In mathematics, it is often noted that pupils suffer a “dip” in their knowledge from Year 6 to Year 7. Secondary teachers often remark that pupils who scored well on key stage 2 Sats don’t know how to do some of the mathematics that their score implies they should be able to do.
If this is true (and this does need to be questioned) then it implies two big questions:
1) Why is it happening?
2) What do we do about it?
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One possible answer to the first question is that it isn’t really happening, but it can appear as if it is early on.
Anxiety over school transition
If we consider how disorientating the change of school is, amid all the things happening both externally and internally at the age when pupils move into Year 7, it is possibly not surprising that in the first few weeks of transition pupils are not on their “A game”. It may well be that after they have settled in and feel comfortable enough to focus on the mathematics, pupils’ knowledge resurfaces.
The negative effects of anxiety on academic performance have been well established, and the transition from primary to secondary is likely to be a very anxious time for pupils.
This would also affect pupils’ ability to learn new things in their new school. The cognitive load associated with feeling like you have to be “on top of” all of the changes may well completely overwhelm pupils’ working memory, making it virtually impossible for them to actively learn much of anything new until the changes become more routine.
The wrong maths content?
Another factor in this may be aspects of the KS2 curriculum. In his paper "Teaching Mathematics at Secondary Level", eminent mathematics professional Tony Gardiner identifies two apparent issues with the KS2 curriculum that may then affect performance with concepts that also appear in KS3. These are:
A significant amount of material has been included at key stage 2 in a way that is likely to prove developmentally inappropriate;
Some of the listed topics that are entirely appropriate in Year 5 and 6 have been specified rather poorly.
In Gardiner’s view, this makes it likely that, through no fault of the teachers in Year 5 and 6, many pupils entering KS3 will have a somewhat superficial grasp of some key ideas from KS2.
An obvious solution to this is to remove some content from KS2, and use the space created to specify properly the more appropriate concepts.
Of course, schools can find it difficult to make this decision unilaterally, with the pressures of KS2 Sats and the inherent judgements that this might bring about. In reality, this would likely require a change in the government curriculum policy before all schools with KS2 pupils felt comfortable in approaching their teaching in this way.
An alternative is to ensure proper consolidation of these ideas early on in KS3. This actually serves the dual purpose of reducing anxiety in pupils (as they are working with maths they already feel relatively comfortable and familiar with) as well as removing the need for them to learn new things when their brains are simply not ready to cope with it following all of the upheaval.
If we accept this alternative, then we might well wonder, what are the mathematical ideas that need to form the basis of this consolidation time?
Again, the inimitable Tony Gardiner has a possible answer. In the same publication, Tony suggests that the following are examples of “topics which may have been ‘covered’ at Key Stage 2, but which will need serious attention in Years 7 and 8”.
The extension of place value to decimals
The arithmetic of decimals
Work with measures – especially compound measures
The arithmetic of fractions
Ratio and proportion
The use of negative numbers
Work with coordinates in all four quadrants
As a teacher of mathematics, I can recognise that many of the ideas listed above are precisely those that can cause pupils problems when they arrive at secondary school.
Plan for Year 7
So what is my plan for Y7?
1. Reduce anxiety
Use time on both sides of the holiday to set the scene for what is to come – if pupils are suffering anxiety due to the transition, then trying to make them feel as prepared and comfortable as possible for what they will encounter in maths lessons will definitely help.
Try and make sure that maths is on the timetable for any transition days that your school hosts for its arriving pupils on either side of the holiday, and make sure the lessons done in those times do reflect what will be the norm for their maths lessons when new learning starts (while simultaneously trying to soften the impact of any new ways of working so that you don’t cause more anxiety).
It is also really worthwhile considering devoting some time to actually explicitly teaching routines and expectations – in my department we have a standard “expectations” lesson that will introduce pupils to the standard experiences they will get in most maths lessons, but that takes them through this in a way that is not associated to new learning.
This might be particularly helpful for pupils with SEND whose emotional state might be even more heightened than their peers if they rely on “knowing the rules” to help them manage their classroom experience.
2. Delay baseline assessments
Wait before you baseline pupils – if you are in a school that routinely sets pupils on entry, you may as well actually use their KS2 Sats scores. Doing a baseline in the first few days and then using this to set could well be less accurate, despite many people thinking the opposite.
If performance is being upset by anxiety around a new school, then your baseline could well be giving you false results. Even if you do normally set the pupils late in the year, or teach mixed ability for the whole of year 7, try and wait until pupils have settled into the routine of your school before you attempt to do any sort of baseline test that is designed to discriminate based on performance.
In my school, we teach mixed ability in Year 7, but we do use a baseline test to see if there are pupils who would benefit from intervention in numerosity, or, conversely, if there are pupils whose Sats might suggest they do whereas, in fact, they don’t.
For next year I will be changing this practice so that early intervention is planned around KS2 Sats question level analysis, and then the baseline test won’t be conducted until the end of the first unit.
3. Spend the early time consolidating
I know some people like to start Year 7 with something completely new. They want Year 7 or “big school” maths to feel very different to the maths that pupils were exposed to at primary school.
This may well work for some – those who can adjust to the change in environment, teacher and status quickly or who can take these things in their stride.
My concern with this would be those who are so overwhelmed by all the change, that the last thing they need is something else that looks different: “Not even maths is the same!”
Given what Gardiner says about topics from KS2 that will need attention in KS3, I think there is ample scope to begin Year 7 with a focus on consolidation and renewal, rather than new content.
This doesn’t mean it has to be “the same old boring stuff” for pupils who are ready to move on. In my school, we start Year 7 by revisiting integer arithmetic, in particular revisiting the four operations and laws of arithmetic before extending to negative integers.
However, while doing this we introduce thinking about numbers and arithmetic in ways pupils haven’t considered before. We do things like explicitly look at the difference between “Steve had 10 sweets and gave Jemma 4, how many does Steve have left?” and “Steve has 10 sweets and Jemma has 4, how many more does Steve have?”.
The idea here is not to practise answering questions like this (although it does allow us to pick up if any pupil does still have difficulty with number bonds to 10), but rather to motivate two different ways of seeing subtraction. This serves the dual purpose that the ideas are very familiar to pupils and we are still able to use what we are doing to push those pupils who are ready for more to think differently about what they already know.
Over the course of Year 7 and 8 we look at everything on Gardiner's list, either explicitly or at least as a main idea in a different topic (for example, we use coordinates in four quadrants to look at graphing formulae, spending at least an hour just focusing on the plotting of the coordinates generated by substitution into a formula).
Peter Mattock is head of maths at an 11-16 school in Leicestershire and author of Visible Maths