UMA PROPOSTA PARA A FORMAÇÃO DE PROFESSORES DE MATEMÁTICA: O CASO DA ARGUMENTAÇÃO MATEMÁTICA
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Palavras-chave:
argumento
argumentação
formação de professores de matemática
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Edição:
v. 1 n. 1 (2024): junio
Seção: Artículos de Educación Matemática
Resumo
Apresentamos alguns produtos de um processo de investigação de renovação curricular dos programas de formação inicial e contínua de professores de matemática da Universidade Pedagógica Nacional (Colômbia), que procura promover a aprendizagem de aspectos relacionados com a argumentação. Descrevemos e ilustramos como operacionalizámos a nossa posição sobre a argumentação matemática. Centramo-nos numa abordagem metodológica que procura favorecer os processos argumentativos e transformar a argumentação num objeto de estudo na formação inicial e num plano de formação para professores em exercício, que visa apoiar a transformação do seu conhecimento sobre argumentação.
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Molina, O., Camargo, L., Vargas, C., Samper, C., & Perry, P. (2024). UMA PROPOSTA PARA A FORMAÇÃO DE PROFESSORES DE MATEMÁTICA: O CASO DA ARGUMENTAÇÃO MATEMÁTICA. RIME, 1(1), 151-185. https://doi.org/10.32735/S2810-7187202400013356
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Referências
1. Mariotti M. Proof and Proving in Mathematics Education. In Gutiérrez A, Boero P. Handbook of Research on the Psychology of Mathematics Education. Past, Present and Future. Rotterdam, The Netherlands: Sense Publishers; 2006. p. 173-204.
2. Boero P, Douek N, Morselli F, Pedemonte B. Argumentation and proof: a contribution to theoretical perspectives and their classroom implementation. In Pinto MMF, Kawasaky TF, editors. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education; 2010; Belo Horizonte, Brazil: PME. p. 179-204.
3. Durand-Guerrier V, Boero P, Douek N, Epp S, Tanguay D. Argumentation and Proof in the Mathematics Classroom. In Hanna G, de Villiers M. Proof and Proving in Mathematics Education. New York: Springer; 2012. p. 349-368.
4. Hanna G, de Villiers M. Proof and Proving in Mathematics Education New York: Springer; 2012.
5. Reid D, Knipping C. Proof in Mathematics Education. Research, Learning and Teaching Rotterdam: Sense Publishers; 2010.
6. Stylianides A, Bieda K, Morselli F. Proof and Argumentation in Mathematics Education Research. In Guitérrez A, Leder G, Boero P. The Second Handbook of Research on the Psychology of Mathematics Education. Rotterdam: Sense Publishers; 2016. p. 315-352.
7. McNeill KL, Knight AM. Teachers’ pedagogical content knowledge of scientific argumentation: The impact of professional development on k-12 teachers. Science Education. 2013; 97(6): 936–972.
8. Baker M. Argumentative interactions and the social construction of knowledge. In Mirza NM, Perret-Clermont AN. Argumentation and education: Theoretical foundations and practices. Dordrecht: Springer; 2009. p. 127–144.
9. Stylianides A, Ball D. Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education. 2008; 11(4): 307–332.
10. Krummheuer G. The ethnography of argumentation. In Cobb P, Bauersfeld H. The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, New Jersey: Lawrence Erlbaum Associates; 1995. p. 229–269.
11. Yackel E, Cobb P. Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education. 1996; 27(4): 458-477.
12. Duval R. Lettre de la Preuve. [Online].; 1999 [Traducido por Patricio Herbst]. Available from: http://www.lettredelapreuve.org/OldPreuve/Newsletter/
991112Theme/991112ThemeES.html.
13. Perelman C, Olbrechts-Tyteca L. Tratado de la argumentación. La nueva retórica Madrid: Editorial Gredos; 1989.
14. Toulmin S. Los usos de la argumentación Barcelona: Ediciones Península; 2007.
15. Anscombre JC, Ducrot O. La argumentación en la lengua Madrid: Gredos; 1994.
16. van Eemeren FH, Grootendorst RA. Systematic Theory of Argumentation: The pragma-dialectical approach Nueva York: Cambridge University Press; 2004.
17. Ledezma C, Sol T, Sala-Sebastià G, Font V. Knowledge and beliefs on mathematical modelling inferred in the argumentation of a prospective teacher when reflecting on the incorporation of this process in his lessons. Mathematics. 2022; 10: 3339.
18. Reuter F. Explorative mathematical argumentation: a theoretical framework for identifying and analysing argumentation processes in early mathematics learnin. Educational Studies in Mathematics. 2023; 112: 415–435.
19. Pedemonte B. How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics. 2007; 66: 23–41.
20. Camargo L, Samper C, Perry P, Molina O, Echeverry A. Use of dragging as organizer for conjecture validation. In Tzekaki M, Kaldrimidou M, Sakonidis H. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, 2. Thessaloniki, Greece : PME; 2009. p. 257-264.
21. Molina O, Samper C. Tipos de problemas que provocan la generación de argumentos inductivos, abductivos y deductivos. Bolema: Boletim de Educação Matemática. 2019; 32(62).
22. Molina O, Pino-Fan L, Font V. Estructura y dinámica de argumentos analógicos, abductivos y deductivos: un curso de geometría del espacio como contexto de reflexión. Enseñanza de las Ciencias. 2019; 37(1): 93-116.
23. Molina O. Sistema de normas que influyen en procesos de argumentación: un curso de geometría del espacio como escenario de investigación [Tesis Doctoral] Osorno: Universidad de Los Lagos; 2019.
24. Arzarello F, Olivero F, Paola D, Robutti O. A cognitive analysis of dragging practises in Cabri environments. ZDM. 2002; 34(3): 66-72.
25. Arzarello F, Bartolini-Bussi M, Leung A, Mariotti M, Stevenson I. Experimental Approaches to Theoretical Thinking: Artefacts and Proofs. In Hanna G, de Villiers M. Proof and Proving in Mathematics Education.: Springer; 2012. p. 97-146.
26. Baccaglini-Frank A, Mariotti M. Generating Conjectures in Dynamic Geometry: The Maintaining Dragging Model. International Journal of Computers for Mathematical Learning. 2010; 15: 225–253.
27. Pino-Fan L, Godino JD. Perspectiva ampliada del conocimiento didáctico-matemático del profesor. Paradigma. 2015; 36(1): 87-109.
28. Carr W. Una teoría para la educación. Hacia una investigación crítica: Morata; 2002.
2. Boero P, Douek N, Morselli F, Pedemonte B. Argumentation and proof: a contribution to theoretical perspectives and their classroom implementation. In Pinto MMF, Kawasaky TF, editors. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education; 2010; Belo Horizonte, Brazil: PME. p. 179-204.
3. Durand-Guerrier V, Boero P, Douek N, Epp S, Tanguay D. Argumentation and Proof in the Mathematics Classroom. In Hanna G, de Villiers M. Proof and Proving in Mathematics Education. New York: Springer; 2012. p. 349-368.
4. Hanna G, de Villiers M. Proof and Proving in Mathematics Education New York: Springer; 2012.
5. Reid D, Knipping C. Proof in Mathematics Education. Research, Learning and Teaching Rotterdam: Sense Publishers; 2010.
6. Stylianides A, Bieda K, Morselli F. Proof and Argumentation in Mathematics Education Research. In Guitérrez A, Leder G, Boero P. The Second Handbook of Research on the Psychology of Mathematics Education. Rotterdam: Sense Publishers; 2016. p. 315-352.
7. McNeill KL, Knight AM. Teachers’ pedagogical content knowledge of scientific argumentation: The impact of professional development on k-12 teachers. Science Education. 2013; 97(6): 936–972.
8. Baker M. Argumentative interactions and the social construction of knowledge. In Mirza NM, Perret-Clermont AN. Argumentation and education: Theoretical foundations and practices. Dordrecht: Springer; 2009. p. 127–144.
9. Stylianides A, Ball D. Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education. 2008; 11(4): 307–332.
10. Krummheuer G. The ethnography of argumentation. In Cobb P, Bauersfeld H. The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, New Jersey: Lawrence Erlbaum Associates; 1995. p. 229–269.
11. Yackel E, Cobb P. Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education. 1996; 27(4): 458-477.
12. Duval R. Lettre de la Preuve. [Online].; 1999 [Traducido por Patricio Herbst]. Available from: http://www.lettredelapreuve.org/OldPreuve/Newsletter/
991112Theme/991112ThemeES.html.
13. Perelman C, Olbrechts-Tyteca L. Tratado de la argumentación. La nueva retórica Madrid: Editorial Gredos; 1989.
14. Toulmin S. Los usos de la argumentación Barcelona: Ediciones Península; 2007.
15. Anscombre JC, Ducrot O. La argumentación en la lengua Madrid: Gredos; 1994.
16. van Eemeren FH, Grootendorst RA. Systematic Theory of Argumentation: The pragma-dialectical approach Nueva York: Cambridge University Press; 2004.
17. Ledezma C, Sol T, Sala-Sebastià G, Font V. Knowledge and beliefs on mathematical modelling inferred in the argumentation of a prospective teacher when reflecting on the incorporation of this process in his lessons. Mathematics. 2022; 10: 3339.
18. Reuter F. Explorative mathematical argumentation: a theoretical framework for identifying and analysing argumentation processes in early mathematics learnin. Educational Studies in Mathematics. 2023; 112: 415–435.
19. Pedemonte B. How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics. 2007; 66: 23–41.
20. Camargo L, Samper C, Perry P, Molina O, Echeverry A. Use of dragging as organizer for conjecture validation. In Tzekaki M, Kaldrimidou M, Sakonidis H. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, 2. Thessaloniki, Greece : PME; 2009. p. 257-264.
21. Molina O, Samper C. Tipos de problemas que provocan la generación de argumentos inductivos, abductivos y deductivos. Bolema: Boletim de Educação Matemática. 2019; 32(62).
22. Molina O, Pino-Fan L, Font V. Estructura y dinámica de argumentos analógicos, abductivos y deductivos: un curso de geometría del espacio como contexto de reflexión. Enseñanza de las Ciencias. 2019; 37(1): 93-116.
23. Molina O. Sistema de normas que influyen en procesos de argumentación: un curso de geometría del espacio como escenario de investigación [Tesis Doctoral] Osorno: Universidad de Los Lagos; 2019.
24. Arzarello F, Olivero F, Paola D, Robutti O. A cognitive analysis of dragging practises in Cabri environments. ZDM. 2002; 34(3): 66-72.
25. Arzarello F, Bartolini-Bussi M, Leung A, Mariotti M, Stevenson I. Experimental Approaches to Theoretical Thinking: Artefacts and Proofs. In Hanna G, de Villiers M. Proof and Proving in Mathematics Education.: Springer; 2012. p. 97-146.
26. Baccaglini-Frank A, Mariotti M. Generating Conjectures in Dynamic Geometry: The Maintaining Dragging Model. International Journal of Computers for Mathematical Learning. 2010; 15: 225–253.
27. Pino-Fan L, Godino JD. Perspectiva ampliada del conocimiento didáctico-matemático del profesor. Paradigma. 2015; 36(1): 87-109.
28. Carr W. Una teoría para la educación. Hacia una investigación crítica: Morata; 2002.