Mastering a mindset for maths
In my experience at school, and later as a teacher educator in the further education sector (FE), few subjects elicit such strong emotions as maths. How ironic for a subject which is predominantly rule bound and based on logic, writes Sarah Boodt, Senior Lecturer, Placement Lead Post-16 and Further Education.
My recollections of school maths lessons conjure up the smell of stale air in classrooms where the radiators had been left on too long, students sitting in rows listening to the teacher give the rules for something mathematical, and then completing exercises for practice. My learning strategy was to memorise the rules and then try to apply them; but with no understanding I had limited success. Consequently, I associate maths with feelings of stupidity, failure and fear; in short, an indictment of self (Dweck 2000). Many FE students resitting GCSE maths feel the same way.
Since August 2015 it is a condition of 16-19 funding that all full-time students who do not have a Grade C or equivalent in maths must enrol onto a GCSE qualification. The policy rhetoric links numeracy skills to improved employability, increased productivity and economic growth. Whilst there is an undeniable logic to this, what of the students who end up resitting their maths GCSE multiple times, in an (often fruitless) attempt to achieve the set grade? Students who see it as an opportunity to improve their attainment level readily engage, but for others this apparent 'failure' can lead to negative attitudes, a lack of confidence in maths, and low motivation to engage with what they see as 'more of the same'.
Research suggests that students who leave 11-16 education without good grades in English or maths are likely to continue their study in an FE organisation, and are often already demotivated by their experiences in school (Anderson & Peart 2016). This, compounded with the stressful and emotional experience of sitting formal examinations, may explain why the summer 2018 mathematics resit success rate remains 'stubbornly low' at only 23.7% out of over 170,000 candidates. Having spent many years at school without achieving the set GCSE grade, these students not only need support, but frequently also lack a positive mental attitude, motivation and confidence.
Furthermore, resitting and (re-)failing GCSE maths can leave them with a lasting sense of failure and a reinforced negative attitude towards maths, which may prevent them from engaging with learning and using maths in the future. Consequently, to raise maths GCSE success rates in FE organisations, staff must be given professional development opportunities to explore different methods and approaches to teaching maths that enable them to improve students' understanding.
According to constructivist theories, people learn through a process of collective sense-making with their teacher and with each other (Freire 1976). Through interaction, individuals construct meanings from new information which they then apply in new contexts, moving to higher and deeper levels of learning (Bruner 2009). Dialogue is key to this process.
As an ESOL subject specialist, a dialogical approach has always informed my teaching; we learn a language in order to communicate, and it is through communicating that we learn a language, progressing to higher levels of complexity and nuance. But maths is also a language, with its own structures, syntax and collocations. So why will I confidently and enthusiastically engage with a piece of text in any language, but anything mathematical throws me into a state of cortisol-flooded fight or flight?
Mastery approaches to maths teaching in the FE sector
Teaching for mastery can be used to mean belief about learners’ potential, a way of approaching the curriculum and its teaching, and a quality of learning (Boylan & Townsend 2017). It rejects the idea that some students cannot learn maths and instead encourages a mind-set that all are able to learn. We ran an ETF-funded project to identify what mastery approaches to maths teaching might look like in the FE sector. The project team drew on their understanding of mastery teaching in maths, and how these approaches are being adopted in the school sector. We worked with four FE organisations, and observed maths lessons taught using mastery approaches.
The lesson I observed was at 9am on a Monday morning, which was reminiscent of my O' Level year, when my school week began and ended with double maths. As luck would have it, the topic of the lesson was also one of my mathematical nemeses: ratio, but with a Venn diagram twist. However, unlike my school maths lessons, the session started with a card-sort activity that supported interaction between students, helping them recap and develop their understanding of the language of Venn diagrams. Each stage of the lesson built on the previous one, using dialogue to identify what was the same, what was different and what each section of the Venn diagram might represent.
At first, like the student sitting next to me, I was reluctant to initiate discussion and share my answers for fear of looking foolish. We were two students, wrestling our demons in silent isolation. However, as the concept of ratio gradually emerged through the visual representation of the Venn diagram I had my first ever 'aha moment' in maths: I finally understood not only how to work out ratio, but also how my thinking about ratio had led me astray all those years ago. I found myself wanting to talk about maths with the student sitting next to me. We began to compare our answers and when we understood different things at different points of the lesson, we were able to help each other out. For the first time ever, I was enjoying a maths lesson!
I came away from that lesson energised and exhilarated, but also pensive and regretful about what my experience of school maths lessons might have been. The air in the classroom was still stale, the radiators had still been left on too long, but maths had become something to talk about, a set of concepts to be 'played with', something I could visualise and relate to. Every innovation takes time to embed, and arguably we can't afford the additional time needed by mastery approaches. However, if the alternative is repeated failure, a life-time of low self-esteem, and avoidance of maths, perhaps we should ask: can we afford not to?
