Fluid Intelligence Test Scores Across the Schooling: Evidence of Nonlinear Changes in Girls and Boys


The results of the analyses of the changes of fluid intelligence scores measured by the Standard Progressive Matrices test across all school years were presented. Sex differences in fluid intelligence scores for each year of schooling as well as in fluid intelligence changes across schooling were analyzed. A total of 1581 participants (51.1% boys) aged 6.8 to 19.1 years from one public school were involved in this cross-sectional study, of whom 871 were primary schoolchildren (mean age = 9.23; range 6.8–11.6), 507 were secondary schoolchildren (mean age = 14.06; range 10.8–18.0), and 203 were high schoolchildren (mean age = 17.25; range 15.3–19.1). To examine the changes in fluid intelligence both correlation analysis and polynomial regression of the total, boys’ and girls’ samples were performed. Linear, quadratic, and cubic regression models were fitted to the data. To explore sex differences in fluid intelligence in each year of schooling, the series of ANOVA were carried out. The results revealed that the school-age change in fluid intelligence is nonlinear for both girls and boys. The changes for girls during the schooling are best described by a quadratic relationship while those for boys are best reflected by a cubic relationship.

Author Biographies

Tatiana N. Tikhomirova, Lomonosov Moscow State University, Psychological Institute of the Russian Academy of Education, Moscow, Russia

Tatiana N. Tikhomirova is a Doctor of Psychology, Corresponding Member of the Russian Academy of Education, Professor of the Department of Psychology at Lomonosov Moscow State University. She is also a Leading Researcher at the Psychological Institute of the Russian Academy of Education. Dr. Tikhomirova is a winner of the Government of the Russian Federation Award in Education (2021). Tatiana received her MSc in Pedagogical sciences and a PhD in Psychology from the Russian Academy of Sciences. Her current research focuses on the problems of cognitive development and individual differences in educational outcomes using the methods of longitudinal studies and cross-cultural psychology. Tatiana’s studies were supported by grants from the Russian Science Foundation and an Agreement between the Russian Academy of Sciences and British Academy. She is a member of the Russian Psychological Society and the International Society for Intelligence Research. Prof. Tikhomirova supervises BSc, MSc, and PhD students’ research. She was awarded the Vygotsky (2020) and Davydov (2021) Medals for her contribution to the development of psychology.

Artem S. Malykh, Psychological Institute, Russian Academy of Education, Centre of Interdisciplinary Research in Education, Russian Academy of Education, Moscow, Russia

Artem S. Malykh is a researcher at the Psychological Institute of the Russian Academy of Education, a data scientist at the Center of Interdisciplinary Research in Education of the Russian Academy of Education. Artem Malykh received a MSc degree in Computer Science from the National Research Nuclear University (2016). He is a winner of the Government of the Russian Federation Award in Education (2021). Presently, his work is related to the analysis of cognitive development data and use of machine learning approaches in longitudinal studies.

Sergey B. Malykh, Lomonosov Moscow State University, Psychological Institute of the Russian Academy of Education, Moscow, Russia

Sergey B. Malykh is a Laboratory Director at the Psychological Institute of the Russian Academy of Education, a Laboratory Director at the Department of Psychology at Lomonosov Moscow State University. Prof. Sergey Malykh earned a MSc degree in Psychology from Saratov State University (1979) and a PhD in Psychophysiology from the Institute of General and Educational Psychology, Academy of Pedagogical Sciences, USSR (1986). His current research deals with behavior genetics, individual difference, and cognitive development. Prof. Sergey Malykh has been elected as a Member of the Russian Academy of Education, Presidium Member of the Russian Psychological Society and the Standing Science Committee member of the European Federation of Psychological Associations. Prof. Malykh received the Government of the Russian Federation Award in Education (1998), Chelpanov Medal awarded by the Federation of Educational Psychologists of Russia (2007), Ushinski Medal awarded by the Ministry of Science and Education of the Russian Federation (2007), Vygotsky Medal awarded by the Russian Academy of Education (2018).


  • Aichele, S., Rabbitt, P., & Ghisletta, P. (2019). Illness and intelligence are comparatively strong predictors of individual differences in depressive symptoms following middle age. Aging & Mental Health, 23(1), 122–131. https://doi.org/10.1080/13607863.2017.1394440

  • Baltes, P., & Reinert, G. (1969). Cohort effects in cognitive development of children as revealed by cross-sectional sequences. Developmental Psychology, 1(2), 169–177. https://doi.org/10.1037/h0026997

  • Barbey, A. K. (2018). Network neuroscience theory of human intelligence. Trends in Cognitive Sciences, 22(1), 8–20. https://doi.org/10.1016/j.tics.2017.10.001

  • Brinch, C. N., & Galloway, T. A. (2012). Schooling in adolescence raises IQ scores. Proceedings of the National Academy of Sciences of the United States of America, 109(2), 425–430. https://doi.org/10.1073/pnas.1106077109

  • Brouwers, S. A., van de Vijver, F. J. R., & van Hemert, D. A. (2009). Variation in Raven’s Progressive Matrices scores across time and place. Learning and Individual Differences, 19(3), 330–338. https://doi.org/10.1016/j.lindif.2008.10.006

  • Brown, R. E. (2016). Hebb and Cattell: The genesis of the theory of fluid and crystallized intelligence. Frontiers in Human Neuroscience, 10, Article 606. https://doi.org/10.3389/fnhum.2016.00606

  • Cahan, S., & Cohen, N. (1989). Age versus schooling effects on intelligence development. Child Development, 60(5), 1239–1249. https://doi.org/10.2307/1130797

  • Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54(1), 1–22. https://doi.org/10.1037/h0046743

  • Colom, R., & Lynn, R. (2004). Testing the developmental theory of sex differences in intelligence on 12–18 year olds. Personality and Individual Differences, 36(1), 75–82. https://doi.org/10.1016/S0191-8869(03)00053-9

  • Deary, I. J., Strand, S., Smith P., & Fernandes, C. (2007). Intelligence and educational achievement. Intelligence, 35(1), 13–21. https://doi.org/10.1016/j.intell.2006.02.001

  • Deary, I. J., & Johnson, W. (2010). Intelligence and education: Causal perceptions drive analytic processes and therefore conclusions. International Journal of Epidemiology, 39(5), 1362–1369. https://doi.org/10.1093/ije/dyq072

  • Desjardins, R., & Warnke, A. J. (2012). Ageing and skills: A review and analysis of skill gain and skill loss over the lifespan and over time (OECD Education Working Papers, No. 72). OECD Publishing. https://doi.org/10.1787/5k9csvw87ckh-en

  • Flynn, J. R., & Rossi-Casé, L. (2011). Modern women match men on Raven’s Progressive Matrices. Personality and Individual Differences, 50(6), 799–803. https://doi.org/10.1016/j.paid.2010.12.035

  • Frenken, H., Papageorgiou, K. A., Tikhomirova, T., Malykh, S., Tosto, M. D., & Kovas, Y. (2016). Siblings’ sex is linked to mental rotation performance in males but not females. Intelligence, 55, 38–43. https://doi.org/10.1016/j.intell.2016.01.005

  • Ghisletta, P., Rabbitt, P., Lunn, M., & Lindenberger, U. (2012). Two thirds of the age-based changes in fluid and crystallized intelligence, perceptual speed, and memory in adulthood are shared. Intelligence, 40(3), 260–268. https://doi.org/10.1016/j.intell.2012.02.008

  • Hartshorne, J., & Germine, L. (2015). When does cognitive functioning peak? The asynchronous rise and fall of different cognitive abilities across the life span. Psychological Science, 26(4), 433–443. https://doi.org/10.1177/0956797614567339

  • Horn, J. L., & Cattell, R. B. (1966) Refinement and test of the theory of fluid and crystallized general intelligences. Journal of Educational Psychology, 57(5), 253–270. https://doi.org/10.1037/h0023816

  • Irwing, P., & Lynn, R. (2005). Sex differences in means and variability on the progressive matrices in university students: A meta-analysis. British Journal of Psychology, 96(4), 505–524. https://doi.org/10.1348/000712605X53542

  • Jackson, M., Khavenson, T., & Chirkina, T. (2020). Raising the stakes: Inequality and testing in the Russian education system. Social Forces, 98(4), 1613–1635. https://doi.org/10.1093/sf/soz113

  • Kievit, R. A., Davis, S. W., Griffiths, J., Correia, M. M., Cam-CAN, & Henson, R. N. (2016). A watershed model of individual differences in fluid intelligence. Neuropsychologia, 91, 186–198. https://doi.org/10.1016/j.neuropsychologia.2016.08.008

  • Miller, D. I., & Halpern, D. F. (2014). The new science of cognitive sex differences. Trends in Cognitive Sciences, 18(1), 37–45. https://doi.org/10.1016/j.tics.2013.10.011

  • Nisbett, R. E., Aronson, J., Blair, C., Dickens, W., Flynn, J., Halpern, D. F., & Turkheimer, E. (2012). Intelligence: New findings and theoretical developments. American Psychologist, 67(2), 130–159. https://doi.org/10.1037/a0026699

  • Ob obrazovanii v Rossiiskoi Federatsii [On Education in the Russian Federation]. Federal Law of the Russian Federation No. 273-FZ (2012, December 29, rev. on 2021, July 2). http://pravo.gov.ru/proxy/ips/?docbody=&nd=102162745

  • Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499–503. https://doi.org/10.1126/science.1102085

  • Raven, J. J. (2003). Raven Progressive Matrices. In R. S. McCallum (Ed.), Handbook of nonverbal assessment (pp. 223–237). Springer. https://doi.org/10.1007/978-1-4615-0153-4_11

  • Ritchie, S. J., Bates, T. C., & Deary, I. J. (2015). Is education associated with improvements in general cognitive ability, or in specific skills? Developmental Psychology, 51(5), 573–582. https://doi.org/10.1037/a0038981

  • Schneeweis, N., Skirbekk, V., & Winter-Ebmer, R. (2014). Does education improve cognitive performance four decades after school completion? Demography, 51(2), 619–643. https://doi.org/10.1007/s13524-014-0281-1

  • Shangguan, F., & Shi, J. (2009). Puberty timing and fluid intelligence: A study of correlations between testosterone and intelligence in 8- to 12-year-old Chinese boys. Psychoneuroendocrinology, 34(7), 983–988. https://doi.org/10.1016/j.psyneuen.2009.01.012

  • Tikhomirova, T., Kuzmina, Y., Lysenkova, I., & Malykh, S. (2019a). Development of approximate number sense across the elementary school years: A cross-cultural longitudinal study. Developmental Science, 22(4), e12823. https://doi.org/10.1111/desc.12823

  • Tikhomirova, T., Kuzmina, Y., Lysenkova, I., & Malykh, S. (2019b). The relationship between non-symbolic and symbolic numerosity representations in elementary school: The role of intelligence. Frontiers in Psychology, 10(2019), Article 2724. https://doi.org/10.3389/fpsyg.2019.02724

  • Tikhomirova, T., Malykh, A., & Malykh, S. (2020). Predicting academic achievement with cognitive abilities: Cross-sectional study across school education. Behavioral Sciences, 10(10), Article 158. https://doi.org/10.3390/bs10100158

  • Tucker-Drob, E., & Briley, D. (2014). Continuity of genetic and environmental influences on cognition across the life span: A meta-analysis of longitudinal twin and adoption studies. Psychological Bulletin, 140(4), 949–979. https://doi.org/10.1037/a0035893

  • von Stumm, S., & Plomin, R. (2015). Socioeconomic status and the growth of intelligence from infancy through adolescence. Intelligence, 48, 30–36. https://doi.org/10.1016/j.intell.2014.10.002

  • Zilles, D., Lewandowski, M., Vieker, H., Henseler, I., Diekhof, E., Melcher, T., Keil, M., & Gruber, O. (2016). Gender differences in verbal and visuospatial working memory performance and networks. Neuropsychobiology, 73(1), 52–63. https://doi.org/10.1159/000443174

How to Cite
Tikhomirova, T., Malykh, A., & Malykh, S. (2022). Fluid Intelligence Test Scores Across the Schooling: Evidence of Nonlinear Changes in Girls and Boys. Changing Societies & Personalities, 6(3), 488–503. doi:10.15826/csp.2022.6.3.186