# The Effects of the Unit Concept on Prospective Elementary Teachers' Understanding of Rational Number Concepts.

1994

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

Merlyn J. Behr

## Abstract

The purpose of this study was to follow and describe the cognitive processes of five prospective elementary teachers as they engaged in the formation of units and to examine the role of the unit concept as a possible link between the whole number and rational number domains. An attempt was made to gain an understanding of how the students constructed units and whether or not their attention to and understanding of the unit concept would increase their understanding of rational number concepts and operations. The rational number domain is one that causes great difficulties for students and their teachers. The complexity of this domain is revealed through the many roles in which a rational number can appear--measure, ratio, part-whole, quotient, and operator. In an effort to improve rational number understanding, focus has turned to the unit fraction and the basic concept of unit. It has been suggested that students possess intuitive or informal knowledge of unit formation and this knowledge may be used as a foundation for building rational number understanding. This study examined the role of the unit concept in bridging the gap between whole numbers and rational numbers. The students were five preservice elementary teachers enrolled in a mathematics course designed for elementary education majors. The group of five students was selected based on an inventory and personal interviews. Once selected the students participated in a teaching experiment that consisted of six lessons. Data was collected through videorecording, audiotapes, journals, essays, and students' written work. Results of the study indicated: (a) Students' awareness of their informal knowledge regarding the unit concept promotes understanding; (b) teachers who provide opportunities for students to build on their informal knowledge by working with various whole number units to develop unitizing and norming skills, help students develop schemes for further work with rational numbers; and (c) students who become accustomed to focusing on the unit may more readily recognize intuitive and authentic connections between natural and rational numbers.

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