In my last post, I set out the problems with making predictions about students’ progress by drawing a ‘flight path’ between KS2 and KS4. Instead, I will argue, we should address three interlinked aspects; curriculum, assessment and instruction. In order to make a meaningful statement about where students are right now and what they need to do next, we need to be very clear about where we are hoping they’ll end up.

This post will focus on issues of curriculum.

One of the first things to acknowledge when planning a curriculum is the tension between breadth and focus. Of course students need to make progress towards achieving in a particular qualification, but that examination ought never be the focus of 5 years of education. As I’ve argued before, breadth trumps depth.

The problem of being constrained by exam specifications is compounded by the vogue for ‘planning backwards’ from GCSEs or A levels to determine what should be taught at Key Stage 3. When we plan backwards, our attention is on the build up of a narrow set of knowledge and skill, but when planning forwards we more likely to consider the curriculum in all its messy breadth before later narrowing our focus to the content of specific exams. This allows us to make sure the curriculum includes what Christine Counsell has called the ‘hinterland’ of subject disciplines – areas that are not directly examined but give students the knowledge base to think better.

Secondly, we should acknowledge that the quality of assessment and instruction cannot exceed the quality of the curriculum. As Black and Wiliam set out in Assessment and Classroom Learning, teachers require, “a sound model of students’ progression in the learning of the subject matter, so that the criteria that guide the formative strategy can be matched to students trajectories in learning.” The curriculum is a model of what we want students to know and where we want them to go. If we want to make judgements about progress and attainment, we need a clear understanding of progression within subject disciplines.

What this means is that we should know what it means to get better at maths, French, geography, music, English, science etc. Or, put another way, what is the progression model for each subject? In Devising Learning Progressions, Leahy and Wiliam discuss learning hierarchies and learning progressions as being synonymous, but I don’t this is necessarily the case. Instead, by looking at mark schemes for mathematics, we can see that progression is much clearer in some subjects: students either know how to solve the problems they’re set, or they don’t. Progress is limited by what they know; if they’re struggling to answer questions on trigonometry then they clearly need additional instruction on that aspect of the course; if they’re getting lots of algebra questions wrong, then you can be pretty sure there’s going to be an algebra shaped conceptual gap in their knowledge base. Now, as Leahy and Wiliam point out that the hierarchical nature of progress can sometimes seem inevitable:

it seems inconceivable that someone could master multiplication before addition. It might be possible to define multiplication in some other way than as repeated addition, but it is hard to imagine how one could prevent a child from discovering addition before they reached the level of maturity needed to understand an abstract definition of multiplication. A learning hierarchy of this kind could therefore be seen as

natural. (p.2)

But, other ‘natural’ hierarchies are more the result of habit and tradition. For instance, multiplication is almost always taught as a precursor to teaching division despite the evidence that division is often conceptually easier for children to understand. Part of effective curriculum design must be to determine which hierarchies are natural and which are not.

In English literature, for instance, GCSE mark schemes point to a model of progression which is hierarchical and actively unhelpful. We get statements such as “convincing, critical analysis and exploration” at the top of the hierarchy to “clear understanding” to “simple, explicit comments”. It’s then up to individual examiners to decide whether a particular student’s work meets these vague criteria. Basing a curriculum on this sort of thing would make it impossible to assess where students are now and how to help them get where we want them to be.

So, in order to solve the problem of progression across the curriculum, maybe we need to make English a bit more like maths. By that, what I mean is that we should determine in advance what students will need to know in order to be able to do well on an assessment and ensure that these things are taught in such a way that allow students to make progress.

The implicit assumption made by English literature GCSE mark schemes is that it doesn’t matter what you study as long as you can show evidence of “convincing, critical analysis and exploration”. Clearly, this is not quite true as the course will also specify content so, it’s no use being able to convincingly and critically explore the Harry Potter novels, you have to demonstrate your critical analysis on a Shakespeare play and a Victorian novel. The trouble is, when schools ‘plan backwards’ from GCSE to determine what to teach in Key Stage 3, all too often they ignore the specified content and instead design their curriculum around opportunities to critically analyse any old text.

No matter how hard we try to nail down precisely what it is we intend students to learn, our attempts will be open to a depressingly wide range of interpretations. This is hard enough in a subject like maths, let alone English. Consider the objective that students should “Compare two fractions to identify the larger”. Does that mean they can work out whether ⅝ is greater than ⅞? Or whether ¾ is greater than ⅘? Or could it mean that they are able to compare the relative values of ⅜ and ⅗? As should be clear, each of these comparisons fulfil the objective but the third comparison is very much more challenging than the first.

As Leahy and Wiliam point out, “the level of granularity needed by teachers to effectively use learning hierarchies in their own work is generally at a far finer level than those used in educational objectives.” They argue that the work of identifying a progression model must be carried out locally, at the level of individual schools and departments for it to have any real meaning. They are also clear that thinking about progression must be empirical; that is, our assertions about what aspects of the curriculum students struggle with more than others must be rooted in objective data.

In his researchED talk, “Fundamental Measurement for Schools,” Deep Ghataura, neatly summarises these conclusions by stating that learning progressions must be:

- Inherently
**empirical**– based on how children actually learn the thing - Inherently
**local**—*what*we focus on is our choice

This takes us back to the problem we started with in the last post. Currently, progression data based on a flawed prediction of where students should be at a particular point in the curriculum is garbage. The question we will turn to in Part 3 of this series is how we can better measure students’ attainment in order to make better inferences about the progress they are making.

How do we know pupils are making progress? Part 1: The madness of flight paths – David DidauMarch 24, 2019 at 11:39 am[…] Part 2: The curriculum […]

Michael PyeMarch 25, 2019 at 2:08 pmCould you guide me towards the evidence that division is easier to learn then multiplication

Tom BurkardMarch 26, 2019 at 11:35 amThe statement that “if they’re getting lots of algebra questions wrong, then you can be pretty sure there’s going to be an algebra shaped conceptual gap in their knowledge base” isn’t quite right. You are virtually certain to find the gaps–in both conceptual and procedural knowledge–earlier in the curricular progression. For instance, a pupil who hasn’t achieved a high degree of automaticity in fractions will most likely have difficulties with algebra. In other words, more intensive instruction in algebra won’t help much if there are prior gaps. These might not be evident if assessment doesn’t involve timed responses–a pupil who can just about plod through lower-level material will be unable to retrieve fully-developed schemata relevant to the more complex material.

David DidauMarch 26, 2019 at 8:42 pmFair enough, I take your point.

How do we know pupils are making progress? Part 3: Assessment – David DidauMarch 26, 2019 at 8:41 pm[…] predictions about students’ progress by drawing a ‘flight path’ between KS2 and KS4, then, in Part 2, I explained how thinking about the curriculum as a progression model is essential in making […]