Influence of the teaching context on pattern representation in early childhood education

Main Article Content

Yeni Acosta-Inchaustegui

Abstract

According to the Mathematics Teaching Itineraries Approach (EIEM), which proposes intentionalteaching sequences from the concrete to the symbolic, we analyse how the teaching context influencesthe repetition pattern tasks in a group of 24 children during two consecutive school years (4-6 years old).For this purpose, repetition pattern tasks have been implemented in the two extreme contexts of a previouslydesigned and validated itinerary: real situations and graphic contexts, respectively. The data have beenanalysed from ethnographic methodological schemesof participant observation (field diary); pedagogical documentation (audiovisual record); and written productions of the patterns (representations). The mainresults obtained show that: a) in pupils aged 4-5 years, a positive difference of 32.9% of real situations versusgraphic resources has been identified; b) in pupils aged 5-6 years, although the difference between the twocontexts decreases slightly, it continues to be above 30%. It is concluded that the teaching context influences the understanding of repetition patterns, so that it isnecessary to teach patterns from the situational to the formal level.

Article Details

Section
Central Theme
Author Biography

Ángel Alsina

Catedrático de Didáctica de las Matemáticas en la Universidad de Girona

References

Bock, A.M., Cartwright, K.B., McKnight, P.E., Patterson, A.B., Shriver, A.G., Leaf, B.M., Mohtasham, M.K., Vennergrund, K.C., y Pasnak, R. (2018). Patterning, Reading, and Executive Functions. Frontiers in Psychology, 9, 1802.

Björklund, C., y Pramling, N. (2014). Pattern discernment and pseudo-conceptual development in early childhood mathematics education. International Journal of Early Years Education, 22 (1), 9-104. http://10.1080/09669760.2013.809657

Björklund, C., van den Heuvel-Panhuizen, M., y Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM Mathematics Education. https://doi.org/10.1007/s11858-020-01177-3

Bowman, B., Donovan, M., y Burns, M. (2001). Eager to learn: Educating our preschoolers. National Academy Press.

Carruthers, E., y Worthington, M. (2005) Making Sense of Mathematical Graphics: The Development of Understanding Abstract Symbolism. European Early Childhood Educational Research Journal, 13(1), 57-79.

Clements, H.D., y Sarama, J. (2015). El Aprendizaje y la Enseñanza de las Matemáticas a Temprana Edad. Learning Tools LLC.

Creswell, J.W., y Plano Clark, V.L. (2011). Designing and Conducting Mixed Methods Research. 2nd Edition, Sage Publications.

Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publishers.

Kawulich, B.B. (2005). La observación participante como método de recolección de datos. Forum Qualitative Social Research, 6(2).

Korthagen, F. A. (2001). Linking practice and theory. The pedagogy of realistic teacher education. Lawrence Erlbaum Associates.

Laski, E. V., y Siegler, R. S. (2014). Learning from number board games: You learn what you encode. Developmental Psychology, 50(3), 853-864.

Leeuwen, V.T. (2008). Discourse and practice: New tools forcritical discourse analysis. Oxford University Press.

Lüken, M. (2018). Is patterning a mathematical activity?—An analysis of young children’s strategies in working with repeating patterns. In A mathematics education perspective on early mathematics learning—POEM. https://doi.org/10.1007/978-3-030-34776-5_5

Mitchelmore, S. (2018). Providing Insight Through Pedagogical Documentation: Seeing Research as an Everyday Practice. En M. Fleer, y B. van Oers (Eds.), International Handbook of Early Childhood Education Volume I (pp.190-195). Springer.

Mulligan, J. T., y Mitchelmore, M. C. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.

Mulligan, J.T., Oslington, G., y English, L. D. (2020) Supporting early mathematical development through a 'pattern and structure' intervention program. ZDM—International Journal of Mathematics Education, 52, 663-676. https://doi.org/10.1007/s11858-020-01147-9

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. The National Council of Teachers of Mathematics.

NCTM. (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics, Inc.

Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D., Sarama, J., Wolfe, C., y Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Childhood Research Quarterly, 36, 550– 560. https://doi.org/10.1016/j.ecresq.2016.02.003

Papic, M.M. (2015). An Early Mathematical Patterning Assessment: identifying young Australian Indigenous children’s patterning skills. Mathematics Education Research Journal, 27(4), 519-534. https://doi.org/10.1007/s13394-015-0149-8

Papic, M. M., Mulligan, J. T., y Mitchelmore, M. C. (2011). Assessing the development of pre-schoolers' mathematical patterning. Journal for Research in Mathematics Education, 42, 237-268.

Pino-Fan, L., Guzmán, I., Font, V., y Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value function: Two theoretical perspectives. PNA, 11(2), 97-124.

Radford, L., y Sabena, C. (2015). The question of method in a Vygotskyan semiotic approach. En A. Bikner-Ahsbahs, C. Knipping, y N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 157–182). Springer. https://doi.org/10.1007/978-94-017-9181-6_7

Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., y Farran, D. C. (2017). Early math trajectories: Low-income children’s mathematics knowledge from age 4 to 11. Child Development, 88, 1727– 1742. https://doi.org/10.1111/cdev.12662

Rittle-Johnson, B, Zippert, E. L., y Boice, K. L. (2018). The Roles of Patterning and Spatial Skills in Early Mathematics Development. Early Childhood Research Quarterly, 46, 166-178.

Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., y Chauzova, V. (2022). A Systematic Review on Algebraic Thinking in Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2065. https://doi.org/10.29333/ejmste/11486

Tirosh, D., Tsamir, P., Barkai, R., y Levenson, E. (2018). Engaging young children with mathematical activities involving different representations: Triangles, patterns, and counting objects. CEPS Journal, 8(2), 9-30.

Vanluydt, E., Wijns, N., Torbeyns, J., y Dooren, W.V. (2021). Early childhood mathematical development: the association between patterning and proportional reasoning. Educational Studies in Mathematics 107, 93–110. https://doi.org/10.1007/s10649-020-10017-w

Vygotsky, L.S. (1978). Mind in society. The development of higher psychological processes. Harward University Press.

Wijns, N., Torbeyns, J., Bakker, M., De Smedt B., y Verschaffel, L. (2019). Four-year olds' understanding of repeating and growing patterns and its association with early numerical ability. Early Childhood Research Quarterly, 49, 152-163.

Wijns, N., Verschaffel, L., De Smedt, B., y Torbeyns, J. (2021). Associations between repeating patterning, growing patterning, and numerical ability: A longitudinal panel study in four- to six-year olds. Child Development, 92, 1354-1368. https://doi.org/10.1111/cdev.13490

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