Abstract or Concrete Examples in Learning Mathematics? A Replication and Elaboration of Kaminski, Sloutsky, and Heckler's Study

Kaminski, Sloutsky, and Heckler (2008a) published in Science a study on “The advantage of abstract examples in learning math,” in which they claim that students may benefit more from learning mathematics through a single abstract, symbolic representation than from multiple concrete examples. This publication elicited both enthusiastic and critical comments by mathematicians, mathematics educators, and policymakers worldwide. The current empirical study involves a partial replication–but also an important validation and extension–of this widely noticed study. The study's results confirm Kaminski et al.'s findings, but the accompanying qualitative data raise serious questions about their interpretation of what students actually learned from the abstract concept exemplification. Moreover, whereas Kaminski et al. showed that abstract learners transferred what they had learned to a similar abstract context, this study shows also that students who learned from concrete examples transferred their knowledge into a similar concrete context.