By Paul Clopton
Fuzzy Math refers to the many newer
mathematics programs that reflect
current fads in mathematics education and are generally inadequate for effective learning. The word "fuzzy" connotes "warm and fuzzy" or "fuzzy" thinking, and does not refer to advanced topics like fuzzy logic.
Fuzzy Math programs emphasize process over content and even correct answers, and are deficient in mathematical depth and breadth. Fuzzy Math takes many forms, but here are some of the more common varieties:
- No textbook - Publishers are selling instructional materials including overheads, software, dice, spinners, and building blocks instead of textbooks, which have clear explanations, worked-out examples, and practice problems.
- MTV - Characterized by lots of color and pictures that often have no relationship to mathematics and do not contribute to learning, parents are right to worry that students cannot hear the mathematics amid all of the noise.
- PC - These math programs often include politically correct lessons, such as writing essays about how to save trees or whales. Grades may be based on political correctness, not math skills and knowledge.
- Discover-It-Yourself - Based on the notion that children learn what they discover on their own, this approach avoids giving direct instruction to students. Learning takes longer this way, so less material is covered, and great demands are placed on teachers and their mathematical knowledge.
- Guesswork - Many of these programs promote guessing (rather than knowing) and devote considerable time to this process. Students are encouraged to work on problems they have no idea how to solve and are discouraged from practicing methods that lead to mastery.
- Anti-Algorithm - Textbooks promoting this method may discuss many ways to multiply but fail to cover the traditional method. They often encourage the use of calculators and pay little attention to manual computation.
- Project and Investigation - Students spend a great deal of time addressing non-mathematical aspects of working on projects. A group of four students may spend a week on a project that actually requires just one student to solve a few simple problems.
- Group Learning and Group Testing - In groups, the faster students often do the work and the slower ones go along for the ride. Group learning and group testing help to equalize grades and enable failing students to pass their classes anyway.
- Integrated Content Some argue that mathematical subjects, such as algebra and geometry, should not be taught in isolation, but should be integrated with other subjects. In practice, the mathematical development becomes so mixed up that it is impossible to determine what children should be learning at any given time. Accountability becomes impractical, and achievement suffers.
- Write About It - Based on the assumption that students should be able to explain their math, precious time is spent writing essays with very little math content. In some cases, most of the math involves figuring out margins and spacing on the word processor.
If fuzzy math has invaded your world, first determine what your children should be learning. See the grade level standards for math in California or visit www.mathematicallycorrect.com on the internet. Next, look for less fuzzy materials your children can use both at home and at school to meet those goals. Stay involved with your children's math and monitor their progress toward the goal for each grade level. This is no easy task, but it is the only way to ensure real success.
Paul Clopton is a biomedical research statistician with the Department of Veterans Affairs in San Diego. He is a cofounder of Mathematically Correct and has worked on the California mathematics frameworks, statewide tests, and textbook adoptions in California. Reprinted by permission from the August, 2001 issue of Parent Power! Helping you make sense of schooling today, published by The Center for Education Reform. Web: www.edreform.com. For a free e-mail subscription to Parent Power!, log onto www.edreform.com/parentpower/signup.htm.