Specialized Understanding of Mathematics: A Study of Prospective Elementary Teachers

This dissertation study informs the field on how, when and where a specialized understanding of math (SUM) might be developed within a teacher education program by focusing on the three following research questions and related methodology.

1) What are the strengths and weaknesses in prospective elementary teacher’s specialized understanding of mathematics as they enter their mathematics methods course?

The Number and Operation and Geometry items from the Content Knowledge for Teaching Mathematics instruments, which have been developed at The University of Michigan’s Learning Mathematics for Teaching Project, were administered to 244 prospective elementary teachers at four universities during the first two weeks of the mathematics methods course. An item analysis sheds light on areas of strengths and weaknesses, and a statistical analysis was conducted to see any relationships between content understanding and quantity and type of content courses. A relationship was found between participants who took specialized content courses and the pretest scores. Another interesting finding was that simply taking more mathematics content courses is not related to higher scores.

2) Does the specialized understanding of mathematics change as they take the mathematics methods course?

The CKTM items were administered as a post test during the last two weeks of the methods course and compared with the pre test to look at changes, both as a paired samples t test and an item analysis. Growth in SUM was found between the pretest and posttest.

3) What learning opportunities during the methods course may improve the specialized understanding of mathematics of prospective elementary teachers?

Interviews were conducted with mathematics methods instructors who saw significant growth on specific items. The general philosophy of the course, as well as specific learning opportunities that may have helped understanding in the specific items that saw growth were explored, and a framework was created of learning opportunities that may impact understanding of mathematics. The learning opportunities that seem to add to improved SUM include readings, communication, experiencing children’s mathematical thinking, mathematics activities, manipulatives, and field experiences.