Arithmetic equality statements: numerical balance and notational substitution

Numerous studies have investigated the benefits of teaching young children that the equals sign means “is the same as” and presenting a variety of statement forms such as a+b=b+a and c=a+b. However, an important and overlooked aspect of equivalence relations is that of replacing one term with another, which implies a “can be substituted for” meaning of the equals sign. I report a trial with a pair of primary pupils working on a computer-based task that requires viewing equality statements in terms of both numerical balance and notational substitution. I present screenshots and transcript excerpts to illustrate how they articulated and coordinated balance and substitution in order to achieve the task goals.