Summary

Mathematics learning encompasses a broad range of processes and skills that change over time. Magnitude and equivalence are two fundamental mathematical ideas that students encounter early and often in their mathematics learning. Numerical magnitude knowledge is knowledge of the relative sizes of numbers, including whole numbers, fractions, and negative numbers, within a given scale. Understanding mathematical equivalence means understanding that two or more specific quantities with the same value can be represented in a variety of ways and remain equal and interchangeable. A major area of research on equivalence is knowledge of the equal sign. Both equal sign knowledge and magnitude knowledge are foundational in that they predict later learning in mathematics, including algebra. Implications for practice include the use of number lines and more variation in the way that arithmetic problems are formatted.