Reinholz, D., Trninic, D., Howison, M., & Abrahamson, D. (2010). It’s not easy being green: embodied artifacts and the guided emergence of mathematical meaning. 

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, pp. 1488 – 1496). Columbus, OH: PME-NA.

ABSTRACT: Situated at the intersection of research on embodied cognition and semiotic mediation, this on-going design-based research study of deep mathematics learning focuses on Grade 4-6 students’ guided task-based interaction with a novel computer-based hand-tracking system built to suggest the limitations of naïve additive schemes and create opportunities to develop core notions of proportionality as elaborations on these schemes, even before engaging numerical semiotic forms. Study participants struggled with canonical issues inherent to rational numbers: embarking from additive expectation expressed as virtual manipulation, they formulated a string of insights leading up to a new type of equivalence class. Reported as a case study of Itamar, a 5th-grade middle-achieving male student, our analyses reveal emergence of conceptually critical mathematical meanings in an activity that initially bears little mathematical significance.