The sense of number and success in teaching mathematics at primary school age: a cross-longitudinal analysis

Publication type Article
Status Published
Occupation: professor
Affiliation: Federal State Budgetary Educational Institution of Higher Education
Address: Russian Federation
Occupation: professor
Affiliation: Federal State Budgetary Institution “Psychological Institute of RAO”
Address: Russian Federation
Journal namePsikhologicheskii zhurnal
EditionVolume 39 № 6

The current article presents the results of a longitudinal investigation of the relationship between number sense and mathematical achievement across the primary school years. We analyzed the data of 133 participants from the Russian Longitudinal Study of Academic Achievement on symbolic and non-symbolic number sense ability and mathematical achievement in Grades 3 and 4. The mean age at Grade 3 was 9.82 years (SD = 0.3) and 10.82 years at Grade 4 (SD = 0.3). We used the cross-lagged analysis to explore the causal relationship between number sense and mathematical achievement. Our analysis revealed that the reciprocal model best described the empirical data suggesting the cross-lagged relation between number sense accuracy and academic achievement in Math. The results of our longitudinal study have shown differences in the association the mathematical achievement with the two aspects of number sense – symbolic and non-symbolic representation. Thus, mathematical achievement in Grade 3 predicted only the symbolic estimation ability in Grade 4. On the contrary, mathematical achievement at Grade 3 had no significant effect on another aspect of number sense, non-symbolic estimation ability, by the end of primary school. We also found differences in the stability of the two aspects of number sense at primary school age. Thus, non-symbolic number sense ability was the most stable over time. The results were discussed in the context of a theoretical problem of the association of cognitive development and school education.

Keywordsnumber sense, mathematical achievement, primary school years, cross-lagged analysis, education, development
AcknowledgmentThe study was supported by the Russian Science Foundation, project No. 17-78-30028.
Publication date22.12.2018
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1. Zhuravlev A. L. Vzaimodejstvie sotsial'no-psikhologicheskikh i sotsial'no-ehkonomicheskikh fenomenov v izmenyayuschemsya obschestve // Sotsial'no-psikhologicheskaya dinamika v usloviyakh ehkonomicheskikh izmenenij / Otv. red. A. L. Zhuravlev, E. V. Shorokhova. M.: Izd-vo “Institut psikhologii RAN”, 1998. S. 11–37.

2. Malykh S. B., Tikhomirova T. N., Zhou S., Vej V., Rodich M., i dr. Struktura vzaimosvyazej kognitivnykh kharakteristik i uspeshnosti v arifmetike u doshkol'nikov: krosskul'turnyj analiz // Voprosy psikhologii. 2012. № 5. S. 133–143.

3. Ponomarev Ya. A. Perspektivy razvitiya psikhologii tvorchestva // Psikhologiya tvorchestva: shkola Ya. A. Ponomareva. M.: Izd-vo “Institut psikhologii RAN”, 2006. S. 145–276.

4. Tikhomirova T. N., Malykh S. B. Kognitivnye osnovy individual'nykh razlichij v uspeshnosti obucheniya. M.; SPb.: Nestor-Istoriya, 2017.

5. Tikhomirova T. N., Malykh S. B., Tosto M. G., Kovas Yu. V. Kognitivnye kharakteristiki i uspeshnost' v reshenii matematicheskikh zadanij v starshem shkol'nom vozraste: krosskul'turnyj analiz // Psikhologicheskij zhurnal. 2014. T. 35. № 1. S. 41–53.

6. Tikhomirova T. N., Misozhnikova E. B., Kuz'mina Yu. V., Malykh S. B. Vzaimosvyaz' neverbal'nogo intellekta i uspeshnosti v matematike v mladshem shkol'nom vozraste: longityudnoe issledovanie // Teoreticheskaya i ehksperimental'naya psikhologiya. 2016. T. 9. № 4. S. 6–22.

7. Tikhomirova T. N., Modyaev A. D., Leonova N. M., Malykh C. B. Faktory uspeshnosti v obuchenii na nachal'noj stupeni obschego obrazovaniya: polovye razlichiya // Psikhologicheskij zhurnal. 2015. T. 36. № 5. C. 43–54.

8. Booth J. L., Siegler R. S. Numerical magnitude representations influence arithmetic learning // Child dev. 2008. V. 79 (4). P. 1016–1031.

9. Dehaene S. The Number Sense: How the mind creates mathematics. Oxford: Oxford University Press USA, 2011.

10. Desoete A., Ceulemans A., De Weerdt F. & Pieters S. Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study // Brit. J. Educ. Psychol. 2012. V. 82(1). P. 64–81.

11. Geary D. C. Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study // Dev. psychol. 2011. V. 47(6). P. 1539.

12. Geary D. C., Hoard M. K., Nugent L., Byrd-Craven J. Development of number line representations in children with mathematical learning disability // Dev. neuropsychol. 2008. V. 33(3). P. 277–299.

13. Halberda J., Ly R., Wilmer J., Naiman D., Germine L. Number sense across the lifespan as revealed by a massive internet-based sample // Proc. Natl. Acad. Sci. 2012. V. 109 (28). P. 11116–11120.

14. Halberda J., Mazzocco M. M., Feigenson L. Individual differences in nonverbal estimation ability predict maths achievement // Nature. 2008. V. 455. P. 665–668.

15. Inglis M., Attridge N., Catchelor S., Gilmore S. Non-verbal number acuity correlates with symbolic mathematics achievement: but only in children // Psychon. Bull. Rev. 2011. V. 18(6). P. 1222–1229.

16. Little T. D., Preacher K. J., Selig J. P., & Card N. A. New developments in latent variable panel analyses of longitudinal data // Int. J. Behav. Dev. 2007. V. 31(4). P. 357–365.

17. Mazzocco M. M.M., Feigenson L., Halberda J. Preschoolers’ Precision of the Approximate Number System Predicts Later School Mathematics Performance // PLoS ONE. 2011. V. 6(9). P. 1–8.

18. Merritt D. J., DeWind N.K., Brannon E. M. Comparative cognition of number representation // T. R. Zentall, E. A. Wasserman (Eds.). The Oxford Handbook of Comparative Cognition. New York, NY: Oxford University Press, 2012. P. 451–476.

19. Opfer J. E., Siegler R. S. Representational change and children’s numerical estimation // Cogn. Psychol. 2007. V. 55. P. 169–195.

20. Rodic M., Zhou X., Tikhomirova T., Wei W., Malykh S., Ismatulina V., Sabirova E., Davidova Y., Tosto M., Lemelin J-P. & Kovas Y. Cross-Cultural Investigation into Cognitive Underpinnings of Individual Differences in Early Arithmetics // Dev. Sci. 2015. V. 18(1). P. 165–174.

21. Siegler R. S., Booth J. L. Development of numerical estimation in young children // Child dev. 2004. V. 75(2). P. 428–444.

22. Siegler R. S., Ramani G. B. Playing linear number board games – but not circular ones – improves low-income preschoolers’ numerical understanding // J. Educ. Psychol. 2009. V. 101 (3). P. 545.

23. Soltesz F., Scoz D., Scoz L. Relationship between magnitude representation, counting and memory in 4- to 7-year old children: A developmental study // Behav. Brain Funct. 2010. V. 6(13). P. 1–14.

24. Tikhomirova T. N. Spatial thinking and memory in Russian high school students with different levels of mathematical fluency // Procedia Soc. Behav. Sci. 2017. V. 237. P. 1260–1264.

25. Whalen J., Gallistel C. R., Gelman R. Nonverbal counting in humans: The psychophysics of number representation // Psychol. Sci. 1999. V. 10(2). P. 130–137.

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