Hidden mechanisms of differentiation: teachers’ beliefs about student diversity

  • Galina LarinaEmail author
  • Valeria Markina


This article provides an empirically grounded analysis for two fundamentally different models of mathematics teachers’ beliefs about student diversity in Russian secondary schools: exclusive and inclusive models. Although teachers’ beliefs are considered a central factor for the differentiated approach, teachers’ beliefs could be stereotyped and, consequently, the evaluation of a student’s ability would be systematically shifted and decisions about the possibility of teaching a student would be incorrect. Semi-structured interviews with 30 mathematics teachers allowed us to investigate what criteria teachers claim to employ while classifying students in the classroom and what expectations they have for each group of students. It was found that within the exclusive model, teachers have an image of a “normal” student and use discrete categories for labelling students with reference to the “normality”. Within the inclusive model, teachers tend not to match students with discrete categories; rather they prefer to compare a student only with herself or himself. Research findings are discussed in the context of a possible “fixed effect” on a student’s development. However, there is a need for further investigation of a connection between teachers’ belief systems, teaching practices and student achievement.


Teachers’ beliefs Ability grouping Mathematics Grounded theory Russia 



The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and supported within the framework of a subsidy by the Russian Academic Excellence Project “5-100”.


  1. Aguirre, J. (2009). Privileging mathematics and equity in teacher education: Framework, counter- resistance strategies, and reflections from a Latina mathematics educator. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.), Culturally responsive mathematics education (pp. 295–319). New York, NY: Routledge Education.Google Scholar
  2. Atweh, B., Bleicher, R., & Cooper, T. (1998). The construction of social context of mathematics classroom: A sociolinguistic analysis. Journal for Research in Mathematics Education, 29(1), 63–82.Google Scholar
  3. Boaler, J. (1997). Experiencing school mathematics: Teaching styles, sex and setting. Buckingham: Open University Press.Google Scholar
  4. Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33, 239–258.Google Scholar
  5. Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey Bass.Google Scholar
  6. Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods. Boston, MA: Allyn and Bacon.Google Scholar
  7. Brown, A. L. (1994). The advancement of learning. Educational Researcher, 23, 4–12.Google Scholar
  8. Butler, R. (2000). Making judgments about ability: The role of implicit theories of ability in moderating inferences from temporal and social comparison information. Journal of Personality and Social Psychology, 78, 965–978.Google Scholar
  9. Campbell, T. (2015). Stereotyped at seven? Biases in teacher judgement of pupils’ ability and attainment. Journal of Social Policy, 44(3), 517–547.Google Scholar
  10. Carnoy, M., Larina, G., & Markina, V. (Eds.). (2019). (Ne)obychnye shkoly: raznoobrazie i neravenstvo [(Un)common schools: Diversity and inequality]. Moscow: HSE Publishing House.Google Scholar
  11. Catsambis, S., Mulkey, L. M., & Crain, R. L. (2001). For better or for worse? A nationwide study of the social psychological effects of gender and ability grouping in mathematics. Social Psychology of Education, 5, 83–115.Google Scholar
  12. Cooper, H., & Good, T. (1983). Pygmalion grows up: Studies in the expectation communication process. New York: Longman.Google Scholar
  13. Davies, P. (2000). Differentiation: Processing and understanding in teachers’ thinking and practice. Educational Studies, 26(2), 191–203.Google Scholar
  14. Dunne, C. (2011). The place of the literature review in grounded theory research. International Journal of Social Research Methodology, 14(2), 111–124.Google Scholar
  15. Dweck, C., Walton, G. M., & Cohen, G. L. (2011). Academic tenacity: Mindsets and skills that promote long-term learning. Seattle, WA: Gates Foundation.Google Scholar
  16. Eccles, J., & Wigfield, A. (1985). Teacher expectations and student motivation. In J. Dusek (Ed.), Teacher expectancies (pp. 185–226). Hillside, NJ: Lawrence Erlbaum Associates.Google Scholar
  17. Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38, 47–64.Google Scholar
  18. Federal’nyj gosudarstvennyj obrazovatel’nyj standart osnovnogo obshchego obrazovaniya [Federal State Educational Standards for Secondary (Complete) General Education]. (2010). Retrieved from Accessed 9 January 2019.
  19. Fives, H., & Buehl, M. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: What are they? Which have been examined? What can they tell us? In K. R. Harris, S. Graham, & T. Urdan (Eds.), APA educational psychology handbook (Vol. 2. Individual differences and cultural and contextual factors) (pp. 471–499). Washington, DC: American Psychological Association.Google Scholar
  20. Good, T. L., & Marshall, S. (1984). Do students learn more in heterogeneous or homogeneous groups? In P. L. Peterson, L. C. Wilkinson, & M. T. Hallinan (Eds.), The social context of instruction: Group organization and group process (pp. 15–38). Orlando, FL: Academic Press.Google Scholar
  21. Greven, C. U., Harlaar, N., Kovas, Y., Chamorro-Premuzic, T., & Plomin, R. (2009). More than just IQ: School achievement is predicted by self-perceived abilities—But for genetics rather than environmental reasons. Psychological Science, 20(6), 753–762.Google Scholar
  22. Gutshall, C. A. (2013). Teachers’ mindsets for students with and without disabilities. Psychology in Schools, 50(10), 1073–1083.Google Scholar
  23. Hallinan, M. T., & Kubitschek, W. N. (1999). Curriculum differentiation and high school achievement. Social Psychology of Education, 3(41), 41–62.Google Scholar
  24. Hanushek, E., & Woßmann, L. (2006). Does educational tracking affect performance and inequality? Differences-in-differences evidence across countries. Economic Journal, 116, 63–76.Google Scholar
  25. Jordan, A., & Stanovich, P. (2003). Teachers’ personal epistemological beliefs about students with disabilities as indicators of effective teaching practices. Journal of Research in Special Educational Needs, 3(1), 1–12.Google Scholar
  26. Jorgensen, R., Gates, P., & Roper, V. (2014). Structural exclusion through school mathematics: Using Bourdieu to understand mathematics as a social practice. Educational Studies in Mathematics, 87(2), 221–239.Google Scholar
  27. Kerckhoff, A. C. (1986). Effects of ability grouping in British secondary schools. American Sociological Review, 51(6), 842–858.Google Scholar
  28. Koncepciya razvitiya matematicheskogo obrazovaniya v rossijskoj federacii [The strategy for development of mathematical education in Russia]. (2013). Retrieved from Accessed 9 January 2019.
  29. Kozlov, V., & Kondakov, A. (Eds.). (2011). Fundamental’noe yadro soderzhaniya obshchego obrazovaniya [The fundamental nucleus of general education curriculum content]. Moscow: Prosveshchenie.Google Scholar
  30. Krapohl, E., Rimfeld, K., Shakeshaft, N. G., Trzaskowski, M., McMillan, A., Pingault, J.-B. J.-B., et al. (2014). The high heritability of educational achievement reflects many genetically influenced traits, not just intelligence. Proceedings of the National Academy of Sciences, 111(42), 15273–15278.Google Scholar
  31. Lawrence-Brown, D. (2004). Differentiated instruction: Inclusive strategies for standards-based learning that benefit the whole class. American Secondary Education, 32(3), 34–62.Google Scholar
  32. Malik, V. (2019). The Russian panel study ‘Trajectories in Education and Careers’. Longitudinal and Life Course Studies, 10(1), 124–144.Google Scholar
  33. Meirink, J. A., Meijer, P. C., Verloop, N., & Bergen, T. C. M. (2009). Understanding teacher learning in secondary education: The relations of teacher activities to changed beliefs about teaching and learning. Teaching and Teacher Education, 25(1), 89–100.Google Scholar
  34. Nicolae, M. (2014). Teachers’ beliefs as the differentiated instruction starting point: Research basis. Procedia - Social and Behavioral Sciences, 128, 426–431.Google Scholar
  35. Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale University Press.Google Scholar
  36. Oakes, J. (1992). Can tracking research inform practice? Technical, normative, and political considerations. Educational Researcher, 21(4), 12–21.Google Scholar
  37. Phillip, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Charlotte, NC: Information Age.Google Scholar
  38. Plomin, R., DeFries, J. C., Knopik, V. S., & Neiderhiser, J. M. (2016). Top 10 replicated findings from behavioural genetics. Perspectives on Psychological Science, 11(1), 3–23.Google Scholar
  39. Rattan, A., Good, C., & Dweck, C. S. (2012). “It’s ok - not everyone can be good at math”: Instructors with an entity theory comfort (and demotivate) students. Journal of Experimental Social Psychology, 48, 731–737.Google Scholar
  40. Riegle-Crumb, C., & Humphries, M. (2012). Exploring bias in math teachers ‘Perceptions of Students’ ability by gender and race/ethnicity. Gender and Society, 26(2), 290–322.Google Scholar
  41. Rosenbaum, J. E. (1976). Making inequality: The hidden curriculum of high school tracking. New York: Wiley.Google Scholar
  42. Rosenthal, R., & Jacobson, L. (1968). Pygmalion in the classroom: Teacher expectations and pupils intellectual development. New York: Holt, Rinehart, and Winston.Google Scholar
  43. Rubie-Davis, C. (2009). Teacher expectations and labeling. In L. J. Saha & A. G. Dworkin (Eds.), International handbook of research on teachers and teaching (pp. 597–707). Boston, MA: Springer.Google Scholar
  44. Scantlebury, K., & Kahle, J. B. (1993). The implementation of equitable teaching strategies by high school biology student teachers. Journal of Research in Science Teaching, 30(6), 537–545.Google Scholar
  45. Scott, J. (2015). Towards a participatory approach to ‘beliefs’ in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education. Exploring a mosaic of relationships and interactions (pp. 3–25). Cham: Springer.Google Scholar
  46. Sirotyuk, A. L., & Duminike, Y. S. (2005). Sovremennye koncepcii obucheniya: tradicionnyj, raznourovnevyj, profil’nyj, individual’nyj, prirodosoobraznyj podhody [Modern conceptions of learning: Traditional, multilevel, cross-sectional, individual, nature-aligned approaches]. Kafedra, 54–63.Google Scholar
  47. Starkova, E. V. (2006). Dostupnost’ vysshego obrazovaniya: ocenka ekspertov [Access to higher education: Experts’ reviews]. Zhurnal issledovanij social’noj politiki, 4(2), 183–205.Google Scholar
  48. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). Thousand Oaks, CA: Sage.Google Scholar
  49. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouwns (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.Google Scholar
  50. Törner, G. (2002). Mathematical beliefs—A search for a common ground: Some theoretical considerations on structuring beliefs, some research questions, and some phenomenological observations. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 73–94). Dordrecht: Kluwer Academic Publisher.Google Scholar
  51. Van Zoest, L. R., & Bohl, J. V. (2005). Mathematics teacher identity: A framework for understanding secondary school mathematics teachers’ learning through practice. Teacher Development, 9(3), 315–345.Google Scholar
  52. Zakharov, A., Carnoy, M., & Loyalka, P. (2013). Which teaching practices improve student performance on high-stakes exams? Evidence from Russia., Series EDU “Education” Moscow: NRU Higher School of Economics.Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.International Laboratory for Educational Policy Analysis, Institute of EducationNational Research University Higher School of EconomicsMoscowRussia

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