Students’ ways of reasoning about nonlinear functions in guess-my-rule games

There is a growing movement toward the introduction of algebra in early grades. This is supported by an increasing number of research studies that have reported success in getting young students to “do” mathematics considered beyond their reach. Yet, the consensus is that more research is needed to provide insights into the processes by which students make sense of algebraic ideas. In particular, more studies are needed on how nonlinear functions can be introduced in early grades. This article reports an algebra research strand that introduced seventh grade students to quadratic functions using Guess-My-Rule games. The article describes several instances of the students engaging successfully with ideas and forms of reasoning involving quadratic functions. The purpose is to contribute to the debate on the introduction of algebra in early grades by providing further evidence of young students’ ability to engage with algebraic ideas usually considered to be beyond their reach.