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What Should Secondary School Mathematics Teachers Know?

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by Johnny W. Lott, NCTM President 2002-2004
NCTM News Bulletin, October 2003

A well-prepared teacher is vitally important to a child's education. So important, in fact, that teacher preparation is one of the focus areas for federal legislation. To give secondary school teachers the best preparation, The Mathematical Education of Teachers, Part I (Conference Board of the Mathematical Sciences 2001) proposes that "prospective high school teachers of mathematics should be required to complete the equivalent of an undergraduate major in mathematics, that includes a 6-hour capstone course connecting their college mathematics courses with high school mathematics." The report recommends that prospective teachers of secondary school have "a knowledge of the mathematical understandings and skills that students acquire in their elementary and middle school experiences, and how they affect learning in high school." Additionally, it is suggested that future teachers need a "knowledge of the mathematics that students are likely to encounter when they leave high school for collegiate study, vocational training or employment" and "mathematical maturity and attitudes that will enable and encourage continued growth of knowledge in the subject and teaching."

These are lofty and desirable goals that NCTM certainly supports but that may rarely be found in teacher preparation programs. Consider what would be required to make these recommendations a reality.

  • "The equivalent of an undergraduate major in mathematics"
    The route to the front of the classroom is being shortened to address teacher shortages; however, current high school mathematics curricula can be taught successfully only by teachers who have a deep knowledge of mathematics. To create a program that includes the courses necessary to satisfy this goal, a joint effort would be required of teacher preparation programs, certification programs, state certification officers, and the U.S. Department of Education. Additionally, it would require rethinking the classes that constitute an undergraduate mathematics major. And, since most mathematics departments are not allowed simply to add a 6-credit capstone course to an existing mathematics major program, several university approvals would be required to institute such a program.
  • "A 6-hour capstone course connecting college mathematics courses with high school mathematics"
    Finding faculty to teach this course would be challenging because mathematicians around the nation who have enough interest in, or knowledge of, the secondary school mathematics curriculum to deliver this course may be rare. The intent of the recommendation is to develop an understanding in preservice teachers of how high school mathematics carries over into advanced mathematics courses. The best potential teachers may be a team composed of a mathematician and a practicing high school teacher. Thus, a rethinking of how to teach prospective teachers is required.
  • "A knowledge of the mathematical understandings and skills that students acquire in their elementary and middle school experiences"
    We might look to our Japanese colleagues to achieve this worthwhile goal. In some Japanese universities, there is a required component of an elementary school practicum in every prospective secondary school teacher's program of studies. This model would require revolutionary thinking in the United States but could help us attain a greater level of cohesiveness in mathematics programs.
  • "A knowledge of the mathematics that students are likely to encounter when they leave high school for collegiate study, vocational training or employment"
    Education should always be forward-looking—preparing students not only with the knowledge for today but with the understanding of mathematics that will enable them to be flexible and "problem solve" in the future. A crystal ball might help us predict the mathematics that they will need to know in the distant future, but the next best thing might be a team composed of a mathematician, a vocational mathematics educator, and a community businessperson who work together to think through the mathematics needed for employment in the future.
  • "Mathematical maturity and attitudes that will enable and encourage continued growth of knowledge in the subject and teaching"
    Fostering mathematical maturity and attitudes for continued growth in the subject and teaching is not a trivial issue. First, we may have to rethink how one gains mathematical maturity and be firmly aware that such maturity will require more than simply participating in coursework. That may be a part of the picture, but it cannot stand alone. We must recognize that there are many different routes to mathematical maturity and a variety of studies; some from other disciplines may be contributory routes. Second, fostering "good" mathematics attitudes may require a concerted effort to change public perception about mathematics.

These goals would all require changes in university teaching but very well could promote good teaching. Are we willing to make a commitment to achieve them?

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