Session for London Maths (ATM/MA) Workshop Teaching mathematics for social justice Pete Wright UCL Institute of Education pete.wright@ucl.ac.uk @PeteWrightIOE

What is teaching mathematics for social justice? An activity from the book … Global Inequality task (Measuring Inequality 1): “Global inequality doubled between 1965 and 1990” Use the information in the table below to justify whether or not the above statement is true.

What is teaching mathematics for social justice? Gini Coefficient task (Measuring Inequality 2): Explain how this Lorenz Curve has been drawn. The Gini Coefficient is the ratio of the area between the curve and the diagonal line divided by the area of the triangle below the diagonal line. How could you find these areas?

Group activity Draw a Lonenz curve and calculate the Gini Coefficient for one of the years: 1965/1970/1980/1990/2000/2007 How did you find the area between the curve and the diagonal? Can you do it another way? What is happening to global inequality over time?

What is teaching mathematics for social justice? Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. (National Curriculum, 2007) A high quality mathematics education therefore provides a foundation for understanding the world … (National Curriculum, 2014)

What is teaching mathematics for social justice? A conceptualisation of TMSJ: Collaborative problem-solving approach to teaching maths for all (Boaler, 2009). Recognise students’ real-life experiences – cultural relevance of maths (D’Ambrosio, 2006). Use maths to develop understanding of social, political, economic, cultural Situation (Gutstein, 2006). Develop agency that enables students to engage in social action (Gutstein, 2006) and realise their foregrounds (Skovsmose, 2011). Develop a critical awareness of the nature of maths and its position/status in society (Skovsmose, 2011).

Why is TMSJ important? Consensus – more engaging and relevant maths curriculum needed – greater emphasis on problem-solving and conceptual understanding (Boaler, 2009; ACME, 2011; OFSTED, 2012). High stakes assessment – many maths classrooms focus on factual recall and procedural understanding – disengagement/disaffection (Nardi & Steward, 2003). Government policies emphasise functional maths – driven by demands of economy – ‘functional literacy’ rather than ‘critical literacy’ (Gutstein, 2006) – ‘prescription readiness’ (Skovsmose, 2011). Discourse of inequity – setting as the norm, ability viewed as innate, parallel curricula – school maths as ‘critical filter’. Evidence-based practice – performativity – distrust of new policies amongst teachers – theory/practice divide.

What is teaching mathematics for social justice? Another activity (from the book): What’s going on here? London European Elections 2014 Results Regional List System using D'Hondt Formula (with divisors 1, 2, 3, …) Party: Labour Conservative UKIP Green Lib Dem Number of votes: MEP’s Elected: Taken from European Election task (Proportional Representation 2)

What is teaching mathematics for social justice? Proportional Representation: Is this method fairer? London European Elections 2014 – Hypothetical Results Regional List System using Sainte-Lague Formula (divisors = 1, 3, 5, …)

Discussion What is the purpose of each of the activities we have looked at so far? What are the implications for teaching mathematics for social justice? How might you use these ideas in your classroom?

TMSJ Research Project Five teacher researchers from four different schools. TMSJ Research Group – 7 meetings over one academic year (2013-14). Participatory action research – three cycles. Data collected through interviews and student surveys. Ideas generated from project used for the TMSJ book. More about the research project: http://maths-socialjustice.weebly.com/

Example TMSJ project: Counting the Votes Group activity: Have a go at the Preference Voting task (Counting the Votes 1 – see handout). What would be the ‘fairest’ way of deciding which film to see? Can you make a case for going to see: Cleopatra? Bobby? Tango? Justify your decision to others.

Example TMSJ project: Counting the Votes Borda’s preferential voting system (from Counting the Votes 2): Voters in an election express preferences for each candidate, ‘1’ for their 1st choice, ‘2’ for their 2nd choice, etc. A sequence is then used to award points for each preference. The points for each candidate are then added together and the one with the largest total wins. Borda count with arithmetic weighting: An arithmetic progression is used, e.g. 1, 2, 3, 4, … For 5 candidates, 5 points are awarded for each 1st preference, 4 for each 2nd preference, etc. Borda count with geometric weighting: A geometric progression, e.g. 1, 2, 4, 8, … For 5 candidates, 16 points are awarded for each 1st preference, 8 for each 2nd preference, etc.

Example TMSJ project: Counting the Votes An Unusual Ballot task (Counting the Votes 3): The 11 ballot papers (in the envelope) are from an imaginary election carried out using a preferential voting system. Decide which candidate would win the election under each of the following methods for counting the votes (refer to handout). Relative majority Absolute majority Condorcet Pair-Wise Counting Borda count with arithmetic weighting Borda count with geometric weighting Patil elected McAleese elected Roussef elected Banda elected

Teaching mathematics for social justice … Discussion: How can learning mathematics help bring about a fairer society? How might a focus on equity affect the way we teach mathematics? What would an engaging, meaningful and empowering mathematics curriculum look like? What is mathematics and why do we spend so much time learning it?

Teaching Mathematics for Social Justice Book+PDF = £18 (ATM members £13.50); PDF only = £12 (ATM members £9) https://www.atm.org.uk/Shop/Newly-Available/Teaching-Mathematics-for-Social-Justice

References Boaler, J., 2009. The elephant in the classroom: helping children learn and love maths. London: Souvenir Press. 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. Nardi, E. & Steward, S., 2003. Is mathematics T.I.R.E.D.? A profile of quiet disaffection in the secondary mathematics classroom. British Educational Research Journal, 29(3), pp. 345-367. Noyes, A., 2008. Mathematical marginalisation and meritocracy: inequity in an English classroom. In: B. Sriraman, ed. International perspectives on social justice in mathematics education. Charlotte, NC: Information Age Publishing, pp. 51-68. Skovsmose, O., 2011. An invitation to critical mathematics education. Rotterdam: Sense Publishers.