Trninic, D., Reinholz, D., Howison, M., & Abrahamson, D. (2010). Design as an object-to-think-with: semiotic potential emerges through collaborative reflective conversation with material. 

In P. Brosnan, Erchick, D., & Flevares, L. (Eds.), Proceedings of the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 32) (Vol. VI, Ch. 18: Technology, 1523 – 1530). Columbus, OH: PME-NA.

We chart a historical analysis of a collaborative design-based research project investigating the emergence of mathematical meaning from embodied interaction with a technological tracking-system supporting the learning of proportionality. Recounting iterative cycles of a conceptually critical perceptual feedback element, we articulate three interconnected images of research-based designers: (a) Janus the two-headed keeper of passageways who sees artifacts alternately as a student would or as an expert would; (b) an investigator searching to explicate design decisions coherently in light of learning-sciences theory; and (c) a reflective practitioner who embraces tradeoffs and is open to constructive criticism and to implementing radical changes to design and theory. Ultimately, we posit, we as researchers are continuously developing professional vision for our own design even as the design changes.