To the Editor:
We are writing in response to an article and subsequent blog post describing what many experts are suggesting is one of the “biggest shifts” associated with the Common Core State Standards for mathematics: the early and ongoing emphasis on “fractions as points on a number line,” rather than “just parts of a whole.” We don’t see this “key shift” as warranted in light of four decades of well-respected research on children’s thinking, funded principally by the National Science Foundation. This cumulative body of research suggests that children’s understanding of fractions develops through activities of equal sharing and reasoning about fractional units in relation to whole units in contexts that involve partitioning and iterating quantities. These activities go far beyond fractions as “just parts of a whole,” and children’s ability to place a fraction on a number line is a result of this process of development, not the foundation for this development.
We are concerned that end-point characterizations of what children are to know, such as new curriculum standards defining fractions as points on a number line, are becoming de facto curricular prescriptions, and are likely to drive out practices that are research-based and conceptually forward-looking. Rather than adopt a new approach to fractions that is essentially untested, the key shift that is needed is to support teachers’ use of the existing research base to attend to children’s thinking and the development of a robust understanding of fractions.
Walter M. Stroup, Susan Empson & Jessica Hunt
STEM Education Program
University of Texas at Austin
A version of this article appeared in the March 18, 2015 edition of Education Week as Let Mathematics Research Base Guide Teaching of Fractions