“ We all play teacher”

1. “We all play teacher” Naturally-occurring student discourse in adult numeracy classrooms Helen OughtonUniversity of Bolton ALM-16 8th July 2009

2. Introduction • Taking advantage of recent increase in collaborative groupwork in adult numeracy classrooms • Source of naturally-occurring discourse for audio recording and analysis • Research questions • How much do students draw on informal numeracy practices and ‘funds of knowledge’? • What else can classroom discourse tell us about experiences of adult numeracy learners?

3. Theoretical perspectives: Numeracy as a Social Practice • Numeracy practiced differently in different domains • Some forms of numeracy more powerful than others • Takes into account beliefs, attitudes, fears and aspirations of people carrying out activities involving numbers • (Street 1984; Barton and Hamilton 1998; Baker 1998; Street, Baker and Tomlin 2005)

4. Theoretical perspectives:Funds of Knowledge • Moll et al (1992) - Ethnographic research among Mexican families in Arizona • Extended by Baker (2005) to adult numeracy learners • knowledge, experiences, histories, identities and images of themselves • attitudes, dispositions, desires, values, beliefs, and social and cultural relations • relationships with learning, teachers and mathematics itself • numeracy practices beyond the classroom

5. Collaborative groupwork as research opportunity • Breaks with IRE tradition • Based on work of Swan and colleagues • (e.g. Swan 2006; Swain and Swan 2007) • Legitimated as good practice by Ofsted (2006)

6. Methodology

7. Classroom talk as data • Many informal numeracy practices invisible • “The facts of greatest value for the study of education are…most readily displayed in classroom talk.” • (Edwards and Westgate 1994:55) • Linguistic Ethnography • Language and social world mutually shaping • Close analysis of naturally-occurring talk givesinsights into social settings and wider structures (Rampton et al 2004)

8. Research Setting • Adult education centres in north of England • Classes chosen where discursive groupwork encouraged • 6-11 students in each class • Working in groups of 3-5 • Participants largely female, white-British • Age range 20-60 years • Working towards Level 1 and Level 2 Adult Numeracy qualifications

9. Method of data collection • Audio recording of student-student discussion during collaborative groupwork • Little intervention from teacher • Naturalistic data? • Mobile phones unobtrusively on classroom tables • Labov(1972) - speakers’ talk becomes more natural when intensely engaged in subject under discussion

10. Method of data collection (contd) • Usual classroom activities – not specially planned for research • Card matching (e.g. dominoes, jigsaws) • Card sorting and categorising • Traditional worksheets and assessment papers • Data collected • 3 centres • 10 sessions • 18 participants • 12 hours of recorded discussion

11. Examples of activities: Thinking Through Mathematics (DfES 2007)

12. Examples of activities: designed by participating teacher

13. Emerging Themes The adult numeracy classroom as a site of social interaction

14. The adult numeracy classroom as a community of practice • Students join groupwork via legitimate peripheral participation (Lave and Wenger 1991) • Classroom has discourse of its own • Regular practices • Administration and accreditation procedures • Laughter prevalent • Humour as a “resource” in adult numeracy classrooms (Baynham 1996) • Excluded from community of practice • ESOL • Disabilities or learning difficulty

15. Uncertainty and Self-deprecation • Lack of self-confidence amongst adult numeracy learners well-recognised • Generally regarded as problematic • Expressions of uncertainty prevalent in my recordings • “…I think” • “…isn’t it?” • “Would that be…?” • “It was just a guess” • “I’m getting myself muddled up“ • “Why can’t I do it?”

16. Uncertainty and Self-deprecation • Expressions of uncertainty acknowledged and accepted by group • By male as well as female students • Used by students to: • Elicit encouragement and support from other students • Invite other students to evaluate contributions • Articulate difficulties and formulate questions for teacher • Elicit suggestions for metacognitive strategies E.g. “I draw pies” (to visualise fractions) • Could almost be regarded as a resource?

17. Uncertainty and Self-deprecation

18. Uncertainty and Self-deprecation

19. Emerging themes Context and Relevance

20. Relevance of classroom maths to adult learners lives? • Students only occasionally drew on “funds of knowledge” • Most often in measure and data handling discussion activities • Least often in traditional word problems, including practice assessment materials

21. Relevance of classroom maths to adult learners lives? • “Contexts” in traditional word problems largely ignored • (Oughton 2009) • Current assessment materials in England consist entirely of word problems • Level 1 and Level 2 Adult Numeracy

22. Alternatives to word problems

23. Alternatives to word problems • allowed students to critique relevance DfES 2007

24. Alternatives to word problems • Seemed to encourage students to relate to out of classroom practices • Conditional tense?

25. Alternatives to word problems

26. Alternatives to word problems

27. Alternatives to word problems • Salaries in a small company used to illustrate how outlying values (e.g. director’s salary) distort mean • Example often used in numeracy classrooms • Given extra impact by randomly distributing cards to each student showing a salary • Students spontaneously seized on chance to role play

28. Alternatives to word problems

29. The relevance of learning to students’ lives • Students’ interests not always in line with government focus on skills for employment! • Body image often seemed to be considered important • Social practice a more useful framework here than funds of knowledge

30. The relevance of learning to students’ lives

31. Emerging themes Implications for Pedagogy

32. Implications for Pedagogy Rarity of formal mathematical discourse (LSIS/Tribal 2008)

33. Implications for Pedagogy Rarity of formal mathematical discourse

34. Implications for Pedagogy Multimodal representation and card activities - scaffolding

35. Implications for Pedagogy Multimodal representation and card activities – referencing abstract ideas

36. Implications for Pedagogy Informal Calculation Strategies • Makes ‘invisible’ practices audible • Multiplication by repeated addition • Addition by counting on

37. Other implications for Pedagogy • ‘Gestalt’ moments audible • Students’ (over-)reliance on algorithms • Groupwork flounders if students tackle work outside ZPD • Potential of this method as a CPD tool for teachers

38. Emerging implications for practice and further research • Simplicity / effectiveness of research method • Irrelevance of ‘contexts’ in word-problem genre • Numeracy ‘funds of knowledge’ not often used • Alternative activities encouraged more links to out-of-classroom numeracies • Has implications for roll-out of ‘Functional Skills’ in England • Expressions of uncertainty not so much a ‘problem’ as a ‘resource’? • Exclusion of some students from participation in collaborative groupwork

39. Limitations and opportunities for further study • Reflects only adults who have chosen to return to study • Data seems ‘naturalistic’, but hard to prove • Audio data only one aspect of classroom interaction • Future directions • How to make collaborative groupwork more inclusive • Potential for teacher CPD • Application to functional skills agenda (in England)

40. References Baker, D. (1998) ‘Numeracy as Social Practice; an adult education context in South Africa’ Journal of Literacy and Numeracy Studies 8(1) pp. 37-50 Baker, D. (2005) ‘Numeracy and “funds of knowledge” ’ Reflect 3 pp. 16-19 Barton, D. and Hamilton, M. (1998) Local Literacies: Reading and writing in one community London: Routledge Baynham, M. (1996) ‘Humour as an Interpersonal Resource in Adult Numeracy Classes’ Language And Education 10 (2&3) pp.187-200 DfES (2007) Thinking Through Mathematics: Strategies for Teaching and Learning London: Department for Education and Skills (Maths4Life) Edwards, A. and Westgate, D. (1994) Investigating Classroom Talk London: Falmer Labov, W. (1972) Sociolinguistic Patterns Philadelphia, PA: University of Pennsylvania Press Lave, J., and E. Wenger (1991). Situated Learning: Legitimate peripheral participation. Cambridge: Cambridge University Press LSIS/Tribal (2008) Key skills application of number/ Adult numeracy Level 2 Test Paper L [Available on-line at www.move-on.org.uk/downloadsFile/ downloads1576/Num_Level2_TestL_Jan08.pdf accessed 27.6.09] Moll, L., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: using a qualitative approach to connect homes and classrooms. Theory into Practice, 31, pp.132-141. Oughton, H. (2007) ‘Constructing the “Ideal Learner”: A Critical Discourse Analysis of the Adult Numeracy Core Curriculum’ Research in Post-Compulsory Education 12 (2) pp.259-275.

41. References Ofsted (2006) Evaluating mathematics provision for 14–19-year-olds. London: HMSO Oughton, H (2008) ‘Mapping the Adult Numeracy Curriculum: Cultural capital and Conscientization’, Literacy and Numeracy Studies 16 (1) pp 39-61 Oughton, H. (2009) ‘A willing suspension of disbelief? “Contexts” and recontextualisation in adult numeracy classrooms’, Adults Learning Mathematics: An International Journal 4(1) pp16-31 Rampton, B., Tusting, K., Maybin, J., Barwell, R., Creese, A. and Lytra, V. (2004) UK Linguistic Ethnography: A discussion paper. Available on line at www.ling-ethnog.org.uk/documents/discussion_paper_jan_05.pdf [accessed 22/07/07] Skillsworkshop (2007) Percentages – Level 2. Available on-line at www.skillsworkshop.org/l2num/l2percentageprobs.pdf [accessed 29/11/08] Street, B. (1984). Literacy in Theory and Practice. Cambridge: Cambridge University Press. Street, B., Baker, D and Tomlin, A. (2005) Navigating Numeracies: Home/School Numeracy PracticesDordrecht: Kluwer Swain, J. and Swan, M. (2007) Thinking Through Mathematics Research Report London: NRDC. Swan, M. (2006) Collaborative Learning in Mathematics: A Challenge to our Beliefs and Practices. London: National Institute for Adult and Continuing Education (NIACE); National Research and Development Centre for adult literacy and numeracy (NRDC).