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We look at a strategy for comparing fractions by simultaneously considering both the numerator (the number of pieces) and the denominator (the size of the pieces). We argue that developing an understanding of this strategy will help prospective teachers develop their fraction number sense and an ability to look at a fraction as a measure—i.e., a/b means a pieces of size 1/b. We share results from both the development and implementation of a task for helping prospective teachers construct an understanding of the comparison strategy, which we call the greater number of larger pieces strategy.
Dana Olanoff, Widener University
Ziv Feldman, Boston University
Rachael M. Welder, Western Washington University
Jennifer M. Tobias, Illinois State University
Eva Thanheiser, Portland State University
Amy Hillen, Kennesaw State University