Making the abstract concrete: Visualizing mathematical solution procedures

This paper reports on an experiment investigating the effects of different kinds of computer-based visualizations on the acquisition of problem-solving skills in the domain of probability theory. Learners received either purely text-based worked examples, text plus an instruction to mentally imagine the examples’ contents, or the possibility of retrieving either static pictures or concrete animations that depicted the problem statement and the problem states achieved by applying a specific solution-step. It could be shown that frequent use of both static pictures and imagining the examples’ contents improved performance on isomorphic problems. Frequent use of animations, in contrast, led to substantial increases in learning time and a decrease in performance. Thus, the use of concrete animations to visualize solution procedures was more harmful than helpful for conveying problem-solving skills. Reasons for these outcomes are discussed in the light of cognitive load theory.