Purposeful planning for maths mastery

I was at the very lovely Dulwich Picture Gallery this summer, visiting their Cutting Edge: Modernist British Printmaking exhibition. I spent a fascinating hour browsing the linocut prints and reading about the visionary artists of the Grovesnor School of Modern Art. As someone interested in maths mastery, I couldn’t help but see the numbers and patterns in these prints – so full of movement – inspired by the rapidly changing world of the 1920s and 1930s. I wonder what the artists would think of the pace of change today! I’m looking forward to sharing some of the images with my students this term to discover what they will see in them. Take a look with your children at prints such as Cyril Power’s Skaters and Gale or Speedway by Sybil Andrews then challenge them to subitise the numbers they can see, or describe the patterns that they’ve spotted.

The Giant Stride – Ethel Spowers, circa 1933
I see 3 + 3 + 1 – what can you see?

On the wall in one of the exhibition rooms in the Picture Gallery was a quote by Sybil Andrews that caught my eye:

This speaks to me on several levels, both privately and as an educator. However, the “THINK what you are doing, and WHY” section particularly resonates. All too often I have observed lessons where planned tasks lack purpose, becoming a job to be done rather than a vehicle for learning. I’ve seen children hustled on to the next question so that they can be finished before break time, with learning opportunities regrettably missed.

I know how busy term time is and sometimes it feels as though ‘wake up and work’ is all that you do! I know that it makes life easier, for example, to pull a worksheet with a bunch of purses with coins off the internet and ask the students to work out how much money each purse contains. Please take a moment though; think what you’re doing, and why. Have you purposefully planned activities that present learning opportunities or have you accidentally slipped into tasks that are more procedural in nature? Wouldn’t it be more powerful to give the students lots of empty purses, tell them that there is a specific amount in the purse and see which different ways they could make that amount? With this task you’ll not only find out if they can recognise and add together coins but also present opportunities to discover and discuss:

  • what strategies they are employing to find the total
  • which resources they are using to help them
  • whether they can work systematically to find all of the possible combinations

Make sure that any adults working with the students understand that the route to the answer presents opportunities to discuss and learn.

My 5 year old daughter completed this task, working systematically when prompted.

Now put a little more thought into it and anticipate the common errors students may make or misconceptions they may have. Choose, for example, 8p or 30p for the total inside the purse rather than 10p or 20p (depending on the age of your students). This little tweak will help you to weed out the students who will make the common error of drawing an 8p or a 30p coin. You wouldn’t spot this misconception if the total in the purse was 10p or 20p.

Couldn’t you then plan to give students who are progressing quickly a little ‘learning nudge’ and say that you forgot to tell them that all the coins in the purse are copper/silver coins, or that all of the coins are the same type of coin, and so add some extra cognitive load?

Having a think about “what you are doing and why”at the planning stage and then making these kinds of small, purposeful tweaks will generate learning discussions and tell you so much more about your students’ knowledge, understanding and skills. And all without massively increasing your workload, thank goodness!

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