Banner Portal
Kindergarten and primary teacher’s specialized knowledge on the topic of division
PORTUGUÊS (Português (Brasil))
INGLÊS (Português (Brasil))

Keywords

MTSK
Division
Kindergarten and primary school
Teacher education

How to Cite

POLICASTROS, Milena Soldá; RIBEIRO, Miguel. Kindergarten and primary teacher’s specialized knowledge on the topic of division. Zetetike, Campinas, SP, v. 29, n. 00, p. e021020, 2021. DOI: 10.20396/zet.v29i00.8661906. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8661906. Acesso em: 22 jul. 2024.

Abstract

Considering teachers’ knowledge plays a central role in their practice and on students’ learning, and as the division is one of the most problematic topic for teachers’ and students’, we focus our attention on the content of kindergarten and primary teachers’ specialized knowledge who participated of a teacher education program in Brazil, related to such topic. Data concerns teachers’ interactions when discussing a task and was analysed according to the Mathematics Teachers’ Specialized Knowledge perspective to characterize the content of such a knowledge on division. From the analysis, emerged a set of descriptors of teachers’ specialized knowledge related to concepts, procedures, properties, foundations and systems of representation in the scope of division. It contributes to improve the way teachers’ training programs are conceptualized, providing elements to intentionally implement effective instruments for the development of such a teacher’s knowledge.

https://doi.org/10.20396/zet.v29i00.8661906
PORTUGUÊS (Português (Brasil))
INGLÊS (Português (Brasil))

References

Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. Journal of the Learning Sciences, 11(1), 25–62.

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. DOI: https://doi.org/10.1177/0022487108324554

Behr, M. J., Harel, G., Post, T., & Lesh, R. (1994). Units of quantity: A conceptual basis common to additive and multiplicative intents. In G. Harel & J. Confrey, The development of multiplicative reasoning in the learning of mathematics (pp. 121–176). Albany, NY: State University of New York Press.

Bicknell, B., Young-Loveridge, J., Lelieved, J., & Brooker, J. (2015). Using multiplication and division contexts with young children to develop part-whole thinking. Journal Issue, 2, 53–59. DOI: http://dx.doi.org/10.18296/set.0018

Bisanz, J., & LeFevre, J.-A. (1992). Chapter 3 Understanding Elementary Mathematics. In J. I. D. Campbell (Org.), Advances in Psychology (Vol. 91, pp. 113–136). North-Holland. DOI: https://doi.org/10.1016/S0166-4115(08)60885-7

Boyd, D. J., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher Preparation and Student Achievement. Educational Evaluation and Policy Analysis, 31(4), 416–440. DOI: https://doi.org/10.3102/0162373709353129

Brocardo, J., Serrazina, L., & Kraemer, J.-M. (2003). Algoritmos e sentido do número. Educação e Matemática, 75(Nov/Dez), 11–15.

Carreño, E., Rojas, N., Montes, M. Á.., & Flores, P. (2013). Mathematics teacher’s specialized knowledge. Reflections based on specific descriptors of knowledge. Proceedings of CERME 8, 2976–2984. Antalya, Turquia: METH.

Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., … Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–256. DOI: https://doi.org/10.1080/14794802.2018.1479981

Clements, D., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. In D. Clements, J. Sarama & A.-M. DiBiase (Orgs.), Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education (pp. 299–317). New Jersey: LEA.

Correa, J., Nunes, T., & Bryant, P. (1998). Young children’s understanding of division: The relationship beteween division terms in a noncomputational task. Journal of Educational Psychology, 90(2), 321–329. DOI: https://doi.org/10.1037/0022-0663.90.2.321

Dooren, W. V., Verschaffel, L., & Onghena, P. (2002). The impact of preservice teachers’ content knowledge on their evaluation of students’ strategies for solving Arithmetic and Algebra words problems. Journal for Research in Mathematics Education, 33(5), 319–351. DOI: https://doi.org/10.2307/4149957

Downton, A. (2009). It Seems to Matters Not Whether it is Partitive or Quotitive Division When Solving One Step Division Problems. In R. Hunter, B. Bicknell & T. Burgess, Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 161–168). Palmerston North, NZ: MERGA.

Fávero, M. H., & Neves, R. S. P. (2012). A divisão e os racionais: Revisão bibliográfica e análise. Zetetiké, 20(37), 33–67. DOI: https://doi.org/10.20396/zet.v20i37.8646635

Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147–164). New York: National Council of Teachers of Mathematics.

Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Reaserch in Mathematics Education, 16(1), 3–17. DOI: https://doi.org/10.5951/jresematheduc.16.1.0003

Fosnot, C. T., & Dolk, M. (2001). Young mathematics at work: Constructing multiplication and division. Portsmouth, NH: Heinemann.

Golden, G., & Shteingold, N. (2001). Systems of representation and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio, The role of representation in school mathematics (pp. 1–23). Boston, Virginia: NCTM.

Gómez, P., & Cañadas, M. C. (2016). Dificultades de los profesores de matemáticas en formación en el aprendizaje del análisis fenomenológico. Revista Latinoamericana de Investigación en Matemática Educativa, 19(3), 311–334. DOI: https://doi.org/10.12802/relime.13.1933

Hiebert, J., & Grouws, D. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 371–404). New York: Information Age Publishing.

Jakobsen, A., Ribeiro, M., & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19, 135–150.

Lautert, S. L., Oliveira, D. C. A.., & Correa, J. (2017). Compreensão de crianças sobre relações inversas sem explicitação numérica. Arquivos Brasileiros de Psicologia, 69(1), 73–89.

Lesser, L. M., & Tchoshanov, M. A. (2005). The effect of representation and representational sequence on students’ understanding. In G. M. Lloyd, M. Wilson, J. L. M. Wilkins & S. L. Behm, Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 813–819). Roanoke, Virginia: Virginia Tech.

Mason, J., Stephens, M., & Watson, A. (2009). Appreciating Mathematical Structure for All. Mathematics Education Research Journal, 21(2), 10–32. DOI: https://doi.org/10.1007/BF03217543

Ribeiro, M. (2011a). A importância do conhecimento do conteúdo matemático na prática letiva de uma professora: Discutindo um modelo de análise. Zetetiké, 19(35), 71–102. DOI: https://doi.org/10.20396/zet.v19i35.8646646

Ribeiro, M. (2011b). Abordagem aos números decimais e suas operações: A importância de uma “eficaz navegação” entre representações. Educação e Pesquisa, 37(2), 407–422.

Ribeiro, M., & Amaral, R. (2015). Early years’ prospective teachers’ specialized knowledge on problem posing. Proceedings of 39th Psychology of Mathematics Education Conference, 4, 81–88. Hobart, Australia: Beswick, K., Muir, T. & Wells, J.

Ribeiro, M., Carrillo, J., & Monteiro, R. (2012). Cognições e tipo de comunicação do Professor de matemática. Exemplificação de um modelo de análise num episódio dividido. Revista latinoamericana de investigación en matemática educativa, 15(1), 93–121.

Ribeiro, M, Almeida, A. R., & Mellone, M. (2019). Desenvolvendo as especificidades do conhecimento interpretativo do professor e tarefas para a formação. In V. Giraldo, J. Viola, & H. R. Elias, Problematizações sobre a Formação Matemática na Licenciatura em Matemática [s.l.]. SBEM. No prelo.

Ribeiro, M, Policastro, M., Mamoré, J., & Di Bernardo, R. (2018). Conhecimento Especializado do professor que ensina Matemática para atribuir sentido à divisão e ao algoritmo. Educação Matemática em Revista – RS, 1(19), 152–167.

Rizvi, N. F. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377–392.

Robinson, K. M., & LeFevre, J.-A. (2012). The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework. Educational Studies in Mathematics, 79(3), 409–428. DOI: https://doi.org/10.1007/s10649-011-9330-5

Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281. DOI: https://doi.org/10.1007/s10857-005-0853-5

Simon, M. A. (1993). Prospective Elementary Teachers’ Knowledge of Division. Journal for Research in Mathematics Education, 24(3), 233–254. DOI: https://doi.org/10.5951/jresematheduc.24.3.0233

Skemp, R. R. (1989). Mathematics in the primary school. London: Routledge Falmer.

Squire, S., & Bryant, P. (2002). From sharing to dividing: Young children’s understanding of division. Developemental Science, 5(4), 452–466. DOI: https://doi.org/10.1111/1467-7687.00240

Timmerman, M. A. (2014). Making Connections: Elementary Teachers’ Construction of Division Word Problems and Representations. School Science and Mathematics, 114(3), 114–124. DOI: https://doi.org/10.1111/ssm.12059

Young-Loveridge, J., & Bicknell, B. (2018). Making connections using multiplication and division contexts. In V. Kinnear, T. Muir & M. Y. Lai (Orgs.), Forging Connections in Early Mathematics Teaching and Learning, Early Mathematics Learning and Development, (pp. 259–272). Brisbane, Autralia: Lyn D. English.

Young-Loveridge, J. M. (2001). Helping children move beyond counting to part-whole strategies. Teachers and Curriculum, 5, 72–78.

Zakaryan, D., & Ribeiro, M. (2018). Mathematics teachers’ specialized knowledge: A secondary teacher’s knowledge of rational numbers. Research in Mathematics Education, 21(3), 1–19. DOI: https://doi.org/10.1080/14794802.2018.1525422

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright (c) 2021 Zetetiké

Downloads

Download data is not yet available.