Which side of the “math wars” is correct?
Reform efforts during the 1980s and 1990s downplayed computational skill, emphasizing instead that students should understand and be able to use math. In extreme cases, students were expected to invent math with little or no assistance. Reactions to these efforts led to increased attention to memorization and computational skill, with students expected to internalize procedures presented by teachers or textbooks. The clash of these contrasting positions has been called the “math wars.”
Which position is correct? Neither. Both are too narrow. When people advocate only one strand of proficiency, they lose sight of the overall goal. Such a narrow treatment of math may well be one reason for the poor performance of U.S. students in national and international assessments.
Math instruction cannot be effective if it is based on extreme positions. Students become more proficient when they understand the underlying concepts of math, and they understand the concepts more easily if they are skilled at computational procedures. U.S. students need more skill and more understanding along with the ability to apply concepts to solve problems, to reason logically, and to see math as sensible, useful, and doable. Anything less leads to knowledge that is fragile, disconnected, and weak.