Commognition as an approach to studying proof teaching in university mathematics lectures

Thomais Karavi; Angeliki Mali; Lucy Avraamidou

doi:10.29333/ejmste/12173

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Thomais Karavi ¹ ^* , Angeliki Mali ¹ , Lucy Avraamidou ¹

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¹ University of Groningen, Groningen, THE NETHERLANDS^* Corresponding Author

Abstract

In this position paper, we propose commognition for the study of proof teaching at university lectures through an integrative literature review. We critically examine studies that focused on proof teaching but did not use the commognitive framework. Through this examination, we gain an understanding of the pedagogical aspects of proof teaching and address gaps in the literature. After we introduce the key principles of the commognitive framework, we review a set of studies that used commognition for the investigation of lecture-type teaching in higher education. In reviewing these studies, we pay special attention to the added value of the use of commognition. We conclude by proposing an approach to the study of proof teaching by using the commognitive framework. This approach offers insights into opportunities provided by lecturers for the de-ritualization of proving routines.

Keywords

commognition
de-ritualization
proving routines
university mathematics
lecture

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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 18, Issue 7, July 2022, Article No: em2132

https://doi.org/10.29333/ejmste/12173

Publication date: 25 Jun 2022

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Article Downloads: 1330

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References

Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. SAGE.
Coles, A., & Sinclair, N. (2019). Ritualisation in early number work. Educational Studies in Mathematics, 101(2), 177-194. https://doi.org/10.1007/s10649-018-9815-6
de Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24(24), 17-24.
Fukawa-Connelly, T. P. (2012). A case study of one instructor’s lecture-based teaching of proof in abstract algebra: Making sense of her pedagogical moves. Educational Studies in Mathematics, 81(3), 325-345. https://doi.org/10.1007/s10649-012-9407-9
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
Gueudet, G., Bosch, M., DiSessa, A. A., Kwon, O. N., & Verschaffel, L. (2016). Transitions in mathematics education. Springer. https://doi.org/10.1007/978-3-319-31622-2
Hemmi, K. (2010). Three styles characterising mathematicians’ pedagogical perspectives on proof. Educational Studies in Mathematics, 75(3), 271-291. https://doi.org/10.1007/s10649-010-9256-3
Heyd-Metzuyanim, E., & Graven, M. (2019). Rituals and explorations in mathematical teaching and learning: introduction to the special issue. Educational Studies in Mathematics, 101(2), 141-151. https://doi.org/10.1007/s10649-019-09890-x
Heyd-Metzuyanim, E., Tabach, M., & Nachlieli, T. (2016). 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
Jaworski, B., Mali, A., & Petropoulou, G. (2017). Critical theorising from studies of undergraduate mathematics teaching for students’ meaning making in mathematics. International Journal of Research in Undergraduate Mathematics Education, 3(1), 168-197. https://doi.org/10.1007/s40753-016-0044-z
Kieran, C., Forman, E., & Sfard, A. (2002). Learning discourse. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48085-9
Kontorovich, I. (2021). Minding mathematicians’ discourses in investigations of their feedback on students’ proofs: A case study. Educational Studies in Mathematics, 107, 213-234. https://doi.org/10.1007/s10649-021-10035-2
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press. https://doi.org/10.1017/CBO9780511815355
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
Lew, K., Fukawa-Connelly, T. P., Mejia-Ramos, J. P., & Weber, K. (2016). Lectures in advanced mathematics: Why students might not understand what the mathematics professor is trying to convey. Journal for Research in Mathematics Education, 47(2), 162-198. https://doi.org/10.5951/jresematheduc.47.2.0162
McCloskey, A., Lloyd, G., & Lynch, C. (2019). Theorizing mathematics instruction using ritual: Tensions in teaching fractions in a fifth grade classroom. Educational Studies in Mathematics, 101(2), 195-213. https://doi.org/10.1007/s10649-017-9779-y
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
Park, J. (2015). Is the derivative a function? If so, how do we teach it? Educational Studies in Mathematics, 89(2), 233-250. https://doi.org/10.1007/s10649-015-9601-7
Petropoulou, G., Jaworski, B., Potari, D., & Zachariades, T. (2020). Undergraduate mathematics teaching in first year lectures: Can it be responsive to student learning needs? International Journal of Research in Undergraduate Mathematics Education, 6(3), 347-374. https://doi.org/10.1007/s40753-020-00111-y
Pinto, A. (2019). Variability in the formal and informal content instructors convey in lectures. The Journal of Mathematical Behavior, 54, 100680. https://doi.org/10.1016/j.jmathb.2018.11.001
Robertson, S. A., & Graven, M. (2019). Exploratory mathematics talk in a second language: A sociolinguistic perspective. Educational Studies in Mathematics, 101(2), 215-232. https://doi.org/10.1007/s10649-018-9840-5
Selden, A. (2011). Transitions and proof and proving at tertiary level. In G. Hanna, & M. de Villiers (Eds.), Proof and proving in mathematics education (pp. 391-420). Springer. https://doi.org/10.1007/978-94-007-2129-6_17
Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. In C. Kieran, E. Forman, & A. Sfard (Eds.), Learning discourse: Discursive approaches to research in mathematics education (pp. 13-57). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48085-9_1
Sfard, A. (2008). Thinking as communicating: Human development, development of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Sfard, A. (2014). University mathematics as a discourse–why, how, and what for? Research in Mathematics Education, 16(2), 199-203. https://doi.org/10.1080/14794802.2014.918339
Sfard, A. (2017). Ritual for ritual, exploration for exploration or what the learners get is what you get from them in return. In J. Adler, & A. Sfard (Eds.), Research for educational change: Transforming researchers’ insights into improvement in mathematics teaching and learning (pp. 39-63). Routledge.
Sfard, A. (2020). Commognition. Encyclopedia of Mathematics Education, 95-101. https://doi.org/10.1007/978-3-030-15789-0_100031
Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different? –Early numerical thinking revisited. Cognition and Instruction, 23(2), 237-309. https://doi.org/10.1207/s1532690xci2302_3
Snyder, H. (2019). Literature review as a research methodology: An overview and guidelines. Journal of Business Research, 104, 333-339. https://doi.org/10.1016/j.jbusres.2019.07.039
Suritsky, S. K., & Hughes, C. A. (1991). Benefits of notetaking: Implications for secondary and postsecondary students with learning disabilities. Learning Disability Quarterly, 14(1), 7-18. https://doi.org/10.2307/1510370
Viirman, O. (2014). The functions of function discourse–University mathematics teaching from a commognitive standpoint. International Journal of Mathematical Education in Science and Technology, 45(4), 512-527. https://doi.org/10.1080/0020739X.2013.855328
Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: A commognitive analysis. International Journal of Mathematical Education in Science and Technology, 46(8), 1165-1181. https://doi.org/10.1080/0020739X.2015.1034206
Viirman, O. (2021). University mathematics lecturing as modelling mathematical discourse. International Journal of Research in Undergraduate Mathematics Education, 7, 466-489. https://doi.org/10.1007/s40753-021-00137-w
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. (2004). Traditional instruction in advanced mathematics courses: A case study of one professor’s lectures and proofs in an introductory real analysis course. The Journal of Mathematical Behavior, 23(2), 115-133. https://doi.org/10.1016/j.jmathb.2004.03.001
Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge University Press. https://doi.org/10.1017/CBO9780511803932
Williams, R. L., & Eggert, A. C. (2002). Notetaking in college classes: Student patterns and instructional strategies. The Journal of General Education, 51(3), 173-199. https://doi.org/10.1353/jge.2003.0006

How to cite this article

APA

Karavi, T., Mali, A., & Avraamidou, L. (2022). Commognition as an approach to studying proof teaching in university mathematics lectures. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2132. https://doi.org/10.29333/ejmste/12173

Vancouver

Karavi T, Mali A, Avraamidou L. Commognition as an approach to studying proof teaching in university mathematics lectures. EURASIA J Math Sci Tech Ed. 2022;18(7):em2132. https://doi.org/10.29333/ejmste/12173

AMA

Karavi T, Mali A, Avraamidou L. Commognition as an approach to studying proof teaching in university mathematics lectures. EURASIA J Math Sci Tech Ed. 2022;18(7), em2132. https://doi.org/10.29333/ejmste/12173

Chicago

Karavi, Thomais, Angeliki Mali, and Lucy Avraamidou. "Commognition as an approach to studying proof teaching in university mathematics lectures". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 7 (2022): em2132. https://doi.org/10.29333/ejmste/12173

Harvard

Karavi, T., Mali, A., and Avraamidou, L. (2022). Commognition as an approach to studying proof teaching in university mathematics lectures. Eurasia Journal of Mathematics, Science and Technology Education, 18(7), em2132. https://doi.org/10.29333/ejmste/12173

MLA

Karavi, Thomais et al. "Commognition as an approach to studying proof teaching in university mathematics lectures". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 7, 2022, em2132. https://doi.org/10.29333/ejmste/12173