Abstract
A methodology is offered for studying problem solving from the inside. This approach is first set in the context of millenia of educational thinkers, and then in the context of providing support for the professional development of teachers of mathematics. The approach is based on the development and strengthening of each teacher's own awareness of their own mathematical thinking so that they can more readily enter and appreciate the thinking of their pupils. It is described and illustrated, through offering experience of working on mathematics, through offering challenging assertions, and through suggesting ways of working on mathematics teaching. Observations are made about validity and validation through this methodology. The heart of the methodology is based on the observation that what really matters in teaching is to be awake to possibilities in the moment, as a lesson unfolds; moments when the teacher experiences the true freedom of a conscious choice. Three extracts from different styles of presentation of mathematics for students at a distance are offered for consideration.
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Mason, J. (1992). Researching Problem Solving from the Inside. In: Ponte, J.P., Matos, J.F., Matos, J.M., Fernandes, D. (eds) Mathematical Problem Solving and New Information Technologies. NATO ASI Series, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58142-7_2
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DOI: https://doi.org/10.1007/978-3-642-58142-7_2
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