Chase, K., & Abrahamson, D. (2013). Rethinking transparency: Constructing meaning in a physical and digital design for algebra.

In J. P. Hourcade, E. A. Miller, & A. Egeland (Eds.), Proceedings of the 12th Annual Interaction Design and Children Conference (IDC 2013) (pp. 475-478). New York: IDC.

ABSTRACT: In the course of developing an experimental algebra unit, the researchers noted variability in their design’s instructional potential across a set of implementation media. In an effort to explain this variability, we revisited the classical theoretical construct of transparency. Transparency is the perceptual and conceptual accessibility of the mechanism, logic, and application of a tool. Corroborating earlier literature, it appears that participants saw only what they had built—transparency is a subjective achievement of a learner rather than an inherent feature of a device. Our first design prompted students with an algebraic proposition, for example “3x+2=4x-1”. The two equivalent expressions were to be interpreted by students as alternative quantifications of a single linear spatial interval; namely, the path that a giant took on two separate occasions to bury and recover treasure. Problem solving required manually adjusting the modeling media to coordinate two types of equivalence: (a) the total length represented by each expression; and (b) the length represented by the variable and known units. The researchers found that successful coordination was predicated on the subjective transparency of the models’ perceptual elements within the media. Therefore, in redesigning the activity as a computer-based application we will have learners first construct tools and only then automatize them.