Research, Reflection, Practice: Algebraic Thinking and Pictorial Growth Patterns

Abstract

Dorothy, a second grader at an at-risk school where 87 percent of the students receive free or reduced lunches, watched intently as Mrs. T laid out pattern blocks to create a sequence of figures shaped like people (see fig. 1). When Mrs. T asked Dorothy, “What will the next one look like?” Dorothy replied, “Well, if you wanted to go from [the first person] all the way to four … you would put a head, then the body, hands, then the feet. And then you would put a hat, and another hat, and another one, and another one …. I think that's heavy for a person.” Dorothy thought the hats looked a bit top-heavy; nevertheless, she extended the pictorial growth pattern by correctly building the fourth person (see fig. 1).