Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback

Jorge Gaona; Romina Menares

doi:10.29333/ejmste/11425

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Jorge Gaona ¹ ^* , Romina Menares ²

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¹ Centro de Estudios Avanzados, Universidad de Playa Ancha, CHILE² Instituto de Matemáticas, Universidad de Valparaíso, CHILE^* Corresponding Author

Abstract

This article reports the argumentation work of a group of trainee mathematics teachers in an experiment carried out in a virtual class (due to the emergence of COVID-19) during 2020. They worked with a task on fractions in an online assessment system with questions with random parameters and infinite possible correct answers. This was followed by a discussion of the strategies and the justifications, arguments and validations of these strategies and other conjectures that emerged. This article analyzes this work from a qualitative approach using the Mathematical Working Space as a theoretical framework. The results show that the discussion work led the trainee teachers to find interpretations for the algorithms processed by the computer, enhancing epistemic discourse and argumentation in the context of the use of technological artifacts. In turn, the same discourses allowed the future teachers to instrumentalize the processes to be used in new tasks.

Keywords

mathematics education
digital technology
proof and discourse
task design
online teaching/learning strategies

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 17, Issue 12, December 2021, Article No: em2055

https://doi.org/10.29333/ejmste/11425

Publication date: 17 Dec 2021

Article Views: 1828

Article Downloads: 1004

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245-274. https://doi.org/10.1023/A:1022103903080
Bachelard. (1938). La formation de l’esprit scientifique. Paris Vrin.
Balacheff, N. (1987). Processus de preuve et situations de validation [Proof process and validation situations]. Educational Studies in Mathematics, 18(2), 147-176. https://doi.org/10.1007/BF00314724
Balacheff, N. (2000). Procesos de prueba en los alumnos de matemáticas [Testing processes in mathematics students]. Una empresa docente.
Belin, M., & Akar, G. K. (2020). The effect of quantitative reasoning on prospective mathematics teachers’ proof comprehension: The case of real numbers. Journal of Mathematical Behavior, 57(June 2018), 100757. https://doi.org/10.1016/j.jmathb.2020.100757
Boyatzis, R. (1998). Transforming qualitative information: Thematic analysis and code development. Sage Publications.
Brousseau, G. (1998). Théorie des situations didactiques [Theory of didactic situations] (La pensée).
Coutat, S., & Richard, P. (2011). Les figures dynamiques dans un espace de travail mathématique pour l’apprentissage des propriétés géométriques [Dynamic figures in a mathematical workspace for learning geometric properties]. Annales de Didactique et de Sciences Cognitives, 16, 97-126.
Creswell, J. W., & Poth, C. N. (2017). Qualitative inquiry and research design: Choosing among five approaches. In Sage Publications.
Duval, R. (1993). Argumenter, demontrer, expliquer: continuité ou rupture cognitive? [Argue, demonstrate, explain: continuity or cognitive rupture ?] Petit x, 31, 37-61.
Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM - International Journal on Mathematics Education, 44(6), 747-759. https://doi.org/10.1007/s11858-012-0425-y
Flores, J., Gaona, J., & Richard, P. (2022). Mathematical work in the digital age: Variety of tools and the role of geneses. In A. Kuzniak, E. Montoya, & P. Richard (Eds.), Mathematical work in educational context - the Mathematical Working Space Theory perspective. Springer International Publishing.
Gaona, J. (2020). Panorama sobre los sistemas de evaluación automática en línea en matemáticas [An overview of online self-assessment systems in mathematics]. Revista Paradigma, 16, 53-81. https://doi.org/10.37618/PARADIGMA.1011-2251.0.p53-80.id853
Gaona, J., Hernández, R., Guevara, F., & Bravo, V. (2021). Influence of a function’s coefficients and feedback of the mathematical work when reading a graph in an online assessment system. https://arxiv.org/pdf/2107.11448.pdf
Hanna, G. (2001). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5-23. https://doi.org/10.1023/A:1012737223465
Henríquez-Rivas, C., & Montoya-Delgadillo, E. (2015). Espacios de trabajo geométrico sintético y analítico de profesores y su práctica en el aula [Synthetic and analytical geometric workspaces of teachers and their practice in the classroom]. Enseñanza de Las Ciencias. Revista de Investigación y Experiencias Didácticas, 33(2), 51. https://doi.org/10.5565/rev/ensciencias.1408
Henríquez-Rivas, C., & Montoya-Delgadillo, E. (2016). El trabajo matemático de profesores en el tránsito de la geometría sintética a la analítica en el liceo [The mathematical work of teachers in the transition from synthetic geometry to analytics in high school]. Bolema - Mathematics Education Bulletin, 30(54), 45-66. https://doi.org/10.1590/1980-4415v30n54a03
Kuzniak, A., & Richard, P. (2014). Espacios de trabajo matemático. Puntos de vista y perspectivas [Mathematical workspaces. Points of view and perspectives]. Revista Latinoamericana de Investigación En Matemática Educativa, 17(4), 1-8. https://doi.org/10.12802/relime.13.1741a
Kuzniak, A., Nechache, A., & Drouhard, J. P. (2016a). Understanding the development of mathematical work in the context of the classroom. ZDM - Mathematics Education, 48(6), 861-874. https://doi.org/10.1007/s11858-016-0773-0
Kuzniak, A., Tanguay, D., & Elia, I. (2016b). Mathematical working spaces in schooling: An introduction. ZDM - Mathematics Education, 48(6), 721-737. https://doi.org/10.1007/s11858-016-0812-x
Lo, J. J., Grant, T. J., & Flowers, J. (2008). Challenges in deepening prospective teachers’ understanding of multiplication through justification. Journal of Mathematics Teacher Education, 11(1), 5-22. https://doi.org/10.1007/s10857-007-9056-6
Mena-Lorca, A., Mena-Lorca, J., Montoya-Delgadillo, E., Morales, A., & Parraguez, M. (2014). El obstáculo epistemológico del infinito actual: Persistencias y categorías de análisis [The epistemological obstacle of the current infinity: Persistence and categories of analysis]. Revista Latinoamericana de Investigación En Matemática Educativa, 17(1), 9-32. https://doi.org/10.12802/relime.13.1832
MINEDUC, C. de E. (2020). Impacto del Covid-19 en los resultados de aprendizaje y escolaridad en Chile [Impact of Covid-19 on Learning and Schooling Outcomes in Chile]. https://chile.un.org/es/102663-impacto-del-covid-19-en-los-resultados-de-aprendizaje-y-escolaridad-en-chile
MINEDUC. (2019). Bases Curriculares 3^o y 4^o medio [Curricular bases 3rd and 4th grade].
Montoya-Delgadillo, E., Mena-Lorca, A., & Mena-Lorca, J. (2014). Circulaciones y génesis en el espacio de trabajo matemático [Circulations and genesis in the mathematical workspace]. Revista Latinoamericana de Investigación En Matemática Educativa, 17(4-1), 191-210. https://doi.org/10.12802/relime.13.1749
Montoya-Delgadillo, E., Mena-Lorca, J., & Mena-Lorca, A. (2016). Estabilidad epistemológica del profesor debutante y espacio de trabajo matemático [Epistemological stability of the beginning professor and mathematical workspace]. Bolema - Mathematics Education Bulletin, 30(54), 188-203. https://doi.org/10.1590/1980-4415v30n54a09
Nagel, K., Schyma, S., Cardona, A., & Reiss, K. (2018). Análisis de la argumentación matemática de estudiantes de primer año [Analysis of the mathematical argumentation of first-year students]. Pensamiento Educativo, 55(1), 1-13. https://doi.org/10.7764/PEL.55.1.2018.10
Peirce, C. S. (1932). Collected papers of Charles Sanders Peirce. II: Elements of logic. Harvard University Press.
Peña, C. N., Pino-Fan, L. R., & Assis, A. (2021). Normas que regulan la gestión de clases virtuales de matemáticas en el contexto COVID-19 [Norms that regulate the management of virtual mathematics classes in the context of COVID-19]. Uniciencia, 35(2), 1-20. https://doi.org/10.15359/ru.35-2.21
Pizarro, N., Albarracín, L., & Gorgorió, N. (2018). Actividades de estimación de medida: La interpretación de los docentes de Educación Primaria [Measurement estimation activities: The interpretation of primary education teachers]. Bolema: Boletim de Educação Matemática, 32(62), 1177-1197. https://doi.org/10.1590/1980-4415v32n62a21
Radford, L. (2014). On the role of representations and artefacts in knowing and learning. Educational Studies in Mathematics, 85(3), 405-422. https://doi.org/10.1007/s10649-013-9527-x
Rodríguez-Jara, M. A., Mena-Lorca, A., Mena-Lorca, J., Vásquez, P., & del Valle, M. (2019). Construcción cognitiva del conjunto solución de un sistema de ecuaciones lineales con dos incógnitas [Cognitive construction of the solution set of a system of linear equations with two unknowns]. Enseñanza de Las Ciencias, 1, 71-92. https://doi.org/10.5565/rev/ensciencias.2194
Solar, H. (2018). Implicaciones de la argumentación en el aula de matemáticas [Implications of argumentation in the mathematics classroom]. Revista Colombiana de Educación, 1(74), 155-176. https://doi.org/10.17227/rce.num74-6902
Solar, H., & Deulofeu, J. (2016). Conditions to promote the development of argumentation competence in the mathematics classroom. Bolema: Boletim de Educação Matemática, 30(56), 1092-1112. https://doi.org/10.1590/1980-4415v30n56a13
Stupel, M., & Ben-Chaim, D. (2017). Using multiple solutions to mathematical problems to develop pedagogical and mathematical thinking: A case study in a teacher education program. Investigations in Mathematics Learning, 9(2), 86-108. https://doi.org/10.1080/19477503.2017.1283179
Stylianides, A., & Stylianides, G. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72(2), 237-253. https://doi.org/10.1007/s10649-009-9191-3
Stylianides, A., Bieda, K., & Morselli, F. (2016). Proof and argumentation in mathematics education research. In Á. Gutierres, G. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (Issue Icmi, pp. 315-351). https://doi.org/10.1007/978-94-6300-561-6_9
Stylianides, G., & Stylianides, A. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40(3), 314-352. https://doi.org/10.5951/jresematheduc.40.3.0314
Stylianides, G., Stylianides, A., & Shilling-Traina, L. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490. https://doi.org/10.1007/s10763-013-9409-9
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423-440. https://doi.org/10.1016/S0732-3123(02)00143-8
Zengin, Y. (2017). The effects of GeoGebra software on pre-service mathematics teachers’ attitudes and views toward proof and proving. International Journal of Mathematical Education in Science and Technology, 48(7), 1002-1022. https://doi.org/10.1080/0020739X.2017.1298855

How to cite this article

APA

Gaona, J., & Menares, R. (2021). Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2055. https://doi.org/10.29333/ejmste/11425

Vancouver

Gaona J, Menares R. Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback. EURASIA J Math Sci Tech Ed. 2021;17(12):em2055. https://doi.org/10.29333/ejmste/11425

AMA

Gaona J, Menares R. Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback. EURASIA J Math Sci Tech Ed. 2021;17(12), em2055. https://doi.org/10.29333/ejmste/11425

Chicago

Gaona, Jorge, and Romina Menares. "Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 12 (2021): em2055. https://doi.org/10.29333/ejmste/11425

Harvard

Gaona, J., and Menares, R. (2021). Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2055. https://doi.org/10.29333/ejmste/11425

MLA

Gaona, Jorge et al. "Argumentation of Prospective Mathematics Teachers in Fraction Tasks Mediated by an Online Assessment System With Automatic Feedback". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 12, 2021, em2055. https://doi.org/10.29333/ejmste/11425