Overview

Making connections between representations of fractions requires a shared understanding of what a fraction is. Establishing and using definitions is a way to develop shared understanding. Definitions play an important role in mathematics. Definitions, along with basic logical principles, are one of the foundations of mathematical reasoning. Mathematical work requires that terms be defined unambiguously and with shared usage. Mathematical definitions provide the precision and shared meaning that is crucial for effective mathematical communication and reasoning.

Definitions are also a fundamental resource for the work of teaching mathematics. Knowledge of definitions supports the inspection of instructional materials and making judgments about the quality and usability of those materials. Because definitions give names and precise meanings to important concepts, teachers can use their knowledge of definitions to support communication, mathematical reasoning, and the reconciliation of classroom disagreement about mathematics.

This part begins to develop a working definition of a fraction. Calling it a “working definition” signals that the definition will be further developed and revised.