Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition

Verónica Martín-Molina; Alfonso J. González-Regaña; Rocío Toscano; José María Gavilán-Izquierdo

doi:10.29333/ejmste/9159

Full Text (PDF)

Verónica Martín-Molina ¹ ^* , Alfonso J. González-Regaña ¹ , Rocío Toscano ¹ , José María Gavilán-Izquierdo ¹

More Detail

¹ Departamento de Didáctica de las Matemáticas, Universidad de Sevilla, SPAIN^* Corresponding Author

Abstract

Undergraduate students’ engagement with mathematical discourse when defining geometric solids is analysed and compared with what their lecturers expect them to do. The theory of commognition is adopted as the theoretical framework, which permits the characterisation and comparison of their discursive activities, and may lead to the identification of potential commognitive conflicts. The participants were forty-five undergraduate students (primary pre-service teachers) and their lecturers. A worksheet with questions about defining geometric solids was used as a data collection instrument. The students, in small groups, had to discuss and write their answers, and the lecturers were asked what they expected from their students. Results show three main areas of mismatch between students’ engagement in mathematical discourse and what their lecturers expected from them. There is no clear consensus across the students on how to define or on what a definition is or on which criterion to use when selecting a definition.

Keywords

defining
mathematical discourse
theory of commognition
undergraduate students

License

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, 2020, Volume 16, Issue 12, Article No: em1917

https://doi.org/10.29333/ejmste/9159

Publication date: 14 Nov 2020

Article Views: 1311

Article Downloads: 737

Open Access References How to cite this article

References

Biza, I., Giraldo, V., Hochmuth, R., Khakbaz, A., & Rasmussen, C. (2016). Research on teaching and learning mathematics at the tertiary level: State-of-the-art and looking ahead. Springer. https://doi.org/10.1007/978-3-319-41814-8
Cooper, J., & Karsenty, R. (2018). Can teachers and mathematicians communicate productively? The case of division with remainder. Journal of Mathematics Teacher Education, 21(3), 237-261. https://doi.org/10.1007/s10857-016-9358-7
De Villiers, M. (1998). To teach definition or to teach to define? In A. Olivier & K. Newstead (Eds.), Proceedings of the 22th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 248-255). PME.
Escudero, I., Gavilán, J. M., & Sánchez-Matamoros, G. (2014). Una aproximación a los cambios en el discurso matemático generados en el proceso de definir [An approach to changes in the mathematical discourse generated in the process of defining]. Revista Latinoamericana de Investigación en Matemática Educativa, 17(1), 7-32. https://doi.org/10.1080/14794802.2014.918338
Fernández-León, A., Gavilán-Izquierdo, J. M., González-Regaña, A. J., Martín-Molina, V., & Toscano, R. (2019). Identifying routines in the discourse of undergraduate students when defining. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-019-00301-1
Freudenthal, H. (1973). Mathematics as an educational task. Reidel. https://doi.org/10.1007/978-94-010-2903-2
Gavilán, J. M., Barroso, R., Ariza, A., & Sánchez, A. (2002). Laboratorio virtual de matemáticas II [Virtual laboratory of Mathematics II]. In J. M. Mesa, R. J. Castañeda, & L. M. Villar (Eds.), La Universidad de Sevilla y la innovación docente, curso 2001-2002 (Vol. 1, pp. 77-85). Instituto de Ciencias de la Educación de la Universidad de Sevilla.
Gavilán-Izquierdo, J. M., Martín-Molina, V., González-Regaña, A. J., Toscano, R., & Fernández-León, A. (2019). Cómo construyen definiciones matemáticas los estudiantes para maestro: Una aproximación sociocultural [How pre-service teachers construct mathematical definitions: A sociocultural approach]. In E. Badillo Jiménez, N. Climent Rodríguez, C. Fernández Verdú, & M. T. González Astudillo (Eds.), Investigación sobre el profesor de matemáticas: Práctica de aula, conocimiento, competencia y desarrollo profesional (pp. 135-155). Ediciones Universidad de Salamanca.
Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82(3), 439-453. https://doi.org/10.1007/s10649-012-9438-2
Heyd-Metzuyanim, E., Tabach, M., & Nachlieli, T. (2015). Opportunities for learning given to prospective mathematics teachers: Between ritual and explorative instruction. Journal of Mathematics Teacher Education, 19(6), 547-574. https://doi.org/10.1007/s10857-015-9311-1
Hohenwarter, M., Borcherds, M., Ancsin, G., Bencze, B., Blossier, M., Elias, J., Frank, K., Gal, L., Hofstätter, A., Jordan, F., Konecny, Z., Kovacs, Z., Lettner, E., Lizelfelner, S., Parisse, B., Solyom-Gecse, C., Stadlbauer, C., & Tomaschko, M. (2018). GeoGebra (version 5.0.507.0). http://www.geogebra.org
Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students’ first encounter with the subgroup test. Mathematics Education Research Journal, 30(2), 117-142. https://doi.org/10.1007/s13394-017-0222-6
Lavie, I., Steiner, A., & Sfard, A. (2019). Routines we live by: From ritual to exploration. Educational Studies in Mathematics, 101(2), 153-176. https://doi.org/10.1007/s10649-018-9817-4
Martín-Molina, V., González-Regaña, A. J., & Gavilán-Izquierdo, J. M. (2018). Researching how professional mathematicians construct new mathematical definitions: A case study. International Journal of Mathematical Education in Science and Technology, 49(7), 1069-1082. https://doi.org/10.1080/0020739X.2018.1426795
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education, 16(2), 182-198. https://doi.org/10.1080/14794802.2014.918338
Ouvrier-Buffet, C. (2011). A mathematical experience involving defining processes: In-action definitions and zero-definitions. Educational Studies in Mathematics, 76(2), 165-182. https://doi.org/10.1007/s10649-010-9272-3
Rasmussen, C., Zandieh, M., King, K., & Teppo, A. (2005). Advancing mathematical activity: A practice-oriented view of advanced mathematical thinking. Mathematical Thinking and Learning, 7(1), 51-73. https://doi.org/10.1207/s15327833mtl0701_4
Sánchez, V., & García, M. (2014). Socio-mathematical and mathematical norms related to definition in pre-service primary teachers’ discourse. Educational Studies in Mathematics, 85(2), 305-320. https://doi.org/10.1007/s10649-013-9516-0
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 567-615. https://doi.org/10.1080/10508400701525253
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Stadler, E. (2011). The same but different—Novice university students solve a textbook exercise. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 2083-2092). University of Rzeszów and ERME.
Tabach, M., & Nachlieli, T. (2015). Classroom engagement towards using definitions for developing mathematical objects: The case of function. Educational Studies in Mathematics, 90(2), 163-187. https://doi.org/10.1007/s10649-015-9624-0
Thoma, A., & Nardi, E. (2016). A commognitive analysis of closed-book examination tasks and lecturers’ perspectives. In E. Nardi, C. Winsløw, & T. Hausberger (Eds.), Proceedings of the First Conference of the International Network for Didactic Research in University Mathematics (pp. 306-315). University of Montpellier and INDRUM.
Thoma, A., & Nardi, E. (2018). Transition from school to university mathematics: Manifestations of unresolved commognitive conflict in first year students’ examination scripts. International Journal of Research in Undergraduate Mathematics Education, 4(1), 161-180. https://doi.org/10.1007/s40753-017-0064-3
Toscano, R., Gavilán-Izquierdo, J. M., & Sánchez, V. (2019). A study of pre-service primary teachers’ discourse when solving didactic-mathematical tasks. EURASIA Journal of Mathematics, Science and Technology Education, 15(11), em1762, 1-16. https://doi.org/10.29333/ejmste/108631
Viirman, O., & Nardi, E. (2019). Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics, 101(2), 233-252. https://doi.org/10.1007/s10649-018-9861-0
Weber, K., & Mejia-Ramos, J. P. (2013). Effective but underused strategies for proof comprehension. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 260-267). University of Illinois at Chicago.
Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning. The Journal of Mathematical Behavior, 29(2), 57-75. https://doi.org/10.1016/j.jmathb.2010.01.001
Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317-347.

How to cite this article

APA

Martín-Molina, V., González-Regaña, A. J., Toscano, R., & Gavilán-Izquierdo, J. M. (2020). Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), em1917. https://doi.org/10.29333/ejmste/9159

Vancouver

Martín-Molina V, González-Regaña AJ, Toscano R, Gavilán-Izquierdo JM. Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition. EURASIA J Math Sci Tech Ed. 2020;16(12):em1917. https://doi.org/10.29333/ejmste/9159

AMA

Martín-Molina V, González-Regaña AJ, Toscano R, Gavilán-Izquierdo JM. Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition. EURASIA J Math Sci Tech Ed. 2020;16(12), em1917. https://doi.org/10.29333/ejmste/9159

Chicago

Martín-Molina, Verónica, Alfonso J. González-Regaña, Rocío Toscano, and José María Gavilán-Izquierdo. "Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition". Eurasia Journal of Mathematics, Science and Technology Education 2020 16 no. 12 (2020): em1917. https://doi.org/10.29333/ejmste/9159

Harvard

Martín-Molina, V., González-Regaña, A. J., Toscano, R., and Gavilán-Izquierdo, J. M. (2020). Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition. Eurasia Journal of Mathematics, Science and Technology Education, 16(12), em1917. https://doi.org/10.29333/ejmste/9159

MLA

Martín-Molina, Verónica et al. "Differences between how Undergraduate Students Define Geometric Solids and what their Lecturers Expect from them through the Lens of the Theory of Commognition". Eurasia Journal of Mathematics, Science and Technology Education, vol. 16, no. 12, 2020, em1917. https://doi.org/10.29333/ejmste/9159