Is Learning Data in the Right Shape?

Anthony E. Kelly


In this short thought-piece, I attempt to capture the type of freewheeling discussions I had with our late colleague, Mika Seppälä, a research mathematician from Helsinki. Mika, not being a psychometrician or learning scientist, was blissfully free from the design constraints that experts sometimes ingest, unwittingly. I also draw on delightful conversations with the German research mathematician, Heinz-Otto Peitgen, a polyglot whose work includes advances in medical imaging and explorations in fractal geometry for K–12 students. Together, they taught me to reconsider foundational assumptions about learning, how to describe it, and how to grow it. Accordingly, I use this set of papers as a prompt for examining assumptions that numerical precision ensures scientific insight, that linear models best capture growth in learning, and that relaxing a fixation with time (exemplified by the reification of pre- and post-testing) might open up new topologies for describing, predicting, and promoting learning in its myriad manifestations.


Learning; modeling; linearity; complexity theory

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