Seventh-grade students’ representations for pictorial growth and change problems

The purpose of this teaching experiment was to investigate eight seventh-grade pre-algebra students’ development of algebraic thinking in problems related in growth and change pattern structure. The teaching experiment was designed to help students (1) identify and generalise patterns in relationships between quantities in the pictorial growth and change problems, (2) represent these generalisations in verbal and symbolic representations, and (3) build effective connections between their external and internal representations for pattern finding and generalising. Findings from the study demonstrated that the students recognized patterns in related problems that enabled them to describe generalised quantitative relationships in the problems. Students modeled their thinking using different external representations—drawing diagrams, creating tables, writing verbal generalisations, and constructing generalised symbolic expressions. Seven of the eight students primarily created and interpreted diagrams as a way to generalise verbally and then symbolically.