Can Entropy Predict the Creativity Potential of Mathematical Tasks? An Exploratory Study in Mathematics Education

Creativity is a key goal in contemporary mathematics education, yet teachers often rely on intuition when selecting tasks intended to elicit creative thinking. This study proposes Creativity-Eliciting Potential Entropy (CEPE), an entropy-inspired theoretical framework that conceptualises the creative potential of mathematical tasks in terms of their structural openness across the stages of Start, Process, and Goal. CEPE focuses on the diversity of possible solution strategies, assumptions, and representations provided by a task, rather than on learners’ observed performance. An exploratory study was conducted with 32 mathematics teachers from Japan and Germany, who ranked three task types—a geometrical proof task, a mathematical modelling task, and a Fermi problem—according to their perceived creativity-eliciting potential. Teachers’ rankings showed a weak but statistically significant consensus and a significant alignment with CEPE-based predictions, particularly in the high evaluation of Fermi problems. However, substantial individual variability remained, reflecting teachers’ consideration of learner characteristics and instructional constraints. The findings suggest that CEPE provides a theoretically grounded lens that supports, but does not replace, teachers’ professional judgement in task selection.