A prospective teacher’s reflection on the teaching and learning of algebra through mathematical modelling

Authors

DOI:

https://doi.org/10.22481/intermaths.v2i2.9644

Keywords:

Critérios de adequação didática, Ensino de Álgebra, Modelagem Matemática, Reflexão na formação de professores

Abstract

There is a broad consensus on the importance of working on mathematical competencies at all educational levels, among which mathematical modelling stands out. Due to its relevance as a tool to solve real-context problems, this article addresses this competence from the perspective of a prospective mathematics teacher’s reflection. In this line, the reflection made by a prospective teacher in her Master’s Final Project on the role of mathematical modelling in a teaching learning of algebra process is analysed. To this end, the Didactic Suitability Criteria tool was used, which was the same with which the prospective teacher developed her reflection. In methodological terms, a content analysis of this reflection was carried out and, in terms of its extension, a case study was developed in the context of a professionalising master’s program in mathematics teachers training. From the results obtained, it is stressed that the prospective teacher privileged the epistemic, cognitive, and ecological criteria when she made comments regarding mathematical modelling in her reflection. Furthermore, it is concluded that the Didactic Suitability Criteria tool allowed to make evident the theoretical- procedural notions on modelling underlying her reflection.

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Author Biographies

Carlos Ledezma, Universitat de Barcelona, España

Mestre em Didática da Matemática pelo Instituto de Matemática da Pontificia Universidad Católica de Valparaíso (IMA-PUCV). Atualmente cursa o doutorado na linha de pesquisa de Didática das Ciências Experimentais e da Matemática na Universitat de Barcelona (UB). Seu tema de pesquisa é a modelagem matemática na formação de professores.

Adriana Breda, Universitat de Barcelona, España

Estágio pós-doutoral pela Freie Universität Bozen. Pós-doutora pela Universitat de Barcelona (UB). Mestra e Doutora em Educação em Ciências e Matemática pela Pontifícia Universidade Católica do Rio Grande do Sul (PUCRS). Atualmente é professora e pesquisadora na Universitat de Barcelona (UB). Seu tema de pesquisa é o desenvolvimento da reflexão na formação de professores de matemática.

Alicia Sánchez, Universitat de Barcelona, España

Doutora em Formação de Professores pela Universitat de Barcelona (UB), com estágio doutoral na National and Kapodistrian University of Athens (UA). Professora e pesquisadora na Universitat de Barcelona (UB). Seu tema de pesquisa é o desenvolvimento da criatividade na formação de professores de matemática

References

G. Kaiser, “Mathematical modelling and applications in education”, em Encyclopedia of Mathematics Education, 2da ed., S. Lerman, Ed. Cham, Suíça: Springer, 2020, pp. 553-561. https://doi.org/10.1007/978-3-030-15789-0_101

G. Kaiser e S. Brand, “Modelling competencies: Past development and further perspectives”, em Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences, G. Stillman, W. Blum e M. S. Biembengut, Eds. Cham, Suíça: Springer, 2015, pp. 129–149. https://doi.org/10.1007/978-3-319-18272-8_10

OECD, PISA 2018: Assessment and Analytical Framework. Paris, França: OECD Publishing, 2019. https://doi.org/10.1787/b25efab8-en

W. Blum, “Can modelling be taught and learnt? Some answers from empirical research”, em Trends in Teaching and Learning of Mathematical Modelling: ICTMA 14, G. Kaiser, W. Blum, R. Borromeo e G. Stillman, Eds. Dordrecht, Países Baixos: Springer, 2011, pp. 15–30. https://doi.org/10.1007/978-94-007-0910-2_3

H. M. Doerr e R. Lesh, “Models and modelling perspectives on teaching and learning mathematics in the twenty-first century”, em Trends in Teaching and Learning of Mathematical Modelling: ICTMA 14, G. Kaiser, W. Blum, R. Borromeo e G. Stillman, Eds. Dordrecht, Países Baixos: Springer, 2011, pp. 247–268. https://doi.org/10.1007/978-94-007-0910-2_26

W. Blum e R. Borromeo, “Mathematical modelling: Can be modelling be taught and learnt?”, Journal of Mathematical Modelling and Application, vol. 1, no. 1, pp. 45–58, 2009.

D. A. Schön, The Reflective Partitiones: How Professionals Think in Action. Nova York, NY: Basic Books, 1983.

D. A. Schön, Educating the Reflective Partitiones: Towards a New Design for Teaching and Learning in the Professions. São Francisco, CA: Jossey-Bass Publishers, 1987.

A. H. Schoenfeld e J. Killpatrick, “Towards a theory of proficiency in teaching mathematics”, em The International Handbook of Mathematics Teacher Education Vol. 2: Tools and Processes in Mathematics Teacher Education, D. Tirosh e T. Woods, Eds. Rotterdam, Países Baixos: Sense Publishers, 2008, pp. 321–354.

A. Breda, “Características del análisis didáctico realizado por profesores para justificar la mejora de la enseñanza de las matemáticas”, BOLEMA: Boletim de Educação Matemática, vol. 34, no. 66, pp. 69–88, 2020. https://doi.org/10.1590/1980-4415v34n66a04

A. Breda, V. Font, V. M. R. Lima e M. Villela, “Componentes e indicadores de los criterios de idoneidade didáctica desde la perspectiva del enfoque ontosemiótico”, Transformación, vol. 14, no. 2, pp. 162–176, 2018.

A. Breda e V. M. R. Lima, “Estudio de caso sobre el análisis didáctico realizado en un trabajo final de un máster para profesores de matemáticas en servicio”, REDIMAT: Journal of Research in Mathematics Education, vol. 5, no. 1, pp. 74–103, 2016. https://doi.org/10.17583/redimat.2016.1955

J. Basallote, “Variables y Expresiones Algebraicas en Primero de ESO: Propuesta de Mejora”, dissertação final de mestrado, Universitat de Barcelona, Barcelona, Espanha, 2021.

R. Borromeo, “Theoretical and empirical differentiations of phases in the modelling process”, Zentralblatt für Didaktik der Mathematik, vol. 38, no. 2, pp. 86–95, 2006. https://doi.org/10.1007/bf02655883

A. Abassian, F. Safi, S. Bush e J. Bostic, “Five different perspectives on mathematical modeling in mathematics education”, Investigations in Mathematics Learning, vol. 12, no. 1, pp. 56–65, 2020. https://doi.org/10.1080/19477503.2019.1595360

W. Blum, “Mathematical modelling in mathematics education and instruction”, em Teaching and Learning Mathematics in Context, T. Breiteig, I. Huntley e G. Kaiser-Messmer, Eds. Chichester, Inglaterra: Ellis Horwood, 1994, pp. 3–14.

W. Blum, “ICMI Study 14: Applications and modelling in mathematics education - Discussion document”, Educational Studies in Mathematics, vol. 51, no. 1-2, pp. 149–171, 2002. https://doi.org/10.1023/a:1022435827400

K. Maaß, “Classification scheme for modelling tasks”, Journal für Mathematik-Didaktik, vol. 31, no. 2, pp. 285-311, 2010. https://doi.org/10.1007/s13138-010-0010-2

R. Borromeo, Learning How to Teach Mathematical Modeling in School and Teacher Education. Cham, Suíça: Springer, 2018. https://doi.org/10.1007/978-3-319-68072-9

T. Palm, “Feature and impact of the authenticity of applied mathematical school tasks”, em Modelling and Applications in Mathematics Education: The 14th ICMI Study, W. Blum, P. L. Galbraith, H.-W. Henn e M. Niss, Eds. Boston, MA: Springer. 2007, pp. 201–208. https://doi.org/10.1007/ 978-0-387-29822-1_20

A. H. Schoenfeld, Ed. Mathematical Thinking and Problem Solving. Hillsdale, MI: Erlbaum, 1994.

R. Lesh e H. M. Doerr, “Foundations of a models and modeling perspective on mathematics teaching, learning and problem solving”, em Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching, R. Lesh e H. M. Doerr, Eds. Mahwah, NJ: Lawrence Erlbaum, 2003, pp. 3–33.

C. Julie e V. Mudaly, “Mathematical modelling of social issues in school mathematics in South Africa”, em Modelling and Applications in Mathematics Education: The 14th ICMI Study, W. Blum, P. L. Galbraith, H.-W. Henn e M. Niss, Eds. Boston, MA: Springer, 2007, pp. 503–510. https://doi.org/10.1007/978-0-387-29822-1_58

J. D. Godino, C. Batanero e V. Font, “The onto-semiotic approach to research in mathematics education”, ZDM - Mathematics Education, vol. 39, no. 1, pp. 127–135, 2007. https://doi.org/10.1007/s11858-006-0004-1

J. D. Godino, C. Batanero e V. Font, “The onto-semiotic approach: Implications for the prescriptive character of didactics”, For the Learning of Mathematics, vol. 39, no. 1, pp. 38-43, 2019.

C. Ledezma, G. Sala, A. Breda e A. Sánchez, “Analysis of a preservice teacher’s reflection on the role of mathematical modelling in his master’s thesis”, em Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, M. Inprasitha, N. Changsri e N. Boonsena, Eds. Khon Kaen, Tailândia: PME, 2021, pp. 195–204.

L. Cohen, L. Manion e K. Morrison, Research Methods in Education, 8va ed. Nova York, NY: Routledge, 2018.

M. Schreier, Qualitative Content Analysis in Practice. Thousand Oaks, CA: SAGE, 2012.

R. E. Stake, “Qualitative case studies”, em The SAGE Handbook of Qualitative Research, 3ra ed., N. K. Denzin e Y. S. Lincoln, Eds. Thousand Oaks, CA: Sage, 2005, pp. 443–466.

W. Blum e D. Leiss, “How do students and teachers deal with modelling problems?”, em Mathematical Modelling (ICTMA 12): Education, Engineering and Economics, C. Haines, P. Galbraith, W. Blum e S. Khan, Eds. Chichester, Inglaterra: Horwood, 2007, pp. 222–231. https://doi.org/10.1533/9780857099419.5.221

A. Breda, D. Farsani e R. Miarka, “Political, technical and pedagogical effects of the COVID-19 pandemic in mathematics education: An overview of Brazil, Chile and Spain”, INTERMATHS, vol. 1, no. 1, pp. 3–19, 2020. https://doi.org/10.22481/intermaths.v1i1.7400

C. Ledezma, V. Font e G. Sala, “Análisis de la reflexión realizada por un futuro profesor sobre el papel de la modelización matemática en la mejora de un proceso de instrucción para enseñar trigonometría”, PARADIGMA, vol. 42, no. Extra 2, pp. 290–312, 2021. https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p290-312.id1043

V. Font, J. Giménez, J. F. Zorrilla, V. Larios, N. Dehesa, A. Aubanell e A. Benseny, “Competencias del profesor y competencias del profesor de matemáticas. Una propuesta”, em Competencias del Profesor de Matemáticas de Secundaria y Bachillerato, V. Font, J. Giménez, V. Larios e J. F. Zorrilla, Eds. Barcelona, Espanha: Publicacions i Edicions de la Universitat de Barcelona, 2012, pp. 59–68.

Departament d’Educació, Currículum Educació Secundària Obligatòria. Barcelona, Espanha: Generalitat de Catalunya, 2019.

A. Sánchez, V. Font e A. Breda, “Significance of creativity and its development in mathematics classes for preservice teachers who are not trained to develop students’ creativity”, Mathematics Education Research Journal, artigo individual, 2021. https://doi.org/10.1007/s13394-021-00367-w

D. Hidalgo-Moncada, Y. Vanegas e J. Díez-Palomar, “Prácticas de autorregulación del aprendizaje de las matemáticas promovidas por futuros profesores”, em Investigación en Educación Matemática XXIV, P. D. Diago, D. F. Yáñez, M. T. González-Astudillo e D. Carrillo, Eds. Valencia, Espanha: SEIEM, 2021, pp. 339–346.

A. Sánchez, V. Font e A. Breda, “Secondary school preservice teachers’ references to the promotion of creativity in their master’s degree final projects”, em Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education, U. T. Jankvist, M. Van den Hauver-Panhuizen e M. Veldhuis, Eds. Utrecht, Países Baixos: Freudenthal Group & Freudenthal Institute, Utrecht University, ERME, 2019, pp. 4004–4011.

J. Basallote, “Generalitzem per construir una piscina!”, GeoGebra, 2021. [Em linha]. Disponivel em: <https://www.geogebra.org/m/ukydpfhb>. [Acessado: 01-out-2021]

A. Arcavi, P. Drijvers e K. Stacey, The Learning and Teaching of Algebra: Ideas, Insights, and Activities. Nova York, NY: Routledge, 2017.

C. Kieran, “The learning and teaching of school algebra”, em Handbook of Research on Mathematics Teaching and Learning, D. A. Grouws, Ed. Reston, VA: National Council of Teachers of Mathematics, 1992, pp. 390–419.

C. Michelsen, “Functions: A modelling tool in mathematics and science”, Zentralblatt für Didaktik der Mathematik, vol. 38, no. 3, pp. 269–280, 2006. https://doi.org/10.1007/bf02652810

H. M. Doerr e L. D. English, “A modeling perspective on students’ mathematical reasoning about data”, Journal for Research in Mathematics Education, vol. 34, no. 2, pp. 110–136, 2003. https://doi.org/10.2307/30034902

H. Freudenthal, Revisiting Mathematics Education: China Lectures. Dordrecht, Países Baixos: Kluwer Academic Publisher, 2002. https://doi.org/10.1007/0-306-47202-3

Published

2021-12-28

How to Cite

Ledezma, C., Breda, A., & Sánchez, A. (2021). A prospective teacher’s reflection on the teaching and learning of algebra through mathematical modelling. INTERMATHS, 2(2), 227-244. https://doi.org/10.22481/intermaths.v2i2.9644

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