Richard Kitchen is an assistant professor in the College of Education at the University of New Mexico in Albuquerque, New Mexico. His primary interests are problem solving and alternative assessment formats.
E-mail: kitchen@unm.edu

Julie DePree is an associate professor in the Department of Mathematics and Statistics at the University of New Mexico- Valencia Campus in Los Lunas, NM. She teaches many of the mathematics courses for teachers and also teaches statistics and algebra courses.
E-mail: jdepree@unm.edu

In this article, the authors describe their efforts to assess prospective K-8 teachers’ knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers’ work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students.

In general, the prospective teachers used good estimation strategies and were capable of engaging in proportional reasoning, but many had misconceptions about fractions, decimals, and proportions. In particular, the prospective teachers had difficulties converting between decimals and fractions. Because of errors made when working with fractions and decimals, most failed to correctly solve the task. The prospective teachers’ errors and misconceptions highlighted the difficulties they had making sense of fractions and decimals.

The lack of facility when converting between a decimal and a fraction illustrated that the prospective teachers need multiple experiences making sense of decimals and fractions, and converting between them. To address prospective teachers’ deficiencies in making sense of fractions and decimals, converting between them, and working with proportions, the authors are placing more emphasis on these concepts in their mathematics content and methods courses for prospective K–8 teachers.