Early childhood teachers’ specialised knowledge to promote algebraic thinking as from a task of additive decomposition

  1. Muñoz-Catalán, M. Cinta 1
  2. Ramírez-García, Mónica 2
  3. Joglar-Prieto, Nuria 3
  4. Carrillo-Yáñez, José 4
  1. 1 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  2. 2 La Salle Centro Universitario
  3. 3 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

  4. 4 Universidad de Huelva
    info

    Universidad de Huelva

    Huelva, España

    ROR https://ror.org/03a1kt624

Journal:
Journal for the Study of Education and Development, Infancia y Aprendizaje

ISSN: 0210-3702 1578-4126

Year of publication: 2022

Volume: 45

Issue: 1

Pages: 37-80

Type: Article

More publications in: Journal for the Study of Education and Development, Infancia y Aprendizaje

Abstract

In this article we aim to deepen our understanding of the content and nature of the early childhood teacher’s knowledge, focusing on those aspects which might promote students’ algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model Mathematics Teachers’ Specialised Knowledge, we analyse the specialised knowledge in a classroom of five-year-olds handled by an experienced teacher in a lesson on the decomposition of the number 6. Moreover, alternative management of the session is proposed in order to promote early algebraic thinking. In the domain of mathematical knowledge, this analysis has revealed the specificity of the knowledge that this professional must have of the natural number. In the domain of pedagogical content knowledge, it has highlighted the many elements of the knowledge of mathematics teaching that should be possessed to promote algebraic thinking at this educational stage. These elements appear to be more closely related to a profound knowledge of the mathematics taught than to pedagogical knowledge of a more general nature.

Funding information

This work has been partially supported by the project ‘Specialised knowledge of mathematics teachers and teacher training’ (RTI2018-096547-B-I00, from the Ministry of Science, Innovation and Universities, Spain). It is also linked to the Ibero-american MTSK Network of the Asociación Universitaria Iberoamericana de Posgrado (AUIP). / Este trabajo se ha desarrollado en el marco del proyecto: ‘Conocimiento especializado del profesorado de matemáticas y formación del profesorado’ (RTI2018-096547-B-I00, del Ministerio de Ciencia, Innovación y Universidades, España). Asimismo, está vinculado a la Red MTSK de la Asociación Universitaria Iberoamericana de Posgrado (AUIP).

Bibliographic References

  • Adelman, C. (1999). Answers in the toolbox: Academic intensity, attendance patterns, and bachelor’s degree attainment. U.S. Department of Education Office of Educational Research and Improvement. [Google Scholar]
  • Atkinson, R., Campling, R., & Wing, T. (2015). Numicon Infantil 5 años, Bases firmes. Cuaderno de Ejercicios [Numicon 5 years, firm bases. Workbook]. Oxford University Press. [Google Scholar]
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554 [Crossref], [Web of Science ®], [Google Scholar]
  • Bassey, M. (1999). Case study research in educational settings. Open University press. [Google Scholar]
  • Cañadas, M. C., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about linear functional relationships. The Journal of Mathematical Behavior, 41(5), 87–103. https://doi.org/10.1016/j.jmathb.2015.10.004 [Crossref], [Google Scholar]
  • Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann. [Google Scholar]
  • Carraher, D., Schliemann, A., & Brizuela, B. (2000). Early-algebra, early-arithmetic: Treating operations as functions. Plenary Presentation at PME-NA XXII, PME. [Google Scholar]
  • Carrillo, J., Climent, N., Contreras, L. C., & Ribeiro, C. M. (2017). Mathematics teacher’s specialised knowledge (MTSK) in the “Dissecting an equilateral triangle” problem. RIPEM - International Journal for Research in Mathematics Education, 7(2), 88–107. http://sbem.iuri0094.hospedagemdesites.ws/revista/index.php/ripem/article/view/1233 [Google Scholar]
  • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–253. https://doi.org/10.1080/14794802.2018.1479981 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Castro, E., Cañadas, M. C., & Molina, M. (2017). Pensamiento funcional mostrado por estudiantes de Educación Infantil. Edma 0-6: Educación Matemática en la Infancia, 6(2), 1–13. https://www.edma0-6.es/index.php/edma0-6/article/view/35 [Google Scholar]
  • Clements, D. H., Baroody, A. J., & Sarama, J. (2013). Background research on early mathematics. National Governor’s Association, Center Project on Early Mathematics. http://www.nga.org/files/live/sites/NGA/files/pdf/2013/1311SEME-Background.pdf [Google Scholar]
  • Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. Routledge. [Crossref], [Google Scholar]
  • Clements, D. H. (2004). Part 1: Major themes and recommendations. In D. H. Clements, J. Sarama, & A.M. DiBiase (Eds.), Engaging young children in Mathematics: Standards for early childhood mathematics education (pp. 7–76). Lawrence Erlbaum. [Google Scholar]
  • Common Core State Standards Initiative. (2010) . Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers. [Google Scholar]
  • Denzin, N. (1989). The research act (3rd ed.). Prentice Hall. [Google Scholar]
  • Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243–275). Macmillan & Co. [Google Scholar]
  • Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288. https://www.researchwithrutgers.com/en/publications/professional-development-focused-on-childrens-algebraic-reasoning [Web of Science ®], [Google Scholar]
  • Kaput, J. J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. In National Council of Teachers of Mathematics, Mathematical Sciences Education Board, & National Research Council (Ed.), The nature and role of algebra in the K-14 curriculum: Proceedings of a national symposium (pp. 25–26). National Research Council, National Academy Press. [Google Scholar]
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 18(1), 139–151. [Google Scholar]
  • Kvale, S. (1996). Interviews: An introduction to qualitative research interviewing. Sage. [Google Scholar]
  • Liñán, M. M. (2017). Conocimiento especializado en Geometría en un aula de 5º de Primaria [Unpublished Doctoral Dissertation]. Universidad de Huelva. [Google Scholar]
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the US. Lawrence Erlbaum Associates, Publishers. [Crossref], [Google Scholar]
  • Molina, M., Castro, E., & Ambrose, R. (2006). Trabajo con igualdades numéricas para promover pensamiento relacional. PNA, 1(1), 33–46. https://revistaseug.ugr.es/index.php/pna/article/view/6218 [Google Scholar]
  • Morales, R., Cañadas, M. C., & Castro, E. (2017). Generación y continuación de patrones por dos alumnas de 6-7 años en tareas de seriaciones. PNA, 11(4), 233–252. https://revistaseug.ugr.es/index.php/pna/article/view/6241 [Crossref], [Google Scholar]
  • Mosvold, R., Bjuland, R., Fauskanger, J., & Jakobsen, A. (2011). Similar but different – Investigating the use of MKT in a Norwegian kindergarten setting. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 1802–1811). PME. [Google Scholar]
  • Muñoz-Catalán, M. C., Liñán-García, M. M., & Ribeiro, M. (2017). El conocimiento especializado para enseñar la operación de resta en Educación Infantil. Cadernos de Pesquisa, 24, 4–19. https://doi.org/10.18764/2178-2229.v24n.especialp4-19 [Crossref], [Google Scholar]
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. [Google Scholar]
  • Parks, A. N., & Wager, A. A. (2015). What knowledge is shaping teacher preparation in early childhood mathematics? Journal of Early Childhood Teacher Education, 36(2), 124–141. https://doi.org/10.1080/10901027.2015.1030520 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Ramírez, M., & Rodríguez, P. (2011). Interpretaciones del signo igual. Un estudio de libros de texto. Unión, revista Iberoamericana de Educación Matemática, 26, 41–55. https://eprints.ucm.es/id/eprint/25467/ [Google Scholar]
  • Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31, 101–112. https://doi.org/10.1016/j.ecresq.2015.01.005 [Crossref], [Web of Science ®], [Google Scholar]
  • Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85–104. https://doi.org/10.1037/a0021334 [Crossref], [Web of Science ®], [Google Scholar]
  • Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153–172. https://doi.org/10.1007/s10763-017-9859-6 [Crossref], [Web of Science ®], [Google Scholar]
  • Schoenfeld, A. (2000). Models of the teaching process. Journal of Mathematical Behavior, 18(3), 243–261. https://doi.org/10.1016/S0732-3123(99)00031-0 [Crossref], [Google Scholar]
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004 [Crossref], [Google Scholar]
  • Silverman, J., & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499–511. https://doi.org/10.1007/s10857-008-9089-5 [Crossref], [Google Scholar]
  • Socas, M. (2011). La enseñanza del Álgebra en la Educación Obligatoria. Aportaciones de las investigaciones. Números, 77, 5–34. [Google Scholar]
  • Strauss, A., & Corbin, J. (1994). Grounded theory methodology: An overview. In N. K. Denzin, & Y. Lincoln (Eds.), Handbook of qualitative research (pp. 273–285). Sage. [Google Scholar]