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Spontaneous Mathematical Focusing Tendencies in Mathematical Development and Education

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Book cover Constructing Number

Part of the book series: Research in Mathematics Education ((RME))

Abstract

A growing body of evidence reveals the need for research on, and consideration for, children’s and students’ own—self-guided—spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this chapter, we review existing research on SFON and SFOR tendencies in the broader context of the development of mathematical skills and knowledge and examine how the state-of-the-art evidence on SFON and SFOR is relevant for the field of mathematics education. We discuss individual differences in SFON and SFOR, associations between spontaneous focus on mathematical features and mathematics achievement, the contributions of situational contexts that implicitly prompt attention to number, and ways to increase children’s focus on number regardless of their baseline level tendencies. We conclude that children’s and students’ tendencies to focus on number and quantitative relations–spontaneous or otherwise–are key components of mathematical development and education.

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Notes

  1. 1.

    It should be noted that, at the moment, we do not distinguish between different aspects of quantitative relations, though most existing research examines either multiplicative relations with late primary school students or part-whole relations in preschoolers. SFOR tasks usually include discrete quantities and underlying exact numbers are a foil and/or a prerequisite for focusing on the relational aspects of the task.

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Acknowledgements

Drs. Michèle Mazzocco and Jenny Yun-Chen Chan’s contributions to this chapter were supported by Grant #1644748 from the National Science Foundation, awarded to Dr. Mazzocco.

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Authors and Affiliations

  1. Department of Teacher Education and Centre for Research on Learning and Instruction, University of Turku, Turku, Finland

    Jake McMullen & Minna M. Hannula-Sormunen

  2. Institute of Child Development, University of Minnesota—Twin Cities, Minneapolis, MN, USA

    Jenny Yun-Chen Chan & Michèle M. M. Mazzocco

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  1. Jake McMullen
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  4. Minna M. Hannula-Sormunen
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Correspondence to Jake McMullen .

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  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

    Anderson Norton

  2. Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA

    Martha W. Alibali

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McMullen, J., Chan, J.YC., Mazzocco, M.M.M., Hannula-Sormunen, M.M. (2019). Spontaneous Mathematical Focusing Tendencies in Mathematical Development and Education. In: Norton, A., Alibali, M.W. (eds) Constructing Number. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-00491-0_4

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