Abstract
In this chapter, we give an example of practice-oriented research in small group tutorials at university level, focusing on the tutor’s pedagogical practice for promoting her students’ mathematics meaning-making (MMM) and her own developing knowledge in teaching practice. In particular, we analyse, using grounded theory techniques, episodes from a tutorial in Linear Algebra. We focus on the interactions between the tutor and the students and the tutor’s interpretations of students’ MMM. Adopting an Activity Theory perspective, we seek relationships between the tutor’s actions and goals in the activity of tutoring, with emerging tensions related to students’ outcomes. Our analysis in the different layers of the activity indicates the complexity of the tutoring, identifying contradictions internal to the activity. These contradictions can be seen as central to practice, as revealed in practice-oriented research, and to a methodology in developing mathematics tutoring.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abboud, M., Goodchild, S., Jaworski, B., Potari, D., Robert, A., & Rogalski, J. (2018). Use of activity theory to make sense of mathematics teaching: A dialogue between perspectives. In Annales de didactique et de sciences cognitives (pp. 61–92). Special Issue English-French. http://mathinfo.unistra.fr/irem/publications/adsc/#c82018
Alsina, C. (2001). Why the professor must be a stimulating teacher: Towards a new paradigm of teaching mathematics at university level. In D. Holton (Ed.), The teaching and learning of mathematics at university level. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_1
Artemeva, N., & Fox, J. (2011). The writing’s on the board: The global and the local in teaching undergraduate mathematics through chalk talk. Written Communication, 28(4), 345–379. https://doi.org/10.1177/0741088311419630
Barab, S. A., Barnett, M., Yamagata-Lynch, L., Squire, K., & Keating, T. (2002). Using activity theory to understand the systemic tensions characterizing a technology-rich introductory astronomy course. Mind, Culture, and Activity, 9(2), 76–107. https://doi.org/10.1207/S15327884MCA0902_02
Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45(1), 35–65. https://doi.org/10.1023/A:1013809201228
Chapman, O., & Heater, B. (2010). Understanding change through a high school mathematics teacher’s journey to inquiry-based teaching. Journal of Mathematics Teacher Education, 13(6), 445–458. https://doi.org/10.1007/s10857-010-9164-6
Cobb, P., Wood, T., & Yackel, E. (1990). Classrooms as learning environments for teachers and researchers. In R. B. Davis, C. Maher, & N. Noddings (Eds.), Constructivist views on teaching and learning mathematics (pp. 125–146). Journal for Research in Mathematics Education, Monograph series no 4, Reston, Virginia: NCTM. https://doi.org/10.2307/749908
Il’encov, E. (1977). Dialectics of the abstract and the concrete in Marx’s Capital (S. Kuzyakov, Trans.). Progress. (Original work published in 1974).
Jaworski, B. (2002). Sensitivity and challenge in university mathematics teaching. Educational Studies in Mathematics, 51(1), 71–94. https://doi.org/10.1023/A:1022491404298
Jaworski, B., & Didis, M. (2014). Relating student meaning-making in mathematics to the aims for and design of teaching in small group tutorials at university level. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 3, pp. 377–384). PME. https://hdl.handle.net/2134/18211
Kilpatrick, J., Hoyles, C., & Skovsmose, O. (Eds.). (2005). Meaning in mathematics education. Springer. https://doi.org/10.1007/0-387-24040-3_2
Leont’ev, A. N. (1979). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in soviet psychology (pp. 37–71). M. E. Sharpe.
Mali, A. (2016). Lecturers’ tools and strategies in university mathematics teaching: An ethnographic study. Unpublished doctoral dissertation, Loughborough University.
Mason, J. (2002). Researching your own practice: The discipline of noticing. Psychology Press. https://doi.org/10.4324/9780203471876
Nardi, E. (2008). Amongst mathematicians: Teaching and learning mathematics at university level. Springer. https://doi.org/10.1007/978-0-387-37143-6
Nardi, E., Jaworski, B., & Hegedus, S. (2005). A spectrum of pedagogical awareness for undergraduate mathematics: From “tricks” to “techniques”. Journal for Research in Mathematics Education, 36(4), 284–316. https://doi.org/10.2307/30035042
Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings. Educational Studies in Mathematics, 33(2), 203–233. http://www.jstor.org/stable/3482643
Potari, D., & Jaworski, B. (2002). Tackling complexity in mathematics teaching development: Using the teaching triad as a tool for reflection and analysis. Journal of Mathematics Teacher Education, 5(4), 351–380. https://doi.org/10.1023/A:1021214604230
Pritchard, D. (2010). What’s right with lecturing? MSOR Connections, 10(3), 3–6. https://doi.org/10.11120/msor.2010.10030003
Roth, W. M., & Lee, Y. J. (2007). “Vygotsky’s neglected legacy”: Cultural-historical activity theory. Review of Educational Research, 77(2), 186–232. http://www.jstor.org/stable/4624893
Scott, P. (1998). Teacher talk and meaning making in science classrooms: A Vygotskian analysis and review. Studies in Science Education, 32(1), 45–80. https://doi.org/10.1080/03057269808560127
Stouraitis, K., Potari, D., & Skott, J. (2017). Contradictions, dialectical oppositions and shifts in teaching mathematics. Educational Studies in Mathematics, 95(2), 203–217. https://doi.org/10.1007/s10649-017-9749-4
Sweeney, J., O'donoghue, T., & Whitehead, C. (2004). Traditional face-to-face and web-based tutorials: A study of university students’ perspectives on the roles of tutorial participants. Teaching in Higher Education, 9(3), 311–323. https://doi.org/10.1080/1356251042000216633
Wyse, D., Brown, C., Oliver, S., & Poblete, X. (2018). The BERA close-to-practice research project: Research report. British Educational Research Association. https://www.bera.ac.uk/researchers-resources/publications/bera-statement-on-close-to-practice-research (March 2021)
Yackel, E. (2004). Theoretical perspectives for analyzing explanation, justification and argumentation in mathematics classrooms. Communications of Mathematical Education, 18(1), 1–18. http://www.koreascience.or.kr/article/JAKO200418317189001.pdf
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Jaworski, B., Potari, D. (2022). Developing Mathematics Teaching in University Tutorials: An Activity Perspective. In: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., Winsløw, C. (eds) Practice-Oriented Research in Tertiary Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-14175-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-14175-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-14174-4
Online ISBN: 978-3-031-14175-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)