A PROPOSAL FOR PRESERVICE MATHEMATICS TEACHERS: THE CASE OF MATHEMATICAL ARGUMENTATION
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Keywords:
argument
argumentation
mathematics teacher education
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Issue:
Vol. 1 No. 1 (2024): junio
Section: Artículos de Educación Matemática
Abstract
We present some products of a research process of curricular renovation for preservice and in-service mathematics teachers’ programs at the Universidad Pedagógica Nacional (Colombia), which seeks to promote learning on aspects related to argumentation. We describe and illustrate how we have operationalized our point of view on mathematical argumentation. We focus on a methodological approach that seeks to favor argumentative processes and turn argumentation into an object of study, which aims to support the transformation of their knowledge on argumentation.
Article Details
Molina, O., Camargo, L., Vargas, C., Samper, C., & Perry, P. (2024). A PROPOSAL FOR PRESERVICE MATHEMATICS TEACHERS: THE CASE OF MATHEMATICAL ARGUMENTATION. RIME, 1(1), 151-185. https://doi.org/10.32735/S2810-7187202400013356
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References
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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.
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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.