Challenges faced by preservice teachers in planning and exploring tasks that promote mathematical reasoning
Tipo de documento
Autores
Lista de autores
Mendes, Fátima, Delgado, Catarina y Brocardo, Joana
Resumen
Background: mathematical reasoning is fundamental for mathematics learning from the first years of schooling. It is a challenge for students and teachers, so it is relevant to deepen ways to develop this ability with the prospective teachers. Objectives: identify the challenges in supervised practice with a view to developing students’ mathematical reasoning, seeking to answer the following question: what challenges do prospective teachers face in planning and exploring tasks that promote mathematical reasoning? Design: it is based on a formative experiment and follows an interpretive methodology. Setting and participants: this experiment was conducted during 13 sessions of the curricular unit (CU) Didactics of Mathematics of the 2nd year of the master’s course in Pre-School Education and Teaching of the 1st Cycle of Basic Education, in a class of 25 students. The participants were four students - two pairs in teaching practice- whose selection followed the following criteria: not having any of the researchers as teaching practice supervisors and regularly intervening in class. Data collection and analysis: the data were collected through participant observation of the CU classes, interviews, and document collection. Results: students face more challenges associated with mathematical reasoning during monitoring phases of the exploration of the tasks and their final discussion. Conclusions: these results point to the need for initial training programs to prioritise activities that support prospective teachers in the understanding of mathematical reasoning processes and that involve them in the planning of tasks and analysing practical exploration that will enhance their development.
Fecha
2022
Tipo de fecha
Estado publicación
Términos clave
Inicial | Interpretativo | Otro (razonamiento) | Reflexión sobre la enseñanza | Tareas
Enfoque
Nivel educativo
Educación primaria, escuela elemental (6 a 12 años) | Educación superior, formación de pregrado, formación de grado | Formación en posgrado
Idioma
Revisado por pares
Formato del archivo
Volumen
24
Número
4
Rango páginas (artículo)
147-182
ISSN
21787727
Referencias
Adeeb, M. J. (2020). The Challenges Faced by Pre-Service Mathematics Teachers during their Teaching Practice in the UAE: Implications for Teacher Education Programs. International Journal of Learning, Teaching and Educational Research 19(7), 23-34. https://doi.org/10.26803/ijlter.19.7.2 Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33–52. https://doi.org/10.1007/s10857-006-9005-9 Ball, D. L., Thames, M. H., Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407. https://doi.org/10.1177/0022487108324554 Battista, M. (2017). Mathematical reasoning and sense making. Em M. Battista, J. M. Baek, K. Cramer, & M. Blanton (Eds.), Reasoning and sense making in the mathematics classroom. Grades 3-5 (pp. 1-22). NCTM. Brocardo, J., Delgado, C., Mendes, F., & Ponte, J. P. (no prelo). Ações do professor e desenvolvimento do raciocínio matemático durante a discussão coletiva de uma tarefa. Educación Matemática. Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms (K. Brodie, ed.). https://doi.org/10.1007/978-0-387- 09742-8 Chizhik, E. W. & Chizhik. A. W. (2018). Using activity theory to examine how teachers’lLesson plans meet students’ learning needs. The Teacher Educator 53(1), 67–85. https://doi.org /10.1080/08878730.2017.1296913 Delgado, C. (2013). As Práticas do professor e o desenvolvimento do sentido de número: Um estudo no 1.º ciclo. (Tese de Doutoramento). Delgado, C., Oliveira, H. & Brocardo, J. (2017). Práticas do professor na discussão de tarefas que visam o desenvolvimento do sentido de número: um estudo no Ensino Básico. Bolema 31(57), 323-343. https://doi.org/10.1590/1980-4415v31n57a16 Desfitri, R. (2018). Pre-service teachers’ challenges in presenting mathematical problems. J. Physics: Conference Series, 948 012035. https://doi.org/10.1088/1742-6596/948/1/012035 Erickson, F. (1986). Qualitative methods in research on teaching. In M. Wittrockk (Ed.), Handbook of research on teaching (3rd ed., pp. 119- 161). MacMillan. Herbert, S., Vale, C., Bragg, L. A., Loong, E., & Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26–37. https://doi.org/10.1016/j.ijer.2015.09.005 Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/S10649-017-9761- 8 König, J. Bremerich-Vos, A., Buchholtz, C., Fladung, I., & Glutsch, N. (2020). Pre–service teachers’ generic and subject-specific lesson- planning skills: On learning adaptive teaching during initial teacher education, European Journal of Teacher Education, 43(2), 131-150. https://doi.org/10.1080/02619768.2019.1679115 Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press. Lannin, J., Ellis, A., & Elliot, R. (2011). Developing essential understanding of mathematical reasoning: Pre-K-Grade 8. NCTM. Livy, S., & Downton, A. (2018). Exploring experiences for assisting primary pre-service teachers to extend their knowledge of student strategies and reasoning. The Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2017.11.004 Maher, C. A., Palius, M. F., Maher, J. A., Hmelo-Silver, C. E., & Sigley, R. (2014). Teachers can learn to attend to students' reasoning using videos as a tool. Issues in Teacher Education, 23(1), 31-47. Mallart, A., Font, V., & Diez, J. (2018). Case study on mathematics pre- service teachers’ difficulties in problem posing. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1465-1481. https://doi.org/10.29333/ejmste/83682 Martins, G. O., Gomes, C. S., Brocardo, J. L., Pedroso, J. V., Acosta Carrillo, J. L., Ucha, L. M., Encarnação, M., Horta, M. J., Calçada, M. T., Nery, R. V., Rodrigues, S. V. (2017). Perfil dos Alunos à Saída da Escolaridade Obrigatória. Ministério da Educação. Homologado pelo Despacho n.º 6478/2017, de 26 de julho. https://dge.mec.pt/sites/default/files/Curriculo/Projeto_Autonomia_e_ Flexibilidade/perfil_dos_alunos.pdf Martins, M., Mata-Pereira, J., & Ponte, J. P. (2021). Os desafios da abordagem exploratória no ensino da Matemática: aprendizagens de duas futuras professoras através do estudo de aula. Bolema, 35(69), 343–364. https://doi.org/10.1590/1980-4415v35n69a16. Mata-Pereira, J., & Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169– 186. https://doi.org/10.1590/1980-4415v32n62a02 ME-DGE (2021). Aprendizagens essenciais de Matemática. https://www.dge.mec.pt/noticias/aprendizagens-essenciais-de- matematica Mendes, F., Delgado, C., Brocardo, J., & Ponte, J. P. (2021). Raciocínio matemático e ações do professor durante a discussão coletiva de uma tarefa. Em N. Branco, S. Colaço, L. Serrazina, R. Ferreira, R. Santos, & A. P. Canavarro (Eds), Capacidades matemáticas transversais. Livros de atas do EIEM 2021. (pp. 123-133). SPIEM. McNeal, B. & Simon, M. A. (2000). Mathematics culture clash: negotiating new classroom norms with prospective teachers. The Journal of Mathematical Behavior 18(4), 475-509. https://doi.org/10.1016/S0732-3123(00)00027-4 Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teacherslLearn? Journal for Research in Mathematics Education, 40(5), 491–529. https://doi.org/10.5951/JRESEMATHEDUC.40.5.0491 NCTM (2007). Princípios e normas para a matemática escolar. APM. NCTM (2017). Princípios para a ação: Assegurar a todos o sucesso em matemática. APM. Ponte, J. P., & Chapman, O. (2006). Mathematics teachers' knowledge and practices. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 461-494). Sense. Ponte, J. P., Santos, L., Oliveira, H., & Henriques, A. (2017). Research on teaching practice in a Portuguese initial secondary mathematics teacher education program. ZDM Mathematics Education, 49, 291– 303. https://doi.org/10.1007/s11858-017-0847-7 Ponte, J. P., Branco, N., & Quaresma, M. (2014). Exploratory activity in the mathematics classroom. In Y. Li, E. Silver, & S. Li. (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 103-125). Springer. https://doi.org/10.1007/978-3-319- 04993-9_7 Ponte, J. P. do Brocardo, J.; Oliveira, H. (2003). Investigações Matemáticas na sala de Aula. Autêntica. REASON (2020). Princípios para elaboração de tarefas para promover o raciocínio matemático nos alunos (versão draft). Santos, l., Oliveira, H., Ponte, J. P., & Henriques, A. (2019). Pre-service teachers’ experiences in selecting and proposing challenging tasks in secondary classrooms. In Proceedings of CERME 11, 11th Congress of European Research in Mathematics Education (pp. 3762-3769), University of Utrecht. 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 Stylianides, G.J., Stylianides, A.J., & Shilling-Traina, L.N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Educational, 11, 1463–1490. https://doi.org/10.1007/s10763-013-9409-9 Tirosh, D. (2000). Enhancing prospective teachers‟ knowledge of children‟s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31, 5-25. https://doi.org/10.2307/749817 UNESCO (2017). Organização das Nações Unidas para a Educação, a Ciência e a Cultura.Education for Sustainable Development Goals: learning objectives.