competition that he was offered a scholarship to Waterloo University. Seeing how several of his students were developing as mathematicians, Mighton decided to backtrack and revisit his tutorial methods. He discovered great benefits if he reduced his explanations to simple steps.

Mighton then started a program for elementary students using similar approaches--JUMP. Explanations of initial concepts are followed by a sequence of small mechanical steps, and the students teach themselves mathematical concepts without any assistance. New abilities emerge from entirely mechanical work. With each step, Mighton gives several examples and then writes out two or three questions, leaving enough room under each question for the students to work. After several tests of this sort, when he is sure the students could reproduce the steps automatically, he moves on to the next step. With lessons that teach all steps at once, a weaker student will not be able to remember the first step by the time he reaches the last. The JUMP method proceeds one step at a time, allowing time for repetition.

This remedial program is successful because it is as much psychological as mathematical. Children enjoy discovering mathematical ideas for themselves, through experiments and open-ended activities. In the JUMP method, students learn to recognize patterns, select appropriate algorithms, and carry out complex sequences of operations. The material is designed to train students' attention and build confidence. Reviewed by Isabel Rodriguez-Dehmer, College Prep Instructor, Miami-Dade College North Campus, Miami, FL