Selecting and sequencing mathematics tasks: seeking mathematical knowledge for teaching
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In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two mathematical tasks taken from the 2010 NDBE Grade 2 and Grade 3 Numeracy Workbooks. Teachers were required to justify the selection and sequencing of the two mathematical tasks for teaching multiplication. In so doing, they provide some indication of what they know or do not know about the mathematical concepts in the tasks; about the connections between mathematical concepts; about the representations of those concepts, and about how learners learn those concepts. Teachers’ responses varied from an articulation of the pedagogic and mathematical intentions of the tasks, to the use and consequences of pictorial representations in the tasks and how learners would respond to the tasks. The variation in responses reflected different criteria that teachers used to justify the selection and sequencing of the tasks. The analysis raises critical questions regarding the interplay between teachers’ subject-matter knowledge, their pedagogic content knowledge and curricular knowledge, which they bring to bear on pedagogic decisions. The analysis raises further critical questions concerning the pedagogic and mathematical explicitness of tasks in the NDBE Numeracy Workbooks. The analysis suggests that careful consideration must be given to the construction of mathematical tasks in Grade 3, and probably the Foundation Phase, to ensure that the mathematical purpose of tasks is explicit, and that ‘contextual noise’ is not introduced that distracts from the pedagogic and mathematical intent of the tasks.