RESEARCH PAPER
Mathematics teacher argumentation in a didactic perspective
 
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Universidad de Antioquia, Medellín, COLOMBIA
 
 
Online publication date: 2023-07-23
 
 
Publication date: 2023-09-01
 
 
EURASIA J. Math., Sci Tech. Ed 2023;19(9):em2322
 
KEYWORDS
ABSTRACT
The teacher’s argumentation is considered essential to promote the student’s mathematical education; the teacher’s argumentation is linked to the teacher’s didactic-mathematical knowledge and the achievement of instructional objectives. In this sense, a pragmatic proposal is required that links the teacher’s didactic-mathematical knowledge with argumentation. Toulmin’s (2007) model makes it possible to study the structure of teacher or student argumentation; in contrast, pragma-dialectic considers that in the face of a difference of opinion, the parties involved try to persuade their counterpart while observing argumentative discourse standards. In the context of an argumentative class, both argumentation models do not consider the particularities of the argumentation of a didactic nature that the teacher uses. This document presents a proposal for argumentation suited to mathematics education, based on a mapping of literature and a model of the teacher’s knowledge, contrasted in an actual class. The analysis and discussion of data let us conclude that a teacher’s argumentation is characterized by epistemic, cognitive, interactional, emotional, and communicative features that reaffirm not only the complexity of educational practices but also the teacher’s argumentation for educational purposes and the adequacy of the proposed definition.
REFERENCES (85)
1.
Anderson, R. C., Nguyen-Jahiel, K., McNurlen, B., Archoudidou, A., Kim, S., Retznitskaya, A., Tillmanns, M., & Gilbert, L. (2001). The snowball phenomenon: Spread of ways of talking and ways of thinking across groups of children. Cognition and Instruction, 19, 1-46. https://doi.org/10.1207/S15326....
 
2.
Andriessen, J., Baker, M., & Suthers, D. (2003). Argumentation, computer support, and the educational context of confronting cognitions. In J. Andriessen, M. Baker, & D. Suthers (Eds.), Arguing to learn (pp. 1-25). Springer. https://doi.org/10.1007/978-94....
 
3.
Asterhan, C., & Schwarz, B. (2016). Argumentation for learning: Well-trodden paths and unexplored territories. Educational Psychologist, 51, 164-187. https://doi.org/10.1080/004615....
 
4.
Ayalon, M., & Even, R. (2016). Factors shaping students’ opportunities to engage in argumentative activity. International Journal of Science and Mathematics Education, 14, 575-601. https://doi.org/10.1007/s10763....
 
5.
Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ attention to potential classroom situations of argumentation. The Journal of Mathematical Behavior, 49, 163-173. https://doi.org/10.1016/j.jmat....
 
6.
Azmon, S., Hershkowitz, R., & Schwarz, B. B. (2011). The impact of teacher-led discussions on students’ subsequent argumentative writing. In Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education: Developing Mathematical Thinking (pp. 73-87).
 
7.
Baker, M. (2009). Argumentative interactions and the social construction knowledge. In N. Muller Mirza, & A. Perret-Clermon (Eds.), Argumentation and education: Theoretical foundations and practices. (pp. 127-144). Springer. https://doi.org/10.1007/978-0-....
 
8.
Baker, M. (2016). The negotiation of meaning in epistemic situations. International Journal of Artificial Intelligence in Education, 26, 133-149. https://doi.org/10.1007/s40593....
 
9.
Baker, M., Andriessen, J., & Schwarz, B. (2019). Collaborative argumentation-based learning. In N. Mercer, R. Wegerif, & L. Major (Eds.), The Routledge international handbook of research on dialogic education (pp. 76-88). Routledge. https://doi.org/10.4324/978042....
 
10.
Billig, M. (1997). Arguing and thinking: A rhetorical approach to social psychology. Cambridge University Press.
 
11.
Bleiler, S., Thompson, D., & Krajcevski, M. (2014). Providing written feedback on students’ mathematical arguments: Proof validations of prospective secondary mathematics teachers. Journal of Mathematics Teacher Education, 17, 105-127. https://doi.org/10.1007/s10857....
 
12.
Boero P., Dapueto C., & Parenti, L. (1996) Didactics of mathematics and the professional knowledge of teachers. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education. Springer. https://doi.org/10.1007/978-94....
 
13.
Castro, W. F., Pino-Fan, L., & Velásquez-Echavarría, H. (2018). A proposal to enhance pre-service teachers noticing. Eurasia Journal of Mathematics, Science & Technology Education, 14(11), em1569. https://doi.org/10.29333/ejmst....
 
14.
Castro, W., Durango-Urrego, J., & Pino-Fan, L. (2021). Preservice teachers' argumentation and some relationships to didactic-mathematical knowledge features. Eurasia Journal of Mathematics, Science and Technology Education, 17(9), em2002. https://doi.org/10.29333/ejmst....
 
15.
Cecchini, M., Tonucci, F., Pinto, M. A., & Dubs, E. (1972). Teacher training, pedagogical method and intellectual development. Instituto de Psicología [Institute of Psychology].
 
16.
Conner, A. (2008). Expanded Toulmin diagrams: A tool for investigating complex activity in classrooms. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (pp. 361-368). Cinvestav-UMSNH.
 
17.
Conner, A. (2022). Adaptive instruction that supports collective argumentation. The Journal of Mathematical Behavior, 66, 100969. https://doi.org/10.1016/j.jmat....
 
18.
Conner, A., & Singletary, L. M. (2021). Teacher support for argumentation: An examination of beliefs and practice. Journal for Research in Mathematics Education, 52(2), 213-247. https://doi.org/10.5951/jresem....
 
19.
Conner, A., Singletary, L., Smith, R., Wagner, P., & Francisco, R. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401-429. https://doi.org/10.1007/s10649....
 
20.
Demiray, E., Isiksal-Bostan, M., & Saygi, E. (2022). Types of global argumentation structures in conjecture-generation activities regarding geometry. International Journal of Science and Mathematics Education, 20, 839-860. https://doi.org/10.1007/s10763....
 
21.
Erduran, S., Guilfoyle, L., & Park, W. (2022). Science and religious education teachers’ views of argumentation and its teaching. Research in Science Education, 52, 655-673. https://doi.org/10.1007/s11165....
 
22.
Evagorou, M., & Osborne, J. (2013). Exploring young students’ collaborative argumentation within a socio-scientific issue. Journal of Research in Science Teaching, 50(2), 209-237. https://doi.org/10.1002/tea.21....
 
23.
Forman, E., Larreamendy-Joerns, J., Stein, M., & Brown, C. (1998). “You’re going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527-548. https://doi.org/10.1016/S0959-....
 
24.
Freeman, J. B. (2005). Systematizing Toulmin’s warrants: An epistemic approach. Argumentation, 19(3), 331-346. https://doi.org/10.1007/s10503....
 
25.
Freinet, C. (1969). Para uma escola do povo [To a people’s school]. Presença [Presence].
 
26.
Gainsburg, J., Fox, J., & Solan, L. (2016). Argumentation and decision making in professional practice. Theory Into Practice, 55(4), 332-341. https://doi.org/10.1080/004058....
 
27.
Gee, J. P. (2008). Social linguistics and literacies: Ideologies in discourses. Routledge. https://doi.org/10.4324/978020....
 
28.
Giannakoulias, E., Mastorides, E., Potari, D., & Zachariades, T. (2010). Studying teachers’ mathematical argumentation in the context of refuting students’ invalid claims. Journal of Mathematical Behavior, 29, 160-168. https://doi.org/10.1016/j.jmat....
 
29.
Goddu, G. C. (2011). Is ‘argument’ subject to the product/process ambiguity? Informal Logic, 31(2), 75-88. https://doi.org/10.22329/il.v3....
 
30.
Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education, 39(1), 127-135. https://doi.org/10.1007/s11858....
 
31.
Godino, J. D., Font, V., Wilhelmi, M. R., & Castro, C. (2009) Aproximación a la dimensión normativa en Didáctica de la Matemática desde un enfoque ontosemiótico [An onto-semiotic approach to the normative dimension in mathematics education]. Enseñanza de las Ciencias, 27(1), 59-76. https://doi.org/10.5565/rev/en....
 
32.
Graff, G. (2003). Clueless in academe: How schooling obscures the life of the mind. Yale University Press.
 
33.
Hershkowitz, R., Tabach, M., Rasmussen, C., & Dreyfus, T. (2014). Knowledge shifts in a probability classroom: A case study coordinating two methodologies. ZDM Mathematics Education, 46, 363-387. https://doi.org/10.1007/s11858....
 
34.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400. https://doi.org/10.5951/jresem....
 
35.
Hunter, A. (2001). Hybrid argumentation systems for structured news reports. The Knowledge Engineering Review, 16(4), 295-329. https://doi.org/10.1017/S02698....
 
36.
Joiner, R., Jones, S., & Doherty, J. (2008). Two studies examining argumentation in asynchronous computer mediated communication. International Journal of Research & Method in Education, 31(3), 243-255. https://doi.org/10.1080/174372....
 
37.
Kazemi, E., Ghousseini, H., Cordero-Siy, E., Prough, S., McVicar, E., & Fox, A. (2021). Supporting teacher learning about argumentation through adaptive, school-based professional development. ZDM Mathematics Education, 53, 435-448. https://doi.org/10.1007/s11858....
 
38.
Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interactions. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp.75-101). Springer. https://doi.org/10.1007/978-94....
 
39.
Kosko, K., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26, 459-476. https://doi.org/10.1007/s13394....
 
40.
Krummheuer, G. (2011). Representation of the notion ‘‘learning-as-participation’’ in everyday situations of mathematics classes. ZDM Mathematics Education, 43, 81-90. https://doi.org/10.1007/s11858....
 
41.
Kuhn, D. (2005). Education for thinking. Harvard University Press.
 
42.
Kuhn, D., Shaw, V., & Felton, M. (1997). Effects of dyadic interaction on argumentative reasoning. Cognition and Instruction, 15, 287-315. https://doi.org/10.1207/s15326....
 
43.
Lin, Pi-Jen., & Tsai, Wen-Huan. (2016). Enhancing students’ mathematical conjecturing and justification in third-grade classrooms: The sum of even/odd numbers. Journal of Mathematics Education, 9(1), 1-15.
 
44.
McAlister, S., Ravenscroft, A., & Scanlon, E. (2004). Combining interaction and context design to support collaborative argumentation using a tool for synchronous CMC. Journal of Computer Assisted Learning, 20(3), 194-204. https://doi.org/10.1111/j.1365....
 
45.
Metaxas, N., Potari, D., & Zachariades, T. (2009). Studying teachers’ pedagogical argumentation. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (pp. 121-128). PME.
 
46.
Metaxas, N., Potari, D., & Zachariades, T. (2016). Analysis of a teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes. Educational Studies in Mathematics, 93, 383-397. https://doi.org/10.1007/s10649....
 
47.
Molina, O., Font, V., & Pino-Fan, L. (2019). Estructura y dinámica de argumentos analógicos, abductivos y deductivos: Un curso de geometría del espacio como contexto de reflexión [Structure and dynamic of analogical, abductive and deductive arguments: A course on solid geometry as a context for reflection]. Enseñanza de las Ciencias [Science Education], 37(1), 93-116. https://doi.org/10.5565/rev/en....
 
48.
Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1-20. https://doi.org/10.1080/247274....
 
49.
Muller-Mirza, N., Perret-Clermont, A.-N., Tartas, V., & Iannaccone A. (2009). Psychosocial processes in argumentation. In N. Muller Mirza, & A.-N. Perret-Clermont (Eds), Argumentation and education. Theoretical foundations and practices (pp. 67-90). Springer. https://doi.org/10.1007/978-0-....
 
50.
Nardi, E., Biza, I., & Zachariades, T. (2012). ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157-173. https://doi.org/10.1007/s10649....
 
51.
Osborne, J. (2010). Arguing to learn in science: The role of collaborative, critical discourse. Science, 328(5977), 463-466. https://doi.org/10.1126/scienc....
 
52.
Pedemonte, B., & Balacheff, N. (2016). Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin model. The Journal of Mathematical Behavior, 41, 104-122. https://doi.org/10.1016/j.jmat....
 
53.
Peldszus, A., & Stede, M. (2016). An annotated corpus of argumentative microtexts. In Argumentation and Reasoned Action: Proceedings of the 1st European Conference on Argumentation (Vol. 2, pp. 801-816). College Publications.
 
54.
Pino-Fan, L., & Godino, J. D. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor [An expanded view of teachers’ didactic–mathematical knowledge]. PARADIGMA, 36(1), 87-109.
 
55.
Pino-Fan, L., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/euras....
 
56.
Pino-Fan, L., Castro, W., & Font, V. (2022). A macro tool to characterize and develop key competencies for the mathematics teacher’ practice. International Journal of Science and Mathematics Education, 21, 1407-1432. https://doi.org/10.1007/s10763....
 
57.
Pino-Fan, L., Godino, J., & Font, V. (2016). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education, 21, 63-94. https://doi.org/10.1007/s10857...- 9349-8.
 
58.
Planas, N., García-Honrado, I., & Arnal-Bailera, A. (2018). El discurso matemático del profesor: ¿Cómo se produce en clase y cómo se puede investigar? [The teacher’s mathematical discourse: How is it produced in the classroom and how can it be researched?] Enseñanza de las Ciencias [Science Education], 36(1), 45-60. https://doi.org/10.5565/rev/en....
 
59.
Rigotti, E., & Greco-Morasso, S. (2009). Argumentation as an object of interest and as a social and cultural resource. In N. Muller Mirza, & A. N. Perret-Clermont (Eds.), Argumentation and education: Theoretical foundations and practices. Springer. https://doi.org/10.1007/978-0-....
 
60.
Rowland, T. (2000). The pragmatics of mathematics education: Vagueness in mathematical discourse. Falmer.
 
61.
Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. https://doi.org/10.1007/s10857....
 
62.
Ruthven, K., & Hofmann, R. (2016). A case study of epistemic order in mathematics classroom dialogue. PNA Revista de Investigación en Didáctica de la Matemática [PNA Research Journal on Mathematics Didactics], 11(1), 5-33. https://doi.org/10.30827/pna.v....
 
63.
Ryve, A. (2011). Discourse research in mathematics education: A critical evaluation of 108 journal articles. Journal for Research in Mathematics Education, 42(2), 167-198. https://doi.org/10.5951/jresem....
 
64.
Sampson, V., & Schleigh, S. (2013). Scientific argumentation in biology: 30 classroom activities. National Science Teachers Association.
 
65.
Schoenfeld, A. H., & Kilpatrick, J. (2008). Towards a theory of proficiency in teaching mathematics. In D. Tirosh, & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 321-354). Sense Publishers. https://doi.org/10.1163/978908....
 
66.
Schwartz, B. B., Neuman, Y., Gil, J., & Ilya, M. (2003). Construction of collective and individual knowledge in argumentative activity. The Journal of the Learning Sciences, 12(2), 219-256. https://doi.org/10.1207/S15327....
 
67.
Sfard A. (2020) Commognition. In S. Lerman (Eds.), Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-3-....
 
68.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/001318....
 
69.
Silverman, J., & Thompson, P. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499-511. https://doi.org/10.1007/s10857....
 
70.
Simon, S. (2008). Using Toulmin’s argument pattern in the evaluation of argumentation in school science. International Journal of Research & Method in Education, 31(3), 277-289. https://doi.org/10.1080/174372....
 
71.
Solar, H., & Deulofeu, J. (2016). Condiciones para promover el desarrollo de la competencia de argumentación en el aula de matemáticas. [Conditions to promote the development of argumentation competence in the mathematics classroom]. Bolema, 30, 1092-1112. https://doi.org/10.1590/1980-4....
 
72.
Staples, M., & Newton, J. (2016). Teachers’ contextualization of argumentation in the mathematics classroom. Theory into Practice, 55(4), 294-301. https://doi.org/10.1080/004058....
 
73.
Terenzini, P. T., Springer, L., Pascarella, E. T., & Nora, A. (1995). Academic and out-of-class influences on students’ intellectual orientations. The Review of Higher Education, 19(1), 23-44. https://doi.org/10.1353/rhe.19....
 
74.
Toro, J., & Castro, W. (2020). Condiciones que activan la argumentación del profesor de matemáticas durante la discusión de tareas en clase [Conditions that activate the argumentation of the mathematics teacher in classroom]. Revista Chilena de Educación Matemática, 12(1), 35-44. https://doi.org/10.46219/rechi....
 
75.
Toulmin, S. (2007). Los usos de la argumentación [The uses of argument]. Ediciones Península [Peninsula Editions].
 
76.
van Eemeren, F., & Grootendorst, R. (2011). Una teoría sistemática de la argumentación. La perspectiva pragmadialéctica [A systematic theory of argumentation. The pragma-dialectical approach]. Editorial Biblos.
 
77.
van Eemeren, F., Grassen, B., Krabbe, E., Snoeck Henkemans, F., Verheij, B. & Wagemans, J. (2014). Handbook of argumentation theory. Springer. https://doi.org/10.1007/978-90....
 
78.
van Eemeren, F., Grootendorst, R. y Snoeck, F. (2006). Argumentación: Análisis, evaluación, presentación [Argumentation: Analysis, evaluation, presentation]. Editorial Biblos.
 
79.
Vygotsky, L. S. (1978). Mind in society. Harvard University Press.
 
80.
Vygotsky, L. S. (1986). Mind in society. The development of higher psychological processes. Harvard University Press.
 
81.
Weinberger, A., & Fischer, F. (2006). A framework to analyze argumentative knowledge construction in computer-supported collaborative learning. Computers & Education, 46, 71-95. https://doi.org/10.1016/j.comp....
 
82.
Willard, C. A. (1976). On the utility of descriptive diagrams for the analysis and criticism of arguments. Communication Monographs, 43, 308-319. https://doi.org/10.1080/036377....
 
83.
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior, 21, 21, 423-440. https://doi.org/10.1016/S0732-....
 
84.
Yopp, D. (2012). Valuing informal arguments and empirical investigations during collective argumentation. PRIMUS, 22(8), 643-663. https://doi.org/10.1080/105119....
 
85.
Zarefsky, D. (2014). Product, process, or point of view? In Rhetorical perspectives on argumentation. Argumentation library. Springer. https://doi.org/10.1007/978-3-....
 
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