Models, Structures and Analogical Thinking in Early Childhood Education and Care and Primary School: A Qualitative Study on Teachers’ Perception about Those Concepts
The objective of this study was to investigate ECEC teachers and primary school teachers’ perspective about recognizing models, structures and using analogical thinking as a key to facilitate children’s learning process. Without discussing in-depth the definition of a mathematical structure or model, teachers reflected about the possibilities and the reasons why？to？use？models, structures and an analogical approach in teaching. Both ECEC teachers and primary school teachers showed a comprehension about those concepts, but mainly related to a theoretical approach. The idea that recognizing structures and models can help to identify what is known and what is new when we try to solve a problem has been discussed. An analogical approach that can help teachers to sustain children in the transition from what is known and what is not has been evaluated,？connected to the zone of proximal development (Vygotsky) and to scaffolding (Bruner). Reflections about the Framework Plan for Kindergartens and the Framework for basic skills in primary school are reported.？Both ECEC teachers and primary school teachers evaluated the concepts of “models” and “structures” as important, agreeing with Van Hiele and Bartha’s definition. Both groups？of teachers also recognized the importance of analogical thinking, where structures and models are useful for defining a starting point in the learning process.
References
[1]
Bartha, P. (2013). Analogy and Analogical Reasoning. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2019 Edition) (P. 80). Metaphysics Research Lab, Stanford University.
https://plato.stanford.edu/archives/spr2019/entries/reasoning-analogy/
[2]
Benjamin, B. (2011). Jean Piaget-Le structuralisme (1968). Publications Pimido.
[3]
Bruner, J. S. (2006). In Search of Pedagogy Volume I: The Selected Works of Jerome Bruner, 1957-1978. Routledge. https://doi.org/10.4324/9780203088609
[4]
Byl, J. (2003). Mathematical Models & Reality. In Proceedings of the 2003 Conference on Association of Christians in the Mathematical Sciences (pp. 33-48). Langley, BC, Canada. https://pillars.taylor.edu/acms-2003/11/
[5]
Clements, D. H., & Battista, M. T. (1992). Geometry and Spatial Reasoning. In Handbook of Research on Mathematics Teaching and Learning (pp. 420-464). Macmillan Library Reference.
[6]
Corry, L. (1992). Nicolas Bourbaki and the Concept of Mathematical Structure. Synthese, 92, 315-348. http://www.jstor.org/stable/20117057
https://doi.org/10.1007/BF00414286
[7]
Dieudonné, J. (1982). The Work of Bourbaki during the Last Thirty Years. Notices of the American Mathematical Society, 29, 618-623.
[8]
Gandillac, M., Goldmann, L., & Piaget, J. (2015). Entretiens sur les notions de genèse et de structure (Vol. 9). Walter de Gruyter GmbH & Co KG.
[9]
Gentner, D., & Smith, L. (2012). Analogical Reasoning. In Encyclopedia of Human Behavior (2nd ed., pp. 130-136). Elsevier.
https://doi.org/10.1016/B978-0-12-375000-6.00022-7
[10]
Giere, R. N. (2004). How Models Are Used to Represent Reality. Philosophy of Science, 71, 742-752. https://doi.org/10.1086/425063
[11]
Goddu, M. K., Lombrozo, T., & Gopnik, A. (2020). Transformations and Transfer: Preschool Children Understand Abstract Relations and Reason Analogically in a Causal Task. Child Development, 91, 1898-1915. https://doi.org/10.1111/cdev.13412
[12]
Goswami, U. (2013). Analogical Reasoning in Children. Psychology Press.
[13]
Harrison, A. G., & Treagust, D. F. (2006). Teaching and Learning with Analogies. In Metaphor and Analogy in Science Education (pp. 11-24). Springer.
https://doi.org/10.4324/9781315804729
[14]
Heywood, D., & Parker, J. (1997). Confronting the Analogy: Primary Teachers Exploring the Usefulness of Analogies in the Teaching and Learning of Electricity. International Journal of Science Education, 19, 869-885. https://doi.org/10.1080/0950069970190801
[15]
Heywood, D., & Parker, J. (2009). The Role of Analogies in Learning. In The Pedagogy of Physical Science (pp. 39-64). Springer. https://doi.org/10.1007/978-1-4020-5271-2_3
[16]
Hofstadter, D., & Sander, E. (2013). L’analogie, coeur de la pensée. Odile Jacob.
https://doi.org/10.3917/sh.dorti.2014.01.0354
[17]
Lesh, R. E., & Doerr, H. M. (2003). Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching. Lawrence Erlbaum Associates Publishers. https://doi.org/10.4324/9781410607713
[18]
Maharaj-Sharma, R. (2011). An Examination of Types and Usefulness of Analogies Generated by Upper Primary School Students—A Case Study.
[19]
Marker, D. (2006). Model Theory: An Introduction (Vol. 217). Springer Science & Business Media.
[20]
Matlen, B. J., Atit, K., Goksun, T., Rau, M. A., & Ptouchkina, M. (2012). Representing Space: Exploring the Relationship between Gesturing and Geoscience Understanding in Children. In International Conference on Spatial Cognition (pp. 405-415). Springer.
https://doi.org/10.1007/978-3-642-32732-2_26
[21]
Nguyen, H. T. (2000). Some Mathematical Structures for Computational Information. Information Sciences, 128, 67-89. https://doi.org/10.1016/S0020-0255(00)00039-6
[22]
Noddings, N. (1987). The World’s a Stage. Journal for Research in Mathematics Education, 18, 5. https://doi.org/10.2307/749088
[23]
Norwegian Directorate for Education and Training (2017). Framework plan for kindergartens.
https://www.udir.no/globalassets/filer/barnehage/rammeplan/framework-plan-for-kindergartens2-2017.pdf
[24]
Norwegian Directorate for Education and Training (2020). Loereplan i matematikk fellesfag 2P-Y-Vg3 pabygging til generell studiekompetanse.
[25]
Ozdem-Yilmaz, Y., & Bilican, K. (2020). Discovery Learning—Jerome Bruner. In Science Education in Theory and Practice (pp. 177-190). Springer.
https://doi.org/10.1007/978-3-030-43620-9_13
[26]
Resnik, M. D. (1981). Mathematics as a Science of Patterns: Ontology and Reference. Nous, 14, 529-550. https://doi.org/10.2307/2214851
[27]
Resnik, M. D. (1982). Mathematics as a Science of Patterns: Epistemology. Nous, 16, 95-105. https://doi.org/10.2307/2215419
[28]
Richland, L. E., & Begolli, K. N. (2016). Analogy and Higher Order Thinking: Learning Mathematics as an Example. Policy Insights from the Behavioral and Brain Sciences, 3, 160-168. https://doi.org/10.1177/2372732216629795
[29]
Schoenfeld, A. H. (2014). Mathematical Problem Solving. Academic Press.
[30]
Sibley, D. F. (2009). A Cognitive Framework for Reasoning with Scientific Models. Journal of Geoscience Education, 57, 255-263. https://doi.org/10.5408/1.3559672
[31]
Takaya, K. (2008). Jerome Bruner’s Theory of Education: From Early Bruner to Later Bruner. Interchange, 39, 1-19. https://doi.org/10.1007/s10780-008-9039-2
[32]
Thibaut, J. P., & Goldwater, M. B. (2017). Generalizing Relations during Analogical Problem Solving in Preschool Children: Does Blocked or Interleaved Training Improve Performance? In Proceedings of the 39th Annual Meeting of the Cognitive Science Society (p. 6). Austin, TX.
[33]
Vakil, E., Lifshitz, H., Tzuriel, D., Weiss, I., & Arzuoan, Y. (2011). Analogies Solving by Individuals with and without Intellectual Disability: Different Cognitive Patterns as Indicated by Eye Movements. Research in Developmental Disabilities, 32, 846-856.
https://doi.org/10.1016/j.ridd.2010.08.006
[34]
Van Hiele, P. M. (1986). Structure and Insight: A Theory of Mathematics Education. Academic Press.
[35]
Vitz, P. C. (2017). The Origin of Consciousness in the Integration of Analog (Right Hemisphere) & Digital (Left Hemisphere) Codes. Journal of Consciousness Exploration & Research, 8, 881-906.
[36]
Vygotsky, L. S. (2012). The Collected Works of LS Vygotsky: Scientific Legacy. Springer Science & Business Media.
[37]
Weisberg, M. (2012). Simulation and Similarity: Using Models to Understand the World. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199933662.001.0001
