Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

This study examined above-grade-level abstract reasoning abilities of 150 students (grades 2-6). Understanding of abstract concepts varied by age for only four of eight subscales or concepts: probability, proportion, momentum, and frames of reference. Performance varied widely within age level for the understanding of volume, correlation,…

Two studies investigated how social class and race are associated with mathematical thinking. The first study compared poor Black preschoolers with a group of both Black and White middle-class children; the second study compared Black and White children of lower- and middle-class status. Children were drawn from both preschool and kindergarten…