Making Pedagogical Rationale Explicit to Mathematics Learners

1. BSRLM Conference – 10th June 2017 (Oxford)Critical Mathematics Education Working GroupStructure of session12.00-12.30:A discussion of an idea for a future research project on Making pedagogical rationale explicit to mathematics learners(led by Pete Wright, UCL Institute of Education)12.30-1.00:A discussion of possible foci for future meetings and potential areas of research that resonate with the working group’s aims(Chaired by Heather Mendick)

2. BSRLM Conference – 10th June 2017 (Oxford)Critical Mathematics Education Working GroupMaking pedagogical rationale explicit to mathematics learnersA discussion led by …Pete WrightUCL Institute of Educationpete.wright@ucl.ac.uk@PeteWrightIOE

3. Rationale for session • As a PGCE Secondary Maths tutor, I regularly observe lessons taught by student teachers (STs). • Clear from reflective discussions that STs have a clear (and often highly advanced) pedagogical rationale. • However, I have become increasingly aware of an apparent reluctance to share this pedagogical rationale with learners. • Bernstein’s notion of strong and weak ‘framing’ suggests that working-class children may be disadvantaged by open-ended approaches to learning mathematics (see following slides). • Does this mean that such pedagogical approaches should be avoided? Or should we continue to explore ways for student teachers to engage with these teaching approaches whilst making their rationale more explicit to learners?

4. Background • Strong association between maths attainment and family income (Boaler et al., 2011); • Reproduction of inequities through ‘cultural capital’ (Bourdieu & Passeron, 1990; Jorgensen et al., 2014). • Alternative pedagogical approaches advocated to address issues of equity/social justice: • problem-solving, discussion, group work (Boaler, 2009); • building on real-life experiences (D’Ambrosio, 2006); • inquiries that develop understanding of social/cultural/political/economic situations (Gutstein, 2006); • students making decisions about the direction of learning (Skovsmose, 2011).

5. Theoretical framework (Bernstein, 2000) • Mathematics has strong ‘classification’ – separate from other subjects – specialised rules for communication and behaviour. • Maths involves strong ‘framing’ – teacher viewed as transmitting knowledge – substantial control over discursive and social order. • Success in maths depends on students’ ability to decipher the ‘rules of the game’: • ‘recognition rules’ – identifying relevant meaning from tasks set; • realisation rules’ – formulating appropriate responses/legitimate actions. • ‘Rules of the game’ are less explicit when tackling more open-ended tasks – framing is weaker. • Students from working-class backgrounds further disadvantaged – less able to create own framing to make effective use of realisation rules.

6. Theoretical framework (Lerman & Zevenbergen, 2004) • Lubianski: working-class students in US disadvantaged by model of inquiry-based teaching using relevant/meaningful contexts. • Dilemma for those advocating investigative approaches to teaching maths, in which learners are given less direction and greater autonomy, and who wish to achieve equitable outcomes. • “Some work needs to be done, both theoretically and practically, to mitigate the effects of invisible pedagogies - such as through modifying the strength of framing” (L&Z, 2004, p. 37). • Teachers need to reflect carefully on their own expectations of students from different social backgrounds and become more aware of how these influence their responses to classroom tasks. This will help teachers to avoid interpreting misrecognition of implicit classroom norms as non-compliant misbehaviour.

7. Extract from brief analysis of data:

8. Discussion • Potential for conducting collaborative research into developing strategies for making pedagogical rationale explicit? • Who might be involved in conducting the research? Teacher educators? Experienced teachers? Early career teachers? Student teachers? • What might such research look like? Methodology? • What teaching approaches and classroom management strategies might be explored? • How might we assess the impact of the research on teachers and learners? • How might the impact on the reproduction of inequities through existing mathematics teaching practice be assessed? • What might be the outcomes of the research? CPD module?

9. References • Bernstein, B., 2000. Pedagogy, Symbolic Control and Identity: Theory, Research, Critique. Revised edition. Lanham, Maryland: Rowman and Littlefield. • Boaler, J., 2009. The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press. • Boaler, J., Altendorf, L. and Kent, G., 2011. “Mathematics and Science Inequalities in the United Kingdom: When Elitism, Sexism and Culture Collide.” Oxford Review of Education 37 (4): 457-484. • Bourdieu, P., and Passeron, J.-C., 1990. Reproduction in Education, Society and Culture. 2nd ed. London: Sage. • D’Ambrosio, U., (2006). Ethnomathematics: Link between traditions and modernity. Rotterdam: Sense Publishers. • Gutstein, E. 2006. Reading and Writing the World with Mathematics: Toward a Pedagogy for Social Justice. New York: Routledge. • Jorgensen, R., Gates, P. and Roper, V., 2014. “Structural Exclusion Through School Mathematics: Using Bourdieu to Understand Mathematics as a Social Practice.” Educational Studies in Mathematics 87: 221-239. • Lerman, S., and Zevenbergen, R., 2004. “The Socio-Political Context of the Mathematics Classroom: Using Bernstein’s Theoretical Framework to Understand Classroom Communications.” In Researching the Socio-Political Dimensions of Mathematics Education, edited by P. Valero and R. Zevenbergen, 27-42. Dordrecht: Kluwer. • Skovsmose, O., 2011. An Invitation to Critical Mathematics Education. Rotterdam: Sense. R.

10. BSRLM Conference – 10th June 2017 (Oxford)Critical Mathematics Education Working GroupA discussion of possible foci for future meetings and potential areas of research that resonate with the working group’s aims: 1. Focus and future activities? 2. Structure and organisation? 3. Influencing others?Chaired by Heather MendickThank you to Peter Gates, Tatiana Rostovtseva and Pete Wright for suggesting questions.

11. 1. Focus and future activities? • What is the purpose of a CME (BSRLM) Working group?Is it for intellectual discussion, activism, disruption …? • How can the group promote sharing ideas, mutual support and collaboration amongst its members? • What is Critical Mathematics Education (CME)?Is the description in the abstract (2nd/3rd sentences) accurate? • What strategies work to pull teachers away from dominant narratives to critical narratives? • Should we undertake lesson/task design to foster critical maths education. • Should we focus on one theme at a time?What about ‘ability grouping’, ‘decolonizing maths ed’ …?

12. 2. Structure and organisation? • Are you happy for Suman Ghosh and Pete Wright to act as coordinators for the group? Any other volunteers? • Are we ready to request a space on the BSRLM website’s ‘Working Groups’ page? http://www.bsrlm.org.uk/working-groups/Reports from meetings? • Should we adopt the structure of today’s meeting for future meetings?If so, any suggestions for next meeting?(11th November 2017 @ Liverpool Hope) • Other ideas for sustaining the momentum of the group?Discussion Forum?

13. 3. Influencing others? • How can we convince others of the relevance and importance of CME? • How do we turn outputs into impact? • How can we ACTUALLY influence policy? • Should we orient ourselves to the Labour Party and work to influence policy? • Should we engage with other parties?Left-leaning or broader audience? • Should we reach out to other organisations?Which ones?