Since 2000, a body of research has
studied students' covariational reasoning, that is,
students' conceptions and imagery of how two real-valued
quantities vary together. Last year Ely & Ellis
formulated the new category of scaling-continuous
covariation. A series of task-based interviews reveal how
this type of reasoning manifested in a 7th grader's
thinking and supported his robust conceptualization of
constant, constantly-changing, and instantaneous rates of
change. I will also make some historical notes as well as
discuss how scaling-continuous reasoning can support
learning in differential calculus.
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