Abstract
Current reforms in geometry seek to challenge prevailing ideas about “what it means to do mathematics” (Stephan et al., 2015, p. 139) by engaging learners in “the grasping of space” (Freudenthal, 1973; Hansen et al., 1998, p. 241). This study takes up this challenge by investigating problematizing activity as an embodied phenomenon among 21 eighth-grade learners who engaged with spatial and dimensional concepts during a series of investigations around Flatland. Using a phenomenological research approach, we examined classroom discourse as well as learners’ blog postings, lived-experience descriptions, and interviews. The analysis revealed three manifestations of problematizing activity—provocation, impasse, and questioning and conjecturing activity. Embodiment was evidenced through perceptuo-motor-imaginary activity as learners juxtaposed naturally continuous space with discrete notions of space emphasized in K−12 settings.
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