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Abstract
Communication plays a key role in teaching and learning processes. Questions are a communicational act greatly used by teachers to structure their discourse, establish dynamics, and foster interaction between the different participants in the classroom. In view of these potentialities of questions in the classroom context, we have developed a teaching experiment with the aim of understand the role of the teacher's question in the learning of topics on functions. Considering the nature of this aim, a methodology of qualitative and interpretative nature was used. The data collection was based on the students’ written productions and on the audio and video recordings of a mathematics class of a Grade 10 educational group (in northern Portugal). Data analysis is based on content analysis techniques, crossing collected data and categories emerging from the literature. The study revealed that the teacher’s questions alternated between confirmation, focalization, and inquiry, with inquiry prevailing. Questions aimed at testing the student’s knowledge gave both the teacher and actual student important information. Questions that focused the student’s attention on a particular detail enabled the students to organize their reasoning and structure their answer. Questions that required the students to explain or justify their thoughts were those that proved to most contribute to the development of the student’s reasoning process.
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References
- Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797-810. https://doi.org/10.1007/s11858-013-0506-6
- Baran, A., & Kabael, T. (2021). An investigation of eighth grade students’ mathematical communication competency and affective characteristics. The Journal of Educational Research, 114(4), 367-380. https://doi.org/10.1080/00220671.2021.1948382
- Canavarro, A., Oliveira, H., & Menezes, L. (2014). Práticas de ensino exploratório da Matemática: Ações e intenções de uma professora. In J. P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 219-236). Instituto de Educação da Universidade de Lisboa. http://hdl.handle.net/10174/13631
- Chapman, O. (2004). Facilitating peer interactions in learning mathematics: Teachers' practical knowledge. In M. J. Høines, & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 191–198.
- Chin, C. (2006). Teacher questioning in science classrooms: What approaches stimulate productive thinking? International Science Education Conference, 183–192. http://hdl.handle.net/10497/4744
- Guerreiro, A., Tomás Ferreira, R., Menezes, L., & Martinho, M. H. (2015). Comunicação na sala de aula: A perspetiva do ensino exploratório da matemática. Zetetiké: Revista de Educação Matemática, 23(4), 279-295. https://doi.org/10.20396/zet.v23i44.8646539
- Lomibao, L. S., Luna, C. A., & Namoco, R. A. (2016). The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research, 4(5), 378-382. https://doi.org/10.12691/education-4-5-3
- Love, E., & Mason, J. (1995). Telling and asking. In P. Murphy, M. Selinger, J. Bourne, & M. Briggs (Eds.), Subject learning in the primary curriculum: Issues in English, Science, and Mathematics (pp. 252–270). Routledge.
- McMillan, J., & Schumacher, S. (2014). Research in Education Evidence-Based Inquiry. Pearson Education Limited.
- Menezes, L. (1995). Concepções e práticas de professores de matemática: contributos para o estudo da pergunta. Master’s Dissertation, Universidade de Lisboa.
- Menezes, L., Guerreiro, A., Martinho, M. H., & Tomás Ferreira, R. (2013). Essay on the Role of Teachers’ Questioning in Inquiry-Based Mathematics Teaching. Sisyphus - Journal of Education, 1(3), 44-75. https://doi.org/10.25749/sis.3706
- Menezes, L., Ferreira, R. T., Martinho, M. H., & Guerreiro, A. (2014). Comunicação nas práticas letivas dos professores de Matemática. In J. P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 135-164). Instituto de Educação da Universidade de Lisboa. https://doi.org/10.13140/2.1.1731.4885
- Menezes, L., Fernandes, J. A., Viseu, F., Ribeiro, A., & Flores, P. (2020). Perspectivas de Professores de Matemática sobre o Humor e o seu Valor Educacional. Bolema: Boletim de Educação Matemática, 34(66), 332-353. https://doi.org/10.1590/1980-4415v34n66a16
- Moyer, P. S., & Milewicz, E. (2002). Learning to question: categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315. https://doi.org/10.1023/A:1021251912775
- NCTM (2007). Princípios e normas para a Matemática escolar. Associação de Professores de Matemática.
- Newton, L. (2017). Questioning: a window on productive thinking. International Centre for Innovation in Education (ICIE).
- Oliveira, H., Canavarro, A. P., Menezes, L. (2014). Casos de multimédia na formação de professores que ensinam Matemática. In J.P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 13-31). Instituto de Educação da Universidade de Lisboa. https://doi.org/10.13140/RG.2.1.1759.5361
- Oliveira, H., Menezes, L., & Canavarro, A. P. (2013). Conceptualizando o ensino exploratório da Matemática: Contributos da prática de uma professora do 3.º ciclo param a elaboração de um quadro de referência. Quadrante, 22(2), 30–53. https://doi.org/10.48489/quadrante.22895
- Ponte, J. P. (2005). Gestão curricular em Matemática. In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11-34). Associação de Professores de Matemática.
- Rodrigues, C., Ponte, J. P., & Menezes, L. (2020). Práticas discursivas de professores de Matemática na condução de discussões coletivas. Quadrante, 29(2), 24-46. https://doi.org/10.48489/quadrante.22575
- Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
- Wachira, P., Pourdavood, R. G., & Skitzki, R. (2013). Mathematics teacher’s role in promoting classroom discourse. International Journal for Mathematics Teaching and Learning, 13(1), 1-38. https://www.cimt.org.uk/journal/wachira.pdf
References
Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797-810. https://doi.org/10.1007/s11858-013-0506-6
Baran, A., & Kabael, T. (2021). An investigation of eighth grade students’ mathematical communication competency and affective characteristics. The Journal of Educational Research, 114(4), 367-380. https://doi.org/10.1080/00220671.2021.1948382
Canavarro, A., Oliveira, H., & Menezes, L. (2014). Práticas de ensino exploratório da Matemática: Ações e intenções de uma professora. In J. P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 219-236). Instituto de Educação da Universidade de Lisboa. http://hdl.handle.net/10174/13631
Chapman, O. (2004). Facilitating peer interactions in learning mathematics: Teachers' practical knowledge. In M. J. Høines, & A. B. Fuglestad (Eds.), Proceedings of the 28th PME International Conference, 2, 191–198.
Chin, C. (2006). Teacher questioning in science classrooms: What approaches stimulate productive thinking? International Science Education Conference, 183–192. http://hdl.handle.net/10497/4744
Guerreiro, A., Tomás Ferreira, R., Menezes, L., & Martinho, M. H. (2015). Comunicação na sala de aula: A perspetiva do ensino exploratório da matemática. Zetetiké: Revista de Educação Matemática, 23(4), 279-295. https://doi.org/10.20396/zet.v23i44.8646539
Lomibao, L. S., Luna, C. A., & Namoco, R. A. (2016). The influence of mathematical communication on students’ mathematics performance and anxiety. American Journal of Educational Research, 4(5), 378-382. https://doi.org/10.12691/education-4-5-3
Love, E., & Mason, J. (1995). Telling and asking. In P. Murphy, M. Selinger, J. Bourne, & M. Briggs (Eds.), Subject learning in the primary curriculum: Issues in English, Science, and Mathematics (pp. 252–270). Routledge.
McMillan, J., & Schumacher, S. (2014). Research in Education Evidence-Based Inquiry. Pearson Education Limited.
Menezes, L. (1995). Concepções e práticas de professores de matemática: contributos para o estudo da pergunta. Master’s Dissertation, Universidade de Lisboa.
Menezes, L., Guerreiro, A., Martinho, M. H., & Tomás Ferreira, R. (2013). Essay on the Role of Teachers’ Questioning in Inquiry-Based Mathematics Teaching. Sisyphus - Journal of Education, 1(3), 44-75. https://doi.org/10.25749/sis.3706
Menezes, L., Ferreira, R. T., Martinho, M. H., & Guerreiro, A. (2014). Comunicação nas práticas letivas dos professores de Matemática. In J. P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 135-164). Instituto de Educação da Universidade de Lisboa. https://doi.org/10.13140/2.1.1731.4885
Menezes, L., Fernandes, J. A., Viseu, F., Ribeiro, A., & Flores, P. (2020). Perspectivas de Professores de Matemática sobre o Humor e o seu Valor Educacional. Bolema: Boletim de Educação Matemática, 34(66), 332-353. https://doi.org/10.1590/1980-4415v34n66a16
Moyer, P. S., & Milewicz, E. (2002). Learning to question: categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315. https://doi.org/10.1023/A:1021251912775
NCTM (2007). Princípios e normas para a Matemática escolar. Associação de Professores de Matemática.
Newton, L. (2017). Questioning: a window on productive thinking. International Centre for Innovation in Education (ICIE).
Oliveira, H., Canavarro, A. P., Menezes, L. (2014). Casos de multimédia na formação de professores que ensinam Matemática. In J.P. Ponte (Org.), Práticas Profissionais dos Professores de Matemática (pp. 13-31). Instituto de Educação da Universidade de Lisboa. https://doi.org/10.13140/RG.2.1.1759.5361
Oliveira, H., Menezes, L., & Canavarro, A. P. (2013). Conceptualizando o ensino exploratório da Matemática: Contributos da prática de uma professora do 3.º ciclo param a elaboração de um quadro de referência. Quadrante, 22(2), 30–53. https://doi.org/10.48489/quadrante.22895
Ponte, J. P. (2005). Gestão curricular em Matemática. In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11-34). Associação de Professores de Matemática.
Rodrigues, C., Ponte, J. P., & Menezes, L. (2020). Práticas discursivas de professores de Matemática na condução de discussões coletivas. Quadrante, 29(2), 24-46. https://doi.org/10.48489/quadrante.22575
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
Wachira, P., Pourdavood, R. G., & Skitzki, R. (2013). Mathematics teacher’s role in promoting classroom discourse. International Journal for Mathematics Teaching and Learning, 13(1), 1-38. https://www.cimt.org.uk/journal/wachira.pdf