Basic skills versus conceptual understanding in mathematics education: The case of fraction division

The distinction between conceptual understanding and basic skills is as old as mathematics education research itself. It still remains a central issue for many disputes. In this paper, building upon professor Hung-Hsi Wu's rejection of the distinction, I explore three possible accounts of it: (a) conceptual understanding first, (b) explaining the distinction away and emphasizing “procedural-understanding” instead, and finally (c) treating understanding and procedural skill as two separate, irreducible, complementary components. In contrast to Wu who favors the second account, I argue that as far as mathematics teaching is concerned the third view is the preferable one