By now most teachers will have spent a week with their new classes. Inevitably some of you reading this have been throwing your hands up in despair about your new Year 7 class, complaining to colleagues that they are “the weakest you’ve ever taught/taught in years” and lamenting the fact that your primary counterparts have clearly fiddled the data and that the students must have been coached to death through their SATs exams without actually learning anything.
My knowledge of primary education is far too limited to even begin to comment on any of the above issues. However, what is indisputable is that a fairly large number of students, for whatever reason, arrive at secondary school ill-prepared for the demands of the mathematics curriculum.
Rather than trying to unpick why this is the case, I want to outline some of the considerations I find to be particularly important for these ‘low ability’ Mathematics students. Note that this term is imperfect and has far more negative connotations than I would like. To me it implies an inability to improve, something that is the polar opposite of what we as teachers work towards. However, I will use this term a. for lack of a better one and b. because I assume that most at least understand what the term means irrespective of whether or not they agree with my view that it has negative connotations.
Don’t teach them what you ‘should’ be teaching them, teach what they need to know to know now
If students are lacking basic skills and if they do not have certain facts committed to memory, they will not be able to make progress. Fact. Much of the philosophy behind the mastery approach to teaching is predicated upon this idea. Nail the basics so that they do not take up space in students’ working memory, thus allowing them to apply these concepts to more complex problems.
In Mathematics, I would go so far as to say that if the four operations and an understanding of place value and the decimal system is not 100% secure then that is what you as a teacher should be almost exclusively focusing. Trying to teach students to multiply two decimals together, to calculate area and perimeter or to carry out any sort of task involving algebra (as well as most other tasks on a typical Year 7 scheme of work) is likely to be to no avail without these in place first. The added cognitive strain of carrying out these operations whilst applying them to a new context will make committing any new processes to memory nigh on impossible.
And by basic I mean basic. Number bonds to 10, 50, 100. Place value. Chanted multiplication learnt by rote, basic inverse operations and not much else (For more on this, see Bruno Reddy’s account of how King Solomon Academy in London designed a ‘Mastery Curriculum’).
Many Year 7 schemes of work do not start with these ‘basics’. At the previous two schools I have worked in, ‘factors, multiples and primes’ has been the first topic covered in Year 7. Finding the factors of 48 without having multiplication tables committed to memory is an almost impossible task.
If you identify with this and your students are not 100% confident with the ‘building blocks’ of Mathematics, implore the powers that be to let you focus on that at the expense of all else. They will catch up later.
Complaining ‘they should know this by now’ is pointless. Make it your job to teach them this. Right now. And don’t rush. embedding these concepts takes time and once embedded must be periodically recapped to help commit them to long-term memory and to allow them to be effortlessly deployed as and when they are needed. This is a process that takes months and even years, not weeks.
Get them enthused
Even amongst the most disaffected students, it is rare to find a student who does not exhibit at least some excitement in starting secondary school. Harness this. For the love of God grab onto this and don’t let go. Keeping this level of excitement and enthusiasm for the entire year is a tough and seemingly impossible task but if you are constantly stoking that enthusiasm and creating a positive mindset, students will hopefully overcome many of the negative perceptions that they associate with Mathematics. New year, new you etc!
How to do this? Well that is the million dollar question. I only have one real guideline here- get students excited about getting better. Students like being good at things. They like this more than almost anything else. If you can show pupils how they are progressing and getting better (track quiz scores, table tests etc.) and if you can give them real, genuine, praise about their progress, they are more likely to ‘buy into’ your maths lessons. A generally positive learning environment with great relationships underpins this obviously, but you must get students excited about doing and progressing in maths, not about making posters, using technology or anything else.
Planning….or more accurately thinking and rehearsing
Obviously all lessons should be carefully and thoughtfully planned but when teaching lower ability students, meticulous planning is more important than ever. By planning I don’t mean full ‘Ofsted-style’ lesson plans. Rather, I mean taking the time to think through possible misconceptions, requisite prior knowledge and to carefully rehearse explanations, focusing in particular on the language that you are using and the expectations for how the work should look on the page.
Given that the concepts being taught to these students are at the more ‘basic’ end of the spectrum, there is a tendency to almost ignore the explanation and to try to explain it off the cuff in class whereas when teaching (say) a difficult A Level topic, many teachers spend more time considering this aspect of their practice. Given that these concepts are going to underpin the rest of the students’ Mathematical understanding and the fact that these students have almost certainly been taught these topics before but haven’t managed to retain the information, these explanations are the most important you will give as a maths teacher. Take time to get them right.
One area that I am very keen to develop in my own practice is the use of concrete resources to aid explanations. This is something I have never felt confident using myself having received a fairly half-baked 45 minute training session on concrete resources during my ITT year and very little else since other than being told in my NQT year to “just use some Deans Blocks with them” (I imagine this is not uncommon among secondary maths teachers). From what I gather however, if these resources are used correctly, the impact on student understanding can be significant.
There is no shortage of research on feedback and its importance. There is also no shortage of information telling you exactly how to give feedback. It must, of course be written (for parents, senior leadership, Ofsted etc), must give the opportunity for the student to give a written response and should involve peers…..
Whilst this might be applicable in some cases, my personal experience suggests that feedback for lower ability students should, by and large be immediate and is most effective when given verbally. Students who struggle in maths tend not to be able to effectively link the written feedback on a page with answers and solutions that they wrote down a day or two previously. Immediate verbal feedback given while circulating the classroom and mini whiteboard work combined with regular low-stakes quizzes to assess learning are far more effective than written comments in books for these students in particular.
Additionally, I find that, whilst students can be ‘trained up’ to be fairly effective peer markers, the opportunity cost of doing so (using time that could be spent doing maths) more than negates the relatively small benefits of being able to review another piece of work and almost all of the benefits derived from peer marking can be given through teacher produced model answers.
Scaffold the transition
One thing I am often struck by when entering a primary classroom (something I do not do enough of, especially given I work in a very large ‘all through’ school) is how different it is to secondary classrooms and in particular, my ‘unfashionable’ classroom layout with students seated in rows facing the board.
Whilst I am convinced that seating students like this has a positive impact on student learning, I am also of the view that for Year 7 students in particular, this sort of classroom environment can be something of a shock to the system. Similarly, having students work on questions from the board rather than on worksheets or listen in their seats rather than in carpet spaces can be very difficult for students who haven’t experienced it before. While the end goal for me is to get students to a position where they are able to work effectively in a traditional secondary setting, secondary teachers must acknowledge these challenges and try to wean students away from the primary mentality but must do so gradually.
If you have a space to do some work ‘on the carpet do it. Use worksheets. Sit down with students and work through problems together. Occasionally group tables together and move students around. Interleave ‘primary’ methods with ‘secondary’ methods and over time begin to move away from the former and towards the latter. Even if you are able to keep up this ‘primary-style’ approach, for better or for worse it is likely that your colleagues will not and students need to be prepared for the realities of secondary education.
This obviously isn’t a ‘how to’ guide. It is just a set of reflections from my experience teaching so-called ‘low ability’ students in mathematics. I’d love to hear the experiences of others and what works and doesn’t work for you.
Teaching these classes can be challenging but, at the risk of sounding sanctamonious, can be the most rewarding classes to teach. The planning and delivery of these lessons requires patience and takes time to get right but, when the students start making steady and sustained progress, the sense of personal satisfaction is right up there with some of the best feelings in teaching.