By Mark Dawes, September 2023
Last June there were questions asked on Twitter about why secondary maths departments don’t make use of the vast amounts of data about the pupils who will shortly join them at the start of Year 7. It is possible for secondary schools to download the number of marks that every pupil gained on each part of each question in their SATs tests. Surely this would be a treasure-trove of information for schools to have and to be able to use?
After all, at the start of Year 7 we don’t want to start from the very beginning of mathematics, and we certainly need to build on what the pupils already know. So why aren’t the vast majority of schools using SATs data to help with this?
Here is an example of a SATs question (2018 P2):
What do pupils need to be able to do to get this question right?
Know what a ‘net of a cube’ is
Realise that in a cube the side-lengths are all the same, so you can divide 20cm by 4 to get the length of one side
Be able to carry out 20 ÷ 4 accurately
Recall what volume means
Know that to find the volume of a cube you need to cube the side-length
Know that this means 5 × 5 × 5 (and not 5 × 3)
Be able to carry out 5 × 5 × 5 accurately
In addition to this, there are non-mathematical things that need to happen:
Not spending too much time on previous questions, so they get to this one
Not rushing so they misread the question
Not miscopying the number 20 from the question or miscopying their answer into the box
Not turning over two pages and omitting this question accidentally
Not losing focus and deciding not to answer the question
Notice that the question is worth 1 mark. If the pupil doesn’t get that mark, what do we know? We actually know very little. They might not understand the concept of ‘volume’ at all. They might have worked out 52 by mistake and need to clarify the difference between area and volume. They might just have messed up the calculation of 20 ÷ 4 or 5 × 5 × 5, which means they have numerical weaknesses, even though they have secure knowledge of volume.
If they got the correct answer, what can we assume? They certainly won’t have guessed that the answer is 125 out of the blue, but they might have been unsure about whether to use the formula for area or volume and guessed between the two. Alternatively, they might have happened to do a similar question the previous day, or to have talked about the volume of a cube earlier that morning with a parent or older sibling. They might have known all of the maths listed above at the start of May when they took their SATs, but not have used some of it since and forgotten it. Depending on the school’s scheme of work, they might not study volume until later in Yr 7 (or not at all during that year), which could exacerbate the risk of them ‘losing’ some maths. We also don’t know whether they understand volume in full, or whether they just know the formula for the volume of a cube.
In short, if they got the question right, we don’t know whether they ever understood what volume was, or (if they did) whether they can still recall it when they meet it again at secondary school. And if they got the question wrong, we don’t know what it is that caused the problem (or even whether there was actually a problem in the first place).
In terms of knowing what individual pupils already know, the SATs are useless. We do however need to have something in place to find this out and it is, according to the recent Ofsted mathematics subject report, not something that is done well. The secondary part of the report, Coordinating mathematical success, (published in July 2023) states:
108. In all schools, leaders said that teachers would routinely make sure that pupils had securely learned conceptual knowledge before starting new learning that built on it. However, this assertion was consistently accurate in very few of the schools visited.
109. Teachers used a range of approaches to assess pupils’ pre-existing knowledge/understanding. These included quick low-stakes quizzes, with pupils’ answers displayed on mini-whiteboards or electronic devices. When used with well-considered questions, these approaches gave teachers appropriate assurance that pupils had the knowledge and understanding necessary to move on to the next stage of the curriculum.
Checkpoints
One possible solution to this is to use the NCETM’s Checkpoint resources.
During Covid the SATS tests were cancelled, so pupils arrived at their secondary school without KS2 data, meaning we knew very little about the prior attainment (on a topic level) of our pupils. The NCETM accordingly created a new set of resources to deal with this: Checkpoints. The original Yr 7 versions were designed to be used diagnostically with a class as a way to find out what the pupils already know and what gaps they might have. The Checkpoints are not a ‘test’, and because they are placed in a context they give the pupils an opportunity to explore and discuss the concept/idea while working on it. This allows for a certain amount of revision of the topic and then the opportunity to show what they know about that topic. The Checkpoints were so positively received that the NCETM then created more of them, which they have described as ‘Year 8 Checkpoints’.
Here is an edited sample, selected from the Year 8 resource ‘Perimeter, Area and Volume 2’:
There are some nice features of this task, which is designed to take only a short amount of time in a lesson. The teachers’ notes point out that pupils have studied nets at primary school, so this is not brand new. There is an opportunity for pupils to remind themselves of what a net is and then to think about the nets for several different shapes.
There are different reasons why these fail at being nets: (c) has a superfluous face, (b) has the right number of correctly-shaped faces, but at least one needs to be moved elsewhere, (e) has the ‘ends’ being different sizes, (a) also has the correct faces, but two of them need to be swapped over, while in (d) two of the rectangles have the wrong heights.
Teachers can use one diagram at a time or can show all of them at once. Pupils can be given printouts to annotate or could use mini whiteboards or their exercise books, and there are opportunities for oracy and literacy too, with a big focus on explaining the problems that each ‘net’ has.
The task also gives new learning opportunities. For example, there are so many occasions where maths has one right answer, such as in the answer to calculations, the solving of linear equations in one variable, the derivation of a probability, or the prime factorisation of a number, so it might be a surprise to some pupils that there are multiple different possible nets even for a seemingly simple shape such as a cube.
While it has lots of different features, and can be used in lots of different ways, this checkpoint activity focuses on a single area of mathematics (nets) rather than the multiple areas involved in the SATs question, which means it is ideal for telling us whether pupils understand the concept of a net.
My colleagues and I are looking forward to using Checkpoints as a way to help our new Yr 7 pupils to build on the work they have done during KS2.