We have an accountability system that has encouraged schools to check that children are making a certain number of sub-levels of progress each year. This is the basis on which headteachers monitor (and now pay) teachers and on which Ofsted judges schools. Yet there is little hard science underpinning the system in use: take a child’s attainment at Key Stage One (age 7), look up the average attainment for children at the same level by Key Stage Two (age 11) and draw a straight line between the two assuming that linear progress will be made in each of the four intervening years.

For example, a child deemed to be working at Level 2C at Key Stage One is expected to reach Level 4C by their Key Stage Two tests, Level 5C by Key Stage Three and at least Level 5A by Key Stage Four.

But do children normally take such smooth learning journeys as they acquire knowledge and understanding in a subject as our accountability system assumes? And is it reasonable to deem children as ‘on target’ or ‘in need of intervention’ using this approach?

Linear progress of pupils from their Key Stage One assessment forms the basis of targets. Note: Average attainment, grouped by Key Stage One sub-level, for children age 16 between 2008 and 2010 Key Stage One = average English and maths levels; Key Stage Two and Key Stage Three = average English and maths test fine grades; Key Stage Four = average English and maths GCSE grades (A*=10; G=3)

### Only 1 in 10 pupils make linear progress at each Key Stage

Linear progress at each Key Stage can be defined as attaining within one third of a Level (i.e. +/- a sub-Level) of the national average for all pupils who start with the same Key Stage One attainment. Yet by reviewing the data, we find that only 9% of pupils take the expected pathways through Key Stage Two, Key Stage Three and Key Stage Four Levels. If we look at each Key Stage separately, 55% of pupils make the anticipated linear progress to reach the Key Stage Two Level that is predicted for them from their Key Stage One score. The rest either overperform or underperform.  Moreover, the capacity of the model to accurately predict pupil’s attainment falls in secondary schools, with 45% of pupils making the anticipated linear progress between Key Stage Two and Key Stage Three, and just 33% making the anticipated linear progress between Key Stage Three and Key Stage Four. This suggests that the model’s assumption of consistent progress for a group of children at the same starting point is already weak between the first two stages of schooling, and that the numbers of children judged to be outperforming or underperforming targets is higher still in secondary school.

### There are many pathways to achieving ‘expected’ attainment

By using this model of consistent linear progression, most children will perform better or worse than their expected Key Stage attainment on one or two occasions, and some consistently outperform or underperform throughout their school career. Others do achieve the level of GCSE attainment that we might expect, given their age 7 starting point, but their route to doing so is far from linear and predictable. Here, we show the numerous pathways to achieving an ‘expected’ age 16 attainment for the large group of children receiving a Level 2B at Key Stage One, tracking their progress through to their average GCSE grade achieved. These children would be expected to achieve a Level 4B at Key Stage Two, a Level 5A at Key Stage Three and average GCSE grades just below a grade C.

More children get to the ‘right’ place in the ‘wrong’ way, than get to the ‘right’ place in the ‘right’ way!

One third of these children will indeed get an average grade C at Key Stage Four. But of these children who meet their predictions, the majority will do so via a route that includes periods of both slower and more rapid progress. If targets are simply set based on the last Key Stage test results available, this leads to almost all children being deemed as underperforming at some stage of their schooling career.

### Children with low initial attainment have particularly unpredictable future attainment

The predictability of progress and attainment as children pass through schools is particularly poor for those with low levels of attainment at Key Stage One. For children achieving a Level 1C, B or A at this stage, their development is so unpredictable that most will either outperform or underperform any Key Stage Two target that might be set. It would seem important that these children are not unthinkingly receiving curriculum restriction through placement in lower ability teaching groups or given low targets for attainment, because many of them will go on to achieve success later in their school career.

#### The variation in children’s learning trajectories varies by initial starting point of the child

Note: we exclude Key Stage One Levels W, 3A and 4C for brevity in this table but they are included in the total

### The setting of expectations and targets for pupils must be done with care

Our evidence suggests that the assumptions of many pupil tracking systems and Ofsted inspectors are probably incorrect. The vast majority of pupils do not make linear progress between each Key Stage, let alone across all Key Stages. This means that identifying pupils as “on track” or “off target” based on assumptions of linear progress over multiple years is likely to be wrong. This is important because the way we track pupils and set targets for them influences teaching and learning practice in the classroom, contributes to headteacher judgements of teacher performance and is used to judge whether schools are performing well or not. Providing pupils with the curriculum diet that is deemed suitable for the ‘Level’ they are working at may be doing them a profound disservice, if in reality their trajectories are much more varied.

Of course, this data tells us nothing about why pupil learning trajectories are so diverse. Children are likely to make cognitive leaps and pauses at different times for a variety of reasons. Indeed, if researchers were able to observe termly test score data, the patterns we show above would be accentuated even more. There are also more practical reasons as to why children do not track through the Key Stage levels as smoothly as we ask them to: all tests have a considerable measurement error and assessments may not be good matches for the knowledge and skills we might ideally measure.

All of the points raised above highlight the importance of using tracking systems carefully, putting to one side ‘average progress’ as the key target by which children should be judged where it clearly doesn’t mirror teacher experiences of the child’s potential. Monitoring systems that trigger rewards or warnings if deviation from the mean average takes place can only work if these deviations are relatively rare. The way that children learn is too idiosyncratic to do this and so pupil target setting should be more flexible and take into account a range of likely outcomes rather than a single number.

For example, we could monitor whether pupils are making progress within the range of attainment levels that is the case for, say, 60% of pupils with similar prior attainment. Pupils making progress in the 20% above or 20% below these ranges could then be more reasonably identified as overperforming or underperforming and in need of investigation to understand why. How wide we should set these ranges will depend on how the target is to be used: the higher the penalties to the teacher or school for underperforming the range, the wider the range must be.

Numbers need to be treated with care. Statisticians know this. In particular they recognise that the single number summary of a disparate dataset through the production of an average score hides as much as it reveals. At a stroke, it removes from view the variation in the dataset. Yet good teaching relies on keeping in view the variation in pupils’ responses to what and how teachers teach. We lose sight of this when numbers set a uniform path for every pupil to follow. It is refreshing to see the first fruits of a more sophisticated analysis here that is challenging some of the core assumptions upon which much monitoring of teachers’ practice rests and is reminding the profession to expect the unexpected, not rely on simplistic mantras to keep children on track.

Gemma Moss, Professor of Education, University of Bristol

This shows that expected progress measures should never be seen as more than indicative. Yet unfortunately it seems they are treated as a science – and indeed teacher performance and even pay are being evaluated on the supposition that progress is linear. My interest is in social disadvantage, which is of course correlated with low initial attainment, and I would like to see how these trajectories differ by social class. The analysis shows that many low initial attainers go on to achieve very good education success, but most do not. This highlights the urgency of focusing policy and practice on supporting lower attainers.

Becky Francis, Professor of Education and Social Justice, King’s College London