Research Commentary: A Rejoinder Foregrounding Procedural Knowledge

In this rejoinder to Baroody and colleagues (2007), I point out that there are several areas of agreement between my position and that of Baroody et al.— most notably that both procedural knowledge and conceptual knowledge are of critical importance in students' learning of mathematics. However, there are issues on which Baroody et al. and I do not agree. In particular, I elaborate on the idea that procedures can be known deeply, flexibly, and with critical judgment—positive learning outcomes that are exclusively about students' knowledge of procedures and not necessarily a result of connections to conceptual knowledge.