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New Thinking about the Mathematical Education of Teachers

alanby Alan Tucker
October 2000

A forthcoming Conference Board on Mathematical Sciences report calls for rethinking the mathematical education of teachers at U.S. colleges and universities. (See CBMS Mathematical Education of Teachers Project Report at Recently, realization has been growing that more substantial mathematical content knowledge is needed for teaching school mathematics than was previously believed. For example, this knowledge should prepare an elementary school teacher to assess the validity of the following subtraction algorithm proposed by a student, by using properties of the place-value system of numbers:

43 – 27 = (40 – 20) + (3 – 7), where 40 – 20 is tens-place subtraction and 3 – 7 is ones-place subtraction,
= 20 + –4
= 16

International studies have also highlighted the importance of continuing study as an integral part of a teacher's school week. Thus, college mathematics courses should prepare teachers to learn much of the mathematics that they will need to know in the future rather than try to cram everything into the initial college education.

A preliminary draft form of some key recommendations in the report includes the following:

  1. Future teachers need mathematics courses that develop an in-depth understanding of the mathematics that they will teach.

    Courses about school mathematics should focus on a thorough development of basic mathematical ideas. Attention to the broad and flexible applicability of basic ideas and modes of reasoning is preferable to superficial coverage of many topics. All courses designed for future teachers should develop careful reasoning and mathematical common sense in analyzing conceptual relationships and in applied problem solving. Future teachers should learn how basic mathematical ideas combine to form the skeleton on which specific mathematics lessons are built. For example, the ideas of function, of algebraic representation of information, and of graphical representation (analytic geometry) form the basis of most of high school algebra and trigonometry.

  2. Elementary school teachers should take at least 9 semester hours of mathematics. Middle school teachers of mathematics (grades 5–8) should take at least 21 semester hours of mathematics. High school teachers of mathematics should complete the equivalent of an undergraduate major in mathematics.

    Elementary and middle school programs should include at least 9 semester hours in the mathematical knowledge needed to teach school mathematics well. High school programs should have at least 6 semester hours in the foundations of high school mathematics.

  3. Teacher education must be recognized as an important part of the mission of mathematics departments at institutions that educate teachers.

    Mathematics departments need to devote commensurate resources to designing and offering courses for teachers. They need to value and properly reward faculty members who are heavily involved in teacher education. In return, mathematics departments should receive the resources that they need to follow through on their commitment to high-quality teacher education.

    Mathematics departments engaged in teacher preparation should establish a committee on teacher education. In addition to monitoring teacher education, this committee can serve as a vehicle to engage more faculty in teacher preparation. Mathematics departments that grant doctoral degrees are encouraged to incorporate teacher education as a part of the instructional component of doctoral training.


Alan Tucker,, is a professor of applied mathematics and statistics at the State University of New York, Stony Brook, and is the lead writer on the Math Education of Teachers Project of the Conference Board of Mathematical Sciences.



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