Skip to main content
SpringerLink
Log in

Affect and emotions in mathematics education: toward a holistic psychology of mathematics education

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Emotions and affect have become an area of interest to mathematics research. However, both tend to be intellectualized and approached as external to and separate from intellect. As far back as in the 1930s, Vygotsky considered the split between affect and intellect as psychology’s greatest defect. To address that defect, over the last 18–24 months of his life, he sketched the barebones of a different psychology but died before he could develop his ideas into a theory of emotions. His ideas provided us with a roadmap for developing an approach in which intellect and affect are united to constitute a central part in the life of the whole person. Such a position, conceived here in dramatic terms, remains virtually unknown, in part because of the unavailability of specific texts and personal notes until a few years ago. In this study, we develop Vygotsky’s seeds and go beyond what he actually stated. We focus our conceptualization of affect on mathematics classroom practices and exemplify our theoretical perspective with empirical data drawn from a number of studies.

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

Similar content being viewed by others

Notes

  1. In dialectics, two opposing terms (e.g., intellect and affect) not only form a unity but also are identical such that there is difference at the heart of identity (cf. Marx & Engels, 1975). The expression “unity and identity” (Vygotsky, in Zavershneva & van der Veer, 2018, p. 245) reflects the dual meanings of Marx’s German Einheit and Vygotsky’s Russian edinstvo.

  2. From Roth and Radford (2011, p. 161 French, p. 167 English). Transcription was augmented with permission. The transcription conventions used here include (0.87) = pauses in seconds; ((pounds)) = transcriber’s description; “=” = latching of sounds;:: = lengthening of sound, 0.1 s per colon; [com] = shading indicates correspondence with image to the right; tiENs = capitalization marks emphasis (by means of intonation or intensity); [] = brackets in consecutive lines indicate overlapping speech; . = punctuation marks intonation, period for strongly falling.

References

  • Attard, C., & Curry, C. (2012). Exploring the use of iPads to engage young students with mathematics. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia (pp. 75–82). Singapore: MERGA.

    Google Scholar 

  • Bailey, J. (2014). Mathematical investigations for supporting pre-service primary teachers repeating a mathematics education course. Australian Journal of Teacher Education, 39, 86–100.

    Article  Google Scholar 

  • Bakhtin, M. M. (1993). Toward a philosophy of the act. Austin: University of Texas Press.

    Google Scholar 

  • Batchelor, S., Torbeyns, J., & Verschaffel, L. (2019). Affect and mathematics in young children: An introduction. Educational Studies in Mathematics, 100, 201–209.

    Article  Google Scholar 

  • Bateson, G. (1979). Mind and nature: A necessary unity. New York, NY: E. P. Dutton.

    Google Scholar 

  • Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127–147.

    Article  Google Scholar 

  • Butler, J., & Scott, J. (Eds.). (1992). Feminists theorize the political. New York, NY: Routledge.

    Google Scholar 

  • Clarke, D. (2015). Reaction to section 1: Faith, hope and charity: Theoretical lenses on affect. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 119–134). Dordrecht, the Netherlands: Springer.

  • Code, L. (1995). Rhetorical spaces: Essays on gendered locations. New York, NY: Routledge.

    Google Scholar 

  • Collins, R. (2004). Interaction ritual chains. Princeton, NJ: Princeton University Press.

    Book  Google Scholar 

  • Dewey, J. (1938). Logic: The theory of inquiry. New York, NY: Henry Holt.

    Google Scholar 

  • Dewey, J. (2008). Art as experience. In J.-A. Boydston (Ed.),  John Dewey: The later works 1925–1953 vol. 10. Carbondale: Southern Illinois University Press (First published in 1934).

  • Dowker, A., Cheriton, O., Horton, R., & Mark, W. (2019). Relationships between attitudes and performance in young children’s mathematics. Educational Studies in Mathematics, 100, 211–230.

    Article  Google Scholar 

  • Evans, J. (2000). Adults’ mathematical thinking and emotions. A study of numerate practices. London, UK: RoutledgeFalmer.

  • Foucault, M. (1988). The ethic of care for the self as a practice of freedom. Cambridge, MA: MIT Press.

    Google Scholar 

  • Goldin, G. A. (2004). Characteristics of affect as a system of representation. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Psychology of Mathematics Education vol. 1 (pp. 109–114). Bergen, Norway: Bergen University College.

    Google Scholar 

  • Hannula, M. S. (2004). Introduction—RF01: Affect in mathematics education—Exploring theoretical frameworks. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Psychology of Mathematics Education vol. 1 (pp. 107–109). Bergen, Norway: Bergen University College.

    Google Scholar 

  • Hegel, G. W. F. (1807). System der Wissenschaft. Erster Teil, die Phänomenologie des Geistes [system of science. Part 1, the phenomenology of spirit]. In Bamberg & Würzburg. Germany: Joseph Anton Goebhardt.

    Google Scholar 

  • Heyd-Metzuyanim, E. (2015). Vicious cycles of identifying and mathematizing: A case study of the development of mathematical failure. Journal of the Learning Sciences, 24, 504–549.

    Article  Google Scholar 

  • Holzkamp, K. (1993). Lernen: Subjektwissenschaftliche Grundlegung [Learning: Foundation in a science oft he subject]. In Frankfurt/M. Germany: Campus.

    Google Scholar 

  • Il’enkov, E. V. (1977). Dialectical logic: Essays on its history and theory. Moscow, USSR: Progress.

    Google Scholar 

  • James, W. (1909). The pluralistic universe. New York, NY: Longmans, Green.

    Google Scholar 

  • Lacan, J. (1977). The four fundamental concepts of psycho-analysis. London, UK: Hogarth Press.

  • Leont’ev, A. N. (1981). Problems of the development of the mind. Moscow, USSR: Progress.

    Google Scholar 

  • Malmivuori, M.-L. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63, 149–164.

    Article  Google Scholar 

  • Mannheim, K. (2004). Beiträge zur Theorie der Weltanschauungs-Interpretation. In J. Strübing & B. Schnettler (Eds.), Methodologie interpretativer Sozialforschung: Klassische Grundlagentexte (pp. 103–153). Konstanz, Germany: UVK.

    Google Scholar 

  • Marx, K., & Engels, F. (1975). Werke Band 20. Berlin, Germany: Dietz.

  • Marx, K., & Engels, F. (1978). Werke Band 3. Berlin, Germany: Dietz.

  • Mead, G. H. (1932). The philosophy of the present. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Mead, G. H. (1972). Mind, self, and society: From the standpoint of a social behaviorist. Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Merleau-Ponty, M. (1945). Phénoménologie de la perception [Phenomenology of perception]. Paris, France: Gallimard.

  • Mikhailov, F. T. (2001). The “other within” for the psychologist. Journal of Russian and East European Psychology, 39(1), 6–31.

    Article  Google Scholar 

  • Nietzsche, F. (1967). The will to power. New York, NY: Random House.

    Google Scholar 

  • 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, 193–207.

    Article  Google Scholar 

  • Planalp, S. (1999). Communicating emotion: Social, moral, and cultural processes. Cambridge, UK: Cambridge University Press.

  • Politzer, G. (1928). Critique des fondements de la psychologie. Paris, France: Rieder.

  • Politzer, G. (1929). Les fondements de la psychologie: Psychologie mythologique et psychologie scientifique. La Revue de la Psychologie Concrète, 1, 9–64.

    Google Scholar 

  • Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80, 101–118.

    Article  Google Scholar 

  • Ricœur, P. (1984). Time and narrative (Vol. 1). Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Roth, W.-M. (2011). Geometry as objective science in elementary classrooms: Mathematics in the flesh. New York, NY: Routledge.

    Book  Google Scholar 

  • Roth, W.-M. (2015). Meaning and the real life of language: Learning from “pathological” cases in science classrooms. Linguistics and Education, 30, 42–55.

    Article  Google Scholar 

  • Roth, W.-M. (2016). On the social nature of mathematical reasoning. For the Learning of Mathematics, 36(2), 34–39.

    Google Scholar 

  • Roth, W.-M. (2019). Transactional psychology of education: Toward the social in a strong sense. Cham, Switzerland: Springer.

  • Roth, W.-M. (forthcoming). Adventures in mind and mathematics. Cham, Switzerland: Springer.

  • Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam, the Netherlands: Sense.

    Book  Google Scholar 

  • Scherer, K. R. (1989). Vocal correlates of emotional arousal and affective disturbance. In H. Wagner & A. Manstead (Eds.), Handbook of social psychophysiology (pp. 165–197). New York, NY: John Wiley & Sons.

    Google Scholar 

  • Schukajlow, S., Rakoczy, K., & Pekrun, R. (2017). Emotions and motivation in mathematics education: Theoretical considerations and empirical contributions. ZDM: Mathematics Education, 49, 307–322.

    Article  Google Scholar 

  • Sheets-Johnstone, M. (2009). The corporeal turn: An interdisciplinary reader. Exeter, UK: Imprint Academic.

    Google Scholar 

  • Sheets-Johnstone, M. (2011). The primacy of movement (2nd ed.). Amsterdam, the Netherlands: John Benjamins.

  • Turner, J. C., Warzon, K. B., & Christensen, A. (2010). Motivating mathematics learning: Changes in teachers’ practices and beliefs during a nine-month collaboration. American Educational Research Journal, 48, 718–762.

    Article  Google Scholar 

  • Veresov, N. (2004). Zone of proximal development (ZPD): The hidden dimension? In A.-L. Østern & R. Heilä-Ylikallio (Eds.), Språk som kultur—betydningar i tid och rum (pp. 13–30). Vasa, Sweden: Åbo Akademi.

    Google Scholar 

  • Vološinov, V. N. (1930). Marksizm i folosofija jazyka: osnovye problemy sociologičeskogo metoda b nauke o jazyke [Marxism and the philosophy of language: Main problems of the sociological method in linguistics]. Leningrad, USSR: Priboj.

    Google Scholar 

  • Vygotsky, L. S. (1987). The collected works of L. S. Vygotsky, vol. 1: Problems of general psychology. New York, NY: Springer.

    Google Scholar 

  • Vygotsky, L. S. (1989). Concrete human psychology. Soviet Psychology, 27(2), 53–77.

    Article  Google Scholar 

  • Vygotsky, L. S. (1997). The collected works of L. S. Vygotsky, vol. 4: The history of the development of higher mental functions. New York, NY: Springer.

    Google Scholar 

  • Vygotsky, L. S. (1999). The collected works of L. S. Vygotsky, vol. 6: Scientific legacy. New York, NY: Springer.

    Google Scholar 

  • Vygotsky, L. S. (2010). Two fragments of personal notes by L. S. Vygotsky from the Vygotsky family archive. Journal of Russian and East European Psychology, 48(1), 91–96.

    Article  Google Scholar 

  • Walden, R., & Walkerdine, V. (1982). Girls and mathematics: The early years: A review of literature and an account of original research. London, UK: University of London Institute of Education.

  • Walshaw, M. (1999). Paradox, partiality and promise: A politics for girls in school mathematics. Unpublished doctoral dissertation. In Massey University. New Zealand: Palmerston North.

    Google Scholar 

  • Walshaw, M. (2014). Who can know mathematics? For the Learning of Mathematics, 34(2), 2–6.

    Google Scholar 

  • Whitehead, A. N. (1919). An enquiry concerning the principles of natural knowledge. Cambridge, UK: Cambridge University Press.

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

    Article  Google Scholar 

  • Zavershneva, E., & van der Veer, R. (Eds.). (2018). Vygotsky’s notebooks: A selection. Singapore: Springer.

    Google Scholar 

  • Zavershneva, E. I. (2010a). The Vygotsky family archive: New findings. Notebooks, notes, and scientific journals of L. S. Vygotsky (1912–1934). Journal of Russian and East European Psychology, 48(1), 34–60.

    Article  Google Scholar 

  • Zavershneva, E. I. (2010b). The way to freedom. Journal of Russian and East European Psychology, 48(1), 61–90.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Victoria, MacLaurin Building A567, Victoria, BC, V8P 5C2, Canada

    Wolff-Michael Roth

  2. Massey University, Palmerston North, New Zealand

    Margaret Walshaw

Authors
  1. Wolff-Michael Roth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Margaret Walshaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wolff-Michael Roth.

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

Roth, WM., Walshaw, M. Affect and emotions in mathematics education: toward a holistic psychology of mathematics education. Educ Stud Math 102, 111–125 (2019). https://doi.org/10.1007/s10649-019-09899-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-019-09899-2

Keywords

Search

Navigation