Skip to main content
SpringerLink
Log in

The Influence of Making Predictions on the Accuracy of Numerosity Estimates in Elementary-Aged Children

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

Estimation supports the development of higher level mathematical thinking and reasoning; however, has received relatively little research attention. We examined whether making predictions influences the accuracy of numerosity estimates in elementary-aged children, and whether the amount of information available to the estimator determines the accuracy of their subsequent estimate. The study was conceptualized on the basis of five different conditions for estimating, based on the contention that estimates will become more accurate as additional information becomes available to the estimator. To test this idea, the study utilized two tasks to examine the responses of year 2 (grade 2) and year 6 (grade 6) students (n = 110) when using prediction-first and estimation-only strategies. Across both tasks, we found a direct linear relationship between the accuracy of students’ estimates and the amount of information available. Moreover, there was some evidence that being given an opportunity to make an initial prediction improved the accuracy of final estimates; however, these conclusions were tempered by task and age. Overall, our findings support a strategy sophistication effect, whereby the amount of information available to the estimator, and the ability to use that information effectively, increases the accuracy of the estimate.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. To be consistent with the estimation literature, we refer to the term “decomposition” throughout this paper when discussing this idea, however within the mathematics education literature more broadly, the term multiplicative partitioning or equipartitioning would be considered more accurate.

  2. Note that condition 5 was not considered in the current study. Indeed, in the context of the sorts of tasks we explored with our participants, condition 5 remains essentially theoretical, as attempting to enact it would restructure the task in a manner that would undermine the flow of the interview, and actually change the nature of the task (e.g., moving from beans to cube-shaped beans).

References

  • Alvarez, J., Abdul-Chani, M., Deutchman, P., DiBiasie, K., Iannucci, J., Lipstein, R., & Sullivan, J. (2017). Estimation as analogy-making: Evidence that preschoolers’ analogical reasoning ability predicts their numerical estimation. Cognitive Development, 41, 73–84.

    Article  Google Scholar 

  • Anobile, G., Cicchini, G. M., & Burr, D. C. (2016). Number as a primary perceptual attribute: A review. Perception, 45(1–2), 5–31.

    Article  Google Scholar 

  • Australian Curriculum and Assessment Authority (ACARA). (2015). The Australian Curriculum: Mathematics. Retrieved from: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1.

  • Baroody, A. J., & Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. Journal for Research in Mathematics Education, 22(1), 59–68.

    Article  Google Scholar 

  • Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189–201.

    Article  Google Scholar 

  • Brod, G., Hasselhorn, M., & Bunge, S. A. (2018). When generating a prediction boosts learning: The element of surprise. Learning and Instruction, 55, 22–31.

    Article  Google Scholar 

  • Case, R., & Sowder, J. T. (1990). The development of computational estimation: A neo-Piagetian analysis. Cognition and Instruction, 7, 79–104.

    Article  Google Scholar 

  • Charles, R. I., & Carmel, C. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education, 7(3), 9–24.

    Google Scholar 

  • Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, M., McDonough, A., . . . Clarke, B. (2002). Early numeracy research project final report. Melbourne: Australian Catholic University.

  • Crites, T. (1992). Skilled and less skilled estimators’ strategies for estimating discrete quantities. The Elementary School Journal, 92(5), 601–619.

    Article  Google Scholar 

  • Downton, A., & Sullivan, P. (2017). Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections. Educational Studies in Mathematics, 95(3), 303–328.

    Article  Google Scholar 

  • Gandini, D., Lemaire, P., & Dufau, S. (2008). Older and younger adults’ strategies in approximate quantification. Acta Psychologica, 129(1), 175–189.

    Article  Google Scholar 

  • Ganor-Stern, D. (2016). Solving arithmetic problems approximately: A developmental perspective. PLoS One, 11, e0155515.

    Article  Google Scholar 

  • Hegarty, M., Kriz, S., & Cate, C. (2003). The roles of mental animations and external animations in understanding mechanical systems. Cognition and Instruction, 21(4), 209–249.

    Article  Google Scholar 

  • Huntley-Fenner, G., & Cannon, E. (2000). Preschoolers’ magnitude comparisons are mediated by a preverbal analog mechanism. Psychological Science, 11(2), 147–152.

    Article  Google Scholar 

  • Kahneman, D., & Egan, P. (2011). Thinking, fast and slow (Vol. 1). New York: Farrar, Straus and Giroux.

    Google Scholar 

  • Kasmer, L. A., & Kim, O. K. (2012). The nature of student predictions and learning opportunities in middle school algebra. Educational Studies in Mathematics, 79(2), 175–191.

    Article  Google Scholar 

  • Kim, O.-K., & Kasmer, L. (2007). Using “prediction” to promote mathematical reasoning. Mathematics Teaching in the Middle School, 12(6), 294–299.

    Article  Google Scholar 

  • LeFevre, J. A., Greenham, S. L., & Waheed, N. (1993). The development of procedural and conceptual knowledge in computational estimation. Cognition and Instruction, 11, 95–132.

    Article  Google Scholar 

  • Lemaire, P., & Lecacheur, M. (2011). Age-related changes in children’s executive functions and strategy selection: A study in computational estimation. Cognitive Development, 26, 282–294.

    Google Scholar 

  • Lim, K. H., Buendia, G., Kim, O. K., Cordero, F., & Kasmer, L. (2010). The role of prediction in the teaching and learning of mathematics. International Journal of Mathematical Education in Science and Technology, 41(5), 595–608.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., & Hegarty, M. (2019). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20(5), 729–751.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Opfer, J. E., & Siegler, R. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55(3), 169–195.

    Article  Google Scholar 

  • Patahuddin, S. M., Rokhmah, S., & Ramful, A. (2020). What does teaching of spatial visualisation skills incur: An exploration through the visualise-predict-check heuristic. Mathematics Education Research Journal, 32(2), 307–329.

    Article  Google Scholar 

  • Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present, and future (pp. 205–235). Rotterdam: Sense Publishers.

    Google Scholar 

  • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.

    Article  Google Scholar 

  • Rittle-Johnson, B., & Star, J. R. (2011). The power of comparison in learning and instruction: Learning outcomes supported by different types of comparisons. In J. Mestre & B. Ross (Eds.), Psychology of learning and motivation (Vol. 55, pp. 199–225). Oxford: Elsevier.

    Chapter  Google Scholar 

  • Rivera, F. (2011). Toward a visually-oriented school mathematics curriculum: Research, theory, practice, and issues (Vol. 49). Springer Science & Business Media.

  • Russo, J. (2018). Dynamic estimation: A guided approach to refining student estimates. Australian Primary Mathematics Classroom, 23(3), 4–7.

    Google Scholar 

  • Siegel, A. W., Goldsmith, L. T., & Madson, C. R. (1982). Skill in estimation problems of extent and numerosity. Journal for Research in Mathematics Education, 13(3), 211–232.

    Article  Google Scholar 

  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. Campbell (Ed.), Handbook of mathematical cognition (pp. 197–212). New York: Psychology Press (Taylor & Francis Group).

    Google Scholar 

  • Smith, H. D. (1999). Use of the anchoring and adjustment heuristic by children. Current Psychology, 18(3), 294–300.

    Article  Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Charlotte: Information Age Publishing.

    Google Scholar 

  • White, R., & Gunstone, R. (1992). Prediction-observation-explanation. In R. White & R. Gunstone (Eds.), Probing understanding (Vol. 4, pp. 44–64). London: The Falmer Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Education, Monash University, Wellington Rd, Clayton, VIC, 3800, Australia

    James Russo & Toby Russo

  2. Early Childhood Mathematics Education, School of Education, Charles Sturt University, PO Box 789, Albury, NSW, 2640, Australia

    Amy MacDonald

Authors
  1. James Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amy MacDonald
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Toby Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to James Russo.

Supplementary Information

ESM 1

(DOCX 641 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Russo, J., MacDonald, A. & Russo, T. The Influence of Making Predictions on the Accuracy of Numerosity Estimates in Elementary-Aged Children. Int J of Sci and Math Educ 20, 531–551 (2022). https://doi.org/10.1007/s10763-021-10156-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-021-10156-3

Keywords

Search

Navigation