Publication 448

Tillema E. S. & Hackenberg A. J. (2011) Developing systems of notation as a trace of reasoning. For the Learning of Mathematics 31(3): 29–35.
In this paper, we engage in a thought experiment about how students might notate their reasoning for taking a fraction of a fraction and determining its size in relation to the whole. We situate this discussion within a radical constructivist framework for learning in order to articulate how developing systems of notation with students can contribute to their learning. In particular, we posit that developing systems of notation with students is likely to contribute to what Piaget called reflected abstractions – a retroactive thematization of one’s reasoning.
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