Creative thinking for learning algebra: Year 10 students' problem solving and problem posing with quadratic figural patterns

There is increasing focus on giving all students opportunities to develop their creative thinking in mathematics. In a fine-grained qualitative case study, Australian Year 10 (15-16-year-old) students experienced problem-solving and problem-posing tasks in a learning sequence designed to elicit creative thinking through visualization and with algebraic (functional) concepts. This article shares findings on two pairs' creative processes and work products for generalizing and creating quadratic figural growing patterns, related to the cognitive, affective, and aesthetic dimensions of learning. Post-sequence data on the class's preferences for types of creative thinking tasks are also shared. Students were found to exhibit different creativity aspects in their problem solving and varying levels of meta-representational competency in their problem posing. The students evidenced diverse affective responses to the different types of tasks, with proportionally more students preferring problem solving to problem posing. Some implications for engaging secondary mathematics students in creative thinking tasks are shared along with recommendations for future research.