Skip to main content

Young Children’s Early Mathematical Competencies: The Role of Mathematical Focusing Tendencies

  • Chapter
  • First Online:
Mathematics Education in the Early Years

Abstract

In this chapter we review and discuss a relatively new line of research in the domain of early mathematical development that addresses the dispositional rather than the ability aspect of children’s early mathematical competence, namely their tendencies to attend to and focus on various mathematical elements in their environment and its relation with (later) mathematical development in school. So far, most of this research has been done on young children’s spontaneous focusing on numerosity (SFON), but to a much lesser extent, similar efforts have been made for Arabic number symbols (SFONS), quantitative relations (SFOR), and mathematical patterns (SFOP). Our review and discussion of these four mathematical focusing tendencies are organized around the following four themes: definition, measurement, development, and stimulation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Andrews, P., & Sayers, J. (2015). Identifying opportunities for grade one children to acquire foundational number sense: Developing a framework for cross cultural classroom analyses. Early Childhood Education Journal, 43(4), 257–267. https://doi.org/10.1007/s10643-014-0653-6

    Article  Google Scholar 

  • Aunio, P., & Niemivirta, M. (2010). Predicting children’s mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20, 427–435. https://doi.org/10.1016/j.lindif.2010.06.003

    Article  Google Scholar 

  • Baroody, A. J., & Purpura, D. J. (2017). Early number and operations: Whole numbers. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 308–354). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Batchelor, S. (2014). Dispositional factors affecting children’s early numerical development (Doctoral thesis, Loughborough University, Leicestershire, United Kingdom). Retrieved from https://dspace.lboro.ac.uk/2134/17474

  • Batchelor, S., Inglis, M., & Gilmore, C. (2015). Spontaneous focusing on numerosity and the arithmetic advantage. Learning and Instruction, 40, 79–88. https://doi.org/10.1016/j.learninstruc.2015.09.005

    Article  Google Scholar 

  • Bojorque, G., Torbeyns, J., Hannula-Sormunen, M. M., Van Nijlen, D., & Verschaffel, L. (2016). Development of SFON in Ecuadorian kindergartners. European Journal of Psychology Education, 1–14. https://doi.org/10.1007/s10212-016-0306-9

  • Chan, J. Y.-C., & Mazzocco, M. M. M. (2017). Competing features influence children’s attention to number. Journal of Experimental Child Psychology, 156, 62–81. https://doi.org/10.1016/j.jecp.2016.11.008

    Article  Google Scholar 

  • Choudhury, A., McCandliss, B., & Hannula, M. M. (2007). Individual differences in spontaneous focusing on numerosity are related to numerical skills at school age. In B. McCandliss (Chair), Developmental changes in number skills reflect the emergence of children’s ability to focus attention on different aspects of number. Symposium conducted at the 19th Annual Convention for Psychological Science, Washington DC, USA.

    Google Scholar 

  • Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46, 1176–1191. https://doi.org/10.1037/a0019672

    Article  Google Scholar 

  • De Smedt, B., Janssen, R., Bouwens, K., Verschaffel, L., & Ghesquière, P. (2009). Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade. Journal of Experimental Child Psychology, 103, 186–201. https://doi.org/10.1016/j.jecp.2009.01.004

    Article  Google Scholar 

  • Degrande, T., Verschaffel, L., & Van Dooren, W. (2017). Spontaneous focusing on quantitative relations: Towards a characterization. Mathematical Thinking and Learning, 19, 260–275. https://doi.org/10.1080/10986065.2017.1365223

    Article  Google Scholar 

  • Edens, K. M., & Potter, E. F. (2013). An exploratory look at the relationships among math skills, motivational factors and activity choice. Early Childhood Educational Journal, 41, 235–243. https://doi.org/10.1007/s10643-012-0540-y

    Article  Google Scholar 

  • Fox, J. (2005). Child-initiated mathematical patterning in the pre-compulsory years. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 313–320). Melbourne: PME.

    Google Scholar 

  • Garrick, R., Threlfall, J., & Orton, A. (2005). Pattern in the nursery. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 1–17). London: Continuum.

    Google Scholar 

  • Gray, S. A., & Reeve, R. A. (2016). Number-specific and general cognitive markers of preschoolers’ math ability profiles. Journal of Experimental Child Psychology, 147, 1–21. https://doi.org/10.1016/j.jecp.2016.02.004

    Article  Google Scholar 

  • Gunderson, E. A., & Levine, S. C. (2011). Some types of parent number talk count more than others: Relations between parents’ input and children’s cardinal-number knowledge. Developmental Science, 14, 1021–1032. https://doi.org/10.1111/j.1467-7687.2011.0150.x

    Article  Google Scholar 

  • Hannula, M. M. (2005). Spontaneous focusing on numerosity in the development of early mathematical skills (Doctoral thesis, University of Turku, Turku, Finland). Retrieved from http://www.doria.fi/handle/10024/102190

  • Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15, 237–256. https://doi.org/10.1016/j.learninstruc.2005.04.005

    Article  Google Scholar 

  • Hannula, M. M., Lepola, J., & Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107, 394–406. https://doi.org/10.1016/j.jecp.2010.06.004

    Article  Google Scholar 

  • Hannula, M. M., Mattinen, A., & Lehtinen, E. (2005). Does social interaction influence 3 year-old children’s tendency to focus on numerosity? A quasi-experimental study in day-care. In L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds.), Powerful learning environments for promoting deep conceptual and strategic learning (Vol. 41, pp. 63–80). Leuven, Belgium: Leuven University Press.

    Google Scholar 

  • Hannula, M. M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9, 51–57. https://doi.org/10.1080/10986060709336605

    Article  Google Scholar 

  • Hannula-Sormunen, M. M. (2015). Spontaneous focusing on numerosity and its relation to counting and arithmetic. In R. Cohen-Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 275–290). Oxford, UK: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.018

    Chapter  Google Scholar 

  • Hannula-Sormunen, M. M., Alanen, A., McMullen, J., Kyttälä, M., & Lehtinen, E. (2015, October). Training of kindergartners’ arithmetical skills by a computer game “Fingu” integrated with everyday activities and SFON enhancement. Paper presented at the 2nd meeting of the Scientific Research Community: WO.008.14N Developing competencies in learners: From ascertaining to intervening, Leuven, Belgium.

    Google Scholar 

  • Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Preschool children’s spontaneous focusing on numerosity, subitizing and counting skills as predictors of their mathematical performance 7 years later at school. Mathematical Thinking and Learning, 17, 155–177. https://doi.org/10.1080/10986065.2015.1016814

    Article  Google Scholar 

  • Jordan, N. C., Kaplan, D., Olah, L. N., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153–175. https://doi.org/10.1111/j.1467-8624.2006.00862.x

    Article  Google Scholar 

  • Kucian, K., Kohn, J., Hannula-Sormunen, M. M., Richtmann, V., Grond, U., Käser, T., et al. (2012). Kinder mit Dyskalkulie fokussieren spontan weniger auf Anzahligkeit. Lernen und Lernstörungen, 1, 241–253. https://doi.org/10.1024/2235-0977/a000024

    Article  Google Scholar 

  • Lepola, J., Hannula-Sormunen, M., & Lehtinen, E. (2019). SFON and early motivation as predictors of arithmetical development from kindergarten to grade 2. Educational Studies in Mathematics, 100, 251–269.

    Article  Google Scholar 

  • Mattinen, A. (2006). Huomio lukumääriin: Tutkimus 3-vuotiaiden lasten matemaattisten taitojen tukemisesta päiväkodissa [Focus on numerosities: A study on supporting 3-year-old children’s mathematical development in day care] (Doctoral Dissertation). University of Turku, Finland: Painosalama.

    Google Scholar 

  • McKillip, W. D. (1970). “Patterns”—A mathematics unit for three- and four-year-olds. The Arithmetic Teacher, 17(1), 15–18.

    Article  Google Scholar 

  • McMullen, J. (2014). Spontaneous focusing on quantitative relations and the development of rational number conceptual knowledge (Doctoral Dissertation). University of Turku, Turku.

    Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., Kainulainen, M., Kiili, K., & Lehtinen, E. (2019). Moving mathematics out of the classroom: Using mobile technology to enhance spontaneous focusing on quantitative relations. British Journal of Educational Technology, 50, 562–573. https://doi.org/10.1111/bjet.12601

    Article  Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., Laakkonen, E., & Lehtinen, E. (2016). Spontaneous focusing on quantitative relations as a predictor of the development of rational number conceptual knowledge. Journal of Educational Psychology, 108, 875–868. https://doi.org/10.1037/edu0000094

    Article  Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2013). Young children’s recognition of quantitative relations in mathematically unspecified settings. Journal of Mathematical Behavior, 32, 450–460. https://doi.org/10.1016/j.jmathb.2013.06.001

    Article  Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2014). Spontaneous focusing on quantitative relations in the development of children’s fraction knowledge. Cognition and Instruction, 32, 198–218. https://doi.org/10.1080/07370008.2014.887085

    Article  Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2015). Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later. ZDM Mathematics Education, 47, 813–824. https://doi.org/10.1007/s11858-015-0669-4

    Article  Google Scholar 

  • McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (2017). Spontaneous focusing on quantitative relations as a predictor of rational number and algebra knowledge. Contemporary Educational Psychology, 51(6), 356–365. https://doi.org/10.1016/j.cedpsych.2017.09.007

    Article  Google Scholar 

  • Moll, K., Snowling, M. J., Göbel, S. M., & Hulme, C. (2015). Early language and executive skills predict variations in number and arithmetic skill in children at family-risk of dyslexia and typically developing controls. Learning and Instruction, 38, 53–62. https://doi.org/10.1016/j.learninstruc.2015.03.004

    Article  Google Scholar 

  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. https://doi.org/10.1007/BF03217544

    Article  Google Scholar 

  • Neumann, M. M., Hood, M., Ford, R. M., & Neumann, D. L. (2013). Letter and numeral identification: Their relationship with early literacy and numeracy skills. European Early Childhood Education Research Journal, 21, 489–501. https://doi.org/10.1080/1350293X.2013.845438

    Article  Google Scholar 

  • Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40, 27–52. https://doi.org/10.1207/s15326985ep4001_3

    Article  Google Scholar 

  • Pasnak, R. (2018). Empirical studies of pattering. Psychology, 8, 2276–2293. https://doi.org/10.4236/psych.2017.813144

    Article  Google Scholar 

  • Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. British Journal of Educational Psychology, 82, 42–63. https://doi.org/10.1111/j.2044-8279.2011.02039.x

    Article  Google Scholar 

  • Poltz, N., Wyschkon, A., Hannula-Sormunen, M. M., von Aster, M., & Esser, G. (2014, August). Spontaneous focusing on numerosity and the development of mathematical skills: Stability and prediction in kindergarten. Paper presented at the Biennial EARLI SIG 5 Conference “Learning and Development in Early Childhood”, Jyväskylä, Finland.

    Google Scholar 

  • Purpura, D. J., & Ganley, C. M. (2014). Working memory and language: Skills-specific or domain-general relations to mathematics? Journal of Experimental Child Psychology, 122, 104–121. https://doi.org/10.1016/j.jecp.2013.12.009

    Article  Google Scholar 

  • Purpura, D. J., & Lonigan, C. J. (2013). Informal numeracy skills: The structure and relations among numbering, relations, and arithmetic operations in preschool. American Educational Research Journal, 50(1), 178–209. https://doi.org/10.3102/0002831212465332

    Article  Google Scholar 

  • Ramani, G. B., Rowe, M. L., Eason, S. H., & Leech, K. A. (2015). Math talk during informal learning activities in Head Start families. Cognitive Development, 35, 15–33. https://doi.org/10.1016/j.cogdev.2014.11.002

    Article  Google Scholar 

  • Rathé, S., Torbeyns, J., De Smedt, B., Hannula-Sormunen, M. M., & Verschaffel, L. (2018). Verbal and behavioral measures of kindergartners’ SFON and their associations with number-related utterances during picture book reading. British Journal of Educational Psychology, 88, 550–565. https://doi.org/10.1111/bjep.12201

    Article  Google Scholar 

  • Rathé, S., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Spontaneous focusing on Arabic number symbols and its association with early mathematical competencies. Early Childhood Research Quarterly, 48, 111–121.

    Article  Google Scholar 

  • Rathé, S., Torbeyns, J., Hannula-Sormunen, M. M., De Smedt, B., & Verschaffel, L. (2016). Spontaneous focusing on numerosity and the development of mathematical competence: A review of recent research. Mediterranean Journal for Research in Mathematics Education, 15, 1–25.

    Google Scholar 

  • Rathé, S., Torbeyns, J., Hannula-Sormunen, M. M., & Verschaffel, L. (2016). Kindergartners’ spontaneous focusing on numerosity in relation to their number-related utterances during numerical picture book reading. Mathematical Thinking and Learning, 18, 125–141. https://doi.org/10.1080/10986065.2016.1148531

    Article  Google Scholar 

  • Sella, F., Berteletti, I., Lucangeli, D., & Zorzi, M. (2016). Spontaneous non-verbal counting in toddlers. Developmental Science, 19, 329–337. https://doi.org/10.1111/desc.12299

    Article  Google Scholar 

  • Seo, K.-H., & Ginsburg, H. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics (pp. 91–104). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Sharir, T., Mashal, N., & Mevarech, Z. R. (2015, August). To what extent can young children spontaneously recognize mathematical structures? Paper presented at the Biennial Conference of the European Association for Research on Learning and Instruction (EARLI), Limassol, Cyprus.

    Google Scholar 

  • Tian, J., & Siegler, R. (2015, March). Spontaneous focusing on numerosity in early math development: A cross-national study of American and Chinese preschoolers. Poster presented at the Society for Research in Child Development Biennial Meeting, Philadelphia, Pennsylvania, USA.

    Google Scholar 

  • Torbeyns, J., Gilmore, C., & Verschaffel, L. (2015). The acquisition of preschool mathematical abilities: Theoretical, methodological and educational considerations. An introduction. Mathematical Thinking and Learning, 17, 99–115. https://doi.org/10.1080/10986065.2015.1016810

    Article  Google Scholar 

  • Vamvakoussi, X., Vraka, L., Lioliousi, A., & McMullen, J. (2016, July). Young children’s spontaneous focusing on simple multiplication relations. Paper presented at the 13th International Congress on Mathematical Education, Hamburg, Germany.

    Google Scholar 

  • Van Hoof, J., Degrande, T., Verschaffel, L., & Van Dooren, W. (2016). The relation between learners’ spontaneous focusing on quantitative relations and their rational number knowledge. Studia Psychologica, 58, 156–170. https://doi.org/10.21909/sp.2016.02.714

    Article  Google Scholar 

  • Verschaffel, L., Torbeyns, J., & De Smedt, B. (2017). Young children’s early mathematical competencies: Analysis and stimulation [Powerpoint slides]. Plenary lecture presented at the Congress of European Research in Mathematics Education (CERME), Dublin, Ireland. Retrieved from: http://cerme10.org/wp-content/uploads/2016/01/CERME10-Plenary-Lecture-Verschaffel.pdf

  • Wijns, N., Torbeyns, J., De Smedt, B., & Verschaffel, L. (in press). Are preschoolers who spontaneously create patterns better in mathematics? British Journal of Educational Psychology.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lieven Verschaffel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Verschaffel, L. et al. (2020). Young Children’s Early Mathematical Competencies: The Role of Mathematical Focusing Tendencies. In: Carlsen, M., Erfjord, I., Hundeland, P.S. (eds) Mathematics Education in the Early Years. Springer, Cham. https://doi.org/10.1007/978-3-030-34776-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34776-5_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34775-8

  • Online ISBN: 978-3-030-34776-5

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics