# The co-construction of learning difficulties in mathematics—teacher–student interactions and their role in the development of a disabled mathematical identity

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## Abstract

Leaning on a communicational framework for studying social, affective, and cognitive aspects of learning, the present study offers a new look at the construction of an identity of failure in mathematics as it occurs through teaching–learning interactions. Using the case of Dana, an extremely low-achieving student in 7th grade mathematics, I attempt to unearth the mechanisms of interaction between Dana and myself, her teacher, that instead of advancing Dana, perpetuated her failure. Through examining the interactional routines followed by Dana and me, I show how Dana’s deviations from normative routines resulted in my identification of Dana as “clueless” in mathematics. This identification, shared both by Dana and by me, was accompanied by adherence to ritual rule following that did not enable Dana’s advancement in mathematical discourse. This case points to the need to re-examine permanent difficulties in mathematics in light of the reciprocal nature of such difficulties’ (re)construction in teaching-and-learning interactions.

### Keywords

Learning difficulties Social interaction Identity Communicational framework### References

- Anderson, K. T. (2009). Applying positioning theory to the analysis of classroom interactions: Mediating micro-identities, macro-kinds, and ideologies of knowing.
*Linguistics and Education, 20*(4), 291–310.CrossRefGoogle Scholar - Andersson, A. (2011).
*Engagement in education: Identity narratives and agency in the contexts of mathematics education*. (Unpublished doctoral thesis). Aalborg University: Aalborg.Google Scholar - Ben-Yehuda, M. (2003).
*Using discourse analysis to investigate arithmetical thinking processes of students with learning difficulties*. (Unpublished doctoral thesis) (Hebrew). University of Haifa: Haifa.Google Scholar - Ben-Yehuda, M., Lavy, I., Linchevski, L., & Sfard, A. (2005). Doing wrong with words, what bars students’ access to arithmetical discourses.
*Journal for Research in Mathematics Education, 36*(3), 176–247.Google Scholar - Bishop, J. P. (2012). She’s always been the smart one. I’ve always been the dumb one: Identities in the mathematics classroom.
*Journal for Research in Mathematics Education, 43*(1), 34–74.CrossRefGoogle Scholar - Black, L. (2004a). Differential participation in whole-class discussions and the construction of marginalised identities.
*Journal of Educational Enquiry, 5*(1), 34–54.Google Scholar - Black, L. (2004b). Teacher–pupil talk in whole-class discussions and processes of social positioning within the primary school classroom.
*Language and Education, 18*(5), 347–360.CrossRefGoogle Scholar - Boaler, J. (1997). Reclaiming school mathematics: The girls fight back.
*Gender and Education, 9*(3), 286–306.CrossRefGoogle Scholar - Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.),
*Multiple perspectives on mathematics education*(pp. 171–200). Westport: Ablex.Google Scholar - Brophy, J. E. (1983). Research on the self-fulfilling prophecy and teacher expectations.
*Journal of Educational Psychology, 75*(5), 631–661.CrossRefGoogle Scholar - Brubaker, R., & Cooper, F. (2000). Beyond “identity”.
*Theory and Society, 29*(1), 1–47.CrossRefGoogle Scholar - Butterworth, B. (2005). Developmental dyscalculia. In J. I. D. Campbell (Ed.),
*Handbook of mathematical cognition*(pp. 455–468). New York: Psychology Press.Google Scholar - Cazden, C. B. (2001).
*Classroom discourse: The language of teaching and learning*(2nd ed.). Portsmouth: Heinemann.Google Scholar - Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms.
*Journal for Research in Mathematics Education, 40*(1), 40–68.Google Scholar - Cobb, P., Yackel, E., & Wood, T. (1992). Interaction and learning in mathematics classroom situations.
*Educational Studies in Mathematics, 23*, 99–122.CrossRefGoogle Scholar - Darley, J. M., & Fazio, R. H. (1980). Expectancy confirmation processes arising in the social interaction sequence.
*American Psychologist, 35*(10), 100–122.CrossRefGoogle Scholar - Davies, B., & Harré, R. (1990). Positioning: The discursive production of selves.
*Journal for the Theory of Social Behaviour, 20*(1), 43–63.CrossRefGoogle 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.CrossRefGoogle Scholar - Eisenmann, T., & Even, R. (2011). Enacted types of algebraic activity in different classes taught by the same teacher.
*International Journal of Science and Mathematics Education, 9*, 867–891.CrossRefGoogle Scholar - Evans, J., Morgan, C., & Tsatsaroni, A. (2006). Discursive positioning and emotion in school mathematics practices.
*Educational Studies in Mathematics, 63*(2), 209–226.CrossRefGoogle Scholar - Fletcher, J. M., & Vaughn, S. (2009). Response to intervention: Preventing and remediating academic difficulties.
*Child Development Perspectives, 3*(1), 30–37.CrossRefGoogle Scholar - Fuchs, L. S., Compton, D. L., Fuchs, D., Paulsen, K., Bryant, J. D., & Hamlett, C. L. (2005). The prevention, identification, and cognitive determinants of math difficulty.
*Journal of Educational Psychology, 97*(3), 493–515.CrossRefGoogle Scholar - Geary, D. C. (2004). Mathematics and learning disabilities.
*Journal of Learning Disabilities, 37*(1), 4–15.CrossRefGoogle Scholar - Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics. In J. I. D. Campbell (Ed.),
*Handbook of mathematical cognition*(pp. 253–267). New York and Hove: Psychology Press.Google Scholar - Gee, J. P. (2000–2001). Identity as an analytical lens for research in education.
*Review of Research in Education, 25*(99–125).Google Scholar - Ginsburg, H. P. (1997). Mathematics learning disabilities: A view from developmental psychology.
*Journal of Learning Disabilities, 30*(1), 20–33.CrossRefGoogle Scholar - Goffman, E. (1967/2005).
*Interaction ritual: Essays in face*-*to*-*face behavior*/*Erving Goffman; with a new introduction by Joel Best*. Transaction Publishers: New Brunswick.Google Scholar - González, J. E. J., & Espínel, G. A. I. (1999). Is IQ-achievement discrepancy relevant in the definition of arithmetic learning disabilities?
*Learning Disability Quarterly, 22*(4), 291–301.CrossRefGoogle Scholar - Graven, M. (2011). Creating new mathematical stories: Exploring potential opportunities within maths clubs. In H. Venkat & A. Assien (Eds.),
*Proceedings of the Seventeenth National Congress of the Association for Mathematics Education of South Africa*(pp. 161–170). Johannesburg: AMESA.Google Scholar - Habermas, T., & Bluck, S. (2000). Getting a life: The emergence of the life story in adolescence.
*Psychological Bulletin, 126*(5), 748–769.CrossRefGoogle Scholar - Harré, R., & Gillette, G. (1994).
*The discursive mind*. Thousand Oaks: Sage.Google Scholar - Harré, R., & van Langenhove, L. (Eds.). (1999).
*Positioning theory*. Oxford: Blackwell.Google Scholar - Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety.
*Journal for Research in Mathematics Education, 21*(1), 33–46.CrossRefGoogle Scholar - Heyd-Metzuyanim (2012).
*Emotional aspects of learning mathematics – How the interaction between identifying and mathematizing influences the effectiveness of learning*. (Unpublished doctoral thesis). University of Haifa: Haifa.Google Scholar - Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom—learning mathematics as interplay between mathematizing and identifying.
*International Journal of Educational Research, 51–52*, 128–145.CrossRefGoogle Scholar - Ingram, N. (2011).
*Affect and identity: The mathematical journeys of adolescents*. (Unpublished doctoral thesis). University of Otago: Dunedin.Google Scholar - Jones, E. D., Wilson, R., & Bhojwani, S. (1997). Mathematics instruction for secondary students with learning disabilities.
*Journal of Learning Disabilities, 30*(2), 151–163.CrossRefGoogle Scholar - Jussim, L. (1989). Teacher expectations: Self-fulfilling prophecies, perceptual biases, and accuracy.
*Journal of Personality and Social Psychology, 57*(3), 469–480.CrossRefGoogle Scholar - Kosc, L. (1974). Developmental dyscalculia.
*Journal of Learning Disabilities, 7*(3), 164–177.CrossRefGoogle Scholar - Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching.
*American Educational Research Journal, 27*, 29–63.CrossRefGoogle Scholar - Lange, T. (2009).
*Difficulties, meaning and marginalisation in mathematics learning as seen through children’s eyes*. (Unpublished doctoral thesis). Aalborg University: Aalborg.Google Scholar - Lave, J., & Wenger, E. (1991).
*Situated learning: Legitimate peripheral participation*. New York: Cambridge University Press.CrossRefGoogle Scholar - Leander, K. M. (2002). Locating Latanya: The situated production of identity artifacts in classroom interaction.
*Research in the Teaching of English, 37*(2), 198–250.Google Scholar - Leder, G. C., & Forgasz, H. J. (2006). Affect and mathematics education. In A. Gutierrez & P. Boero (Eds.),
*Handbook of research on the psychology of mathematics education: Past, present and future*(pp. 403–427). Rotterdam: Sense Publishers.Google Scholar - Lefstein, A. (2008). Changing teacher practice through the National Literacy Strategy: A micro-Interactional perspective.
*American Journal of Education Research, 45*(3), 701–737.CrossRefGoogle Scholar - Linchevski, L., & Kutscher, B. (1998). Tell me with whom you’re learning, and I’ll tell you how much you’ve learned: Mixed-ability versus same-ability grouping in mathematics.
*Journal for Research in Mathematics Education, 29*(5), 533–554.CrossRefGoogle Scholar - Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics.
*Journal for Research in Mathematics Education, 30*(5), 520–540.CrossRefGoogle Scholar - Mazzocco, M. M. (2005). Challenges in identifying target skills for math disability screening and intervention.
*Journal of Learning Disabilities, 38*(4), 318–323.CrossRefGoogle Scholar - Mazzocco, M. M., & Myers, G. (2003). Complexities in identifying and defining mathematics learning disability in the primary school-age years.
*Annals of Dyslexia, 53*, 218–252.CrossRefGoogle Scholar - McAdams, D. P. (2001). The psychology of life stories.
*Review of General Psychology, 5*(2), 100–122.CrossRefGoogle Scholar - McCall, G. J., & Simmons, J. L. (1966).
*Identities and interactions*. New York: The Free Press.Google Scholar - McDermott, R. P. (1993). The acquisition of a child by a learning disability. In S. Chaiklin & J. Lave (Eds.),
*Understanding practice*(pp. 269–305). Cambridge: Cambridge University Press.CrossRefGoogle Scholar - 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). New York: Macmillan Publishing Company.Google Scholar - Mehan, H. (1979).
*Learning lessons: Social organization in the classroom*. Cambridge: Harvard University Press.Google Scholar - Montague, M. (2007). Self-regulation and mathematics instruction.
*Learning Disabilities Research and Practice, 22*(1), 75–83.CrossRefGoogle Scholar - Nasir, N. S. (2002). Identity, goals, and learning: Mathematics in cultural practice.
*Mathematical Thinking and Learning, 4*(2), 213–247.CrossRefGoogle Scholar - Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students.
*Contemporary Educational Psychology, 24*, 124–139.CrossRefGoogle Scholar - Pajares, F., & Kranzler, J. (1995). Self-efficacy beliefs and general mental ability in mathematical problem-solving.
*Contemporary Educational Psychology, 20*(4), 426–443.CrossRefGoogle Scholar - Roth, W. M., & Radford, L. (2011).
*A cultural-historical perspective on mathematics teaching and learning*. Rotterdam: Sense Publishers.CrossRefGoogle Scholar - Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior.
*Journal for Research in Mathematics Education, 20*(4), 338–355.CrossRefGoogle Scholar - Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint.
*The Journal of the Learning Sciences, 16*(4), 565–613.CrossRefGoogle Scholar - Sfard, A. (2008).
*Thinking as communicating*. New York: Cambridge University Press.CrossRefGoogle Scholar - Sfard, A., & Lavie, I. (2005). Why cannot children see as the same what grown-ups cannot see as different?—early numerical thinking revisited.
*Cognition and Instruction, 23*(3), 237–309.CrossRefGoogle Scholar - Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity.
*Educational Researcher, 34*(4), 14–22.CrossRefGoogle Scholar - Shalev, R. S., Manor, O., Kerem, B., Ayali, M., Badichi, N., Friedlander, Y., et al. (2001). Developmental dyscalculia is a familial learning disability. (Statistical data included).
*Journal of Learning Disabilities, 34*(1), 59–65.CrossRefGoogle Scholar - Solomon, Y. (2007). Experiencing mathematics classes: Ability grouping, gender and the selective development of participative identities.
*International Journal of Educational Research, 46*(1–2), 8–19.CrossRefGoogle Scholar - Steedly, K., Dragoo, K., Arefeh, S., Luke, S. D. (2008). Effective mathematics instruction, evidence for education.
*3*(1). Downloaded on October, 12, 2012 from http://nichcy.org/wp-content/uploads/docs/eemath.pdf. - Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics.
*Educational Studies in Mathematics, 26*, 275–298.CrossRefGoogle Scholar - Wenger, E. (1998).
*Communities of practice: Learning, meaning, and identity*. New York: Cambridge University Press.Google Scholar - Wittgenstein, L. (1953).
*Philosophical investigations*(trans: Anscombe, G.E.M.). Oxford: Blackwell.Google Scholar - Witzel, B. S., Smith, S. W., & Brownell, M. T. (2001). How can I help students with learning disabilities in algebra?
*Intervention in School and Clinic, 37*(2), 101–105.CrossRefGoogle Scholar - Wood, M. B. (2008).
*Mathematizing, identifying, and autonomous learning: Fourth grade students engage mathematics*. (Unpublished doctoral dissertation). Michigan State University: East Lansing, MI.Google Scholar - Wood, M. B., & Kalinec, C. A. (2012). “What? A Black brother can’t talk?” Possibilities for learning mathematics in small group interactions.
*International Journal of Educational Research, 51–52*, 109–127.CrossRefGoogle Scholar - Wortham, S. (2006).
*Learning identity: The joint emergence of social identification and academic learning*. New York: Cambridge University Press.Google Scholar