Abstract: A substitution conception of equivalence involves recognition that a mathematical object can be substituted with an equivalent object, e.g., for problem-solving purposes. Liang (2021) proposes that attention to equivalence – and, more specifically, substitution – can be used “as a thread to pull different levels of mathematical concepts together” (p. 41). Thus, I conducted task-based clinical interviews to investigate the connections that students identified across mathematical contexts, paying particular attention to whether students identified equivalence or substitution as part of their solution methods. In this talk, I will discuss my task design, methodological decisions, and themes I’ve noticed so far in my preliminary data analysis.
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