#467: A First Grader Making Sense of Graphs: A Knowledge-in-Pieces Account of Functional Thinking

We present the case of Lucca (pseudonym), a six-year-old who participated in three interviews before, during, and after a classroom teaching experiment on function graphs. We analyzed his reasoning by identifying the resources he drew on: seeds of algebraic thinking and resources tied to the graph. Lucca’s functional thinking can be understood through the lens of Knowledge in Pieces: recursive and functional reasoning was supported by his coordination of resources. As his functional thinking developed, the seeds he used remained consistent, but the resources tied to the graph he coordinated were different.