Using Abstraction to Make it Easier to Apply Learning"It is very difficult to extract mathematical principles from story problems. Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching."
That's what Vladimir Sloutsky, a professor of psychology at Ohio State University, had to say in talking about the relative merits of abstract examples vs. concrete examples when teaching math principles.
In a study led by Jennifer Kaminski, a research scientist at Ohio State University's Center for Cognitive Science, of which Sloutsky is the director, experiments showed that students were better able to apply principles to a variety of situations if they were taught the principlpes in the abstract, rather than via scenarios built from concrete details.1
The example cited in OSU's press release about the research is "the classic problem of two trains that leave different cities heading toward each other at different speeds. Students are asked to figure out when the trwo trains will meet." Even if they are able to get the correct answer, it turns out that solving the train problem does not much help when they encounter an equivalent problem with different details, such as levels of water rising over time.
The problem seems to be that "extraneous information about marbles or containers [typical props in concrete examples] divert attention from the real mathematics behind it all."
Even while recognizing that people have different learning styles, there is a lesson here for business trainers who, all too often, overdo cutesy examples in their courses.
On the other hand, it is important to note that the above is not an argument against training that uses examples taken directly from the on-the-job context in which learning is to be applied. On the contrary, such an approach is advisable because it reflects important principles of adult learning.
1 Jennifer Kaminski, Vladimir M. Sloutsky, and Andrew Heckler, "The Advantage of Abstract Examples in Learning Math," Science, Vol. 320, No. 5875 (April 25, 2008), pp. 454-455. You can read a New York Times report on this research, including a few caveats, here.