Research One class and their maths

ONE CLASS AND THEIR MATHS

Pupils’ perspectives on learning mathematics within their classroom environment. Recently retired Senior Maths Teacher Rosemarie Frost on unlocking the joy of learning in all pupils – whatever their ability.

Teaching is not only about imparting knowledge; it is also about instilling a love of learning – but ‘love of learning’ is an elusive concept. My dissertation for an MEd at the University of Cambridge focused on this very aspect of teaching. The research was a case study for which the participants were my Year 11 Mathematics class who were about to complete their IGCSE course. Although they were in set five out of six, they enjoyed their mathematics lessons and did not seem intimidated by the subject’s challenges. This contradicted the findings of studies on the attitude of pupils in lower sets towards mathematics (Boaler, 1997; Boaler, Wiliam and Brown, 2000). Why had these pupils ‘bucked the trend’? In his seminal work The Hidden Lives of Learners, Nuthall stated that ‘a teacher needs to understand how different students experience the classroom, and how their experiences shape the changes that are going on in their minds’ (2007, p.15). This informed my research, which explored my pupils’ experiences in their mathematics classroom. I asked them to complete two narratives and to take part in semi-structured interviews. The findings revealed that they had developed a high degree of self-efficacy because of three mediating factors that were inter-related, as illustrated in Figure 1.

Figure 1: Factors that endanger self-efficacy in pupils

Positive relationships with each other and successful collaborative learning had developed gradually, thanks to a classroom ethos that ensured a non-threatening and non-judgmental environment. I received feedback like: 'When I walk into maths and see the smiles of my friends, I feel instantly relieved. No judgment, no patronising smiles when you answer something wrong.’ The atmosphere facilitated risk-taking, since pupils were always, and patiently, given strategies to address misconceptions, along with assurances that they were capable of ‘getting it’. Pupils indicated that the classroom was a safe place where they could look honestly at their own and each other’s mistakes, a typical comment being: 'I have never felt patronised or insecure about my maths ability because we all have the same attitude and like to help each other learn. Sometimes I will ask an obvious or stupid question, and nobody seems to care – I think this has helped a lot of us be honest about what we struggle with because there is no fear of judgement.’ Collaborative learning, in particular, was mentioned enthusiastically by all pupils.

Many of the pupils’ attitudes towards mathematics had been negative in the past but, by the time they were in Year 11, they had developed a positive perception of the subject. Whilst they still did not necessarily love mathematics itself, they now loved learning it and felt they could achieve well in the subject if they wanted to. In other words, their mindset had changed from from ‘fixed’ to ‘growth’ (Dweck, 2006). One said: 'In Year 11, the more challenging questions have given me a confidence boost after realising that nothing is impossible if you work hard enough to get there.’ This came about because they had developed self-efficacy. Self-efficacy refers to beliefs concerning one’s capability to organise and execute courses of action that produce certain attainments (Bandura, 1997). Pupils with a high degree of self-efficacy work harder, participate more readily, persist longer, and have fewer adverse emotional reactions when they encounter difficulties (Bandura, 1997; Hattie, 2012). These attributes were evident in all the pupils. In addition, there was evidence of intrinsic motivation, where motivation is related to enjoyment in the task.

The classroom environment was key. A major factor in creating the environment was the way in which the ownership of lessons was shared. Each lesson was planned meticulously, applying the principles of Cognitive Load Theory (Sweller, Ayres and Kalyuga, 2011), but the pupils owned the lesson as much as I did, and those who were secure in their understanding of a particular problem were often asked to explain it to others on my behalf. This required a style of classroom management based on teamwork between teacher and pupils. A typical comment was: 'I can discuss with my friends and chat freely. Personally, this makes maths lessons more enjoyable and often leads to completing more work. A quieter, stricter classroom or an unhealthy relationship with my peers would negatively impact my learning as I tend to work well with others. Mrs Frost allows for such an environment to be maintained. My class and I can quickly become loud and distracted as we are all close friends, however Mrs Frost controls an amicable balance of productivity and sociability.’

Conclusion

Evidence-based teaching methods, such as those based on Cognitive Load Theory, play a valuable role in pupils’ learning. However, affective dimensions and classroom ethos play a powerful part too, not only in pupils’ learning, but also in their perception of success. My pupils were coming to the end of a mathematical journey. Although mathematics was still a challenging and effortful subject for them, they relished doing and learning mathematics together with their peers. They knew they would meet IGCSE questions with which they would struggle. Nevertheless, they felt competent and comfortable with mathematics.

Whilst their mathematical ability would be measured by their IGCSE grade, the success of their journey should not be judged by that measure alone. The purpose of teaching should be more than academic achievement in the form of examination results. It should also be about instilling a love of learning. No teacher would deny that, but ‘love of learning’ is not measurable, so it may be overlooked. In participating in this study and describing their experiences and thoughts, these pupils offered an interpretation of the meaning of ‘love of learning’: they had developed mathematical confidence, become at ease with the subject, and taken ownership of it.

References:

Bandura, A., 1997. Self-efficacy: the exercise of control. W. H. Freeman. Boaler, J., 2002. Experiencing school mathematics. Taylor and Francis. Boaler, J., Wiliam, D. and Brown, M., 2000. Students' experiences of ability grouping – disaffection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631–648. Dwek, C. S., 2006. Mindset: the new psychology of success. Random House. Hattie, J., 2012. Visible learning for teachers maximizing impact on learning. Routledge. Nuthall, G., 2007. The hidden lives of learners. New Zealand Council for Educational Research (NZCER) Press. Sweller, J., Ayres, P. and Kalyuga, S., 2011. Cognitive load theory. Springer. 11