Solving algebra problems with interactive diagrams: Demonstration and construction of examples

We investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID. Students who worked with the ID that offered limited representations and tools (illustrating ID) looked for ways to bypass the designed constraints: they changed the representation of the data or built new representations, but did not create new examples in any form. Working with another type of diagram (narrating ID), students treated the specific given example as a generic example and were able to reach a generalization in a process of systematic change and comparison. The variety of tools and representations offered in the design of the third type of ID (elaborating ID) yielded diverse strategies: students constructed, without guidance, various examples and initiated further inquiry that sometimes resulted in the systematic construction of examples, although the ID provided no tools for systematic change.