Evidence for Cognitive Science Principles that Impact Learning in Mathematics

In the present chapter, we review the evidence for several principles that are especially promising for improving mathematics instruction. Using the classification scheme proposed by Koedinger et al. (2013), we begin with principles that focus on improving memory and fluency: scaffolding, distributed practice, and feedback. We then move to worked examples, interleaved practice, and abstract and concrete representations, which primarily promote induction and refinement. Finally, we review principles that are geared towards improving sense making and understanding: Error reflection and analogical comparison. In each section, we first describe the principle and the instructional implications. We then evaluate the evidence for the effectiveness of the principle for promoting mathematics learning, first from laboratory studies and then from classroom studies. Finally, we summarize what is and is not known about how these principles relate to mathematics learning, and identify gaps to be addressed in further translational research. The chapter concludes with an overall evaluation of the current state of evidence regarding how the use of these cognitive principles can influence mathematics instruction, both for simple and for more complex skills and concepts; we also suggest research priorities necessary to maximize the potential impact of cognitive science for mathematics instruction. [This chapter was published in D. C. Geary (Ed.), D. B. Berch (Ed.), R. Ochsendorf (Ed.), K. M. Koepke (Ed.), "Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts, Volume III" (p297-325). New York, NY: Elvesier.]