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Predicting students' performance on geometric problem-solving tasks: the roles of cognitive reflection, fluid
Alicia Rubio-Sánchez1,2, Isabel Gómez-Veiga3, Inés M Gómez-Chacón4
1Escuela Internacional de Doctorado, Universidad Nacional de Educación a Distancia (UNED), Madrid, Spain.
Frontiers in Psychology
|June 25, 2026
Summary
Cognitive skills like fluid intelligence and cognitive reflection, along with prior math achievement, significantly predict geometry problem-solving in secondary students. Mathematics beliefs did not add predictive value beyond these factors.
Area of Science:
- Cognitive Psychology
- Mathematics Education
- Educational Psychology
Background:
- Understanding student reasoning in mathematics requires integrating cognitive and affective factors.
- Geometric problem-solving is a key area for assessing mathematical reasoning.
- Adolescent cognitive development influences mathematical abilities.
Purpose of the Study:
- Investigate the relationship between geometric problem-solving performance and cognitive skills (fluid intelligence, cognitive reflection).
- Examine the predictive role of mathematics-related beliefs and prior achievement on geometry performance.
- Explore potential gender and academic year differences in geometric problem-solving.
Main Methods:
- Surveyed 303 secondary students (years 8-11) on geometric problem-solving, cognitive reflection, fluid intelligence, and math beliefs.
- Collected prior mathematics achievement data from school records.
- Employed correlational, hierarchical regression, mediation, and moderation analyses.
Main Results:
- Significant differences in geometry performance were found across academic years, but not by gender.
- Cognitive reflection, fluid intelligence, and prior math achievement were significant predictors of geometry performance.
- Mathematics-related beliefs did not explain additional variance in geometry performance beyond cognitive and achievement variables.
Conclusions:
- Reasoning processes are crucial for adolescents' geometric problem-solving.
- Cognitive factors and prior achievement are key predictors of geometry success.
- Mathematics beliefs play a less direct role than cognitive abilities in geometry performance.
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