Freedom to learn and teach: Towards a relevant, meaningful and empowering school mathematics
Institute of Education, London
The school curriculum currently disempowers both learners and teachers of mathematics. Students are commonly taught mathematics in a way that they find tedious, irrelevant and meaningless (Nardi & Steward, 2003). Teachers feel pressured to adopt traditional approaches to teaching mathematics which focus on following routines and standard procedures, and completing repetitive exercises from a text book or worksheets (Boaler, 2009). The result is high levels of alienation and disengagement of students from mathematics, resulting in generally negative attitudes towards mathematics amongst children and adults alike (Black, et al., 2009). Thus, the huge amount of time spent learning mathematics at school (approximately 2000 hours by the age of 16) fails to equip students with the mathematical skills they need to become active citizens and to solve problems they come across in employment, higher education or real life.
It doesn’t have to be this way. There is a consensus amongst the mathematics education community, which has grown steadily since the publishing of the Cockcroft (1982) Report, that alternative teaching approaches are needed with a greater focus on mathematical thinking and reasoning, and developing conceptual understanding and problem-solving skills. Students need to be encouraged to work collaboratively and to discuss, explain and justify their results mathematically. Several research projects have aimed to demonstrate how such pedagogies can be put into practice (Sebba, et al., 2012). There are numerous colleagues, in school mathematics departments across the country, struggling to incorporate such approaches into their schemes of work and classroom practice. Unfortunately, these efforts are routinely thwarted by restrictive educational policies, introduced by successive governments (Wright, 2012), and the conditions that currently prevail in schools.
The new National Curriculum programmes of study (DFE, 2013) include a promising introductory statement advocating mathematical fluency, reasoning and problem-solving. Unfortunately, the remainder of the document then focuses exclusively on discrete areas of mathematics, cramming in even more subject content, rather than promoting deeper understanding and a greater appreciation of the links between different topics. Unlike the previous version of the National Curriculum, which argued that working collaboratively and tackling open-ended tasks are integral to learning (QCA, 2007), the new document does little to challenge traditional approaches to teaching mathematics. In contrast, it completely avoids providing guidance on how to teach the subject content, claiming that this decision is better left to teachers’ own professionalism. This is somewhat disingenuous given the growing pressures teachers face on a day-to-day basis from excessive workload, high-stakes testing, and ever-increasing levels of monitoring and scrutiny. These pressures result in a tendency to ‘teach to the tests’, rush through schemes of work, and adopt ‘low-risk’ teaching strategies, in which students get on with their work quietly and produce lots of written work in their exercise books. To a senior member of staff (most likely not a subject specialist), deciding to carry out an unannounced five-minute monitoring visit (a more and more common occurrence), it might appear that students are making good progress.
Performance management of teachers often involves setting targets based on implementing pre-selected research findings, rather than encouraging teachers to engage in and with research themselves (Hammersley, 2004). Hoping to influence education policy in such a climate might appear to be somewhat futile. However, there is another way of challenging the status quo by adopting a bottom-up, rather than top-down, approach to bringing about change in practice. Participatory action research involves teachers and researchers working collaboratively to develop, try out and reflect upon new classroom activities and teaching approaches. Such an approach offers a systematic and rigorous approach to generating research findings which are of direct relevance to other classroom practitioners. Skovsmose and Borba (2004) propose a critical model of participatory action research, in which teacher researchers reflect critically upon their current practice and try out alternative approaches, taking into account both theoretical knowledge and the constraints that teachers face on a day-to-day basis.
From May 2013 to July 2014, I facilitated a research project, based on the above research model, working with five teacher researchers in London schools with relatively high levels of social deprivation. The aim of the project was to develop classroom practices and approaches to learning which promote teaching mathematics for social justice. Through interrogating their own practice in relation to previous research findings, the teacher researchers developed a deeper understanding of the nature of school mathematics. They began to appreciate how traditional teaching approaches and perceptions of mathematics contribute towards disadvantaging particular groups of students and reproducing inequities in society. Through the collaborative planning and evaluation of classroom activities, teacher researchers generated ideas which significantly increased student engagement, helping them to appreciate how school mathematics can be made more relevant and meaningful. Activities focusing on social issues with strong links to mathematics, such as voting systems, measuring global inequality and Fair Trade, enabled students to appreciate how mathematics can provide a powerful means for better understanding their own situation and how it relates to the world around them. Through groups choosing a social issue of interest to them, and using mathematics to develop an argument for a change they would like to see made, students were encouraged to develop mathematical agency.
This research project offers a means of challenging traditional (and outdated) modes of teaching mathematics. It provides an alternative vision of how teachers and researchers can work together, providing the mutual support necessary, to overcome the current constraints which prevent more effective teaching approaches from being adopted. Further details of the project can be found at:
Black, L., Mendick, H. & Solomon, Y., 2009. Mathematical relationships in education: Identities and participation. New York: Routledge.
Boaler, J., 2009. The elephant in the classroom: helping children learn and love maths. London: Souvenir Press.
Cockcroft, W. H., 1982. Mathematics counts: report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the chairmanship of W.H. Cockcroft, London: Her Majesty’s Stationery Office.
DFE, 2013. Mathematics programmes of study: Key stage 3. London: Department for Education.
Hammersley, M., 2004. Some questions about evidence-based practice in education. In: G. Thomas & R. Pring, eds. Evidence-based practice in education. Maidenhead, UK: Open University Press, pp. 133-149.
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.
QCA, 2007. The National Curriculum for England at key stages 3 and 4, London: Qualifications and Curriculum Authority.
Sebba, J. et al., 2012. Raising Expectations and Achievement Levels for All Mathematics Students (REALMS): Final report to the Esmée Fairbairn Foundation, Falmer: University of Sussex.
Skovsmose, O. & Borba, M., 2004. Research methodology and critical mathematics education. In: P. Valero & R. Zevenbergen, eds. Researching the socio-political dimensions of mathematics education. Dordrecht, Netherlands: Kluwer Academic Publishers, pp. 207-226.
Wright, P., 2012. The Math Wars: Tensions in the Development of School Mathematics Curricula. For the Learning of Mathematics, 32(2), pp. 7-13.