O CONHECIMENTO ESPECIALIZADO DO CONTEÚDO EM GEOMETRIA E MEDIDA
ANÁLISE DO DESEMPENHO DE PROFESSORES DOS 1.º E 2.º CICLOS
Palavras-chave:
Conhecimento Matemático para ensinar, conhecimento especializado do conteúdo, geometria, professores do ensino básico, formação de professores.
Resumo
Este estudo investiga o Conhecimento Matemático para Ensinar (MKT) de professores portugueses dos 1.º e 2.º ciclos do Ensino Básico, com foco no Conhecimento Especializado do Conteúdo (SCK) na área da Geometria e Medida. A investigação adota um desenho metodológico misto, combinando análise quantitativa e qualitativa. A amostra é composta por 61 professores, que responderam a um questionário baseado no MKT, seguido de entrevistas cognitivas com dois docentes selecionados. A análise dos dados permitiu identificar dificuldades significativas na interpretação de definições geométricas, na avaliação de afirmações matemáticas e na validação de argumentos dos alunos. Os resultados destacam a necessidade de reforçar a formação inicial e contínua dos professores, de modo a promover um ensino mais estruturado e eficaz da Geometria.
Referências
Arwadi, F., Sidjara, S., & Suarlin. (2023). The Pedagogical Content Knowledge of Mathematics Pre-Service Teachers on Geometry Topic in Universitas Negeri Makassar. Mosharafa: Jurnal Pendidikan Matematika, 12(4), 759–770. https://doi.org/10.31980/mosharafa.v12i4.1189
Ball, D.L., Hill, H. & Bass, H. (2005). Knowing Mathematics for Teaching. Who knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide? American Educator, p. 14-46.
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
Barber, M. & Mourshed, M. (2007). How the world’s best performing school systems come out on top. McKinsey & Company.
Bardin, L. (2009). Análise de conteúdo. Edições 70.
Baumert, J., Kunter,M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M. & Tsai, Y. (2010). Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, v.47, n.1, p.133-180.
Browning, C. A., Edson, A. J., Kimani, P. M., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 241-272. https://doi.org/10.54870/15513440
Brunheira, L., Serrazina, L., & Rodrigues, M. (2023). Preservice and In-Service Primary Teachers’ Knowledge of Mathematical Reasoning Processes in the Context of a Geometry Task. Acta Scientiae, 24(8), 567–591. https://doi.org/10.17648/acta.scientiae.7122.
Carmo, H., & Ferreira, M. M. (2008). Metodologia da Investigação - Guia para Auto-Aprendizagem (2.ª Edição). Universidade Aberta.
Charalambous, C. (2008). Mathematical knowledge for teaching and the unfolding of tasks in mathematics lessons: Integrating two lines of research. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 281-288). PME.
Cole, Y. A. (2009). Mathematical knowledge for teaching: Transferability and use in the Ghanaian context: A pilot study. Paper presented at the AERA Annual Meeting.
Couto, A. (2015). A Formação Inicial de Professores do Ensino Básico e a Geometria: Um estudo de dois casos [Tese de Doutoramento não publicada]. Departamento de Ciências da Educação e do Património da Universidade Portucalense.
Delaney, S. (2008). Adapting and using U. S. measures to study Irish teachers’ Mathematical Knowledge for Teaching. Unpublished Doctoral Dissertation. University of Michigan.
Desai, S., Bush, S., & Safi, F. (2021). Mathematical representations in the teaching and learning of geometry: A review of the literature from the United States. The Electronic Journal for Research in Science & Mathematics Education, 25(4), 6-22.
Elbaz, F. (1983). Teacher thinking: A study of practical knowledge. Croom Helm.
Gomes, A. (2003). Um estudo sobre o Conhecimento matemático de (futuros) professores do 1.º Ciclo – O problema dos conceitos fundamentais em geometria [Tese de Doutoramento não publicada]. Instituto de Estudos da Criança, Universidade do Minho.
Gomes, A. (2021). Que conhecimento matemático para ensinar nos anos iniciais? Desafios para a formação. Roteiro, 46, e23839. https://doi.org/10.18593/r.v46i.23839.
Gonçalves, C. V. (2020). O conhecimento matemático de professores portugueses de matemática dos primeiros anos [Tese de Doutoramento não publicada]. Universidade do Minho.
Haycock, K. (2006). Improving achievement and closing gaps, Pre-K through college. Retrieved December 10, 2006. Disponível em: http://www2.edtrust.org/EdTrust/ Product+Catalog/recent+presentations.
Hiebert, J., & Grouws, D. A. (2007). The Effects of Classroom Mathematics Teaching on Students’ Learning. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 371-404). Information Age.
Hiebert, J. &. Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In: J. H. Hiebert (Ed.), Conceptual and procedural knowledge: the case of Mathematics, 1-27. Lawrence Erlbaum Associates.
Hill, H. C., Schilling S. G. & Ball, D. L. (2004). Developing Measures of Teachers' Mathematics Knowledge for Teaching. The Elementary Journal, 105 (1), 11-30.
Kim, Y. (2024). A study on the development and analysis of a test of pedagogical content knowledge (PCK) of elementary school pre-service teachers in the areas of geometry and measurement. Korean Association For Learner-Centered Curriculum And Instruction, 24(20), 777–792. https://doi.org/10.22251/jlcci.2024.24.20.777
Kurt-Birel, G., Deniz, Ş., & Önel, F. (2020). Analysis of primary school teachers’ knowledge of geometry. International Electronic Journal of Elementary Education, 12(4), 303-309.
Kwon, M. (2009). Validating the adapted mathematical knowledge for teaching (MKT) measures in Korea. Paper presented at the AERA 2009 Annual Meeting.
Liñán-García, M.d.M.; Muñoz-Catalán, M.C.; Contreras, L.C.; Barrera-Castarnado, V.J. (2021). Specialised Knowledge for Teaching Geometry in a Primary Education Class: Analysis from the Knowledge Mobilized by a Teacher and the Knowledge Evoked in the Researcher. Mathematics, 9, 2805. https:// doi.org/10.3390/math9212805
Ma, L. (1999). Saber e Ensinar Matemática Elementar. Gradiva.
Mariotti, M. A. & Fischbein, E. (1997). Defining in classroom activities. Educational Studies in Mathematics, 34 (3), 219-248.
Mosvold, R., Fauskanger, J, Jakobsen, A. & Melhus, K. F. (2009). Translating test items into Norwegian - without getting lost in translation? Nordic Studies in Mathematics Education, 14 (4), 9-31. http://doi.org.10.7146/nomad.v14i4.148213
Mukuka, A., & Alex, J. K. (2024). Student teachers’ knowledge of school-level geometry: Implications for teaching and learning. European Journal of Educational Research, 13(3), 1375-1389. https://doi.org/10.12973/eu-jer.13.3.1375
National Council of Teachers of Mathematics (NCTM). (1991). Professional Standards for Teaching Mathematics.
Ng, D. (2012). Using the MKT measures to reveal Indonesian teachers’ mathematical knowledge: challenges and potentials. ZDM—The International Journal on Mathematics Education, pp.: 1–13.
Nurnberger-Haag, J., Singh, R. ,& Wernet, J.L. (2020). An Atypical Approach to Improve Typical Issues with pre-service teachers’ geometric shape knowledge. IUMPST: The Journal. Vol 1 (Content Knowledge).
Ribeiro, C., M. & Martins, F. (2010). (Des)Conhecimento matemático para ensinar Otd que possuem futuros professores dos primeiros anos. In APM (Ed.), Actas do XXV Encontro Nacional de Professores de Matemática – ProfMat 2010. APM.
Sanders, W.L., & Rivers, J.C. (1996). Cumulative and residual effects of teachers on future student academic achievement. Research Progress Report. University of Tennessee Value-Added Research and Assessment Center.
Schön, D. A. (1983). The reflective practiotioner: How professionals think in action. Avebury.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher.
Tashakkori, A. & Creswell, J. W. (2007). Exploring the nature of research questions in mixed methods research. Journal of Mixed Methods Research, 1, 207-211.
Zazkis, R. & Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics 69, 131–148. https://doi.org/10.1007/s10649-008-9131-7
Ball, D.L., Hill, H. & Bass, H. (2005). Knowing Mathematics for Teaching. Who knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide? American Educator, p. 14-46.
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
Barber, M. & Mourshed, M. (2007). How the world’s best performing school systems come out on top. McKinsey & Company.
Bardin, L. (2009). Análise de conteúdo. Edições 70.
Baumert, J., Kunter,M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M. & Tsai, Y. (2010). Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, v.47, n.1, p.133-180.
Browning, C. A., Edson, A. J., Kimani, P. M., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 241-272. https://doi.org/10.54870/15513440
Brunheira, L., Serrazina, L., & Rodrigues, M. (2023). Preservice and In-Service Primary Teachers’ Knowledge of Mathematical Reasoning Processes in the Context of a Geometry Task. Acta Scientiae, 24(8), 567–591. https://doi.org/10.17648/acta.scientiae.7122.
Carmo, H., & Ferreira, M. M. (2008). Metodologia da Investigação - Guia para Auto-Aprendizagem (2.ª Edição). Universidade Aberta.
Charalambous, C. (2008). Mathematical knowledge for teaching and the unfolding of tasks in mathematics lessons: Integrating two lines of research. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 281-288). PME.
Cole, Y. A. (2009). Mathematical knowledge for teaching: Transferability and use in the Ghanaian context: A pilot study. Paper presented at the AERA Annual Meeting.
Couto, A. (2015). A Formação Inicial de Professores do Ensino Básico e a Geometria: Um estudo de dois casos [Tese de Doutoramento não publicada]. Departamento de Ciências da Educação e do Património da Universidade Portucalense.
Delaney, S. (2008). Adapting and using U. S. measures to study Irish teachers’ Mathematical Knowledge for Teaching. Unpublished Doctoral Dissertation. University of Michigan.
Desai, S., Bush, S., & Safi, F. (2021). Mathematical representations in the teaching and learning of geometry: A review of the literature from the United States. The Electronic Journal for Research in Science & Mathematics Education, 25(4), 6-22.
Elbaz, F. (1983). Teacher thinking: A study of practical knowledge. Croom Helm.
Gomes, A. (2003). Um estudo sobre o Conhecimento matemático de (futuros) professores do 1.º Ciclo – O problema dos conceitos fundamentais em geometria [Tese de Doutoramento não publicada]. Instituto de Estudos da Criança, Universidade do Minho.
Gomes, A. (2021). Que conhecimento matemático para ensinar nos anos iniciais? Desafios para a formação. Roteiro, 46, e23839. https://doi.org/10.18593/r.v46i.23839.
Gonçalves, C. V. (2020). O conhecimento matemático de professores portugueses de matemática dos primeiros anos [Tese de Doutoramento não publicada]. Universidade do Minho.
Haycock, K. (2006). Improving achievement and closing gaps, Pre-K through college. Retrieved December 10, 2006. Disponível em: http://www2.edtrust.org/EdTrust/ Product+Catalog/recent+presentations.
Hiebert, J., & Grouws, D. A. (2007). The Effects of Classroom Mathematics Teaching on Students’ Learning. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 371-404). Information Age.
Hiebert, J. &. Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In: J. H. Hiebert (Ed.), Conceptual and procedural knowledge: the case of Mathematics, 1-27. Lawrence Erlbaum Associates.
Hill, H. C., Schilling S. G. & Ball, D. L. (2004). Developing Measures of Teachers' Mathematics Knowledge for Teaching. The Elementary Journal, 105 (1), 11-30.
Kim, Y. (2024). A study on the development and analysis of a test of pedagogical content knowledge (PCK) of elementary school pre-service teachers in the areas of geometry and measurement. Korean Association For Learner-Centered Curriculum And Instruction, 24(20), 777–792. https://doi.org/10.22251/jlcci.2024.24.20.777
Kurt-Birel, G., Deniz, Ş., & Önel, F. (2020). Analysis of primary school teachers’ knowledge of geometry. International Electronic Journal of Elementary Education, 12(4), 303-309.
Kwon, M. (2009). Validating the adapted mathematical knowledge for teaching (MKT) measures in Korea. Paper presented at the AERA 2009 Annual Meeting.
Liñán-García, M.d.M.; Muñoz-Catalán, M.C.; Contreras, L.C.; Barrera-Castarnado, V.J. (2021). Specialised Knowledge for Teaching Geometry in a Primary Education Class: Analysis from the Knowledge Mobilized by a Teacher and the Knowledge Evoked in the Researcher. Mathematics, 9, 2805. https:// doi.org/10.3390/math9212805
Ma, L. (1999). Saber e Ensinar Matemática Elementar. Gradiva.
Mariotti, M. A. & Fischbein, E. (1997). Defining in classroom activities. Educational Studies in Mathematics, 34 (3), 219-248.
Mosvold, R., Fauskanger, J, Jakobsen, A. & Melhus, K. F. (2009). Translating test items into Norwegian - without getting lost in translation? Nordic Studies in Mathematics Education, 14 (4), 9-31. http://doi.org.10.7146/nomad.v14i4.148213
Mukuka, A., & Alex, J. K. (2024). Student teachers’ knowledge of school-level geometry: Implications for teaching and learning. European Journal of Educational Research, 13(3), 1375-1389. https://doi.org/10.12973/eu-jer.13.3.1375
National Council of Teachers of Mathematics (NCTM). (1991). Professional Standards for Teaching Mathematics.
Ng, D. (2012). Using the MKT measures to reveal Indonesian teachers’ mathematical knowledge: challenges and potentials. ZDM—The International Journal on Mathematics Education, pp.: 1–13.
Nurnberger-Haag, J., Singh, R. ,& Wernet, J.L. (2020). An Atypical Approach to Improve Typical Issues with pre-service teachers’ geometric shape knowledge. IUMPST: The Journal. Vol 1 (Content Knowledge).
Ribeiro, C., M. & Martins, F. (2010). (Des)Conhecimento matemático para ensinar Otd que possuem futuros professores dos primeiros anos. In APM (Ed.), Actas do XXV Encontro Nacional de Professores de Matemática – ProfMat 2010. APM.
Sanders, W.L., & Rivers, J.C. (1996). Cumulative and residual effects of teachers on future student academic achievement. Research Progress Report. University of Tennessee Value-Added Research and Assessment Center.
Schön, D. A. (1983). The reflective practiotioner: How professionals think in action. Avebury.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher.
Tashakkori, A. & Creswell, J. W. (2007). Exploring the nature of research questions in mixed methods research. Journal of Mixed Methods Research, 1, 207-211.
Zazkis, R. & Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics 69, 131–148. https://doi.org/10.1007/s10649-008-9131-7
Publicado
2025-11-25
Secção
Secção 1: Investigação em Educação em Ciências, Matemática e Tecnologia
