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Relating students’ emotions during argumentative discourse to their learning of real-life functional situations

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Abstract

Argu mentative problem solving in mathematics classrooms is a crucial practice that supports important student learning goals via collaborative deliberation and consensus building, but also places substantial cognitive and affective demands on both students and teacher. In this in-depth qualitative study, we considered how students’ emotions during argumentative discourse relate to their learning of real-life functional situations, an area of mathematics highlighted in the literature as foundational yet difficult. Observations, written reflections, and interviews of six Year 9 (14–15-year-old) students’ experience of argument construction, critique, and consensus building were analyzed for insights into emotions experienced during small-group argumentative problem solving, and how various emotions might support or hinder students’ mathematics learning. The emotion of frustration was experienced frequently and was found to facilitate persistence and the correction of misconceptions, but also to hinder the learning in contributing to ongoing tension and eventual resignation. Peer critique was found to stimulate negative emotions but positive learning processes, such as seeking other ways to explain one’s reasoning, and re-evaluating one’s own incorrect solutions.

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Notes

  1. See electronic supplementary material for an example of the argumentation tasks (Cycle 2).

  2. File no. 10367.

References

  • Anderson, R. C., Nguyen-Jahiel, K., McNurlen, B., Archodidou, A., Kim, S., Reznitskaya, A., … Gilbert, L. (2001). The snowball phenomenon: Spread of ways of talking and ways of thinking across groups of children. Cognition and Instruction, 19(1), 1–46.

  • Andriessen, J. (2006). Arguing to learn. In K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 443–459). Cambridge University Press.

    Google Scholar 

  • Asterhan, C. S., & Schwarz, B. B. (2016). Argumentation for learning: Well-trodden paths and unexplored territories. Educational Psychologist, 51(2), 164–187.

    Article  Google Scholar 

  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, 49, 163–173.

    Article  Google Scholar 

  • Ayalon, M., Watson, A., & Lerman, S. (2018). Comparison of students’ understanding of functions in classes following English and Israeli national curricula. Educational Studies in Mathematics, 97(3), 255–272.

    Article  Google Scholar 

  • Chua, B. I. (2016). Justification in Singapore secondary mathematics. In P. C. Toh & B. Kaur (Eds.), Developing 21st century competencies in the mathematics classroom (pp. 165–188). World Scientific.

    Chapter  Google Scholar 

  • Clement, J. (1985). Misconceptions in graphing. In Proceedings of the Ninth International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 369–375). Utrecht University. ‏

  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts during mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 117–148). Springer.

    Chapter  Google Scholar 

  • DeBellis, V. A., & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131–147.

    Article  Google Scholar 

  • Ellsworth, P. C. (2013). Appraisal theory: Old and new questions. Emotion Review, 5(2), 125–131.

    Article  Google Scholar 

  • Else-Quest, N. M., Hyde, J. S., & Hejmadi, A. (2008). Mother and child emotions during mathematics homework. Mathematical Thinking and Learning, 10(1), 5–35. https://doi.org/10.1080/10986060701818644.

    Article  Google Scholar 

  • Evans, J., Morgan, C., & Tsatsaroni, A. (2006). Discursive positioning and emotion in school mathematics practices. Educational Studies in Mathematics, 63(2), 209–226.

    Article  Google Scholar 

  • Feldman Barrett, L. (2012). Emotions are real. Emotion, 12(3), 413–429.

    Article  Google Scholar 

  • Fischer, A. H., & Manstead, A. S. R. (2008). Social functions of emotion. In M. Lewis, J. M. Haviland-Jones, & L. F. Barrett (Eds.), Handbook of emotions (pp. 456–468). The Guilford Press.

    Google Scholar 

  • Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. The Journal of Mathematical Behavior, 24(3–4), 361–372.

    Article  Google Scholar 

  • Goldenberg, E. (1987). Believing is seeing: How preconceptions influence the perception of graphs. Proceedings of the 11th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 197–204). IGPME.

  • Goldin, G. A. (2000). Affective pathways and representations in mathematical problem solving. Mathematical Thinking and Learning, 17(2), 209–219.

    Article  Google Scholar 

  • Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59–72). Kluwer.

    Google Scholar 

  • Gómez-Chacón, I. M. (2017). Emotions and heuristics: The state of perplexity in mathematics. ZDM-Mathematics Education, 49, 323–338.

  • Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.

    Article  Google Scholar 

  • Hannula, M. S. (2006). Motivation in mathematics: Goals reflected in emotions. Educational Studies in Mathematics, 63(2), 165–178.

    Article  Google Scholar 

  • Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: Embodied and social theories. Research in Mathematics Education, 14(2), 137–161.

    Article  Google Scholar 

  • Hannula, M. S. (2015). Emotions in problem solving. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 269–288). Springer.

    Chapter  Google Scholar 

  • Hernandez-Martinez, P., & Harth, H. (2016). Emotions in undergraduate modelling group work. Paper presented at the 13th international congress on mathematical education, Hamburg, Germany.

  • Hershkowitz, R., & Schwarz, B. B. (1999). Reflective processes in a technology-based mathematics classroom. Cognition and Instruction, 17, 65–91.

    Article  Google Scholar 

  • Horn, I. S. (2008). Accountable argumentation as a participation structure to support learning through disagreement. In A. J. Schoenfeld & N. Pateman (Eds.), A study of teaching: Multiple lenses, multiple views: Journal for Research in Mathematics Education, Monograph #14 (pp. 97–126). NCTM.

  • Immordino-Yang, M. H., & Damasio, A. (2007). We feel, therefore we learn: The relevance of affective and social neuroscience to education. Mind, Brain, and Education, 1(1), 3–10.

    Article  Google Scholar 

  • Janvier, C. (1981). Use of situations in mathematics education. Educational Studies in Mathematics, 12(1), 113–122.

    Article  Google Scholar 

  • Lampert, M., Rittenhouse, P., & Crumbaugh, C. (1996). Agreeing to disagree: Developing sociable mathematical discourse. In D. Olson & N. Torrance (Eds.), Handbook of education and human development (pp. 731–764). Blackwell.

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.

    Article  Google Scholar 

  • Lindquist, K. A., & Feldman Barrett, L. (2008). Emotional complexity. In M. Lewis, J. M. Haviland-Jones & L. Feldman Barrett (Eds.), Handbook of emotions (3rd edn., pp. 513–530). The Guilford Press.

  • McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 575–596). MacMillan.

    Google Scholar 

  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded source book (2nd ed.). Sage.

    Google Scholar 

  • Mischo, C. (2003). Cognitive, emotional, and verbal responses in unfair everyday discourse. Journal of Language and Social Psychology, 22(1), 119–131.

    Article  Google Scholar 

  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20.

    Article  Google Scholar 

  • Op’tEynde, P., de Corte, E., & Verschaffel, L. (2006). “Accepting emotional complexity”: A socio-constructivist perspective on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 63(2), 193–207.

    Article  Google Scholar 

  • Schoenfeld, A. (1985). Mathematical problem solving. Academic.

    Google Scholar 

  • Schwarz, B. B., & Baker, M. J. (2017). Dialogue: Argumentation and education: History, theory and practice. Cambridge University Press.

  • Slakmon, B., & Schwarz, B. B. (2019). Deliberative emotional talk. International Journal of Computer-Supported Collaborative Learning, 14(2), 185–217.

    Article  Google Scholar 

  • Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25, 161–217.

    Article  Google Scholar 

  • Staples, M., & Newton, J. (2016). Teachers’ contextualization of argumentation in the mathematics classroom. Theory into Practice, 55(4), 294–301.

    Article  Google Scholar 

  • Stein, N. L., & Albro, E. R. (2001). The origins and nature of arguments: Studies in conflict understanding, emotion, and negotiation. Discourse Processes, 32(2–3), 113–133.

    Article  Google Scholar 

  • Thompson, P. W. (1994). Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics, 26(2–3), 229–274.

    Article  Google Scholar 

  • Van Eemeren, F. H., & Grootendorst, R. (2004). A systematic theory of argumentation: The pragma-dialectical approach (Vol. 14). Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge.

  • Webb, N. M., Nemer, K. M., & Zuniga, S. (2002). Short circuits or superconductors? Effects of group composition on high-achieving students’ science assessment performance. American Educational Research Journal, 39, 943–989.

    Article  Google Scholar 

  • Webb, N. M., Franke, M. L., Ing, M., Wong, J., Fernandez, C. H., Shin, N., & Turrou, A. C. (2014). Engaging with others’ mathematical ideas: Interrelationships among student participation, teachers’ instructional practices, and learning. International Journal of Educational Research, 63, 79–93.

    Article  Google Scholar 

  • Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247–261.

    Article  Google Scholar 

  • Whitenack, J., & Yackel, E. (2002). Making mathematical arguments in the primary grades: The importance of explaining and justifying ideas. Teaching Children Mathematics, 8(9), 524–528.

    Article  Google Scholar 

  • Whiting, D. (2020). Emotions as original existences. Springer.

    Book  Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

  • Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63(2), 113–121.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics Education, University of Haifa, Haifa, Israel

    Michal Ayalon & Katrin Hajjar Eid

  2. Faculty of Education, Monash University, Melbourne, Australia

    Karina J. Wilkie

Authors
  1. Michal Ayalon
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  2. Karina J. Wilkie
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Correspondence to Michal Ayalon.

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Supplementary file1 (DOCX 1890 kb)

Appendix. Post-cycle interview: focus group and teacher

Appendix. Post-cycle interview: focus group and teacher

Student

  1. 1.

    How did you decide on your own graph initially? (Look at the handout together.)

  2. 2.

    What differences were there between your own initial graph and the initial graph of your group? Were you happy with the group decision for this graph?

  3. 3.

    What differences were there between your initial and final group graphs? Were the three student example-graphs helpful for making your final group graph? Why / why not? Were you happy with the group decision for the final graph?

  4. 4.

    Did anything surprise you about the different group graphs presented to the whole class?

  5. 5.

    I noticed that during the lesson, you ………… (events observed). Can you explain to me what was happening from your perspective?

  6. 6.

    From your perspective, how have these emotions you described impacted your engagement and learning? Why?

  7. 7.

    I see you wrote that you learnt …………… (last two questions on written reflection handout).

  8. 8.

    Is there anything else you would like to mention?

Teacher

  1. 1.

    What do you remember as a ‘stand-out’ from the two lessons about (the story situation)?

  2. 2.

    Did you experience any surprising or interesting or difficult moments during the lessons?

  3. 3.

    What do you think about the engagement of the class during the cycle (was it different or similar to usual for this class)?

  4. 4.

    What did you notice about the students’ responses to the tasks?

  5. 5.

    In the first/second lesson in the cycle, I noticed that……… (critical event noticed by researcher). Can you explain what you noticed from your perspective?

After third cycle:

  1. 1.

    What do you think about the students’ progress in learning with these tasks over the whole sequence?

  2. 2.

    If you repeated the sequence, what do you think you would do differently (give reason)? Grouping? Discussions? Sequencing? Tasks?

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Ayalon, M., Wilkie, K.J. & Eid, K.H. Relating students’ emotions during argumentative discourse to their learning of real-life functional situations. Educ Stud Math 110, 23–48 (2022). https://doi.org/10.1007/s10649-021-10121-5

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