Mathematics Clusters Reveal Strengths and Weaknesses in Adolescents’ Mathematical Competencies, Spatial Abilities, and Mathematics Attitudes

ABSTRACT

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of pre-algebra strengths and weaknesses and if variation between clusters was related to mathematics attitudes, anxiety, or for a subsample (n = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters. Lower-performing students had pronounced deficits in their understanding of mathematical equality, fractions magnitudes, and the fractions number line. Higher-performing students had particular advantages in whole number and fractions arithmetic, and the fractions number line. Students could be reliably placed into clusters based on their mathematics self-efficacy and a combination of intelligence and spatial abilities. The results contribute to our understanding of key aspects of students’ mathematical development, highlight areas in need of intervention for at-risk students, and identify cognitive areas in which scaffolds might be incorporated into these interventions.

Acknowledgments

The study was supported by grants DRL-1659133 from the National Science Foundation and R01 HD087231 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development. We thank Dana Hibbard of Columbia Public Schools, as well as the staff, faculty, students and families of Columbia Public Schools for their assistance with the logistics of the study. We thank Kristin Balentine, Mandar Bhoyar, Amanda Campbell, Maria Ceriotti, Felicia Chu, Anastasia Compton, Danielle Cooper, Alexis Currie, Kaitlynn Dutzy, Amanda Evans, James Farley, Amy Jordan, Bradley Lance, Kate Leach, Joshua McEwen, Kelly Mebruer, Heather Miller, Natalie Miller, Sarah Peterson, Nicole Reimer, Laura Roider, Brandon Ryffe, Logan Schmidt, Jonathan Thacker, Zehra Unal, and Melissa Willoughby for their assistance with data collection and processing.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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Additional information

Funding

This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development [R01 HD087231]; National Science Foundation [DRL-1659133].