Guiding students’ learning with an interactive diagram: The case of equations

The article reports on a study of the resources and constraints designed in interactive diagrams to guide students’ development of ways to solve quadratic equations and perform algebraic manipulations. We report qualitatively on an experiment in which four 14- and 15-year-old students were challenged by a task presented as an interactive diagram (ID). The study provides evidence of the way IDs help students in their exploration. We provide a scheme to follow the development of new mathematical knowledge. Knowledge development begins with students’ spontaneous ideas relating to the context of the task, and it evolves through guided explorations supported by the design of the ID.