for the learning of mathematics


Carlos Castillo-Garsow ,  Heather Lynn Johnson and  Kevin C. Moore - Vol. 33 Num. 3 (2013)
 Chunky and smooth images of change

31-37
 ABSTRACT:

Characterizing how quantities change (or vary) in tandem has been an important historical focus in mathematics that extends into the current teaching of mathematics. Thus, how students conceptualize quantities that change in tandem becomes critical to their mathematical development. In this paper, we propose two images of change: chunky and smooth. Chunky images of change are based in imagining change as occurring countable and completed amounts, whereas smooth images of change are based in imagining a continually changing experience. Using empirical examples of student work, we illustrate these images of change and their implications.

 


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