Does Practice and Knowledge Equal Knowledge and Practice?

Debate surrounds the value of procedural practice in learning conceptual material in mathematical domains (Schoenfeld, 2004). We investigated whether purely procedural practice could lead to conceptual gains and explored cognitive load theory as a mechanism for those gains (Sweller, 1988). In a laboratory experiment, 93 undergraduates practiced a procedure by solving 30 problems of an algebra analog and were given conceptual tests before, during and after practice. The conceptual tests tapped students’ understanding of the underlying structure of the domain. Participants’ conceptual knowledge increased with procedural practice, particularly between no practice and some practice. Consistent with cognitive load theory performance on the conceptual test after practice was significantly related to procedural performance at the end of practice. However, this relationship between procedural learning and conceptual learning only held if participants had been alerted earlier in practice to the conceptual nature of the task. These results are consistent with the proposal by Rittle-Johnson, Siegler, & Alibali, (2001) that there is an iterative relationship between conceptual understanding and procedural skill.