Cross-Cultural Study of Individual Differences in Number Sense and Mathematics

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

Abstract

Clear cross-cultural differences exist in school mathematical achievement. The latest report by the OECD's Programme for International Student Assessment (PISA, www.pisa.oecd.org), which plots the comparative academic progress of 400,000 15-year-olds in 57 countries, ranks Great Britain’s (average score = 492, rank 23-31 – which is similar to the US: rank 26-36) and Russia’s (average score = 468, rank 38-39) performance in mathematics well below average. The top results are consistently obtained from several Asian countries and Finland (e.g., China’s score = 600, rank 1). Multiple factors are likely to underlie these cross-cultural differences and at least some of them will also contribute to individual variation in mathematics within each culture. One factor that has been proposed to contribute to individual differences in mathematical achievement is variation in numerical intuition or estimation precision – the so called ‘number sense’. Here we report a cross-cultural study that aimed to investigate whether any differences exist between the groups of 16 year-old Russian and British school children in: (1) different aspects of mathematical ability; (2) different aspects of number sense; and (3) relationships between number sense and mathematics. We focus on these two countries for two reasons: (1) although similar according to the PISA, the countries show some meaningful differences in this rating; and (2) both countries have a centralized National Curriculum. A Russian- and English-language versions of the same battery of tests were validated and implemented for on-line web administration in Russia and the UK. The battery included 2 measures of mathematics (math fluency and a general measure of mathematical achievement) and 3 measures of number sense (the Number Line task; the Dot-Number matching task; and Colored Dot task). In addition, the battery included a test of spatial memory and a simple reaction time test. 250 Russian 16 year-olds completed the on-line battery in Russia (51% females). The students were recruited from a public secondary school in a greater Moscow region. 250 British participants were sampled from the large Twins Early Development Study, which includes several thousand children. The UK participants were matched to the Russian participants for sex, age, school type, school location (greater London region), spatial memory, and reaction time. An additional matching was performed for measures of mathematical interest and engagement, which were also collected in both samples using identical assessment tools. First, the data were analyzed in terms of norms and distributions for each measure. These analyses revealed both, cross-cultural similarities and differences. Second, we investigated whether any differences exist in relationships among the number sense and mathematics measures. Here again, we observed both cross-cultural similarities and differences in the structure of the relationships among the measures. For example, different aspects of number sense were differentially related to mathematics, and these relationships were not the same in the two groups of students. We discuss these results in terms of new hypotheses emerging from this study about potential involvement of linguistic, curricula, and other socio-cultural factors in the development of number sense, mathematical achievement, and the relationship between them.

Authors

• 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

• Maja Rodic, University of London - Goldsmiths

• Robert Plomin, Kings College, London

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