Current reforms in geometry seek to challenge prevailing ideas about “what it means to do mathematics” (, p. 139) by engaging learners in “the grasping of space” (; , 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.
Keri Duncan Valentine, Department of Curriculum and Instruction/Literacy Studies, West Virginia University, 607-E Allen Hall, Morgantown, WV 26506; kevalentine@mail.wvu.edu