How Should Examples be Learned in a Production Task? An Experimental Investigation in Mathematical Problem Posing

When using mathematics in problem solving in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, it is an important task in general education to foster learner problem posing. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study experimentally investigated the effects of three learning activities in problem posing: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new and unique problems from a base problem initially given after learning an example by solving, reproducing, or evaluating it. The results indicated that learning by reproducing the example was the most effective in fostering the composition of new problems.