Commentary on Fractions
This commentary raises and discusses questions based on some of the agreements, disagreements, and themes found in the four chapters on fractions. It considers (1) the importance of tasks that are based in perception and readily available activity in light of an emphasis on problem solving in mathematics education, and the role that theories about thinking and learning play in designing such tasks; (2) some potential connections among various theories about thinking and learning as they relate to fractions; (3) the natural number bias and how ideas about natural numbers could serve as a foundation for fractions; and (4) the roles that magnitude, measurement, and linear representations of number play for fractions.
KeywordsFractions Magnitude Measurement Multiplication Ratio Rational numbers
Thanks to Andrew Izsák for helpful comments on a draft of this commentary. This research was supported by the National Science Foundation under Grant No. DRL-1420307. The opinions expressed are those of the author and do not necessarily reflect the views of the NSF.
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