Tip #6: Provide many examples and practice exercises in which the same underlying concept is at work.
Bransford et al. (2000) recommend that teachers provide “many examples in which the same concept is at work”. (p. 20) In a study by Gick and Holyoak (1980), they presented subjects with a story of a general who breaks up his army into several smaller groups to take different roads to avoid setting off mines. They still all arrived at the same time and were able to take over the capital. Then subjects were ask to solve a problem where the doctor had to radiate a tumor with enough force to destroy it but without harming the tissue around it. Subjects were told to use the story as the model to solve the problem and most subjects realized that the strategy is to break up the radiation source into smaller rays and focuses them only on the tumor so that the strongest radiation is only there.
“Hands-on experiments can be a powerful way to ground emergent knowledge…” (Bransford et al., 2000, p. 22) However there are different ways to practice. Consider doing math homework with the use of formulas and theorems. If you just followed the rules of the formula, you may have completed your homework in less time than if you truly went through the formula to fully and deeply understand all the ins and outs of the formula. Students who understand the reasons behind a formula can usually remember it much better and apply it much better in the long run. They may even be able to more easily learn or transfer to related mathematical (or other) information that shares the same abstract underlying core concepts, or knowledge elements. (Anderson, 2000) “In mathematics, experts are more likely than novices to first try to understand the problems, rather than simply attempt to plug numbers into formulas.” (Bransford et al., 2000, p. 41) Paige and Simon (1966) conducted a study where they presented subjects with an algebra problem. The expert group quickly realized that the problem was logically impossible.