Understanding is Not Enough, and First Steps into a Level-Free World

A big thing we’ve been focused on this year is helping pupils to REMEMBER what they’ve learned in maths.

Happily, most pupils seem to feel positive about lessons, although there are – inevitably – the sullen hangers-on (or the hopelessly confused – what a horrible world they inhabit!). Checks and informal assessment in lessons, pupils’ work and their responses in class suggest that they understand what they’re doing in lessons. Almost everyone does their homework and it’s typically of a good standard (except where there are fundamental issues with understanding or a pupil has drawn a total blank). So far, so good. Lucky teachers. 

Nonetheless, pupils outside of set 1* (and some in set 1) weren’t actually remembering things once we’d moved on from them. This had been a chronic issue in my last school, and it continues in my current one. I was both relieved and disheartened to see this issue happens in other schools: see Kris’s excellent post on memory/recall here for a good discussion of this problem. 

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The solution we came up with – and it is somewhat galling to realise now that it’s probably a reinvention of a (relatively new?) wheel – has been to spend a lot longer on content, taking each topic or concept much further, and to do a lot more ‘small’ assessments that aren’t counted (except to plan intervention) in the build up to a significant single assessment that counts for a lot (from the pupil’s point of view). 

The strategy has been: 

– A baseline assessment four times in the year that is (effectively) the end-of-term assessment, but with different numbers and the very toughest questions removed. This gives an indication if the pupils are unexpectedly strong or weak in one area but also a bit of notice so that plans can be tweaked (as it covers roughly 9 weeks’ worth of content). It also gives them a baseline percentage (they know it’s fine if it’s really low – plenty get 0%). Pupils can also revisit this assessment and start to connect new content with the kind of questions that could be asked (we’re trying to sort out the difference between “didn’t know the content” and “knows the content but didn’t recognise it”). 

– Cover content in class, spending longer than usual but extending it beyond the normal ‘cognitive ceiling’ (e.g. for Y7/8**, 6 hours + homework for Pythagorean Theorem, but extending to 3 dimensions and finding distance between points on a 2D plane; 3 weeks just on fractions in Y7, etc. Choosing what to cut/delay has been pretty painful). We’ve been making more use of stories, images and contexts in the lessons to help pupils remember concepts and results (e.g. calculations with negative numbers in the (initial) context of adding or removing bad players from a football team). That said, I’m still not keen on anything totally contrived (e.g. I get what the car and bee story is about, but it doesn’t ring true for me as a way to remember. That said, I concede that I have no idea how I *do* remember it, and perhaps something beats nothing).  

– Homework set on the topic 3-4 lessons after the topic has been started (i.e., remembering earlier content when learning the later content or just after the topic is finished). The homework is split into routine practice (find the length of this side) and a more intriguing puzzle or application. 

– A weekly ‘mini test’ that is split into ‘critical content’ (e.g. label the hypotenuse, find the length of this side to 2 significant figures, etc) and ‘mastery questions’ (e.g. What is the greatest possible length of the third side if the other sides are 5cm and 6cm? If your only measuring implement was your thumbnail, could you estimate if this is a right-angled triangle?***). 

– Using the results of the weekly mini test and homework to pick up any pupils for one-off catch-up who don’t “get” it (as opposed to aren’t remembering it) or who are making fundamental errors. In lessons, using the tests and homework, pupils compile rough lists of ‘things I keep forgetting’ so that their revision is focused on recalling the things they ‘get, but forget’ or ‘get, but mix up’. This is quite quick – it’s usually part of a growing list in the back of their book, or just highlighting questions where their response is “I can’t believe I forgot that!”. Within a few weeks some pupils had already started filling their rough list in as they did the test (“I’ve forgotten how to explain how I know when a number is a prime – I’m going to highlight it now”), which suggests that it makes sense to them as a way of operating. 

We’ve been pretty pleased with the results so far – if exhausted by the sheer volume of marking it generates. We’ve just collated the results after the first ‘quarterly assessment’; most pupils made great gains from their baseline – which represented 2 months’ worth of ‘memorisation’ – so I’m cautiously optimistic. Of course, some pupils didn’t do as well as they should have (although most pupils whose scores were disappointing admitted that they hadn’t revised).

The pupils’ results are broken down by topic (e.g. indices, rounding and estimation) and they’re ‘BRAGged’ (red/amber/green/blue) for each one. The somewhat unsustainable threat for pupils who didn’t improve ‘enough’ from the baseline score, or got red/amber in a topic, has been that they have to keep coming to catch up until they can are green on that section of the test. I’m not sure how long our commitment/ organisational skills fare in the face of that task. 

That said, I don’t have a strategy in place – or even in mind – to help them recall the content from this ‘quarter’ as we move into the next one. The only plan so far is that ‘just finished’ content is included in the questions and contexts pupils face in later topics. It would be great to know of more strategies to help pupils recall techniques, methods and facts, and to generally help them revise/retain. I know the main revision strategy for maths is ‘doing maths,’ but that feels like a horribly vague thing to say to a Y7, and lacks a clear endpoint.

Have you tried different strategies for assessing and measuring pupils’ progress? Have you tried anything different to help their memory and retention? Please do let me know!

 

* I find the (seemingly) better memories of pupils in set 1 very interesting; which way does the causality work? Do they have better capacity to form and recall memories, which helped them to do well academically and, causing them to end up in set 1? Or do they understand concepts more easily, with better abstract reasoning, making it easier to work things out from first principles? (An example of the latter: some boys in my Y10s last year never needed to learn or recall a method to find the area of sectors, or find the volume or surface area of cylinders – they just reasoned it out from scratch each time, but quickly enough that it was as though they were recalling a well-memorised fact). 

** In future it will just be Y7, but we’re trying to fill gaps as the current Y8s had a different curriculum last year. 

***This will be our first attempt at getting the pupils to think about non-obvious units of measure. I AM ON TENTERHOOKS. 

3 Comments

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3 responses to “Understanding is Not Enough, and First Steps into a Level-Free World

  1. Sounds like you’re really trying hard to address a very common problem. It will be interesting to hear how this progresses.
    Thinking about your question about the better memories of your Set 1 students, I wonder if it is because they have good conceptual understanding and so are able to make connections between different topics which means there’s less to learn. The lower ability students probably have much less conceptual understanding and so are learning facts and techniques in isolation.
    I like the idea of using recent content in questions and contexts for current material to help it stick. I often find that starter activities can be good ways to keep recapping content too.

  2. lw

    I was having a very interesting discussion with our SENCO about learners who have a dyslexic/dyspraxic/discalculic profile and her description was directly related to the idea that the linguistic part of their brain doesn’t work as well so traditional methods (repeating/phonics/any teacher talk/cloze gaps) won’t work as well with them. Instead they need to be manipulating the information into flow charts/mind maps etc to retain it and access it. I’m not sure how definitive this description is, however I do know that with middle ability learners if I do an outline of what you need to know, then memorable activity, then spend time connecting all this together and some deeper learner they engage in it more and are more involved in designing their own mnemonics/ways or remembering/helping each other learn. It’s also easier to tap into later as you can say (remember when we did that really memorable thing).

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