Rachel Rayner is a Primary Mathematics Adviser at Herts for Learning. In this blog Rachel explains why she thinks that teachers can save time by spend less of it looking for ideas online and more time crafting effective examples for themselves. 

So you are probably thinking, well all she has to think about is mathematics, and that would be a fair representation of my day every day.  But, to coin a phrase from the excellent Miranda Hart, please ‘bear with.’  As my schools will testify, if I can teach I will, I get a very real buzz from working with children of all ages on mathematics.  And like all of the advisers I work with, we do have a realistic view of life in schools and the barriers faced.  One of the areas I frequently see as patchy is the curriculum across the school.  Where we look in books across the year groups at one strand, say for example fractions, then it is typical that pupils are engaged in fairly similar content between Year 2 and Year 4.  And if I trawl through popular sites for worksheets I can see why – lots on colouring in shapes and finding fractions of amounts.  Another area that encounters this is statistics.  In how many year groups do pupils need to collect data and draw a bar chart? Again online there are numerous different contexts suggested for collecting data and drawing/building bar charts and pictograms across Years 1 to 4.   There is less emphasis on the interpretation and interrogation of data, there are few examples of pupils being asked to infer meaning from data that I have witnessed for example: Why did no one come to school on a space hopper during walk to school week? Think of at least two reasons.

In summary I think the weighting of shared resources online can lead planning decisions. Without a clear progression (and this isn’t always evident in the programs of study for year groups in the NC) where do teachers look to find specifically what needs to be learned in their year groups so that progression from one year group to the next is clear?  Strand tracking as a subject leader is a great first step as it can help to spotlight where progression slows and/or learning repeats.  This can be discussed and learning expectations clarified allowing teachers to be clearer about their year group expectation.

Once the school plan for strands is in place and the ESSENTIALmaths materials found here and on the PA plus subscription site will support this, then some of the following approaches we have been working on with teachers to craft their lessons may be for you and your colleagues.


Artisan – Pronunciation /ˈɑːtɪzan//ɑːtɪˈzan/                        noun

  1. A worker in a skilled trade, especially one that involves making things by hand.

‘street markets where local artisans display handwoven textiles, painted ceramics, and leather goods’

1.1 as modifier (of food or drink) made in a traditional or non-mechanized way using high-quality ingredients.

‘Britain’s artisan cheeses’

‘the growing appreciation of artisan foods’

Oxford Dictionary


Many of the teachers I work with are born artisans, they know how to choose the right tools, spend time on one feature, make it bespoke to the pupils they work with, choose high quality examples and resources but can lack confidence in their own decisions and knowledge or feel they don’t have the time. One school I have been working with regularly is Huntingdon Primary school in Cambridgeshire. Over several training sessions and working with the maths team and curriculum lead, Kate Rigby, we are working to enable year groups to design their own sequences and to innovate on pre-made resources. At another school Fawbert and Barnard Infants in Hertfordshire Jo Brooker (maths lead and DHT) and her team have also been thinking deeply about breaking down these sequences in order to identify the crucial learning stages.  It’s early days but teachers from both schools have enjoyed and felt enabled by the process of thinking about and breaking down the mathematics they want pupils to learn. And so far the sequences of learning I have seen are remarkable and testament to their efforts.

The schools start by establishing the key features of learning i.e. what the product will look like.  An example I use in training is around the tricky concept of time and duration where I focus on hours, minutes and seconds.

Compare durations of events [for example to calculate the time taken by particular events or tasks] Y3 Pupils will need to be able to –

– understand a unit as 60 in terms of hours, minutes and seconds

-convert between units of time

-find 60 and some more

-add and subtract with time

-understand duration as difference

-estimate duration

-understand how earlier and later link to add, subtract and duration

-deal with duration in mixed units

-compare duration of more than one event

-solve problems of duration – duration unknown, start time unknown and end time unknown problems and difference problems

Teachers also identify that knowledge of the 6x tables is going to be useful too.  Once this has been unpicked it allows us to judge how long we’ll need to spend on this one statement and where this learning fits in with other areas in the long term progression.  For example I recommend teaching the 6x table and multiplying by ten before I tackled this learning.  I’d also ensure the pupils had enough experience of regrouping numbers flexibly before attempting and that they understood the concept of difference.

Next is to identify the right tools for the purpose see the examples below.

Artisan1Understanding 60 as a unit is the lynchpin knowledge in this sequence.  There is very little pupils will be able to build on without this knowledge.  My go to tool here is actually the pattern blocks.  That yellow hexagon is a very useful link to the hour/minute but other resources shown here can also be used.

If the value of the hexagon is 1 hour, what are the blue rhombus, the green triangle and the red trapezium worth?

How many groups of 20 minutes are there in 1 hour?  What would that look like on the clock face?

Repeat for groups of 10 minutes and 30 minutes. 

What if the value of the hexagon is half an hour, what will the blue rhombus, the green triangle and the red trapezium be worth now?

How many groups of 5 minutes are there in 1 hour? Explain how you know. 

How many ways can you make 1 hour using the shapes to help you?

Pupils build their knowledge into the equivalence chart you can see in the graphic and onto part whole models where 60 is always the whole.  What we are looking for is for that first vital component of knowledge to be explored, secured and clarified by the teacher.

Learners require a significant amount of practise for this to be secure.  This is the time artisans give to ensure a quality product, making sure it is perfect.  As Charlie Harber’s blog here shows, pupils need to be presented with a range of examples.  Beadstrings provide a nice opportunity to practice finding complements to 60.  Place a peg after 60 so pupils only use the 60 beads necessary.  Then hide some beads and show what’s left.  How many more to 60?

Artisan2

And then to ensure chances are given to application of knowledge.

For example – How many ways could you make this true?

Artisan3

I know some of the teachers worry that if they spend all of this time on one piece of the learning they won’t cover everything that needs to be covered in one year.  And I sympathise, writing the ESSENTIALmaths materials has made all of us on the maths team appreciate further the time it takes to cover the curriculum well.  But as with everything in teaching this is a trade-off.  We could spend less time on this now and then move on but how much time will be spent bemoaning the fact that pupils haven’t learnt their facts to 60 and having to re-teach it in order that they can progress. Lynchpin learning takes longer, other related learning will (hopefully) be made less painful and less time consuming as a result.  For the teachers I am working with on this currently – they actually see being given permission to craft rather than to race through and repeat as a relief and a release. They know that they won’t get it right all of the time at first but with a little patience and trust in their skills, those evenings trawling on the internet for things that deep down they have a nagging suspicion aren’t right for their class (or them) will be a thing of the past.  Lessons become simple and elegant and focused on the core learning.  So go on chuck out the chintz – and release your inner artisan.

References

Definition of artisan https://en.oxforddictionaries.com/definition/artisan accessed 6th Sept 2017


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