Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Why, when dividing fractions, do we invert and multiply? Prospective secondary school teachers sometimes provide an algebraic explanation. This proof may leverage the elegance of algebraic symbolic manipulation (see fig. 1), but it does not address the underlying relationships that are so important for learners striving to understand fractions. Furthermore, we know that secondary and elementary school preservice teachers have difficulty providing a conceptual explanation for fraction division (Ball 1990; Borko et al. 1992), and we have found that most experienced teachers have not had opportunities to work through, in a meaning-making way, the principles associated with making sense of fraction division.
This article is available to members of NCTM who subscribe to
Teaching Children Mathematics. Don't miss out—join now or upgrade your membership. You may also purchase this article now for online access.
Log In/Create Account
Purchase Article