Supporting Mathematical Problem Posing with a System for Learning Generation Processes through Examples

Problem posing, by which learners create new problems by themselves, is an important activity in mathematics education. However, novice learners have difficulty in posing problems, particularly when formulating appropriate solution structures of problems. Although they are provided with example problems that can serve as hints for composing novel problems, they do not necessarily understand the key ideas used to generate the examples. To improve problem posing for novices, this study discusses an approach that supports learning from examples as a production task. We propose a method of learning from examples through imitation, where a learner reproduces problems identical to given examples. We implement a system that presents examples of problem posing and supports learners in understanding the examples by having the learners reproduce them. We conducted an experimental evaluation in which learners learned from an example that embeds useful ideas to alter solution structures in the system. The results demonstrated that the learners successfully adapted the example when posing their own problems if they learned the example by the reproduction method. Thus, learning from examples through reproduction appears to be effective in the domain of problem posing as a production task.