Using computer programming activities and robots to teach generalization of a geometry concept

Computer science and math education researchers have long believed that a symbiotic relationship exists between their disciplines [7]. In fact, in its early days, computer science education programs were often co-located in a math department. Stenger et al. [13] developed an instructional treatment that uses computer programming as an explicit method for teaching abstraction and generalization in the STEM classroom. This instructional strategy uses computer programming to explore the essential characteristics of a mathematical concept and to push learners to advance in levels of abstraction. In this study, results are shown from a professional learning session using computer programming activities, mathematical arguments, and programming on an S2 robot to push middle and high school computer science, math, and science teachers (N=25) to improve their level of generalization over area expansion of a triangle with respect to the expansion of the sides of the triangle. The programming activities served as a laboratory to expose and explain what happened in the minds of learners as they explored and learned to generalize this geometry concept. The researchers used an initial genetic decomposition to evaluate the learner's level of abstraction. Follow up interviews were conducted with 6 participants. The analysis, using APOS as a framework, categorized mathematical behaviors at the Action, Process or Object level. The data demonstrated how computer programming activities influenced teachers' mental images and pushed them to higher levels of abstraction.