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

Abstract

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.