The Categorizer is an interactive gallery that allows students to upload, share, and categorize their own and their peers’ digital artifacts. Students can observe any underlying rules that generated different artifacts, create their own categorical schemes for sorting and comparing those artifacts, and measure how well they agree or disagree about what artifacts should be grouped.
This project originally emerged from a collaboration with a K-8 school interested in exploring mathematical connections to nature and art. For this project, I created a tool for students to generate their own fractal structures by “writing” the rules to create those fractals geometrically on a computer screen. The fractals are generated using iterated function systems (IFS), and we used the tool with the categorizer to better understand how learners relate their geometric activities on the screen, which define how points in the unit square should map in order to construct the fractal, to set theoretic notions of function; area models of fraction; and different resultant fractal patterns.
A preliminary version of the Categorizer was presented at the 2011 Cyberlearning Tools for STEM Education conference.