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Dr Robyn Jackson, an American maths educator, observes that promises (whether articulated or not) are at the heart of teaching.
She suggests ten promises that are worth making to the children in our classes. In the shadow of Covid, I find the following suggestion of hers particularly pertinent:
I promise to provide you with a physically and psychologically safe learning environment.
While much attention is being paid to making classrooms physically safe, it’s equally important for mathematics lessons to be psychologically safe. I think, however, we sometimes underestimate how ‘at risk’ children can feel in maths lessons.
While a range of opinions on a story might be welcomed in an English lesson, the sense that mathematical offerings are going to be judged on whether or not they are correct can make children anxious about being called on.
Outside school, much of our learning about risk-taking happens through play, both structured and unstructured. Here I offer a few simple, playful maths tasks that may help children feel less anxious about making offerings in class, and help rebuild confidence.
Choose a mental calculation strategy that you think is within the current level of competency of the class and that could usefully be practised. For example:
Tell the class that you’re thinking of a secret rule to apply to numbers, but that you’re not going to tell them what it is. They have to figure it out by giving you numbers and seeing which result you give them, based on applying your secret rule.
Go round the class asking for numbers, recording the pairs of numbers as a table on the board. For example, if your secret rule is ‘add five’, you might record:
In / Out
3 / 8
7 / 12
57 / 62
Explain that if anyone thinks they know what the rule is, they should indicate this by putting a thumb against their chest. As well as getting children to offer you further numbers to act on, select pupils with their thumbs up and give them a number to which they have to apply what they think the rule is.
If they are correct, add the pair of numbers to the table.
Once many children have thumbs up, invite them to offer numbers to apply the rule to that they think will help everyone figure it out. Eventually, ask pupils to turn to a neighbour and agree on what they think the rule is. Can they explain what helped them figure it out?
This can be made more challenging by having a simple two-step rule, for example:
Choose a way of sorting numbers that children should be familiar with. For example:
As for ‘What’s my rule?’, explain that you have secretly chosen a rule for sorting numbers. Draw a horizontal line on the board – children are to give you numbers and if they fit your rule, write it above the line. If it doesn’t, write it below the line.
Take suggestions from children in turn, recording the numbers above or below the line as appropriate.
Again, once anyone thinks they know what the rule is, they should indicate this with a ‘silent’ thumb. When you choose ‘thumbs up’ children, tell them that you want them to give you a number and they must predict whether it will go above or below the line.
Again, as this progresses, invite those who appear to know what they rule is to offer numbers that they think will help anyone still not sure of the rule.
One of the things that often happens when I first play this in class is that, as it progresses, children begin to assume that they have to provide numbers that are ‘correct’, in the sense of going above the line.
It helps to talk about how you can’t be ‘wrong’ in offering a number, and how, often, the numbers below the line can be more helpful in checking what the rule is than those above it. Again, this can be made more challenging by having two criteria for sorting, or a slightly less obvious criterion, for example:
Children each need a set of 0-9 digit cards. Ask pupils to mix up their cards and randomly set aside five of them. Set various challenges for making numbers that the children have to use their remaining cards to show solutions to, for example:
This can be developed into having to make a pair of numbers (still from the five remaining cards) that satisfy certain conditions. For example:
These challenges are helpful for bringing children’s attention to the power of reasoning over working out actual answers.
For example, in looking for two two-digit numbers with a difference of more than 20, children might reason that if they make a number in the 50s, then 20 less than that number is going to be in the 30s, so any number in the 20s or below will satisfy the condition.
Listening out for children’s reasoning and inviting them to share it with the class is a great opportunity for ‘assigning competence’, an idea that I’m grateful to Dr Ruth Trundley for bringing to my attention.
Assigning competence is a strategy for raising the status of children who are not the most confident in lessons by sharing something they’ve said or done with the class and showing how everyone can learn from this.
The work of Ruth and her colleagues demonstrates that assigning competence, done subtly and with a focus on highlighting a child’s thinking rather than them personally, can have a powerful impact on both confidence and attainment.
I’m not going to make any promises that assigning competence is going to make everyone love mathematics, but I recommend you give it a try.
Mike Askew is adjunct professor of education at Monash University, Melbourne and a freelance primary maths consultant. Visit his website at mikeaskew.net and follow him on Twitter at @mikeaskew26.
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