Numbers Count - views from an Every Child Counts National Trainer
Over the years my teaching career has taken a number of twists and turns. Straight out of a PGCE, I was reassured that my “life experience” would compensate for my lack of teaching experience. As it happened, and perhaps unsurprisingly, a previous life as a musician paid dividends in my role as music co-ordinator – albeit with somewhat different protocols regarding the kind of hospitality you might expect at a performance – being “good” at music certainly helped me when it came to teaching it.
Contrary to my expectations though, being a competent mathematician (A-level maths and degree level study of the philosophy of maths and logic) had the opposite effect on my performance as a maths teacher. I had not one about clue how to tackle Y2 maths and no idea what it meant to struggle. My greatest weakness was dealing with my lowest performing mathematicians. I had breezed through the vast majority of my own mathematics education, succumbing briefly to poor teaching at A-level, only to rally during my degree with a genuine passion for philosophy and her estranged sister, mathematics.
Unfortunately for my first primary class (or three), this meant I had never had to deconstruct what it meant to learn mathematics in the early years – or, in fact, at all. In hindsight, and much to my subsequent and abiding embarrassment, I was quite simply a dreadful infant maths teacher. During the eight years I subsequently spent as a LA maths consultant in the South West, frequently observing maths teaching, I often reflected on what my reaction might have been as a consultant on seeing my own maths teaching when I was an NQT. This is a salutary experience. There would have been some very direct words in the head teacher’s office afterwards along the lines of: “...and you’ve got a REAL problem in Y2...” culminating at some point with the words “...consider sacking the feckless fool!”
It strikes me as ironic that now, at what I consider to be the highlight of my career, that I find myself as National Trainer for Every Child Counts for the west region supporting the delivery and development of Numbers Count: a programme designed and developed to support the mathematical learning of the LOWEST performing Y2 children.
This begs the question about teaching Y2 mathematics: am I any better at it? Well, I’d like to think I am. If nothing else, I now no longer think that learning maths is easy, and that if children don’t “get it” then you take the classic approach of the English tourist abroad who, when confronted with a language issue, has only one strategy: to repeat himself more...loudly...and...slowly!
So, what has brought me to recognise (15 years into my career) that learning mathematics can present children (and other people) with real difficulty? In short, diagnostic assessment. As a consultant with Devon LA I worked within an excellent team who placed great store on the diagnosis of children’s strengths and weaknesses. Diagnostic assessment is also perhaps the most important feature of Numbers Count and the main reason for its spectacular success. In the three months that children are on the programme they make an average of around 14 months’ progress – that’s about 1/3 of a month per lesson.
Numbers Count is the daily 1:1 intervention programme devised by Edge Hill University and Lancashire LA under contract to the DCSF in response to Sir Peter Williams’ recent review of primary mathematics and is delivered by a trained specialist teacher – not unlike Reading Recovery (you may have read the article in Issue 23 of the Primary Magazine by Katie Greenwood who is one of our Numbers Count teachers in Devon). Part of my role as National Trainer for ECC is to deliver Numbers Count lessons to two children in a school in Ivybridge. The programme is firmly based on constructivist principles. This means that as NC teachers we focus more on what the children know than on what they don’t. The first two weeks of the 12-week programme are devoted entirely to diagnostic assessment. Not teaching, just presenting the child with mathematical contexts and activities and paying attention to what they do, listening VERY carefully to what they say and thoughtfully and respectfully questioning and probing their understanding. All seven or so sessions are videoed so that the teacher can revisit the “interesting” moments, distilling what they can regarding the child’s understanding and planning what they need to follow up in their remaining sessions.
It is amazing how difficult teachers find this new discipline at first. As teachers we seem to be programmed to intervene as soon as we spot what we think might be some sort of “error”, but in the diagnostic assessment we don’t do this. We allow the child to express their own understanding, flawed and/ or incomplete as it may be and take note, gradually building up a picture and mapping out the landscape of the child’s schema. Teachers new to Numbers Count have to be directed to “sit on their hands” so to speak and learn to keep quiet and listen. Believe me, this is much harder than you may think!
The diagnostic assessment is then used to assemble an individual learning plan for the child, specific to them. This plan should match their needs and indicate how the teacher will support the child in building their mathematical understanding on what they have got already – this is what we mean by a constructivist approach.
It is this attention to the detail of the child’s understanding that really defines the difference between this programme and anything else (excepting Reading Recovery) that I’ve seen in primary education. This level of diagnosis is maintained throughout the programme with the teacher’s planning twisting and turning to follow the curves and parabola of the learning. Truly subordinating teaching to learning as Gattegno might have said. Teachers analyse their regular video recordings of lessons and share their thinking with colleagues as part of Numbers Count professional development. Anyone who teaches primary mathematics should give diagnostic assessment a try. It makes for excellent professional development. Many Numbers Count Teachers report, very early on in training, that were they to return to the classroom they could already see how dramatically their practice would be changed having been involved in Numbers Count. The major impetus for making this judgement is invariably the diagnostic assessment.
What does this tell us about mathematics teaching? Well, in my own case and perhaps that of many of those of my generation, I was taught to “do” mathematics at primary school. Mathematics was presented to me as something you either got right or got wrong. It was not to be discussed particularly, and what I or my peers thought about it was never enquired into. My teachers showed an interest only in the number of ticks and crosses with which they adorned my work. When I came to teach mathematics myself I’m afraid I visited this view upon the children in my care. We all absorb aspects of the culture we are brought up in and, as Vygotsky points out, culture has a formative relationship with our thinking. I have observed that I’m not the only teacher around who has held (or holds) this view, and that should come as no surprise given the way mathematics education has been approached in the UK.
But there is hope. Teachers can hold an outcome-orientated view of mathematics for only as long as they fetish the ticks and crosses. Its tenability is entirely dependent on their attention being focused solely on the outcomes. As soon as you start to attend to the complexities of a child’s thinking processes you start to question the importance of right/wrong, can do/can’t do. In fact, during diagnostic assessment teachers very soon learn that they’ve learnt very little about a child’s mathematics when they’ve found out that a child can do something. In order to support the child’s learning of mathematics it is far more useful to begin to map out the limits of their learning, the edges of their zone of proximal development if you like. This is not to say that we focus on deficit, looking only for gaps and misconceptions. Rather in mapping the limits of learning it becomes possible to see something about what the child can learn next. This is partly determined by what they know and can do and partly by the way they think and approach problems – both are things a teacher can hope to influence.
In my view, good quality mathematics teaching is not about doing: doing a sum, doing a worksheet, doing addition. Nobody doubts that the outcome is important – we don’t want engineers who can’t calculate – but the outcome is not mathematics. Good mathematics teaching is about thinking, it’s about the processes that we and our charges go through together when we engage in mathematical discourse. For me, and for a large number of Numbers Count teachers, this epiphany occurs as a result of diagnostic assessment.
Andy Tynemouth works for Edge Hill University as an Every Child Counts National Trainer.