Skip to main content
Log in

The developmental trajectories of math skills and its relation to math interest in Grades three and five

  • Published:
European Journal of Psychology of Education Aims and scope Submit manuscript

Abstract

Understanding math and the ability to use math in various situations can greatly contribute to a successful life. Different math skills are of importance for understanding and supporting math ability. In addition, math interest may influence math ability. We investigated the relationship between math conceptual and procedural skills, their development over time, and the relation to math interest in Grades three and five. Participants in the study were Estonian students (N = 855), who were in Grade three (2019/2020) during the first testing and in Grade five (2021/2022) during the second testing. Students completed math competence testing which consisted of procedural and conceptual skill tasks and a questionnaire about math interest. Both person- and variable-oriented approaches were used in the analyses. Students’ math conceptual and procedural skills in Grades three and five were moderately related to each other. Furthermore, based on latent profile analysis, three profiles of skills were identified in both grades, distinguishing between students with low, average, and high levels of skills in both skills, with the exception of an approximately average-skill group in Grade five that had low conceptual skills but average procedural skills. Students were likely to remain in similar-skill groups for both Grades three and five. Lastly, there was a significant difference in math interest in Grade three among the groups with stable low, stable average, and stable high skills from Grades three to five. Fostering interest in math may be beneficial for achieving a high level of math proficiency. Future research should prioritize the integration of person-oriented methods into studies aimed at enhancing understanding of math skill development.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data availability

Our data is currently unavailable to access.

References

  • Bailey, D. H., Duncan, G. J., Watts, T., Clements, D. H., & Sarama, J. (2018). Risky business: Correlation and causation in longitudinal studies of skill development. American Psychologist, 73(1), 81.

    Article  PubMed  Google Scholar 

  • Bergman, L. R., & Lundh, L.-G. (2015). Introduction: The person-oriented approach: Roots and roads to the future. Journal of Person-Oriented Research, 1(1–2), 1–6.

    Article  Google Scholar 

  • Bjälkebring, P., & Peters, E. (2021). Money matters (especially if you are good at math): Numeracy, verbal intelligence, education, and income in satisfaction judgments. PLoS One, 16(11), e0259331. https://doi.org/10.1371/journal.pone.0259331

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Campbell, N. K., & Hackett, G. (1986). The effects of mathematics task performance on math self-efficacy and task interest. Journal of Vocational Behavior, 28, 149–162.

    Article  Google Scholar 

  • Celeux, G., & Soromenho, G. (1996). An entropy criterion for assessing the number of clusters in a mixture model. Journal of Classification, 13, 195–212.

    Article  MathSciNet  Google Scholar 

  • Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. John Wiley & Sons.

    Google Scholar 

  • Estonian Government, (2011/2022b). National curriculum for basic schools. Appendix 3. Subject field: Mathematics. Used 11.01.2023 https://www.riigiteataja.ee/tolkelisa/5240/9201/4014/VV1_lisa3.pdf#

  • Estonian Government, (2011/2022a). National curriculum for basic schools. Used 11.01.2023. https://www.riigiteataja.ee/en/eli/524092014014/consolide

  • Fomina, T., & Morosanova, V. (2017). Self-regulation, math self-efficacy, math interest and mathematics achievement. New Trends and Issues Proceedings on Humanities and Social Sciences, 4(6), 33–40.

    Article  Google Scholar 

  • Frenzel, A. C., Goetz, T., Pekrun, R., & Watt, H. M. G. (2010). Development of mathematics interest in adolescence: Influences of gender, family, and school context. Journal of Research on Adolescence, 20(2), 507–537. https://doi.org/10.1111/j.1532-7795.2010.00645.x

    Article  Google Scholar 

  • Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111–127. https://doi.org/10.1207/s15326985ep4102_4

    Article  Google Scholar 

  • Hidi, S. (2006). Interest: A unique motivational variable. Educational Research Review.

  • Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge. The case of mathematics (pp. 1–27). Hillsdale NJ: Erlbaum.

  • Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.

    Article  Google Scholar 

  • Hughes, J. N., & Cao, Q. (2018). Trajectories of teacher-student warmth and conflict at the transition to middle school: Effects on academic engagement and achievement. Journal of School Psychology, 67, 148–162.

    Article  PubMed  Google Scholar 

  • Jõgi, A.-L., Kikas, E., Lerkkanen, M.-K., & Mägi, K. (2015). Cross-lagged relations between math-related interest, performance goals and skills in groups of children with different general abilities. Learning and Individual Differences, 39, 105–113.

    Article  Google Scholar 

  • Kikas, E., Peets, K., Palu, A., & Afanasjev, J. (2009). The role of individual and contextual factors in the development of maths skills. Educational Psychology, 29(5), 541–560. https://doi.org/10.1080/01443410903118499

    Article  Google Scholar 

  • Kubota, M., Hadley, L. V., Schaeffner, S., Könen, T., Meaney, J.-A., Auyeung, B., Morey, C. C., Karbach, J., & Chevalier, N. (2020). Consistent use of proactive control and relation with academic achievement in childhood. Cognition, 203, 104329.

    Article  PubMed  Google Scholar 

  • Laursen, B., & Hoff, E. (2006). Person-centered and variable-centered approaches to longitudinal data. Merrill-Palmer Quarterly, 52, 377–389. https://doi.org/10.1353/mpq.2006.0029

    Article  Google Scholar 

  • Lazarides, R., Viljaranta, J., Aunola, K., & Nurmi, J.-E. (2018). Teacher ability evaluation and changes in elementary student profiles of motivation and performance in mathematics. Learning and Individual Differences, 67, 245–258. https://doi.org/10.1016/j.lindif.2018.08.010

    Article  Google Scholar 

  • Lazarides, R., Gaspard, H., & Dicke, A.-L. (2019). Dynamics of classroom motivation: Teacher enthusiasm and the development of math interest and teacher support. Learning and Instruction, 60, 126–137.

    Article  Google Scholar 

  • Lechner, C. M., Miyamoto, A., & Knopf, T. (2019). Should students be smart, curious, or both? Fluid intelligence, openness, and interest co-shape the acquisition of reading and math competence. Intelligence, 76, 101378.

    Article  Google Scholar 

  • Lee, E. J. (2020). Biased self-estimation of maths competence and subsequent motivation and achievement: Differential effects for high- and low-achieving students. Educational Psychology. https://doi.org/10.1080/01443410.2020.1821869

    Article  Google Scholar 

  • Mädamürk, K., Kikas, E., & Palu, A. (2016). Developmental trajectories of calculation and word problem solving from third to fifth grade. Learning and Individual Differences, 49, 151–161.

    Article  Google Scholar 

  • Mädamürk, K., Kikas, E., & Palu, A. (2018). Calculation and word problem-solving skill profiles: Relationship to previous skills and interest. Educational Psychology. https://doi.org/10.1080/01443410.2018.1495830

    Article  Google Scholar 

  • Nurmi, J.-E. & Aunola, K. (1999). Task-value scale for children (TVS-C). Unpublished test material, University of Jyväskylä, Finland. OECD. (2019). Programme for International Student Assessment (PISA) results from PISA 2018. Used 24.06.2021. https://www.oecd.org/pisa/publications/PISA2018_CN_EST.pdf

  • OECD. (2010). “Main features of the PISA mathematics theoretical framework”, in Learning Mathematics for Life: A perspective from PISA. OECD Publishing.

    Book  Google Scholar 

  • OECD. (2018). PISA 2021 mathematics framework (second draft). Used 05.04.2022 https://www.oecd.org/pisa/pisaproducts/pisa-2021-mathematics-framework-draft.pdf

  • Petersen, J. L., & Hyde, J. S. (2015). Trajectories of self-perceived math ability, utility value and interest across middle school as predictors of high school math performance. Educational Psychology. https://doi.org/10.1080/01443410.2015.1076765

    Article  Google Scholar 

  • Pisher, P. H., Dobbs-Oates, J., Doctoroff, G. L., & Arnolt, D. H. (2012). Early math interest and the development of math skills. Journal of Educational Psychology, 104(3), 673–681.

    Article  Google Scholar 

  • Pittalis, M., Pitta-Pantazi, D., & Christou, C. (2018). A longitudinal study revisiting the notion of early number sense: Algebraic arithmetic as a catalyst for number sense development. Mathematical Thinking and Learning, 20(3), 222–247.

    Article  Google Scholar 

  • R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for statistical computin, Vienna, Austria. URL https://www.R-project.org/. Accessed 30 April 2023

  • Republic of Estonia Ministry of Education and Research. (2020). Pre-school, basic and secondary education. Used 30.03.2022. https://www.hm.ee/en/activities/pre-school-basic-and-secondary-education

  • Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587–597.

    Article  Google Scholar 

  • Rittle-Johnson, B. & Siegler, R. S. (1998). The relation between conceptual and procedural knowledge in learning mathematics: A review. C. Donlan (Ed.), The development of mathematical skill (75–110). Hove, England: Psychology Press.

  • Rodríguez‐Aflecht, G., Jaakkola, T., Pongsakdi, N., Hannula-Sormunen, M., Brezovszky, B. & Lehtinen, E. (2018). The development of situational interest during a digital mathematics game. Journal of Computer Assisted Learning, 1–10, https://doi.org/10.1111/jcal.12239

  • von Eye, A., & Bogat, G. A. (2006). Person-oriented and variable-oriented research: Concepts, results, and development. Merrill-Palmer Quarterly, 52(3), 390–420.

    Article  Google Scholar 

Download references

Funding

This work was supported by Tallinn University (grant number TF/6620) and the Estonian Research Council (grant number PSG741).

Author information

Authors and Affiliations

Authors

Contributions

We confirm that both authors and only the authors have participated in the article preparation and that the manuscript has been read and its submission is approved by both named authors. There are no other persons who satisfied the criteria for authorship. Both of the authors have agreed to the byline order and to the submission of the manuscript in the current form. I, Triinu Kilp-Kabel, will be serving as the corresponding author. I will keep my co-author informed of our progress through the editorial review process, the content of the reviews, and any revisions made. Material preparation and data collection were performed by both authors; literature search, data analysis, and original draft preparation were done by Triinu Kilp-Kabel, and funding acquisition, review, editing, and supervision were done by Kaja Mädamürk.

Corresponding author

Correspondence to Triinu Kilp-Kabel.

Ethics declarations

Ethics approval and consent to participate

This work was approved by the Ethics Committee of Tallinn University (approval number 5). Parents and students signed an informed consent form to link Grade three results to Grade five results. If at least one did not consent to this, their results were not included in the data. The data itself was given to the research team in an encrypted file by a representative of the Exam Infosystem we have in Estonia without students’ personal details which could lead to their identification. In addition, students and parents were allowed to withdraw consent at any time during the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Triinu Kilp-Kabel. School of Natural Sciences and Health, Tallinn University, Narva rd 25, 10120, Tallinn, Estonia. E-mail:triinu.kilp-kabel@tlu.ee

Current themes of research:

Math competence development and its relation to achievement motivation. Enhancing math competence in middle school.

Most relevant publications in the field of Psychology of Education:

No publications as of yet.

Kaja Mädamürk. School of Natural Sciences and Health, Tallinn University, Narva rd 25, 10120, Tallinn, Estonia. E-mail:kaja.madamurk@tlu.ee

Current themes of research:

Reading and math skill development. Learning motivation. Digital engagement in middle school.

Most relevant publications in the field of Psychology of Education:

Kikas, E., Mädamürk, K., & Palu, A. (2020). What role do comprehension‐oriented learning strategies have in solving math calculation and word problems at the end of middle school? British Journal of Educational Psychology, 90, 105-123.

Mädamürk, K., Tuominen, H., Hietajärvi, L., & Salmela-Aro, K. (2021). Adolescent students’ digital engagement and achievement goal orientation profiles. Computers & Education, 161, 104058.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kilp-Kabel, T., Mädamürk, K. The developmental trajectories of math skills and its relation to math interest in Grades three and five. Eur J Psychol Educ (2024). https://doi.org/10.1007/s10212-024-00807-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10212-024-00807-8

Keywords

Navigation