This paper describes some of the research-based principles that I use when designing learning experiences to foster conceptual understanding. These principles are illustrated through the discussion of one type of experience: that of sorting multiple representations. I refer to learning experiences rather than tasks, because tasks are only one component of the design. Close attention is also paid to the role of the teacher in creating an appropriate climate for learning to take place.
After a brief excursion into my own theoretical framework, I describe the educational objectives behind my design and provide a detailed explanation of it in one topic, that of algebraic notation. This is followed with an explanation of the principles that informed the design and the evolution of the task. Finally, I briefly indicate how the design might be generalised to include other topics.
A new journal for educational research has seen the light of day: Educational Designer! The journal is an online journal, and it was established by the International Society for Design and Development in Education. One of the articles in the first issue is written by Malcolm Swan, mathematics education researcher from the University of Nottingham. The article is concerned with Designing a Multiple Representation Learning Experience in Secondary Algebra. Here is the abstract of Swan’s article (but the entire article is available online!):