Learning mathematics with interactive diagrams

The domain of digital interactive mathematics textbooks is new and largely unexplored as yet. In our study we seek to identify practices associated with the design of type of textbook and to focus on the functions of interactive visual representations, which we call interactive diagrams (IDs). An ID is a relatively small and simple software application (an applet) built around a pre-constructed visual example. We are interested in studying the learners' problem solving routines when using IDs. Micro-analysis of the discourse and gestures of a group of 13-14 year old algebra students working with an ID enable us to determine whether and how the designed components of the ID (the example that appears in the diagram, animation, representations, and linking tools) participate and are instrumented in the problem-solving processes. The data show that the small number of animated representations in the diagram, the partial linking between the various visual representations, and the sketchy nature of the representations made the task an interesting challenge for the students and prompted mental work that resembles mathematicians' habits of mind: conjecturing, deriving conclusions and arguing, and logically explaining the conclusions.