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Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I look at the different possibilities offered by the trajectory of second-order models in mathematics education. It seems to me that although possibilities are extended as models become more elaborate, this is only the case if teacher/researchers remain cognisant of a radical constructivist perspective. I also suggest that broad-ranging research on the models affords insight into the “big” mathematical ideas to which all students should have access.
Dooley T. (2014) Second-order models of students’ mathematics: Delving into possibilities. Constructivist Foundations 9(3): 346–348. http://constructivist.info/9/3/346
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