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RESEARCH PAPER
Commognition as an approach to studying proof teaching in university mathematics lectures
1
University of Groningen, Groningen, THE NETHERLANDS
Publication date: 2022-06-25
EURASIA J. Math., Sci Tech. Ed 2022;18(7):em2132
KEYWORDS
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.
REFERENCES (37)
1.
Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. SAGE.
2.
Coles, A., & Sinclair, N. (2019). Ritualisation in early number work. Educational Studies in Mathematics, 101(2), 177-194. https://doi.org/10.1007/s10649....
3.
de Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24(24), 17-24.
4.
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....
5.
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....
6.
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-....
7.
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....
8.
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....
9.
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....
10.
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....
11.
Kieran, C., Forman, E., & Sfard, A. (2002). Learning discourse. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-....
12.
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....
13.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press. https://doi.org/10.1017/CBO978....
14.
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....
15.
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/jresem....
16.
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....
17.
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/10.1080/147948....
18.
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....
19.
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....
20.
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.jmat....
21.
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....
22.
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....
23.
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-....
24.
Sfard, A. (2008). Thinking as communicating: Human development, development of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO978....
25.
Sfard, A. (2014). University mathematics as a discourse–why, how, and what for? Research in Mathematics Education, 16(2), 199-203. https://doi.org/10.1080/147948....
26.
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.
27.
Sfard, A. (2020). Commognition. Encyclopedia of Mathematics Education, 95-101. https://doi.org/10.1007/978-3-....
28.
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/s15326....
29.
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.jbus....
30.
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/10.2307/151037....
31.
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/10.1080/002073....
32.
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/10.1080/002073....
33.
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....
34.
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....
35.
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.jmat....
36.
Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge University Press. https://doi.org/10.1017/CBO978....
37.
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.20....
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