For the first eight years of my teaching career, I had been making a huge mistake. At the start of September each year, confronted by an eager, fresh-faced class of Year 7 students, I had presented topics like ratio, fractions and the most mysterious of all – algebra – as if they were the most miraculous things in the world. Crucially, they were presented as if the students had never seen them before.
Of course, very rarely did a student ever say anything. Perhaps they were too polite, or simply grateful for something familiar at a time of so many changes. Or maybe they assumed it was simply how things worked at Big School. Either way, inside they must have been screaming: sir, we have done this before!
And they would be right.
In planning our new Year 7 and 8 Scheme of Learning, I spent considerable time studying the current Primary Mathematics Framework, and subsequently the new Key Stage 1 and 2 Program of Study released in September 2013. For me, they contained some startling findings.
Let’s play a game. Have a read of the following statutory requirements and guess what school year they refer to (answers at the bottom of the page!):
- know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
- generate and describe linear number sequences
- compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
- add and subtract fractions with the same denominator within one
Are you as surprised as I was?
Indeed, a quick calculation suggested that around 80% of the content that we taught our students in their first two years of high school had already been encountered at primary school. And my experience visiting schools around the country suggests that the style and content of our exiting scheme of learning was very common.
So, is it any wonder there is a national dip in students’ mathematical performance in Years 7 and 8?
Of course you can point to inflated SATs scores and the difficulties of transition that come with being in a new school, with new surroundings, teachers, classmates and challenges. But I suspect there is more to this. Are students who have been solving linear equations and dividing whole numbers by fractions in primary school going to remain engaged when they are presented the concept of a prime number like it is the holy grail? Likewise, students who have struggled with maths throughout primary school, and who now have a genuine fear of the subject, are not going to benefit from being presented with the same material in the same way.
Now, I am by no means saying that consolidation and practise in mathematics are not crucial skills. Of course they are. More so than in any subject. But you only have to take a look in the typical Grade C/D GCSE classroom and witness Year 11 students struggling with adding fractions together or remembering angle facts (topics that they have been studying for at least seven years) to know something has gone wrong along the way. And this problem will only be exacerbated by the new and far more challenging mathematical curriculum that is on the horizon.
And there is another aspect to this problem of transition – and that is the styles of the maths lessons themselves. Now, I am making a broad generalisation here that is based solely upon my own observations of Year 5 and 6 maths lessons in many primary schools compared to Year 7 lessons in secondary schools. The former, in general, are far more focussed on group work, investigation, discovery and independent learning than the latter. Furthermore, I have found differentiation to be far more effective in the primary classroom than in its secondary counterpart, with students entirely comfortable working on different sets of problems at their own pace.
So, students arrive in our classrooms in September and our faced with content they have studied before, taught in a style that they are not used to and which is probably not conducive to their learning. In some cases, this content and style is then repeated for the next five years until many students have a view that mathematics is all about remembering rules and algorithms that make little or no sense, and dislike the subject greatly.
What is to be done about this?
Well, there are two main aspects to our solution. The first was to flip the model that usually happens in the summer term. Instead of Year 6 students coming into our school for taster lessons, we sent Year 7 teachers into our feeder primary schools to observe what maths at Year 6 was really like. And their reaction was exactly the same as mine – surprise about thigh-level that these students were taught, and the impressive style that this content was delivered.
The second change was more significant and took a considerable amount of time. Along with another colleague, I completely rewrote our Year 7 and 8 Schemes of Learning. Content is only to be taught once across the two years. Students are taught fractions in Year 7, but not in Year 8. Likewise, they solve linear equations in Year 8, but not in Year 7. This has two major benefits. Firstly, it avoids the endless repetition that leads to a lack of engagement and, I would argue, serves neither the high nor the low achievers well. We can study the content in greater depth, with a wider variety of resources and activities, instead of the usual two week rush through a topic to be ready for the next assessment.
Secondly, the significant time freed up by this is dedicated to compulsory rich projects that all students in all classes get to enjoy. Many come from NRICH, or the Shell Centre, or the goldmine that is the old GCSE coursework tasks. These activities are investigations that promote group work, problem solving and creativity in mathematics. They are typically “low barrier, high celling”, thus allowing students to access them at all levels, promoting effective differentiation. Because all students in all classes do these tasks, this avoids the “lesson lottery” where students in one class may suffer as their teacher has chosen not to run a particularly high quality activity with them. These rich projects and activities also have the advantage of reinforcing and consolidating the fundamental mathematical skills that students need, but in a more interesting and engaging way.
In addition to this, all students get to enjoy weekly starters on patterns, estimations and number talks. This is based on the latest research from the US that strongly suggests that enabling students at a young age to develop an understanding and flexibility with numbers, together with skills of pattern recognition, can have a significant and positive impact on their mathematical ability, development and enjoyment for the subject. These weekly starters are also displayed on our maths notice board to encourage our students to talk about mathematics outside the classroom.
So, has this been a success?
Well, there have been struggles along the way. For some of our staff this has been a significant change in their usual way of delivery, and we have had to plan carefully the training and support sessions to help with this. But most have risen to the challenge and enjoyed lessons that are filled with student discovery more than perceptive teaching.
And our students? Well, we are still in our first year of this, but the signs are good. Achievement levels are significantly higher for our current Year 7 students than the previous year’s cohort at the same time. But more than this, the lessons feel different. There is an atmosphere of learning and creativity. There is a buzz that was perhaps not there before. Students are talking about maths lessons in a way that they usually reserve for English or Science. And behaviour in lessons, as monitored by recorded incidents on SIMs, has never been better.
So, is the secret to solving the problem of transition to make the mathematics in secondary school more like primary? Possibly. But what is certain is that secondary teachers should be more aware of the mathematical experiences, both in terms of content and style of lessons, that their students have encountered on by the time they arrive in their classrooms in September. This will be of great benefit to all concerned.
1. Year 5 (age 9-10)
2. Year 6 (age 10-11)
3. Year 4 (age 8-9)
4. Year 3 (age 7-8)