The Disappearing "Advantage of Abstract Examples in Learning Math"

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Mathematics Education

Background:

• The presentation of abstract versus concrete examples is a key consideration in teaching novel mathematical concepts.
• A previous study (Kaminski, Sloutsky, & Heckler, 2008a) suggested a general advantage for abstract examples in learning.
• This prior finding has influenced pedagogical approaches in mathematics education.

Purpose of the Study:

• To critically replicate and extend the findings of Kaminski et al. (2008a).
• To investigate whether modifications in learning design alter the perceived advantage of abstract examples.
• To re-evaluate the generalizability of the abstract example advantage in mathematical concept acquisition.

Main Methods:

• A replication and extension of the Kaminski et al. (2008a) experiment was conducted.
• Participants were trained on a novel mathematical concept using either abstract or concrete examples.
• Key modifications were made to the learning design, particularly in the concrete example condition.

Main Results:

• Participants trained with improved concrete examples performed comparably to, or better than, those trained with abstract examples.
• The performance difference observed in the original study was not replicated under the modified conditions.
• The effectiveness of concrete examples was significantly enhanced through design improvements.

Conclusions:

• The previously reported "advantage of abstract examples" may be an artifact of suboptimal concrete examples used in prior research.
• Improved concrete examples can be as effective, if not more effective, than abstract examples for learning mathematical concepts.
• The choice of example type and its design are critical factors in educational interventions for mathematics.