Emphasizing the NCTM Content Standards in Undergraduate Courses for Prospective Teachers

"How can this Abstract Algebra course help me to teach Algebra in high school?" To professors of prospective mathematics teachers, this type of question has a resounding familiarity. Because students are unclear as to the relationship between upper division mathematics courses and the high school curriculum, answering the opening question to the students' satisfaction is almost impossible. These students view calculus and statistics as content courses that need to be learned, but do not reflect on how these courses embody the same mathematical ideas found in high school mathematics. Also, evidence that mathematics majors are entering the teaching profession with insufficient mathematics knowledge points to the further widening of the gap between teachers' undergraduate mathematics experience and their high school mathematics courses. In this paper, the authors describe one effort to close this gap by acquainting the prospective teachers with the National Council of Teachers of Mathematics (NCTM) "Standards." The authors' goal is to raise awareness that in studying mathematics on the lower and upper division levels, future teachers are getting practice with the very ides that they will be conveying to their students. The authors begin with a brief review of the "Standards," followed by detailed examples demonstrating connections between three undergraduate topics and the "Standards." They then describe how they used this exercise in a methods course for mathematics education majors and include the students' suggestions for how this exercise can help in providing answers to this article's opening question.