Supporting Inquiry Learning: an Intellectual Mirror that Describes what It “Sees”

Muchimportant research on the learning of mathematics with technology-supported inquiry has been devoted to learning with multiple-linked representations (MLR) as a mode of feedback. Like a mirror, MLR feedback helps students see their actions in one representation “reflected” in another. Yet, research has followed learning episodes where MLR feedback did not lead to concept formation and the achievement of curricular goals. This article reports on the potential of what might be thought of as a mirror that speaks. In response to example-eliciting tasks, students use interactive diagrams to create examples to which mathematical descriptions are automatically associated. Such descriptions may be thought of as another kind of linked mathematical representation system. Transitions feature in two ways in our analysis of students’ use of this representation. At the level of student activity, we examine when students move between attending to textual descriptions and to the graphs that they describe. We are also interested in how attention to these descriptions and co-ordination with their own use of these words can support students in making a transition in their thinking from considering distance as only total distance traveled, to a co-ordinated view of distance including both total distance traveled and distance from a starting point. This article focuses on two example-eliciting motion tasks and two sets of descriptive words. We found that these sets of words helped students, while and after they were working with the diagram, to distinguish between total distance traveled and position with respect to a starting point.