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BCME 9 Conference (University of Warwick)Workshop on Wednesday 4th April 2018 (2.00-3.30pm)Challenging inequity in mathematics education: Sharing teachers’ pedagogical rationale with learnersPete WrightUCL Institute of Educationpete.wright@ucl.ac.uk@PeteWrightIOEwww.maths-socialjustice.weebly.com(This PowerPoint presentation is available on my weebly site)
Structure of workshop • Brief introduction and rationale for the session. • Flags of the World activity (exemplification of strategies). • Discussion of relevant research literature. • Early findings from the ‘Visible Pedagogies’ project. • Analysing notes from a lesson observation/reflective discussion. • Concluding discussion.
Introduction and rationale for session • Strong and persistent association between maths attainment and family income (Boaler et al., 2011; Ernest, 2016). • Bourdieu’s theory on reproduction of inequities through ‘cultural capital’, etc. (Jorgensen, Gates & Roper, 2014). • Teaching Maths for Social Justice Project: ‘progressive pedagogies’ have potential to address attainment gap through raising motivation and engagement (Boaler, 2008; Wright, 2017). • My own observations/reflections with student teachers: clear pedagogical rationale but reluctance to share this with learners. • Bernstein (2000): working class children less able to interpret ‘rules of the game’ – danger of being further disadvantaged by open-ended (progressive) approaches to learning maths. • Dilemma: Avoid progressive approaches altogether or explore ways to make pedagogical rationale more explicit to learners?
Flags of the World activity • Work in a pair or small group. • Choose a flag from the 7 flags on your table. • Think about how you would find the area shaded in each colour. • Is there more than one way of doing it? • Share your ideas with your partner (or others in your group). • Be ready to present your partner’s ideas. • Do the same for some of the other flags.
Making pedagogies visible • What is the difference between the statements in the two columns of the table? • What do you think was the purpose of separating ‘reasoning’ and ‘working-out’ in the table? • Why do you think I asked you to present your partner’s ideas rather than your own? Other questions I might have asked: • Why did I choose these particular 7 flags (out of 197)? • Why did I let you choose which one(s) to look at? • Why did I ask you to work in a pair/small group? What other questions could I have asked?
Quotes from relevant research literature • Work in a small group (3 or 4). • Discuss the selected quotes from the research literature. • Arrange the quotes in order, starting with those you think are most useful for those wishing to address inequities in mathematics education. • Be ready to justify your arrangement to the rest of the group.
Quote 1: Boaler (2008) The [Railside] students were required to solve conceptual problems that were chosen because they could be solved in many different ways and students were valued for such practices as asking exploratory questions, representing ideas in different ways, and making connections; practices that are often absent in mathematics classrooms. … The pedagogical practices that were developed resulted in equitable relations and the diminishment of achievement differences between students from different cultural groups. Boaler, J. (2008). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed-ability approach. British Educational Research Journal, 34(2), pp. 167-194.
Quote 2: Harris and Williams (2012) These findings suggest that teachers may find it more difficult to handle ideas given by children from poorer backgrounds, in the same way as perhaps these children find it more difficult to handle the ideas of their teachers. It would seem, therefore, that if we seek to counteract the social class disadvantage experienced by many children in poorer areas, we may need to attend more closely to the quality of interactions in the classrooms in less affluent communities. Harris, D. & Williams, J. (2012). The association of classroom interactions, year group and social class. British Educational Research Journal, 38(3), pp. 373-397.
Quote 3: Jorgensen, Gates and Roper (2014) A vicious circle has developed: working class students are disadvantaged on entering the school field as they have a less compatible habitus; this manifests itself in underachievement in tests and in less impressive contributions in the classroom, which results in placement in lower ability sets. Here, they are surrounded by pupils with similar habitus and linguistic incompatibility with the school mathematics discourse, which results in slower progression and continued underachievement in assessments, thus widening the gap between these students and the, largely middle-class, pupils in the higher sets. 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, pp. 221-239.
Quote 4: Rubin (2003) This study suggests that teachers can, in some cases, conflate a commitment to progressive pedagogy with the desire to combat educational inequalities, to the detriment of the latter. In other words, the student-centered, active-learning approach central to progressive educational practice may wrongly be assumed to be the best or sole means for improving the achievement of underserved students. … Several researchers have noted that progressive pedagogy can have the ironic effect of reinforcing the very patterns that equity-minded teachers are ideologically committed to disrupting, by continuing to privilege the cultural capital of children from higher socioeconomic backgrounds over those with fewer economic advantages. Rubin, B. (2003). Unpacking detracking: When progressive pedagogy meets students’ social worlds. American Education Research Journal, 40(2), 539-573.
Quote 5: Thule Lubienski (2004) This study illuminates some of the difficulties that lower SES students may encounter with invisible pedagogies in which the authority of the teacher is downplayed, the official discourse of the classroom is not made explicit, and boundaries between everyday and school knowledge are diminished. ... [Morais and Neves, 2001] argue that teachers must use their authority to make evaluation criteria explicit, while also weakening the hierarchical nature of the teacher–student relationship. In this way students learn the privileged text of schooling, including privileged discourse norms and curricular content while also becoming critical thinkers who can question authority. Thule Lubienski, S. (2004). Decoding mathematics instruction: A critical examination of an invisible pedagogy. In J. Muller, B. Davies, & A. Morais, Reading Bernstein, researching Bernstein (pp.91-122). London: Routledge.
Quote 6: Wright (2017) In order for mathematics learning to become genuinely empowering, teachers need to reflect carefully on the relationships they build with students. The research project highlights how trust needs to be established between teachers and students to enable the adoption and development of alternative pedagogies. Relationships also need to be transparent, with teachers helping students to reflect on their views of mathematics and to make sense of their own learning situations. The challenge is to enable all students, particularly those from disadvantaged backgrounds, to develop the types of behaviour, social skills and dispositions that they need to become successful learners of mathematics.. Wright, P. (2017). Critical relationships between teachers and learners of school mathematics. Pedagogy, Culture and Society, 25(4), pp. 315-330.
Early findings from the ‘Visible pedagogies and equitable outcomes in school mathematics’ project Working with 2 teacher researchers (Tiago & Alba) in N. London comp. school with approx 30% FSM. Tried out 2 strategies with mixed att. Year 7’s, using video-stimulated reflection and surveys. • Students intially did not fully appreciate purpose of strategies, e.g. linked strategies to compliance, e.g. enforcing listening. • Through taking discussions further, students began to appreciate more, e.g. value of learning from others’ ideas. • TRs noticed wider range of students responding appropriately to problem solving tasks and grasping mathematical concepts. • TRs initially felt wary about devoting time to discussing strategies but began to appreciate benefits of doing so. • TRs surprised by students’ willingness to engage with idea of discussing strategies/pedagogy and ability to see its benefits. • Videos/surveys provided evidence for TRs on how all students respond to pedagogies – provides clearer pedagogocial focus.
Discussion • In May 2017, I observed a PGCE Maths student teacher (one of my tutees) towards the end of the second placement. • My notes were designed to capture dialogue and events to act as useful prompts for a post-lesson evaluative discussion. • This discussion focused on the desirability of making the pedagogical rationale clearer to students, e.g. what was the purpose of the starter and are rough sketches of the shapes sufficient? (discussion promted ideas/notes in second column). • The class was a Year 8 lower set. The lesson objective was finding the volume of prisms (starting with cuboids). Refer to the notes from the lesson observation and follow-up reflective discussion as a prompt. Discuss: • What other strategies might be used to make the pedagogical rationale more explicit to learners?
Concluding discussion • What insight have you gained from this workshop? • How will it be useful to you in your future practice?
References • Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory, research, critique. Revised edition. Lanham, Maryland: Rowman and Littlefield. • Boaler, J. (2008). Promoting ‘relational equity’ and high mathematics achievement through an innovative mixed-ability approach. British Educational Research Journal, 34(2), pp. 167-194. • 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), pp.457-484. • Ernest, P. (2016). The scope and limits of critical mathematics education. In P. Ernest, B. Sriraman, & N. Ernest (Eds.), Critical mathematics education: Theory, practice and reality (pp. 99-126). Charlotte, NC: Information Age Publishing. • Harris, D. & Williams, J. (2012). The association of classroom interactions, year group and social class. British Educational Research Journal, 38(3), pp. 373-397. • 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, pp. 221-239. • Rubin, B. (2003). Unpacking detracking: When progressive pedagogy meets students’ social worlds. American Edcuation Research Journal, 40(2), pp. 539-573. • Thule Lubienski, S. (2004). Decoding mathematics instruction: A critical examination of an invisible pedagogy. In J. Muller, B. Davies, & A. Morais, Reading Bernstein, researching Bernstein (pp.91-122). London: Routledge. • Wright, P. (2017). Critical relationships between teachers and learners of school mathematics. Pedagogy, Culture and Society, 25(4), pp. 315-330.
