Building Multiple Models Using Recursive Reasoning
PurposesStudent model building; Reasoning
DescriptionOver the course of the fractions unit, students transitioned from building a single model to justify an answer to building multiple models to support their ideas and represent a single problem. Many students used recursive reasoning, basing the structure of one model on a previous model they had built. Some students progressed further in their reasoning, using the recursive methods to predict other models, as well as form generalization which would describe all the models of a specific type.
In these clips, we see how in the context of three different problems, the fourth graders use recursive reasoning to develop multiple models, predict additional models, as well as form general rules for the creation of models. Alan and Erik use recursive reasoning to model the comparison of one-half and one -fourth and generalize their findings; Alan applies recursive reasoning to build multiple models depicting the comparison of two-fifths and one-half, and predicts the form of larger models; and the class engages in a discussion using recursive reasoning to predict the structure of additional models for comparing two-thirds and three-fourths.
