Abstract
In this paper we share the challenges we encountered while gathering data on young learner mathematical dispositions in the form of written responses to orally administered questionnaires in a context of poor literacy and proficiency in the language of learning and teaching. Drawing on data we gathered from questionnaires with 1208 Grade 3 and 4 learners across twelve schools in the Eastern Cape South Africa we explore what is visible in learner responses and raise issues of concern in relation to aspects of learner dispositions not visible through questionnaires. Differences in literacy levels and competence in the language of instruction affects learner responses in ways that make it difficult to interpret whether differences across schools are as a result of differing mathematical dispositions or rather due to differences in literacy and articulation levels. We open up for discussion both what is gained from the data gathered and explore the challenges of gathering richer data across large numbers of learners with low levels of articulation and literacy.References
Aiken, L. (1974). Two scales of attitudes towards mathematics. Journal for Research in Mathematics Education, 5, 67–71.
Askew, M., Rhodes, V., Brown, M., Wiliam, D. & Johnson, D. (1997). Effective Teachers of Numeracy: Report of a study carried out for the Teacher Training Agency. London.
Bishop, J. P. (2011). ‘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.
Blackwell, L. S., Trzesniewski, K. H. & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: a longitudinal study and an intervention. Child Development, 78(1), 246–263. doi:10.1111/j.1467-8624.2007.00995.x
Bloch, G. (2009). The Toxic Mix: What’s wrong with South Africa’s schools and how to fix it. Cape Town: Tafelberg.
Carnoy, M. & Arends, F. (2012). Explaining mathematics achievement gains in Botswana and South Africa. Prospects, 42(4), 453–468. doi:10.1007/s11125-012-9246-6
Carnoy, M., Chisholm, L., Addy, N., Arends, F., Baloyi, H., Irving, M., . . ., Sorto, A. (2012). The process of learning in South Africa. The quality of mathematics teaching in the North West Province. Technical report. Pretoria.
Carr, M. & Claxton, G. (2002). Tracking the Development of Learning Dispositions. Assessment in Education: Principles, Policy & Practice, 9(1), 9–37.
Chisholm, L. & Chilisa, B. (2012). Contexts of educational policy change in Botswana and South Africa. Prospects, 42(4), 371–388. doi:10.1007/s11125-012-9247-5
Claxton, G. & Carr, M. (2004). A framework for teaching learning: the dynamics of disposition. Early Years, 24(1), 87–97. doi:10.1080/0957514032000179089
Department of Basic Education. (2011a). Curriculum and Assessment Policy Statement Grades 1–3: Mathematics. Policy (0–102). Pretoria: Department of Basic Education, South Africa.
Department of Basic Education. (2011b). Curriculum and Assessment Policy Statement Grades 4–6: Mathematics (1–306). Pretoria: Department of Basic Education, South Africa. doi:10.1787/9789264030206-4-en
Fennema, E. & Sherman, J. A. (1976). Fennema-Sherman Attitude Scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. Journal for Research in Mathematics Education, 7(5), 324–326.
Fleisch, B. (2008). Primary education in crisis: Why South African schoolchildren underachieve in reading and mathematics. Johannesburg: Juta.
Graven, M. (2011). Creating new mathematical stories: exploring opportunities within Maths Clubs. In Proceedings of 17th National Congress of the Association for Mathematical Education of South Africa (AMESA) (161–170). Johannesburg: University of the Witwatersrand.
Graven, M. (2012). Accessing and assessing young learner’s mathematical dispositions. South African Journal of Childhood Education, 2(1), 49–62.
Graven, M. H. (2014). Poverty, inequality and mathematics performance: the case of South Africa’s post-apartheid context. The International Journal of Mathematics Education ZDM. doi:10.1007/s11858-013-0566-7
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, 1791–20, 26–37.
Graven, M. & Heyd-Metzuyanim, E. (2014). Primary learner descriptions of a successful maths learner. In P. Webb, M. G. Villanueva & L. Webb (Eds.), New avenues to transform Mathematics, Science and Technology Education in Africa: Proceedings of the 22nd Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (39–50). Port Elizabeth: Nelson Mandela Metropolitan University.
Graven, M., Venkat, H., Westaway, L. & Tshesane, H. (2013). Place value without number sense: Exploring the need for mental mathematical skills assessment within the Annual National Assessments. South African Journal of Childhood Education, 3(2), 131–143.
Gresalfi, M. S. (2009). Taking up opportunities to learn: Constructing dispositions in mathematics classrooms. Journal of the Learning Sciences, 18(3), 327–369.
Gresalfi, M. S. & Cobb, P. (2006). Cultivating students’ discipline-specific dispositions as a critical goal for pedagogy and equity. Pedagogies: An International journal, 1(1), 49–57.
Hewana, D. & Graven, M. (2014). Grade 4 learners mathematical dispositions: a case study of three learners participating in an after school club. In C. Stevenson-Miln (Ed.), New avenues to transform Mathematics, Science and Technology Education in Africa: Abstracts of the 22nd Annual Meeting of the Southern African Association for Research in Mathematics, Science and Technology Education (49–50). Port Elizabeth: Routledge: Taylor & Francis.
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.
Hoadley, U. (2012a). 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
Hoadley, U. (2012b). 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
Kilpatrick, J., Swafford, J. & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington DC: National Academy Press.
Mulhern, F. & Rae, G. (1998). Development of a shortened form of the Fennema-Sherman Mathematics Attitudes Scales. Educational and psychological Measurement, 58(2), 295–306. doi:10.1177/0013164498058002012
Ndongeni, S. (2014). Examining the nature of the relationship between learners’ conceptual understanding and their mathematical dispositions in the context of multiplication. Unpublished Masters thesis. Rhodes University: Grahamstown.
Schollar, E. (2008). The primary mathematics research project 2004–2007: Towards evidence-based educational development in South Africa. Primary Mathematics. Jhb.
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. doi:10.1207/s1532690xci2302 3
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.
Venkat, H. & Naidoo, D. (2012). Analyzing coherence for conceptual learning in a Grade 2 numeracy lesson. Education as Change, 16(1), 21–33. doi:10.1080/16823206.2012.691686
Wright, R. J., Ellemor-Collins, D. & Tabor, P. D. (2012). Developing Number Knowledge: Assessment, Teaching & Intervention with 7–11 year olds. Los Angeles: Sage Publications.
Wright, R. J., Martland, J. & Stafford, A. K. (2000). Early numeracy: assessment for teaching and intervention. London: Paul Chapman Publishing.