Skip to main content

Advertisement

SpringerLink
Log in

Understanding the choice and use of examples in mathematics teacher education multilingual classrooms

  • Original Paper
  • Published:
ZDM – Mathematics Education Aims and scope Submit manuscript

Abstract

The teaching of mathematics is mostly done with tasks that learners and teachers do or solve, in and outside of class. These tasks, which are used to illustrate concepts in mathematics, are referred to in this paper as examples in mathematics. Examples that teachers choose and use are fundamental to what mathematics is taught and learned, and what opportunities for learning are created in mathematics classrooms. In this paper, I bring together two frameworks which have been used separately in mathematics education research, namely variation theory, and meaning making as a dialogic process framework, in order to understand exemplifying practices in teacher education multilingual classrooms. Lesson transcript data from an introductory class on probability in one teacher education multilingual classroom are used to illustrate how these two theories can be used to examine the choice and use of examples in mathematics teacher education multilingual classrooms. This analysis shows the dialectic relationships among the mathematical object of learning, teacher moves, and the interactional process in which the mathematics content was imbedded.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Adapted from Mortimer and Scott (2003, p. 35)

Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Aguiar, O. G., Mortimer, E. F., & Scott, P. H. (2010). Learning from and responding to students’ questions: The authoritative and dialogic tension. Journal of Research in Science Teaching, 47(2), 174–193.

    Google Scholar 

  • Alexander, R. (2004). Towards dialogic teaching: Rethinking classroom talk. Cambridge: Dialogos.

    Google Scholar 

  • Arzarello, F., Ascari, M., & Sabena, C. (2011). A model for developing students’ example space: The key role of the teacher. ZDM, 43, 295–306. https://doi.org/10.1007/s11858-011-0312-y.

    Article  Google Scholar 

  • Barwell, R. (2020). Learning mathematics in a second language: Language positive and language neutral classrooms. Journal for Research in Mathematics Education, 51(2), 150–178.

    Article  Google Scholar 

  • Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., & Zaslavsky, O. (2006). Exemplification in mathematics education. In J. Novotna (Ed.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Prague: PME.

    Google Scholar 

  • Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483.

    Article  Google Scholar 

  • Erath, K., Ingram, J., Moschkovich, J., & Prediger, S. (2021). Designing and enacting instruction that enhances language for mathematics learning—A review of the state of development and research. ZDM Mathematics Education, 53(2) (in this issue).

  • Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99, 161–179. https://doi.org/10.1007/s10649-018-9830-7.

    Article  Google Scholar 

  • Essien, A. (2014). Examining opportunities for the development of interacting identities within pre-service teacher education classrooms. Perspectives in Education, 32(3), 62–77.

    Google Scholar 

  • Essien, A. (2017). Dialogic and argumentation structures in one quadratic inequalities lesson. In J. Adler & A. Sfard (Eds.), Research for educational change: Transforming researchers’ insights into improvement in mathematics teaching and learning (pp. 82–99). London: Routledge.

    Google Scholar 

  • Goldenberg, P., & Mason, J. (2008). Shedding light on and with example spaces. Educational Studies in Mathematics, 69(2), 183–194. https://doi.org/10.1007/s10649-008-9143-3.

    Article  Google Scholar 

  • Ingram, J. (2018). Moving forward with ethnomethodological approaches to analysing mathematics classroom interactions. ZDM-Mathematics Education, 50, 1065–1075. https://doi.org/10.1007/s11858-018-0951-3.

    Article  Google Scholar 

  • Jung, J., & Schütte, M. (2018). An interactionist perspective on mathematics learning: Conditions of learning opportunities in mixed-ability groups within linguistic negotiation processes. ZDM-Mathematics Education, 50, 1089–1099. https://doi.org/10.1007/s11858-018-0999-0.

    Article  Google Scholar 

  • Kullberg, A., Runesson Kempe, U., & Marton, F. (2017). What is made possible to learn when using the variation theory of learning in teaching mathematics? ZDM-Mathematics Education, 49(4), 559–569. https://doi.org/10.1007/s11858-017-0858-4.

    Article  Google Scholar 

  • Lo, L. (2012). Variation theory and the improvement of teaching and learning. Göteborg: Acta Universitatis Gothoburgensis.

    Google Scholar 

  • Lo, M. L., & Chik, P. P. M. (2016). Two horizons of fusion. Scandinavian Journal of Educational Research, 60(3), 296–308. https://doi.org/10.1080/00313831.2015.1119730.

    Article  Google Scholar 

  • Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Marton, F., & Tsui, A. (2004). Classroom discourse and the space of learning. Mahwah: Lawrence Erlbaum Associates.

    Book  Google Scholar 

  • Mercer, N., Dawes, L., & Staarman, J. K. (2009). Dialogic teaching in the primary science classroom. Language and Education, 23(4), 353–369. https://doi.org/10.1080/09500780902954273.

    Article  Google Scholar 

  • Mortimer, E. F., & Scott, P. H. (2003). Meaning making in secondary science classrooms. Philadelphia: Open University Press.

    Google Scholar 

  • Moschkovich, J. (2013). Issues regarding the concept of mathematical practices. In Y. Li & J. N. Moschkovich (Eds.), Proficiency and beliefs in learning and teaching mathematics: learning from Alan Schoenfeld and Günter Toerner (pp. 257–275). Rotterdam: Sense Publishers.

    Chapter  Google Scholar 

  • Moschkovich, J., & Zahner, W. (2018). Using the academic literacy in mathematics framework to uncover multiple aspects of activity during peer mathematical discussions. ZDM-Mathematics Education, 50, 999–1011. https://doi.org/10.1007/s11858-018-0982-9.

    Article  Google Scholar 

  • Olteanu, C. (2018). Designing examples to create variation patterns in teaching. International Journal of Mathematical Education in Science and Technology, 49(8), 1219–1234. https://doi.org/10.1080/0020739X.2018.1447151.

    Article  Google Scholar 

  • Olteanu, C., & Olteanu, L. (2013). Enhancing mathematics communication using critical aspects and dimensions of variation. International Journal of Mathematical Education in Science and Technology, 44(4), 513–522. https://doi.org/10.1080/0020739X.2012.742153.

    Article  Google Scholar 

  • Pang, M. F., & Marton, F. (2003). Beyond “lesson study”: Comparing two ways of facilitating the grasp of some economic concepts. Instructional Science, 31(3), 175–194. https://doi.org/10.1023/A:1023280619632.

    Article  Google Scholar 

  • Pang, M. F., & Marton, F. (2005). Learning theory as teaching resource: Enhancing students’ understanding of economic concepts. Instructional Science, 33(2), 159–191. https://doi.org/10.1007/s11251-005-2811-0.

    Article  Google Scholar 

  • Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69, 149–163.

    Article  Google Scholar 

  • Runesson, U. (2005). Beyond discourse and interaction. Variation: A critical aspect for teaching and learning mathematics. Cambridge Journal of Education, 35(1), 69–87. https://doi.org/10.1080/0305764042000332506.

    Article  Google Scholar 

  • Schleppegrell, M. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159.

    Article  Google Scholar 

  • Scott, P., Ametller, J., Mercer, N., Kleine Staarman, J., & Dawes, L. (2007). An investigation of dialogic teaching in science classrooms. In: Paper Presented at the NARST, New Orleans.

  • Scott, P., Mortimer, E., & Aguiar, O. (2006). The tension between authoritative and dialogic discourse: A fundamental characteristic of meaning making interactions in high school science lessons. Science Education, 90(4), 605–631.

    Article  Google Scholar 

  • Smit, J., & van Eerde, H. (2011). A teacher’s learning process in dual design research: Learning to scaffold language in a multilingual mathematics classroom. ZDM-The International Journal on Mathematics Education, 43(6), 889–900.

    Article  Google Scholar 

  • Stein, M., Engle, R. A., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: Five practices for helping teacher move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.

    Article  Google Scholar 

  • Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.

    Article  Google Scholar 

  • Wessel, L. (2019). Vocabulary in learning processes towards conceptual understanding of equivalent fractions—Specifying students’ language demands on the basis of lexical trace analyses. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-019-00284-z.

    Article  Google Scholar 

  • Zaslavsky, O. (2010). The explanatory power of examples in mathematics: Challenges for teaching. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 107–128). Boston: Springer.

    Chapter  Google Scholar 

  • Zodik, I., & Zaslavsky, O. (2008). Characteristics of teachers’ choice of examples in and for the mathematics classroom. Educational Studies in Mathematics, 69(2), 165–182. https://doi.org/10.1007/s10649-008-9140-6.

    Article  Google Scholar 

Download references

Acknowledgements

The research was jointly funded by the National Research Foundation (NRF) (Grant no. 114968) and the Mellon Grant. The ideas expressed in this paper are, however, those of the author. My thanks go to Fatou Sey for feedback on the original draft versions of this paper, and to Jenni Ingram, Judit Moschkovich, and the blind reviewers for their insightful comments on earlier versions of the paper.

Author information

Authors and Affiliations

  1. Mathematics Education Division, School of Education, University of the Witwatersrand, Johannesburg, South Africa

    Anthony A. Essien

Authors
  1. Anthony A. Essien
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anthony A. Essien.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Essien, A.A. Understanding the choice and use of examples in mathematics teacher education multilingual classrooms. ZDM Mathematics Education 53, 475–488 (2021). https://doi.org/10.1007/s11858-021-01241-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-021-01241-6

Keywords

Search

Navigation