Preschoolers’ ways of experiencing numbers

Authors

  • Camilla Björklund Department of Education, Communication and Learning, University of Gothenburg, Sweden https://orcid.org/0000-0001-5436-537X
  • Anna-Lena Ekdahl School of Education and Communication, Jönköping University, Sweden https://orcid.org/0000-0002-4685-1594
  • Angelika Kullberg Department of Pedagogical, Curricular and Professional Studies, University of Gothenburg, Sweden https://orcid.org/0000-0002-7698-4590
  • Maria Reis Department of Education, Communication and Learning, University of Gothenburg, Sweden

DOI:

https://doi.org/10.31129/LUMAT.10.2.1685

Keywords:

phenomenography, variation theory, mathematics education, arithmetic, numbers, preschoolers

Abstract

In this paper we direct attention to 5–6-year-olds’ learning of arithmetic skills through a thorough analysis of changes in the children’s ways of encountering and experiencing numbers. The foundation for our approach is phenomenographic, in that our object of analysis is differences in children’s ways of completing an arithmetic task, which are considered to be expressions of their ways of experiencing numbers and what is possible to do with numbers. A qualitative analysis of 103 children’s ways of encountering the task gives an outcome space of varying ways of experiencing numbers. This is further analyzed through the lens of variation theory of learning, explaining why differences occur and how observed changes over a prolonged period of time can shed light on how children learn the meaning of numbers, allowing them to solve arithmetic problems. The results show how observed changes are liberating new and powerful problem-solving strategies. Emanating from empirical research, the results of our study contribute to the theoretical understanding of young children’s learning of arithmetic skills, taking the starting point in the child’s lived experiences rather than cognitive processes. This approach to interpreting learning, we suggest, has pedagogical implications concerning what is fundamental to teach children for their further development in mathematics.

References

Ahlberg, A. (1997). Children's ways of handling and experiencing numbers. Acta Universitatis Gothoburgensis.

Baroody, A. J. (1987). Children’s mathematical thinking. Teachers College Press.

Baroody, A. J. (2016). Curricular approaches to connecting subtraction to addition and fostering fluency with basic differences in grade 1. PNA, 10(3), 161–190. https://doi.org/10.30827/pna.v10i3.6087

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

Björklund, C., Ekdahl, A-L., & Runesson Kempe, U. (2021). Implementing a structural approach in preschool number activities. Principles of an intervention program reflected in learning. Mathematical Thinking and Learning, 23(1), 72–94. https://doi.org/10.1080/10986065.2020.1756027

Björklund, C., Marton, F., & Kullberg, A. (2021). What is to be learnt? Critical aspects of elementary arithmetic skills. Educational Studies in Mathematics, 107(2), 261–284. https://doi.org/10.1007/s10649-021-10045-0

Björklund, C., & Runesson Kempe, U. (2019). Framework for analysing children’s ways of experiencing numbers. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis, (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6–10, 2019). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

Cheng, Z.-J. (2012). Teaching young children decomposition strategies to solve addition problems: An experimental study. The Journal of Mathematical Behavior, 31(1), 29–47. https://doi.org/10.1016/j.jmathb.2011.09.002

Christensen, C. A., & Copper, T. J. (1992). The role of cognitive strategies in the transition from counting to retrieval of basic addition facts. British Educational Research Journal, 18(1), 37–44. https://doi.org/10.1080/0141192920180104

Cross, C., Woods, T., & Schweingruber, H. (Eds.). (2009). Mathematics learning in early childhood. Paths towards excellence and equity. The National Academies Press.

Ellemor-Collins, D. & Wright, R. B. (2009). Structuring numbers 1 to 20: Developing facile addition and subtraction. Mathematics Education Research Journal, 21(2), 50–75. https://doi.org/10.1007/BF03217545

Fuson, K. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). Macmillan Library Reference.

Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Harvard University Press.

Gibson, J. J., & Gibson, E. J. (1955). Perceptual learning: Differentiation – or enrichment? Psychological Review, 62(1), 32–41. https://doi.org/10.1037/h0048826

Lavie, I. & Sfard, A. (2019). How children individualize numerical routines: Elements of a discursive theory in making. Journal of the Learning Sciences, 28(4–5), 419–461. https://doi.org/10.1080/10508406.2019.1646650

Marton, F. (1981). Phenomenography - describing conceptions of the world around us. Instructional Science, 10(2), 177–200. https://doi.org/10.1007/BF00132516

Marton, F. (2015). Necessary conditions of learning. Routledge.

Marton, F., & Booth, S. (1997). Learning and awareness. Lawrence Erlbaum.

Marton, F., & Neuman, D. (1990). Constructivism, phenomenology, and the origin of arithmetic skills. In L. Steffe & T. Wood (Eds.), Transforming children's mathematics education. Lawrence Erlbaum.

Marton, F., & Pong, W. Y. (2005). On the unit of description in phenomenography. Higher Education Research & Development, 24(4), 335–348. https://doi.org/10.1080/07294360500284706

Neuman, D. (1987). The origin of arithmetic skills: A phenomenographic approach. Acta Universitatis Gothoburgensis.

Neuman, D. (2013). Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen [Changing the ways of working and culture in early arithmetic teaching]. Nordic Studies in Mathematics Education, 18(2), 3–46.

Peters, G., De Smedt, B., Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2012). Children’s use of subtraction by addition on large single-digit subtractions. Educational Studies in Mathematics, 79, 335–349. https://doi.org/10.1007/s10649-011-9308-3

Piaget, J. (1952). The child’s conception of number. W.W. Norton & Company Inc.

Piaget, J. (1976[1929]). The child's conception of the world. Litterfield Adams & Co.

Sarama, J., & Clements, D. (2009). Early childhood mathematics education research. Learning trajectories for young children. Routledge.

Smedslund, J. (1977). Piaget’s psychology in practice. British Journal of Educational Psychology 47(1), 1–6.

Starkey, P., & Gelman, R. (1982). The development of addition and subtraction abilities prior to formal schooling in arithmetic. In T. P. Carpenter, J. M. Moser, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 99–116). Lawrence Erlbaum Associates.

Svensson, L. (1997). Theoretical foundations of Phenomenography. Higher Education Research & Development, 16(2), 159–171. https://doi.org/10.1080/0729436970160204

Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2015). Analyzing number composition and decomposition activities in kindergarten from a numeracy perspective. ZDM Mathematics Education, 47(4), 639-651. https://doi.org/10.1007/s11858-015-0668-5

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Published

2022-06-30

How to Cite

Björklund, C., Ekdahl, A.-L., Kullberg, A., & Reis, M. (2022). Preschoolers’ ways of experiencing numbers. LUMAT: International Journal on Math, Science and Technology Education, 10(2), 84–110. https://doi.org/10.31129/LUMAT.10.2.1685

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