- Published: 26/06/2016

For the past year I’ve spent 90 minutes every Friday morning teaching GCSE Maths re-sit students at my local FE/sixth form college. I wanted to do this because post-16 maths for those who don’t achieve at least a grade C in GCSE Maths in Key Stage 4 is something I feel strongly about and consider to be very important, and I wanted to get first-hand knowledge of what current GCSE Maths re-sit teaching is like. I spent seven years of my teaching career in a post-16 college but the last time I taught GCSE re-sit was in 2000, so I felt I was certainly in need of some up-to-date experience to get a realistic perspective on the current situation. I also wanted to do it because I love teaching students generally, and teaching them maths in particular, and get withdrawal symptoms if I stay away from real teaching for too long!

I taught the same small group of students for the whole year (up to 13 of them; a few dropped out, an extra couple joined, but the core of the group remained constant), sharing their teaching with an excellent full-time teacher from the college, who taught them for the other half of their maths lessons. Timetabling restrictions meant they did all of their maths in two 90 minute blocks each week, which is far from ideal, but seems to be the norm in many colleges; four 45 minute slots would be far better. The students were all re-sitting GCSE Maths alongside studying for level 2 vocational programmes at the college. I particularly asked to teach students on vocational programmes as it is these students in particular that I feel are not well-served well by our current post-16 GCSE Maths provision.

Now that the academic year is almost over and the students have taken their exams, I have been reflecting on the year as a whole. In terms of the class dynamic, the students weren’t so different from 16 years ago: They were still generally good natured; they still tried to distract me with discussions about football (I’d forgotten the dangers of admitting to being an Arsenal supporter), and it was still both rewarding and frustrating to teach them. The key difference was that they were conscripts. None would have willingly chosen to re-sit GCSE Maths if they had not been compelled to, and this meant it was a real challenge to motivate them.

The students were following the foundation tier curriculum, and the college had a good scheme of work in place that enabled me and the teacher I was sharing the group with to coordinate our work effectively. Stark realisations I made in the first couple of lessons were:

1) How much these students disliked and feared maths.

2) How little confidence they had with basic, fundamental mathematical facts and ideas.

As a result, most of them strongly resented having to re-sit their GCSE. I don’t think it’s too much of an exaggeration to say that the majority of these students began the course with the view that learning maths is a kind of torture, whose only function was to ‘get a C’. Their view of the education system, at least as far as maths is concerned, was that you study so you can pass exams. They did not believe that the maths they were learning would help them in work and life, only that they needed a C in the exam to have a chance of getting a decent job. They also felt that they had not succeeded because they were ‘crap at maths, so what’s the point’. Working to help them overcome these views (to try to develop a growth mindset in mathematics) was a key part of supporting them to learn maths and (hopefully) to do better in their re-sit exam. I can’t claim great success, but I’d like to think the maths teaching they received at the college did have a positive effect on their attitude towards maths, at least for some of them, and that I contributed to that.

I was shocked to discover their knowledge and understanding of fundamentals, like place value, times tables and number bonds, things that are on the primary school curriculum and that they should have mastered several years ago, were very weak for almost all of the students at the start of the academic year, even though they had achieved grade D in their GCSE Maths at the end of the previous term. Naively, although I knew these areas would be weak, I had not anticipated this would be such a dominant issue. We focused on these areas in the first couple of weeks, and then tried to reinforce them throughout the year through lesson starters and quizzes and whenever they arose (as they do very frequently) within other topics, (e.g. teaching rounding to decimal places and significant figures using a number line is a great way to reinforce understanding of place value). However, it is very hard to develop and build from such weak mathematical foundations post 16.

Arithmetic with negative numbers, order of operations, relationships between fractions, decimals, percentages and ratios, understanding graphs, basic proportional relationships, all were very weak. I suspect that many of the marks they achieved in their GCSE maths exam at the end of Key Stage 4 were earned through rote learning – being taught to recognise standard questions and then ‘remembering’ methods and rules they had been trained to apply to them, not by applying mathematical ideas they had developed fluency with. Exam training built on very shaky mathematical foundations may get some students through the exam, but does little or nothing for their ability to use maths practically, outside of the exam room, and is also very poor basis for further study. I don’t think schools and teachers deserve much of the blame for this. School accountability measures, quite rightly, place a high value on performance in maths, and secondary school maths performance is measured by GCSE Maths grades. The problem is that GCSE Maths examinations have become uninspiring and predictable, encouraging a rote learning approach. If the aspirations of the new GCSE Maths are met, rote learning approaches will not be effective and teaching and mathematical learning should improve.

Throughout the year my colleague and I tried to consolidate earlier work and discuss how topics and ideas were connected, aiming to help the students to develop an appreciation that ‘maths makes sense’ and that if you can become fluent with relatively few key ideas and connections in mathematics, you can ‘work out’ how to use them to solve problems. Many of them thought learning maths was about remembering rules for different topics, and they couldn’t do maths because they couldn’t remember it all. Trying to learn maths in this way is highly inefficient, but it was very difficult to convince the students that learning could be done more effectively by connecting ideas and trying to make sense of them.

In thinking about how to work with these students I drew on ideas from two books, *‘Deep Progress in Mathematics’*^{i} and *‘Collaborative Learning in Mathematics’*^{ii} , that are based on research into teaching students like these, who have not achieved highly in mathematics and may not be well-motivated to learn it. I blended teaching from the front with a combination of small group work, whole class questioning and discussion, trying to break up the 90 minute slot with different activities in an attempt to keep them engaged and thinking about maths for the whole time – this worked some of the time! Mini whiteboards proved a very useful resource.

My colleague and I ‘covered’ (but did the students?!) the whole of the college’s foundation tier scheme of work in this way by the end of March, trying to help the students to make connections between topics and consolidating fundamental ideas on the way. I set homework each week, but it was rare for many to attempt it seriously, despite my efforts to emphasise the importance of consolidation and practice. From the end of March onwards, we focused on exam practice, and there were some encouraging signs. Several said that they felt more able to tackle questions than before and were more confident. Once the exams were looming, the majority became more focused and started to work hard – if only they’d been that focused from the start.

I enjoyed working with the students this year, despite many frustrations, and I really hope the students passed. I definitely intend to do some more post-16 teaching next year, perhaps GCSE resit again (I hope I’d do it better next time), or Core Maths, which, through my MEI work, I was involved in developing - I’ve heard lots of positive things about Core Maths, but I’d like to experience teaching it first-hand.

My main conclusions from my GCSE resit teaching this year are:

1) In the longer-term (5 – 10 years), evidence from schools that have introduced a maths teaching for mastery pedagogy to develop deep mathematical learning suggests that this approach has the potential to solve the problems that held back my re-sit students, and thousands like them. The two features of the students that I noted from the first lesson, that they disliked and feared maths and that they had no confidence with basic, fundamental mathematical facts and ideas, can both be addressed through maths teaching for mastery, starting at primary school and continuing throughout their maths education, giving them the firm foundations and confidence they need to learn maths successfully. This ‘Essence of Maths Teaching for Mastery’ document summarises the approach. Please see our teaching for mastery pages for more detail of the work of the NCETM and the Maths Hubs on maths teaching for mastery.

2) Re-sitting the same GCSE they failed at the end of Key Stage 4 does not meet the needs of students post-16. They need a different qualification that focuses on their need to develop real fluency with the maths they will need for work and life. I have written about this in a previous blog post and my experience of teaching GCSE resit students this year has reinforced that view. Recommendation 5 of MEI’s recently published position paper on the new mathematics GCSEs suggests how this might be done in relation to the new GCSE maths:*‘The needs of students re-sitting GCSE Mathematics can be met with a different post-16 qualification, focused on those aspects of the GCSE Mathematics curriculum that are needed for everyday life and future study and/or employment in fields that do not require advanced level mathematics. This qualification must have equivalent status with employers and universities as a level 2 pass in GCSE Mathematics taken at the end of Key stage 4. The best way to achieve this would be to develop a ‘mature’ version of GCSE Mathematics. The limited content of such a GCSE could be recognised by limiting the maximum grade to that equivalent to a level 2 pass in the Key Stage 4 GCSE Mathematics.’*

It’s vital for many thousands of our young people that we get post-16 GCSE Maths re-sit right. I fear that our current practice of forcing any student with a grade D to re-sit a GCSE designed for the end Key Stage 4 does not meet their mathematical needs and is reinforcing negative views towards maths. The students, and maths, deserve better.

**References**

^{i} Deep Progress in Mathematics, Anne Watson, Els De Geest, Stephanie Prestage, 2003, ISBN 0 903535 68 8^{ii} Collaborative Learning in Mathematics, Malcolm Swan, 2006, ISBN 1 86201 311 X