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The development of computational estimation in the transition from informal to formal mathematics education

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Abstract

The transition from informal to formal mathematics is an important episode in children’s mathematical development. The current study investigated how young children’s computational estimation performance and strategy use develops in this transitional period. The computational estimation performance of 350 children was assessed before the start of formal schooling (i.e., third grade of kindergarten) and again after the start of formal schooling (i.e., first grade of primary school) by means of a computational estimation addition task with manipulatives. Both children’s answer construction and their counting behavior while constructing the answer were observed during task administration. Results showed an age-related increase in children’s estimation accuracy as well as in their proportion of exact answers. Age-related changes in strategy use were also observed. Children demonstrated an increase in their counting behavior while constructing the answer, but no changes in the way the answer was constructed. In both grades, the answer was most often constructed by laying down all manipulatives immediately in one group. These results suggested that children can follow two pathways to solve the estimation problems: (1) relying on the visual representation of the addends without using counting and (2) using the verbal labels provided by the experimenters while using counting. More use of counting in first grade positively influenced children’s estimation accuracy in this grade, suggesting that these children strive for more precision compared to children who do not count.

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Funding

This research was supported by the Grant KU Leuven project C16/16/001 “Development and stimulation of core mathematical competencies.”

Author information

Authors and Affiliations

  1. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Box 3773, 3000, Leuven, Belgium

    Elke Sekeris, Lieven Verschaffel & Koen Luwel

  2. Hogeschool PXL Research, Hasselt, Belgium

    Michaël Empsen

  3. Centre for Educational Research and Development, KU Leuven Campus Brussels, Brussels, Belgium

    Koen Luwel

Authors
  1. Elke Sekeris
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  2. Michaël Empsen
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  3. Lieven Verschaffel
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  4. Koen Luwel
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Correspondence to Elke Sekeris.

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Additional information

Elke Sekeris

Current themes of research:

Mathematics in early childhood. Computational estimation.

Most relevant publications in the field of Psychology of Education:

Peeters, D., Sekeris, E., Verschaffel, L., Luwel, K. (2017). Evaluating the effect of labeled benchmarks on children’s number line estimation performance and strategy use. Frontiers in Psychology, 8:1082.

Sekeris, E., Verschaffel, L., & Luwel, K. (2019). Measurement, development, and stimulation of computational estimation abilities in kindergarten and primary education: A systematic literature review. Educational Research Review, 27, 1–14.

Sekeris, E., Verschaffel, L., Luwel, K. (2019). Predictors of exact arithmetic and computational estimation in kindergarten. In: M. Graven, H. Venkat, A.A. Essien, P. Vale (Eds.), Proceedings of the 43rd conference of the International Group for the Psychology of Mathematics Education (Vol. 3): vol. 3, (312-318). Presented at the Conference of the International Group for the Psychology of Mathematics Education (PME 43), Pretoria, South Africa, 07 Jul 2019-12 Jul 2019. Pretoria, South Africa. ISBN: 978-0-6398215-4-2.

Michaël Empsen

Current themes of research:

Personalized learning. Virtual reality. Student, job market, and education alignment.

Most relevant publications in the field of Psychology of Education:

No publications yet.

Lieven Verschaffel

Current themes of research:

Learning and instruction. Math education. Problem solving.

Most relevant publications in the field of Psychology of Education:

De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematical achievement. Journal of Experimental Child Psychology, 103(4), 469–479.

Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teacher and Teacher Education, 34, 12-25.

Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 7(4), 339-360.

De Corte, E., Greer, B., & Verschaffel, L. (2000). Making sense of word problems. Amsterdam, The Netherlands: Swets & Zeitlinger.

Koen Luwel

Current themes of research:

Development and choice of cognitive strategies. Estimation skills. Cognitive flexibility. Number sense. Problem solving. Numerical and mathematical cognition.

Most relevant publications in the field of Psychology of Education:

Ebersbach, M., Luwel, K., & Verschaffel, L. (2015). The relationship between children’s familiarity with numbers and their performance in bounded and unbounded number line estimations. Mathematical Thinking and Learning, 17 (2), 136-154.

Luwel, K., Siegler, R.S., & Verschaffel, L. (2008). A microgenetic study of insightful problem solving. Journal of Experimental Child Psychology, 99 (3), 210-232.

Schneider, M., Merz, S., Stricker, J., De Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta-analysis. Child Development, 89 (5), 1467-1484.

Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24 (3), 335-359.

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Appendix

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Table 5 Items and corresponding number size from the computational estimation task
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Sekeris, E., Empsen, M., Verschaffel, L. et al. The development of computational estimation in the transition from informal to formal mathematics education. Eur J Psychol Educ 36, 845–864 (2021). https://doi.org/10.1007/s10212-020-00507-z

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