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Toward a Leaner, Meaner Mathematics Education? By George D. Giffen Roosevelt High School Los Angeles Unified School District SUPPORTERS OF THE BACK-TO-BASICS MATHEMATICS STANDARDS seem to have a lot of trouble dealing with uncertainty. As a high school teacher of one of the reform mathematics curricula, I am not pleased with the recent decision of the California State Board of Education. Proponents of traditional mathematics education tend to favor: exercises over applications memorization over discovery precision over estimation direct calculation over calculation by number sense calculation over problem solving beyond the standard formula pencil and paper over calculators and computers In each of the continua above, certainty decreases from left to right. The more uncertain or less evident something is, the harder it is to learn, to teach, to evaluate. But our physical and social worlds are both full of uncertainty. The more we learn, the more we need to find out and the more problems we have to solve. Students need to learn the mathematical language to deal with uncertainty from an early age precisely because it is more difficult to learn than memorize 7 times 8. They also need to develop the habit of problem solving, which means confronting uncertainty. Astrophysicists may use calculus to draw inferences about the universe, but they use probability and statistics to check those inferences where they cannot see directly. Managers use statistics to make billion dollar decisions, assembly-line workers need statistics for quality control, and every citizen needs to understand statistics to evaluate information from the media. What really gets to me is that back-to-basics people assume, obviously without checking out our classrooms, that reform classrooms do not use practice, memorization, and pencil-and-paper calculation, and that our students do not learn algebra, geometry, and precision. These same people use test scores (statistics) as a weapon against reform curricula without ever doing a statistical analysis to see which curricula and what other factors may contribute to those scores. What we need is balance, not a position far to the left or right, and that means learning the mathematics of both certainty and uncertainty.