Specialized knowledge of the future teacher of early childhood education to reflect on algebraic thinking in a professional training task of classification

Autores/as

Agencias de apoyo
This work has been carried out within the framework of the Research Projects with reference PID2021-122180OB-I00 of the MCIN (Government of Spain), ProyExcel_00297 of the Junta de Andalucía (Spain), as an activity of the Instituto Interuniversitario Andaluz de Investigación Educativa (IEDU-Sevilla, Spain), the MTSK Network (sponsored by the AUIP) and the GIEM research group (FQM-226, Andalusia, Spain).

Palabras clave:

Mathematics education, Teacher education, Initial training, Training tasks

Resumen

This article aims to identify elements of the specialized knowledge mobilized by future teachers of Early Childhood Education in initial training on algebraic thinking when they develop a professional formative classification task. The selection was made because we believe that classification is a learning topic in Early Childhood Education that can foster logical-mathematical thinking, which in turn allows us to reflect on and develop algebraic thinking by considering the relationships that are evident in the classification process. Therefore, the theoretical framework we used for this analysis is Mathematics Teacher’s Specialized Knowledge (MTSK). The methodology used was a Teaching Experiment, applied in two initial training classes for early childhood education teachers at the University of Seville. Our results suggest the possibility of advancing discussions about the knowledge early childhood education teachers need regarding the specificities of classification. 

Biografía del autor/a

Edvonete Souza de Alencar, Universidade de Brasília

Post - PhD in Education from the University of Seville. PhD in Mathematical Education from PUC-SP. Professor at the University of Brasília.

Maria de la Cinta Muñoz Catalán, Universidade de Sevilha

Doctor of Mathematics Didactics from the University of Huelva. Professor at the Faculty of Education at the University of Seville.

Maria del Mar Liñán García, Universidade de Sevilha

Doctor of Mathematics Didactics from the University of Huelva. Professor at the Faculty of Education at the University of Seville.

Citas

ACOSTA, Y. Y ALSINA, Á. Learning patterns at three years old: Contributions of a learning trajectory and teaching itinerary. Australasian Journal of Early Childhood, 45(1), pp. 14-29, 2020. https://doi.org/10.1177/1836939119885310. 2020.

ALENCAR, E. A.; MUNHOZ CATALÃN, M. C.; LINAN GARCIA, M. M. Aproximação do conhecimento especializado do professor de educação infantil para ensinar o pensamento algébrico – classificação. Anais [...] VI CIMTSK. Chile, 2023.

BARRERA CASTARNADO, V. J.; CONTRERAS GONZÁLEZ, L. C.; MUÑOZ CATALÁN, M. C.; LIÑÁN GARCÍA, M. M. Conocimiento especializado del profesor: un experimento de enseñanza centrado en una tarea formativa sobre geometría. AIEM - Avances de investigación en educación matemática, 26, pp. 1-19, 2024. https://doi.org/10.35763/aiem26.5359

BASSEY, M. Case study research in educational settings. Buckingham: Open University Press, 1999.

BECK, C. V.; SILVA, J. A. O Estado da Arte das Pesquisas sobre o Pensamento Algébrico com Crianças. REVEMAT, v. 10, pp. 197-208, 2015.

BLANTON, M.; KAPUT, J. Characterizing a classroom practice that promotes algebraic thinking. Journal for Research in Mathematics Education, 36(5), pp. 412-446, 2005.

BLANTON, M.; KAPUT, J. Functional Thinking as a Route into Algebra in the Elementary Grades. In J. Cai, & E. Knuth (Eds.), Early Algebraization, Advances in Mathematics Education. Berlin Heidelberg: Springer-Verlag, 2011. https://doi.org/10.1007/978-3-642-17735-4_2.

BRASIL. Ministério da Educação. Base Nacional Comum Curricular. Brasília: MEC, 2018.

CARRAHER, D. W.; SCHLIEMANN, A. D. Early algebraic thinking and the US mathematics standards for grades K to 5. Infancia y Aprendizage: Journal for the Study of Education and Development, 42(3), pp. 479-522, 2019. https://doi.org/10.1080/02103702.2019.1638570.

CARRILLO-YAÑEZ, J.; CLIMENT, N.; MONTES, M.; CONTRERAS, LUIS C.; FLORES-MEDRANO, E.; ESCUDERO-ÁVILA, D.; VASCO, D., ROJAS, N., FLORES, P., AGUILAR-GONZÁLEZ, A., RIBEIRO, M., & MUÑOZ-CATALÁN, M.C: The mathematics teacher’s specialised knowledge (MTSK) model, Research in Mathematics Education, 2018. https://doi.org/10.1080/14794802.2018.1479981.

JOGLAR PRIETO, N.; LIÑÁN GARCÍA, M. D. M.; CONTRERAS GONZÁLEZ, L. C. MTSK en la formación inicial del profesorado de primaria. En Investigación sobre conocimiento especializado del profesor de matemáticas (MTSK): 10 años de camino (pp. 207-222). Dykinson, 2022.

KAPUT, J. J. What is algebra? What is algebraic reasoning? In: J. J. Kaput; D. W. Carraher; M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York, NY: NCTM & Lawrence Erlbaum Associates, 2008.

LACAMPAGNE C. B., BLAIR W., KAPUT J. J., (Eds.). The algebra initiative colloquium: Vol 1: Plenary and reactor papers. Washington, DC: U.S. Department of Education, Office of Educational Research and Improvement. Vol 2: Working group papers ED385437.pdf, 1995. Available: <https://files.eric.ed.gov/fulltext/ED385436.pdf>.

LORENZATO, SERGIO. Educação Infantil e Percepção Matemática. Campinas/SP. Autores Associados, pp. 23-29, 2008.

MORIEL JUNIOR, J. G. Conhecimento especializado de professores de matemática (MTSK) na Web of Science até 2020. Zetetike, 29(00), e021022, 2021. https://doi.org/10.20396/zet.v29i00.8660030

MUÑOZ-CATALÁN, M. C.; RAMÍREZ-GARCÍA, M.; JOGLAR-PRIETO, N.; CARRILLO J. Mathematics Teacher’s Specialised Knowledge to promote Algebraic Reasoning in Early Childhood Education as from a task of additive decomposition. Infancia y Aprendizaje. Journal for the Study of Education and Development, 45, pp. 37-80, 2022. https://doi.org/10.1080/02103702.2021.1946640.

MUÑOZ-CATALÁN, M.C.; RAMÍREZ-GARCÍA, M.; JOGLAR-PRIETO, N.; CARRILLO-YÁÑEZ, J. Early childhood teachers’ specialised knowledge to promote algebraic thinking as from a task of additive decomposition (El conocimiento especializado del profesor de educación infantil para fomentar el pensamiento algebraico a partir de una tarea de descomposición aditiva). Journal for the Study of Education and Development, 45(1), pp. 37-80, 2021. https://doi.org/10.1080/02103702.2021.1946640.

NCTM [National Council of Teachers of Mathematics]. Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000. Available: <https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Algebra/>.

PINCHEIRA, NATALY; ALSINA, ÁNGEL. Teachers’ mathematics knowledge for teaching early algebra: A systematic review from the mkt perspective. Mathematics, v. 9, n. 20, p. 2590, 2021. Available: . Acesso em: dez. 2022.

PONTE, J. P. et al. Aprendizagens profissionais dos professores através dos estudos de aula. Perspectivas da Educação Matemática, Campo Grande, v. 5, n. temático, pp. 7-24, 2012.

SQUALLI, H. Tout, tout, tout, vous saurez tout sur l’algèbre. Trois-Rivières: Éditions Bande Didactique, 2003.

STEFFE L. P.; THOMPSON P. W. Teaching experiment methodology: Underlying principles and essential elements. In: Lesh R.; Kelly A. E. (eds.). Research design in mathematics and science education. Lawrence Erlbaum, Hillsdale NJ: 267–307, 2000.

Descargas

Publicado

12-12-2025

Cómo citar

SOUZA DE ALENCAR, E.; MUÑOZ CATALÁN, M. de la C.; LIÑÁN GARCÍA, M. del M. Specialized knowledge of the future teacher of early childhood education to reflect on algebraic thinking in a professional training task of classification. Espaço Plural, [S. l.], v. 21, n. 43, p. 26–49, 2025. Disponível em: https://saber.unioeste.br/index.php/espacoplural/article/view/36656. Acesso em: 20 dic. 2025.