1,120
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom

ORCID Icon & ORCID Icon
Pages 115-144 | Received 25 Nov 2019, Accepted 05 Jun 2021, Published online: 25 Aug 2021

References

  • Alcock, L., & Simpson, A. (2004). Convergence of sequences and series: Interactions between visual reasoning and the learner’s beliefs about their own role. Educational Studies in Mathematics, 57(1), 1–32. https://doi.org/10.1023/B:EDUC.0000047051.07646.92
  • Alsina, C. (2002). Why the professor must be a stimulating teacher: Towards a new paradigm of teaching mathematics at university level. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. H. Schoenfeld (Eds.), The teaching and learning of mathematics at university level (Vol. 7, pp. 3–12). Springer.
  • Bergsten, C. (2007). Investigating quality of undergraduate mathematics lectures. Mathematics Education Research Journal, 19(3), 48–72. https://doi.org/10.1007/BF03217462
  • Biggs, J., & Tang, C. (2011). Teaching for quality learning at university. Open University Press.
  • Bligh, D. A. (1972). What’s the use of lectures? (2nd ed.). New Barnet.
  • Calderhead, J. (1981). Stimulated recall: A method for research on teaching. British Journal of Educational Psychology, 51(2), 211–217. https://doi.org/10.1111/j.2044-8279.1981.tb02474.x
  • Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258–277. https://doi.org/10.2307/749781
  • Cooper, J. L., & Robinson, P. (2000). The argument for making large classes seem small. New Directions for Teaching and Learning, 2000(81), 5–16. https://doi.org/10.1002/tl.8101
  • 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. https://doi.org/10.1007/s10649-006-9026-4
  • Ellsworth, P. C., & Scherer, K. R. (2003). Appraisal processes in emotion. In R. J. Davidson, K. R. Scherer, & H. H. Goldsmith (Eds.), Handbook of affective sciences (pp. 572–695). Oxford University Press.
  • Evans, J., Morgan, C., & Tsatsaroni, A. (2006). Discursive positioning and emotion in school mathematics practices. Educational Studies in Mathematics, 63(2), 209–226. https://doi.org/10.1007/s10649-006-9029-1
  • Featherstone, H. (2000). “-Pat + Pat = 0”: Intellectual play in elementary mathematics. For the Learning of Mathematics, 20(2), 14–23.
  • 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
  • Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2(3), 209–219. https://doi.org/10.1207/S15327833MTL0203_3
  • Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391–414). Routledge.
  • Goldin, G. A., Epstein, Y. M., Schorr, R. Y., & Warner, L. B. (2011). Beliefs and engagement structures: Behind the affective dimension of mathematical learning. ZDM Mathematics Education, 43(4), 547–560. https://doi.org/10.1007/s11858-011-0348-z
  • Gómez-Chacón, I. M. (2017). Emotions and heuristics: The state of perplexity in mathematics. ZDM Mathematics Education, 49(3), 323–338. https://doi.org/10.1007/s11858-017-0854-8
  • 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
  • Güçler, B. (2016). Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning. Educational Studies in Mathematics, 91(3), 375–393. https://doi.org/10.1007/s10649-015-9636-9
  • Hannula, M. S. (2006). Motivation in mathematics: Goals reflected in emotions. Educational Studies in Mathematics, 63(2), 165–178. https://doi.org/10.1007/s10649-005-9019-8
  • Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: Embodied and social theories. Research in Mathematics Education, 14(2), 137–161. https://doi.org/10.1080/14794802.2012.694281
  • 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). Cham: Springer.
  • Harré, R., & Gillett, G. (1994). The discursive mind. Sage.
  • Hernandez-Martinez, P., Williams, J., Black, L., Davis, P., Pampaka, M., & Wake, G. (2011). Students’ views on their transition from school to college mathematics: Rethinking ‘transition’ as an issue of identity. Research in Mathematics Education, 13(2), 119–130. https://doi.org/10.1080/14794802.2011.585824
  • Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom: On learning mathematics as an interplay of mathematizing and identifying. International Journal of Educational Research, 51-52, 128–145. https://doi.org/10.1016/j.ijer.2011.12.015
  • Hinton, C., Miyamoto, K., & Della-Chiesa, B. (2008). Brain research, learning and emotions: Implications for education research, policy and practice. European Journal of Education, 43(1), 87–103. https://doi.org/10.1111/j.1465-3435.2007.00336.x
  • Hodkinson, P., & Hodkinson, H. (2001). The strengths and limitations of case study research. In Learning and Skills Development Agency Conference. Cambridge, UK.
  • Jaworski, B. (2002). Sensitivity and challenge in university mathematics tutorial teaching. Educational Studies in Mathematics, 51(1/2), 71–94. https://doi.org/10.1023/A:1022491404298
  • Kieran, C. (2001). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46(1/3), 187–228. https://doi.org/10.1023/A:1014040725558
  • Koichu, B. (2019). A discursively oriented conceptualization of mathematical problem solving. In P. Felmer, P. Liljedahl, & B. Koichu (Eds.), Problem solving in mathematics instruction and teacher professional development (pp. 43–66). Springer.
  • Kontorovich, I., Herbert, R., & Yoon, C. (2019). Students resolve a commognitive conflict between colloquial and calculus discourses on steepness. In J. Monaghan, E. Nardi, & T. Dreyfus (Eds.), Calculus in upper secondary and beginning university mathematics – Conference proceedings (pp. 70–73). MatRIC.
  • LaBar, K. S., & Cabeza, R. (2006). Cognitive neuroscience of emotional memory. Nature Reviews Neuroscience, 7(1), 54–64. https://doi.org/10.1038/nrn1825
  • Lester, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1), 245–278. https://scholarworks.umt.edu/tme/vol10/iss1/12
  • 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
  • Liljedahl, P. G. (2005). Mathematical discovery and affect: The effect of AHA! Experiences on undergraduate mathematics students. International Journal of Mathematical Education in Science and Technology, 36(2–3), 219–234. https://doi.org/10.1080/00207390412331316997
  • Ludmer, R., Dudai, Y., & Rubin, N. (2011). Uncovering camouflage: Amygdala activation predicts long-term memory of induced perceptual insight. Neuron, 69(5), 1002–1014. https://doi.org/10.1016/j.neuron.2011.02.013
  • Malmivuori, M.-L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63(2), 149–164. https://doi.org/10.1007/s10649-006-9022-8
  • Marmur, O. (2017). Undergraduate student learning during calculus tutorials: Key memorable events (Doctoral dissertation). Technion – Israel Institute of Technology.
  • Marmur, O. (2019). Key memorable events: A lens on affect, learning, and teaching in the mathematics classroom. The Journal of Mathematical Behavior, 54, 100673. https://doi.org/10.1016/j.jmathb.2018.09.002
  • Marmur, O., & Koichu, B. (2016). Surprise and the aesthetic experience of university students: A design experiment. Journal of Humanistic Mathematics, 6(1), 127–151. https://doi.org/10.5642/jhummath.201601.09
  • Martínez-Planell, R., & Gaisman, M. T. (2012). Students’ understanding of the general notion of a function of two variables. Educational Studies in Mathematics, 81(3), 365–384. https://doi.org/10.1007/s10649-012-9408-8
  • Martínez-Sierra, G., & García-González, M. D. S. (2016). Undergraduate mathematics students’ emotional experiences in Linear Algebra courses. Educational Studies in Mathematics, 91(1), 87–106. https://doi.org/10.1007/s10649-015-9634-y
  • Marton, F., & Booth, S. (1997). Learning and awareness. Lawrence Erlbaum Associates.
  • Mason, J. (2002). Mathematics teaching practice: Guide for university and college lecturers. Horwood.
  • McGee, D. L., & Martínez-Planell, R. (2014). A study of semiotic registers in the development of the definite integral of functions of two and three variables. International Journal of Science and Mathematics Education, 12(4), 883–916. https://doi.org/10.1007/s10763-013-9437-5
  • McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). Macmillan.
  • McLeod, D. B., & Adams, V. M. (Eds.). (1989). Affect and mathematical problem solving: A new perspective. Springer-Verlag.
  • Moors, A., Ellsworth, P. C., Scherer, K. R., & Frijda, N. H. (2013). Appraisal theories of emotion: State of the art and future development. Emotion Review, 5(2), 119–124. https://doi.org/10.1177/1754073912468165
  • Movshovitz-Hadar, N., & Hazzan, O. (2004). How to present it? On the rhetoric of an outstanding lecturer. International Journal of Mathematical Education in Science and Technology, 35(6), 813–827. https://doi.org/10.1080/00207390412331271384
  • 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
  • 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
  • Nardi, E., & Winsløw, C. (2018). INDRUM2016 special issue editorial. International Journal of Research in Undergraduate Mathematics Education, 4(1), 1–7. https://doi.org/10.1007/s40753-018-0074-9
  • Op’t Eynde, 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. https://doi.org/10.1007/s10649-006-9034-4
  • 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
  • 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
  • Pirie, S. E. B. (1996). Classroom video-recording: When, why and how does it offer a valuable data source for qualitative research? Presented at The Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Panama City, FL.
  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM Mathematics Education, 40(2), 165–178. https://doi.org/10.1007/s11858-008-0086-z
  • Pritchard, D. (2010). Where learning starts? A framework for thinking about lectures in university mathematics. International Journal of Mathematical Education in Science and Technology, 41(5), 609–623. https://doi.org/10.1080/00207391003605254
  • Radford, L. (2015). Of love, frustration, and mathematics: A cultural-historical approach to emotions in mathematics teaching and learning. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions (pp. 25–49). Springer.
  • Rodd, M. (2003). Witness as participation: The lecture theatre as site for mathematical awe and wonder. For the Learning of Mathematics, 23(1), 15–21.
  • Rogalski, M. (2000). The teaching experimented in Lille. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 133–150). Kluwer Academic Publishers.
  • Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Sense Publishers.
  • 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
  • Schroeder, T. L., & Lester, F. K. (1989). Understanding mathematics via problem solving. In P. Trafton (Ed.), New directions for elementary school mathematics (pp. 31–42). National Council of Teachers of Mathematics.
  • Schukajlow, S., Rakoczy, K., & Pekrun, R. (2017). Emotions and motivation in mathematics education: Theoretical considerations and empirical contributions. ZDM Mathematics Education, 49(3), 307–322. https://doi.org/10.1007/s11858-017-0864-6
  • Schwandt, T. A. (2007). The SAGE dictionary of qualitative inquiry (3rd ed.). Sage.
  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.
  • 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., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8(1), 42–76. https://doi.org/10.1207/S15327884MCA0801_04
  • Shkedi, A. (2003). Milim Hamensot Laga’at: Mechkar Eichutani - Teorya Veyisum [Words of Meaning: Qualitative Research - Theory and Practice]. Ramot Publishing House.
  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205
  • Sinclair, N. (2004). The roles of the aesthetic in mathematical inquiry. Mathematical Thinking and Learning, 6(3), 261–284. https://doi.org/10.1207/s15327833mtl0603_1
  • Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with TouchCounts: The role of emotions and the body in mathematical communication. Technology, Knowledge and Learning, 19(1–2), 81–99. https://doi.org/10.1007/s10758-014-9212-x
  • Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258–276. https://doi.org/10.2307/749807
  • Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity, and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495–511). Macmillan.
  • Thomas, D. R. (2006). A general inductive approach for analyzing qualitative evaluation data. American Journal of Evaluation, 27(2), 237–246. https://doi.org/10.1177/1098214005283748
  • Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderman, E. M., Kang, Y., & Patrick, H. (2002). The classroom environment and students’ reports of avoidance strategies in mathematics: A multimethod study. Journal of Educational Psychology, 94(1), 88–106. https://doi.org/10.1037/0022-0663.94.1.88
  • 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
  • Weber, K. (2008). The role of affect in learning real analysis: A case study. Research in Mathematics Education, 10(1), 71–85. https://doi.org/10.1080/14794800801916598
  • Weinberg, A., Wiesner, E., & Fukawa-Connelly, T. (2014). Students’ sense-making frames in mathematics lectures. The Journal of Mathematical Behavior, 33, 168–179. https://doi.org/10.1016/j.jmathb.2013.11.005
  • Wolfe, P. (2006). The role of meaning and emotion in learning. New Directions for Adult and Continuing Education, 2006(110), 35–41. https://doi.org/10.1002/ace.217
  • Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Sage.
  • Yin, R. K. (2011). Qualitative research from start to finish. The Guilford Press.
  • Yoon, C., Kensington-Miller, B., Sneddon, J., & Bartholomew, H. (2011). It’s not the done thing: Social norms governing students’ passive behaviour in undergraduate mathematics lectures. International Journal of Mathematical Education in Science and Technology, 42(8), 1107–1122. https://doi.org/10.1080/0020739X.2011.573877
  • Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63(2), 113–121. https://doi.org/10.1007/s10649-006-9028-2