Why teachers of Foundation Phase mathematics have yet to ‘take up’ progressive roles.

1. Why teachers of Foundation Phase mathematics have yet to ‘take up’ progressive roles. Lise Westaway and Mellony Graven Rhodes University

2. What we argue in this paper Structures (social and cultural) Teachers’ expression of their roles as teachers Reproduction of structures Change in structures CONDITION LEADS TO

3. Context • Learner performance in SA is in crisis (Fleisch, 2008; Reddy et al., 2015 etc) (Robertson & Graven, 2015, p. 13)

4. Teacher-centered practices Learning- and learner– centered practices One-size-fits-all Mediating diverse learner needs Procedural knowledge Number sense and conceptual understanding Systemic roles of the teachers pre- and post-1994

5. Critical and social realism • Ontologically realist and epistemologically relativist. Bhaskar's stratified reality (Bhaskar, 2008, p. 2) • Reality is stratified and differentiated

6. Archer’s social realism and morphogenetic approach Structural and cultural conditioning T1 (pre-1994 & post-1994 systemic roles of teachers, beliefs etc.) Social-cultural interaction T2 T3 (expressing one’s role as a teacher) Structural and cultural elaboration Structural and cultural reproduction T4 (change or reproduction of particular systemic roles, beliefs, classroom interactions etc.)

7. Teacher-centered practices Learning- and learner– centered practices One-size-fits-all Mediating diverse learner needs Procedural knowledge Number sense and conceptual understanding Systemic roles of the teachers pre- and post-1994

8. Claim 1 The two ‘sets’ of systemic roles have created a situational logic of contradiction for the teachers. (Archer, 1995)

9. Methodology • Four Eastern Cape grade 3 teachers in no-fee paying schools where the LoLT was isiXhosa • Life History, Maths History and Practice Interviews and Observations. • Three modes of inference: • Inductive reasoning • Abduction – developing a deeper conception of the phenomenon by framing with a different theory • Retroduction (transfactual questions: what is it about teachers’ identities and their expression in teaching FP mathematics that makes them such?

10. Beliefs that militate against the role of learning mediator • “Mathematics is difficult” / “Not everyone can do mathematics” • “Teachers must explain maths clearly” / “Children must listen attentively”

11. Mathematics is difficult / Not everyone can do maths “Basically I think maths is a very challenging subject, especially to learners, as you can see, look at their faces when they do maths. They look so lost and they know nothing. I don’t know what it is” (Nomsa, MHI, t.114).

12. Mathematics is difficult / Not everyone can do maths “Yes, if my learners have got that (referring to counting and number operations), I’m sure they will pass. Other things like place value, expanded notation, it’s a lot, but I must make sure they can add. These kids it’s so difficult for them.” (Beauty, MHI, t.94) Beauty: Restricted mathematics curriculum and low cognitive demand “Have you noticed that I just did addition, I didn’t do the carrying? I’m afraid, they don’t know how to. It’s few that can [carry]. I’ve done that with the two-digit numbers and we haven’t done it with the three-digit.” (Beauty, MHI, t.96)

13. Mathematics is difficult / Not everyone can do maths Nomsa: Curriculum that is abstract and devoid of sense-making. (Nomsa, FN, pp.10-11) Throughout this section of the lesson, Nomsa’s body faces the ‘first group’ in her class. When asked about this she responded “it’s because I know the answer is going to obviously come from them” (Nomsa, PI2, t.88).

14. Mathematics is difficult / Not everyone can do maths Veliswa: Promotes a proceduralised curriculum. “What is the difference between 35 and 45?” 35+2+2+2+2+2 What is ‘5–5’? ‘10’ IIIII She writes ‘0’ under the units. Together with the children they work out ‘4–3’ and the teacher writes a ‘1’ under the tens column.

15. Mathematics is difficult / Not everyone can do maths 108-66=(100)+(00-60)+(8-6) 309 = 300 + 00 + 9 Write ‘401’ in the house below: Nokhaya: Attempts to make calculating error proof through stating rules for children to follow.

16. Teachers must explain maths clearly / Children must listen attentively “It’s just that the person who taught us that maths, didn’t explain thoroughly how it was done and because I was scared, I didn’t understand it clearly” (Veliswa, MHI, t.112) “I think another problem, when you are doing examples on the board; they are playing, they are not listening. They are not listening at all, especially those ones who are not clever in class. They are the ones who are not listening while you are teaching … When it comes the time to answer questions they know nothing.” (Nomsa, MHI, t.116)

17. Claim 2 The beliefs that teachers hold onto stand in a relation of complementarity with the pre-1994 roles. This has created a situational logic of protection. (Archer, 1995)

18. Why have teachers of Foundation Phase mathematics not yet ‘taken up’ progressive roles?

19. Thank you

20. References • Archer, M. S. (1995). Realist social theory: the morphogenetic approach. Cambridge: Cambridge University Press • Archer, M. S. (1996). Culture and agency: The place of culture in social theory. Cambridge: Cambridge University Press • Archer, M. S. (2000). Being Human: The problem of agency. Cambridge: Cambridge University Press.Archer, M. S. (2007). Making our way through the world: Human reflexivity and social mobility. Cambridge: Cambridge University Press •  Archer, M. S. (2015). The relational subject and the person: self, agent, and actor. In P. Donati, & M. S. Archer (Eds.). The relational subject (pp. 85-122). Cambridge: Cambridge University Press • Bhaskar, R. (2008). A realist theory of science (4thed). London: VersoFleisch, B. (2008). Primary education in crisis: Why South African school children underachieve in reading and mathematics. Cape Town: Juta • Reddy, V., Zuze, T. L., Visser, M., Winnaar, L., Juan, A., Prinsloo, C. H., … Rogers, S. (2015). Beyond Benchmarks: What twenty years of TIMSS data tells us about South African education. Cape Town: HSRC Press • Robertson, S-A., & Graven, M. (2015). Exploring South African mathematics teachers’ experiences of learner migration. Rhodes University, Education Department, Grahamstown.