Contents |
Committee | Preface
| Ch 1 | Ch 2 |
Intro to Ch 3-9 | Ch 3
| Ch 4 | Ch 5 |
Ch 6 | Refs for Part 1
| Other Reports | Ch 7
| Ch 8 | Ch 9

The following three chapters on the mathematical preparation for teachers at various grade levels take a different approach
than the recommendations of the 1991 MAA teacher preparation report *A Call for Change.* That report was built around a broad
inventory, stated in general terms, of the mathematical knowledge and reasoning that K-12 teachers need in order to teach
mathematics well. This report augments those recommendations, by giving more attention to the mathematical conceptions of K-12
students and how their teachers can be better prepared to address these ideas. The conceptions that prospective teachers often
bring to college classes also get considerable attention.

Teachers need to study the mathematics of a cluster of grade levels, both to be ready for the various ways
in which grades are grouped into elementary, middle, and high schools in different school districts, and to understand the larger
mathematical learning context in which the mathematics taught in a specific grade fits.

Consequently, mathematics programs for teachers need some breadth in the grade levels they target. This report calls
for mathematics specialists beginning at least by 5th grade, so that, for example, a mathematics specialist might teach all of the
4th and 5th grade students in a small K-5 elementary school.

Chapters 3, 4, and 5 in Part 1 of this report outline this mathematical foundation. Chapters 7, 8, and 9 (Part 2 of this report) describe this mathematical knowledge in greater detail and illustrate how the need for it arises in teaching. Part 2 is intended for those faculty members who will teach courses in the foundations of school mathematics or who want to broaden their backgrounds in school mathematics instruction. These chapters are also intended to be useful to mathematicians, in general, to make them aware of the pedagogical issues connected with "mathematical knowledge for teaching.''

Mathematicians need to help prospective teachers develop an understanding of the role of proof in mathematics. In the Reasoning
and Proof standard, *Principles and Standards for School Mathematics* says "Proof is a very difficult area for
undergraduate mathematics students. Perhaps students at the postsecondary level find proof so difficult because their only
experience in writing proofs has been in a high school geometry course.'' Prospective teachers at all levels need experience
justifying conjectures with informal, but valid arguments if they are to make mathematical reasoning and proof a part of their
teaching. Future high school teachers must develop a sound understanding of what it means to write a formal proof.

*Student*refers to a child in a K-12 classroom.refers to an instructor in a K-12 classroom, but may also refer to a prospective K-12 teacher in a college mathematics course ("prospective teacher'' is also used in the latter case).

Teacher

*Instructor*refers to an instructor of prospective teachers. In this report, that person will usually be a mathematician.