“Finding Common Ground in the U.S. Math Wars”, Science Magazine, May 19, 2006 describes the 18-month effort initiated by Richard Schaar, mathematician and former president of Texas Instruments, to bridge the gap between professional mathematicians, and math educators. Leaving many issues still to be addressed, the following is their initial statements:
All students must have a solid grounding in mathematics to function effectively in today’s world. The need to improve the learning of traditionally underserved groups of students is widely recognized; efforts to do so must continue. Students in the top quartile are underserved in different ways; attention to improving the quality of their learning opportunities is equally important. Expectations for all groups of students must be raised. By the time they leave high school, a majority of students should have studied calculus.
- Basic skills with numbers continue to be vitally important for a variety of everyday uses. They also provide crucial foundation for the higher-level mathematics essential for success in the workplace which must now also be part of a basic education. Although there may have been a time when being to able to perform extensive paper-and-pencil computations mechanically was sufficient to function in the workplace, this is no longer true. Consequently, today’s students need proficiency with computational procedures. Proficiency, as we use the term, includes both computational fluency and understanding of the underlying mathematical ideas and principles.
- Mathematics requires careful reasoning about precisely defined objects and concepts. Mathematics is communicated by means of a powerful language whose vocabulary must be learned. The ability to reason about and justify mathematical statements is fundamental, as is the ability to use terms and notation with appropriate degrees of precision. By precision, we mean the use of terms and symbols, consistent with mathematical definitions, in ways appropriate for students at particular grade levels. We do not mean formality for formality’s sake.
- Students must be able to formulate and solve problems. Mathematical problem solving includes being able to (a) develop a clear understanding of the problem that is being posed; (b) translate the problem from everyday language into a precise mathematical question; (c) choose and use appropriate methods to answer the question; (d) interpret and evaluate the solution in terms of the original problem, and (e) understand that not all questions admit mathematical solutions and recognize problems that cannot be solved mathematically.
For further elaboration, see Common Ground
Last month, NCTM (National Coucil of Teachers of Mathematics) endorsed a short list of skills, by grade, that every grade and middle school student must master. These “Curriculum Focal Points” are an attempt to correct the “mile-wide, inch-deep” curricula in most schools, which leave most student incapable and ill-prepared for further work in mathematics, science and engineering disciplines. The Focal Points document has not be published at this time.
But, to place these “improvements” into perspective, no one expects these initiative to make improvements by themselves. Further, UC-Berkeley Math Prof Hung-Hsi Wu says “Better mathematics education won’t take place in the next 10 years, I think it will take 30 years.”