Relationships between general giftedness, expertise in mathematics, and mathematical creativity that associated with pattern generalization tasks in different representations

Abstract

The current study investigated creativity-directed problem-solving processing that explicitly requires solving pattern generalization problems in multiple ways. To examine mathematical creativity, we employed a multiple solution tasks approach, asking participants explicitly to solve pattern generalization problems in multiple ways. The participants were engaged with pattern generalization-multiple solution tasks in which patterns were presented numerically, diagrammatically, or contextually. The study aimed to examine whether success and creativity associated with solving pattern generalization-multiple solution tasks are affected (I) by expertise in mathematics (EM) and general giftedness (G) and (II) by task complexity and representation. Two hundred and ninety-eight participants from four research groups that differed in levels of general giftedness (G) and mathematical expertise participated in the study. We found that G affected statistically significant all the components of creativity when solving pattern generalization-multiple solution tasks, independently of task representation. Surprisingly, the effect of EM was lower and dependent on the type of task representation. Also surprising, we found statistically significant interactions between G and EM factors when solving pattern generalization-multiple solution tasks. The findings demonstrate a significant effect of task representation on students’ levels of success and creativity when engaged in solving pattern generalization-multiple solution tasks: contextual representations were approached with the highest level of success and creativity, whereas numerical representations appeared to be tackled with the lowest level of success and creativity. We suggest that mathematical instruction should integrate pattern generalization-multiple solution tasks to promote students’ mathematical expertise and creativity.