UBC Theses and Dissertations
Living mathematics education Renert, Moses Eitan
This dissertation searches for possible sources of life in mathematics pedagogy. It is motivated by my observation that much of mathematics education of today is obstructed by inertia. We teach mathematics today using methods and educational philosophies that have changed little in decades of practice, and we generally avoid the harder question of why do it at all? I use Wilber’s (1995) integral theory, a broad metatheory of psychosocial development, to conceptualize life in general, and aspects of life in mathematics education in particular. Wilber’s epistemological framework, called AQAL, describes reality as manifesting in four quadrants – subjective, objective, intersubjective, and interobjective – and in multiple developmental levels. I use AQAL to examine what is revealed about life in mathematics education through these perspectival lenses. The dissertation studies evolutionary dimensions of five related phenomena in mathematics education: purposes of teaching and learning mathematics, human relations in mathematics classes, the subject matter of mathematics, teachers’ mathematical knowledge, and ecological sustainability. I connect the diverse evolutions of these phenomena to reveal extant developmental pathologies in mathematics education, such as the Platonic barrier and excessive objectification. Moving beyond critique, the synthesis gestures toward a new emergent pedagogy – living mathematics education – that evolves mathematics education past these pathologies. The new pedagogy is elaborated through the examples of an instructional unit on circles and the participatory research methodology of concept study. I provide specific suggestions how living mathematics pedagogy may be practiced through dialogical classes, a new purpose of healing the world, a curriculum of sustainability, a skillful blending of Platonic and non-Platonic mathematics, and an improvisatory disposition towards teaching.
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