What are children learning?

 Ofsted's Coordinating mathematical success: the mathematics subject report came out in 2023 and had a lot to say about Teaching for Mastery, whilst carefully avoiding the phrase "Teaching for Mastery".

As well as highlighting recent improvements in mathematics teaching in England, they had some concerns. One of these was a lack of ambition:

An ambitious curriculum is one that maximises the mathematics that pupils learn. In some schools, teachers move on before ensuring pupils have learned important knowledge and committed that knowledge to long term memory. In schools where this is common, leaders focus on what pupils study, rather than on what pupils learn. Moving on when pupils are not mathematically ready gives the illusion of progress but creates ever greater gaps that will take more time to address in the future. 

Leaders should focus on what pupils learn, not on what pupils study.

 In some schools, teachers teach the curriculum that is put in front of them, then give the children a summative assessment a few times a year to see if they are 'working at age-related expectations'. Not surprisingly, Ofsted also criticise this approach:

Some leaders gain false assurance about the effectiveness of their curriculum design and practice through internal assessments that closely align with ‘expected performance thresholds’ of external assessments. This approach often leads to an acceptance of pupils moving through the mathematics curriculum with significant gaps in their knowledge and leaders failing to make necessary adjustments to their curriculums. In these schools, some pupils would be better served by studying less, but securely learning more.

A more ambitious curriculum would focus on what pupils learn

An ambitious curriculum is one that aims for the most number of pupils to learn the most that they can. Rather than making the expectations more challenging, our ambition should be for more children to securely learn less stuff.

A successful school would focus on their key performance indicators for each year group, and ensure that the children have mastered these before they move on. And if they haven't mastered them, they don't move on. Teachers don't cover the curriculum for their year, they cover the curriculum for the children in front of them. 

What does this look like in practice?

Assess for learning

Start by assessing the pre-requisite content. For example, before starting a year 3 unit on multiplication and division, assess that the children are secure in the relevant key objectives from year 2. You can use the DfE Guidance for this - each Ready to Progress Criteria has a set of assessment questions that cover the key learning and put it into context.

If the children are all secure then you can start to plan. If they are not all secure, then start by covering the key ideas again. Don't worry about the children who are secure at this point - they should be encouraged to think more deeply, explain to their peers and ensure that their understanding is deep enough for what is about to come. Don't be afraid to practice pre-requisite skills first.

Teach for the whole class

Think about the journey from this starting point to the key objectives for your year group. What are the big ideas along the way? The NCETM Professional Development materials provide a journey toward each key objective.

Teach it one step at a time. Give time for enough practice after each step. Don't worry that it seems too easy.

Intervene rapidly

If children aren't successful during the lesson, give the necessary additional support as soon as possible. Work with them directly in the lesson if you can to provide additional, temporary scaffolding. Refer back to the models and language used earlier in the lesson. Give small groups of children short bursts of support after the maths lesson or before the next one.

These rapid pre-, post- or in-lesson interventions are in order that children 'keep up, not catch up'. They are distinct from any ongoing 'gap filling' interventions, that are normally focused on filling gaps from previous years that children lack fluency in.

Age-related expectations: who decides?

The Expected Standard

The Ofsted guidance on assessment contains multiple references such as

pupils achieve the expected standards by the end of year

Unfortunately, there isn't any such thing as 'the expected standard' any more, except for Years 2 and 6. The 2014 National Curriculum has no attainment targets in it, and no levels. 
The DfE only says:

The curriculum must include an assessment system which enables schools to check what pupils have learned and whether they are on track to meet expectations at the end of the key stage.

So who decides what the 'expected standard' is for each year group?

The National Curriculum

It should be easy for Maths. After all the new National Curriculum sets out the suggested teaching objectives for each year group. Surely these make up 'the expected standard'!

But do we expect a child to be able to demonstrate every statement? What about 50%? Or 90%? Maybe some of those teaching objectives are more important than others?

We don't really know what 'the expected standard' is for Year 6 yet either. The abandoned 'Performance Descriptors' talked about 'the majority' of the elements, so that implies 50% of the objectives.  The new tests will cover the teaching from Years 3-6 and have an 'expected score' (which will be scaled to 100); we don't know what this will be yet (it used to change year on year anyway).

Assessment Systems

There seem to be two schools of thought on assessment systems. Some take all the statements and turn the yearly programmes of study into a checklist. Rising Stars has a system like this, exemplifying each statement at three levels for 20 pages. Some stick a set of key statements, often based around the work done by the NAHT.
We still have to decide whether children need all the 'Key Performance Indicators', or a given percentage of the whole lot.

What's the point of Assessment?

We've spent a lot of this year talking about assessment without levels in school. Some of that discussion revolves around why we are assessing children and who the assessments are for.

Ofsted have some helpful ideas (how often do you get to write that?) in their note on the use of assessment information. In the covering letter to schools, Michael Wilshaw writes about 3 purposes for assessment:

1. Raise achievement

The primary reason teachers assess is to make their teaching better. They need to know which children are achieving learning intentions, which children are on the way, and which children need support. With the expectation in maths that most children access the same curriculum at the same pace, it becomes really important that we  know what impact our teaching is having.
There's no point assessing the children's attainment in our classrooms if that information just goes 'up' to leaders, parents and governors. It has to go down too, and be shared with children and impact on planning. The quicker that happens, the more impact the assessment process has.
Good day to day assessment involves having clear objectives, making judgements about how secure the children are and acting on it rapidly to raise the attainment of all, but particularly the children who struggle the most.

2. Identify pupils who are falling behind

As a maths leader, I need to know which children are falling behind the expected standard, and to do something about it. This might be working with the teacher to improve provision in the classroom. It might be working with the intervention leader to plan a focused support. It might be working with the parents or carers to support learning at home.
For me, this involves having a core set of expectations in maths for each year group that are essential by the end of the year. Teachers can then talk about pupils who are missing key skills (often from the previous year), that prevent them making progress.

3. Report to parents

Schools need to let parents know how their children are doing. Ofsted talks about pupils who 'achieve the expected standard', and pupils who 'need to catch up'. That's very black and white: the sheep and the goats.
To be fair, we've been reporting to parents in this way for a while - 'Jane is working at 3b, and that's the expected standard for a year 4'. But it means schools defining 'the expected standard', and how much of it you have to be working at (50%? 90%?)

What does it look like?

I think this gives a sensible model of assessment practice:

Day to day assessment

Teachers plan well-defined objectives for their blocks of lessons, linked to the curriculum, and make judgements about which children are meeting them. They allow enough time for all children in the class to meet the objectives, and intervene to support those who don't.
 This doesn't involve any evidence, tests or external involvement, other than TAs.

Progress meetings

Once or twice a term, teachers make judgements about progress on a set of core objectives (the really important ones) and come to a pupil progress meeting with the subject leader, where they discuss which children need further support. Ideally, the good day to day assessment practice should provide enough support to make these judgements.

Reporting

Lastly, there is an 'end of year' standard which pupils are judged on. Again, if this is based on the 'core objectives', it should not involved any extra testing. It does involve standardisation and moderation, because (like a level judgement) there will be plenty of children on the 'border' between judgements. This standard can be used to judge progress (of children and cohorts) and to report to parents.