Differences between experts in mathematical problem solving

• Mathematical expertise in a school context is not homogeneous • Problem-solving competitors outperformed high-achievers on authentic mathematics tasks • Differences found in flexibility, argumentation, and progression in problem-solving • Working memory and socioeconomic status didn't explain performance differences • Findings suggest need for diverse assessments to capture mathematical expertise Research on expertise in a school mathematics context has traditionally followed the expert-novice paradigm, with few studies exploring its nuances. Mathematical expertise in a school context is often equated with giftedness, despite being distinct concepts, and rarely studied using authentic, complex problems. Our study examined different types of mathematical expertise by comparing two groups of high-school students- “High-Achievers” (HA, n = 24) and “Problem-Solving Competitors” (PSC, n = 19)- as they worked on solving three complex, ill-structured problems. Significant differences with large effect sizes were found between the groups across Progression, Flexibility, and Argumentation in tasks, except for Progression on Task 1. Possible reasons are discussed. Overall, our results suggest that different types of mathematical expertise in a school context manifest in distinct ways, emphasizing the need for a more nuanced understanding of expertise in this field.