ABSTRACT
This chapter presents the role of visual models in the development of fluency with understanding. It talks about two important perspectives to consider when using the progressions in relation to visual models: understanding evidence of the sophistication of student strategies when they solve problems and guiding instructional decisions. The use of a particular model to solve a problem is evidence of the level of sophistication of the strategy and can indicate how students understand multiplicative situations. The transition from equal group models to array models can include a point where students only consider one dimension of the array and as a result may display their objects in an array but still see the equal groups in the array only along one dimension. The chapter also presents the different visual models for multiplication. Visual models for multiplication differ in appearance, sophistication, flexibility, and usefulness beyond whole number multiplication.
