Educational Studies in Mathematics

, Volume 91, Issue 3, pp 349–373 | Cite as

Between people-pleasing and mathematizing: South African learners’ struggle for numeracy

Article

Abstract

The reported research attempts to trace possible reasons for third grade learners’ limited progress in numeracy in a low socioeconomic status (SES) South African context. This is done through two lenses, both stemming from Sfard’s commognitive (The term “commognition” has been offered by Sfard (2008) as an amalgam of “cognition” and “communication,” thus expressing the unity of these concepts. Since its original appearance, some authors (including Sfard herself) have preferred using the word “communicational” to describe Sfard’s framework. We chose to stick with “commognitive” because we believe it clearly points to the specific theoretical stance presented in Sfard (2008), whereas “communicational” might point to many other theories or frameworks that have something to do with human communication.) framework. One lens aims to analyze two learners’ (Mina and Ronaldo (all names are pseudonyms)) mathematical and identity discourse both in one-on-one interviews and in a small group “math club” lesson led by the second author. The other examines the mathematical milieu in which these learners have participated through the analysis of a school mathematics lesson which exemplifies prevalent instructional practices in this milieu. Relying on the distinction between ritual and explorative participation, we show that while Mina was acting in an extremely ritualized manner, Ronaldo was more explorative in his actions. However, the milieu, as seen in the school lesson, encouraged almost exclusively ritual participation. Thus, while Mina was identified as a good student, Ronaldo was identified as an outcast or “troublemaker.” We conclude by drawing implications to the tenacious nature of rituals in the mathematics classroom and the effects that these rituals may have on students’ identities.

Keywords

Commognition Ritual learning Explorative learning Identity Discourse Struggling students Mathematical milieu Learning difficulties 

References

  1. Askew, M., Brown, M., Rhodes, V., Johnson, D., & William, D. (1997). Effective teachers of numeracy. London: King’s College/TTA.Google Scholar
  2. Ben-Yehuda, M., Lavy, I., Linchevsky, 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
  3. DBE. (2012). Report on the annual national assessment 2012: Grades 1 to 6 & 9. Pretoria, South Africa: Basic Education Department.Google Scholar
  4. Department of Basic Education. (2011). Curriculum and assessment policy statement grades 1–3: Mathematics. Pretoria, South Africa: Basic Education Department.Google Scholar
  5. Dweck, C. (1986). Motivational processes affecting learning. American Psychologist, 41(10), 1040–1048.CrossRefGoogle Scholar
  6. Dweck, C. (2000). Self-theories: Their role in motivation, personality, and development. Lillington: Taylor & Francis.Google Scholar
  7. Fleisch, B. (2008). Primary education in crisis: Why South African schoolchildren underachieve in reading and mathematics. Johannesburg: Juta.Google Scholar
  8. Giddens, A. (1984). The constitution of society: Outline of the structuration theory. Cambridge: Polity.Google Scholar
  9. Graven, M. (2011). Creating new mathematical stories: Exploring opportunities within maths clubs. In H. Venkat & A. A. Essien (Eds.), Proceedings of 17th National Congress of the Association for Mathematical Education of South Africa (AMESA) (pp. 161–170). Johannesburg: University of Witswatersrand.Google Scholar
  10. Graven, M. (2012). Accessing and assessing young learner’s mathematical dispositions. South African Journal of Childhood Education, 2(1), 49–62.Google Scholar
  11. Graven, M. (2014). Poverty, inequality and mathematics performance: The case of South Africa’s post-apartheid context. ZDM Mathematics Education, 46, 1039–1049.CrossRefGoogle Scholar
  12. Graven, M., Hewana, D., & Stott, D. (2013). The evolution of an instrument for researching young mathematical dispositions. African Journal of Research in Mathematics, Science and Technology Education, 17, 26–37. doi:10.1080/10288457.2013.826968 Google Scholar
  13. Graven, M., & Heyd-Metzuyanim, E. (2014). Zkoumání omezení a mo ž ností v ý zkumu matematick ý ch schopností u ž ák ů s nízkou úrovní gramotnosti [Exploring the limitations and possibilities of researching mathematical dispositions of learners with low literacy levels]. Scientia in Educatione, 5(1), 1–16.Google Scholar
  14. Gresalfi, M. (2009). Taking up opportunities to learn: Constructing dispositions in mathematics classrooms. Journal of the Learning Sciences, 18(3), 327–369.CrossRefGoogle Scholar
  15. Heyd-Metzuyanim, E. (2013). The co-construction of learning difficulties in mathematics—Teacher–student interactions and their role in the development of a disabled mathematical identity. Educational Studies in Mathematics, 83(3), 341–368.CrossRefGoogle Scholar
  16. Heyd-Metzuyanim, E. (2015). Vicious cycles of identifying and mathematizing—A case study of the development of mathematical failure. Journal of the Learning Sciences. Advance online publication. doi:10.1080/10508406.2014.999270
  17. 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.CrossRefGoogle Scholar
  18. Heyd-Metzuyanim, E., Tabach, M., & Nachlieli, T. (2015). Opportunities for learning given to prospective mathematics teachers: Between ritual and explorative instruction. Journal of Mathematics Teacher Education. Advance online publication. doi:10.1007/s10857-015-9311-1
  19. Hoadley, U. (2012). What do we know about teaching and learning in South African primary schools? Education as Change, 16(2), 187–202. doi:10.1080/16823206.2012.745725 CrossRefGoogle Scholar
  20. Jacobs, J., Hiebert, J., Givvin, K., Hollingsworth, H., Garnier, H., & Wearne, D. (2006). Does eighth-grade mathematics teaching in the United States align with the NCTM standards? Results from the TIMSS 1995 and 1999 video studies. Journal for Research in Mathematics Education, 37(1), 5–32.Google Scholar
  21. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.Google Scholar
  22. McCloskey, A. (2014). The promise of ritual: A lens for understanding persistent practices in mathematics classrooms. Educational Studies in Mathematics, 86(1), 19–38.CrossRefGoogle Scholar
  23. Reddy, B. (2006). Mathematics and science achievement at South African schools in TIMSS 2003. Cape Town: HSRC Press.Google Scholar
  24. Roth, W. M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense.CrossRefGoogle Scholar
  25. Roth, W. M., & Tobin, K. (2007). Science, learning, identity: Sociocultural and cultural-historical perspectives. Rotterdam: Sense.Google Scholar
  26. SANCP. (2015). The South African Numeracy Chair Project, Rhodes University, 2015 indicator report. Grahamstown, South Africa: Rhodes University.Google Scholar
  27. Schollar, E. (2008). Final report—The primary mathematics research project 2004–2007 towards evidence-based educational development in South Africa. Johannesburg, South Africa: Eric Schollar and Associates.Google Scholar
  28. Sfard, A. (2008). Thinking as communicating. New York: Cambridge University Press.CrossRefGoogle Scholar
  29. 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(2), 237–309.CrossRefGoogle Scholar
  30. 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
  31. Spaull, N. (2013). Poverty & privilege: Primary school inequality in South Africa. International Journal of Educational Development, 33(5), 436–447.CrossRefGoogle Scholar
  32. Sztajn, P. (2003). Adapting reform ideas in different mathematics classrooms: Beliefs beyond mathematics. Journal of Mathematics Teacher Education, 6, 53–75.CrossRefGoogle Scholar
  33. Taylor, N., & Vinjevold, P. (Eds.). (1999). Getting learning right: Report of the president’s education initiative research project. Johannesburg: Joint Education Trust.Google Scholar
  34. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  35. Wright, R. J., Martland, J., Stafford, A. K., & Stanger, G. (2006). Teaching number: Advancing children’s skills and strategies (2nd ed.). London: Paul Chapman.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of Education in Science and TechnologyTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Learning Research and Development CenterUniversity of PittsburghPittsburghUSA
  3. 3.Rhodes UniversityGrahamstownSouth Africa

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