Prospective Elementary Teachers' Conceptions of
Rational Numbers

**Dina Tirosh**,
School of Education, Tel-Aviv University, Israel
**Efraim Fischbein**, School of Education, Tel-Aviv
University, Israel
**Anna O. Graeber**,
College of Education, University of Maryland, USA
**James W. Wilson**,
College of Education, University of Georgia, USA
August 8, 1998

**The United State-Israel
Binational Science Foundation**
This research was supported by the United States-Israel Binational
Science Grants (#88-00213/1) and (#92-00276). Any opinions, findings
and conclusions or recommendations expressed in this publication
are those of the authors and do not necessarily reflect the views
of this foundation.

Project 1

## Conceptual Adjustments in Progressing from Whole to
Non-negative Rational Numbers

The Conceptual Adjustments in Progressing from Whole to Non-negative
Rational Numbers project was funded by the United States-Israel
Binational Science Foundation, and four principal investigators
were: James Wilson, from the University of Georgia, Anna Graeber,
from the University of Maryland, and Efraim Fischbein and Dina
Tirosh, from Tel-Aviv University.

### The Main Goals of the Project

The four main aims of this project were:

1. To understand children's and prospective elementary teachers'
conceptions of rational numbers.

2. To develop didactic approaches aimed at helping prospective
teachers extend their own mathematical conceptions of rational
numbers and their knowledge about children's ways of thinking
about them.

3. To involve prospective teachers in activities that encourage
them to expand their notion of mathematics as a human activity.

4. To help prospective teachers decrease their mathematics
anxiety and raise their confidence in their mathematics ability.

Project 2

## Using Multiple Representations to Enhance Teachers'
Mathematical, Pedagogical and Curricular Knowledge of Rational
Numbers

The Using Multiple Representations to Enhance Teachers' Mathematical,
Pedagogical and Curricular Knowledge of Rational Numbers project
is funded by the United States-Israel Binational Science Foundation,
and four principal investigators are: James Wilson, from the University
of Georgia, Anna Graeber, from the University of Maryland, and
Efraim Fischbein and Dina Tirosh, from Tel-Aviv University.

### The Main Goals of the Project

1. To provide a comprehensive description of prospective teachers
mathematical, pedagogical and curricular knowledge of rational
numbers.

2. To develop teaching strategies for enhancing teachers' mathematical,
pedagogical and curricular knowledge of rational numbers and to
evaluate the impact of these strategies.

3. To explore the potential that multiple representations of
rational numbers have as a means of investigating teachers' mathematical,
pedagogical and curricular knowledge of rational numbers and to
investigate the use of multiple representations in facilitating
growth of teachers' rational number knowledge.

## Reports