Experimental study of learning support through examples in mathematical problem posing.

When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures () in problem posing, learning support to improve the composition of solutions is required. 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 discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: 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, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.