The Relationships Among Number Sense, Spatial Abilities, and Mathematics in Mathematically Gifted Students

• In Event: Interdisciplinary and Cross-Cultural Investigations Into Cognitive and Motivational Underpinnings of Mathematical Development

Abstract

Individual differences in mathematics have been associated with variation in spatial ability beyond the association between mathematics and IQ. More recently, research has also found evidence for unique associations between mathematics and several aspects of the ‘number sense’ – estimation and approximation intuitions. However, little is known about whether the association between number sense and mathematics is present throughout development, and whether it can be explained by spatial ability. Moreover, it is currently unknown whether mathematically talented children have particularly well developed number sense or whether the link between mathematics and number sense is not present in these children. To address these research questions, we administered a large battery of mathematical, spatial, and number sense tests to two groups of 16 year old Russian students. The first group was a representative sample of students from a standard public school in Moscow (N = 120, 70 males). The second group was a unique sample of mathematically gifted children (N = 120, 70 males) in Moscow. This special school was set up in 1963 specifically for mathematically gifted children during the final two years of their standard secondary education (age 15-17). The students are accepted into this boarding school from all over the Russian Federation based on an entry examination. A large proportion of the students are winners of the Russian Mathematical Olympic Games and other mathematical competitions. The battery of web-administered tests included 3 number sense tests (Number Line, Colored Dots, and Dot-Number Matching); 2 spatial tasks (3D Mental Rotation, Corsi Block); 2 general cognitive abilities tasks (Raven Matrices, Reaction Time task); and 3 measures of mathematical ability (Math Fluency; General Mathematics; and Mathematics General Exam Grade). Participants completed the battery using computers in their schools, either individually, or in group sessions, under researchers’ supervision. All instructions were standardized and were part of the on-line battery. The data were recorded automatically. The whole assessment took approximately 1 hour 20 minutes. The data were analyzed within each sample and across the two samples to address the research questions. We conducted descriptive analyses to examine whether the distributions and means for each of the measures in these samples were comparable to those previously reported in other samples and ages. We found that for several of the measures the mathematically gifted sample of students showed significantly different distributions to those for students from the ordinary school and to those previously reported in other samples. The results of the ANOVA analyses and of the multiple regressions suggested significant differences between the groups both, in terms of performance on most of the measures, and in terms of the structure of the relationships among the measures. The results of the study are discussed in terms of the role of spatial and number sense abilities in mathematical achievement.

Authors

• Olga Ovcharova, Psychological Institute of the Russian Academy of Education

• Sergei Malykh, Psychological Institute of the Russian Academy of Education

• Tatiana Tikhomirova, Institute of Psychology, Russian Academy of Sciences

• Maria Tosto, University of London - Goldsmiths

• Yulia Kovas, Goldsmiths, University of London and Tomsk State University