The question of how to teach mathematics has become increasingly problematic in recent years as critics from diverse perspectives have offered wide-ranging, and often seemingly incommensurate (=ασύμμετρες), challenges to conventional conceptions of the teacher's task. This article represents an effort to "bring into dialogue" some of the varied commentaries (=ερμηνευτικά σχόλια) on mathematics teaching, using an enactivist (=related to enactivism,a combination of Constructivism and Embodied Cognition, is a theory wherein cognition and environment are inseparable, and learning is drawn from the interaction between learner and environment.) framework to interpret and to propose an alternative way of framing mathematics teaching. In this report, the manner in which the teacher listens is offered as a metaphoric lens through which to reinterpret practice, as a practical basis for teaching action, and as a means of addressing some of the critics' concerns. The report is developed around an extended collaborative research project with a middle school mathematics teacher.
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