Do sweat the small stuff

Headteachers, deputies, union reps and heath and safety officers around the country have recently had to scrutinise every aspect of school life in minute detail – and rightly so. Do we scrutinise what we teach in the same way? Should we? It’s not as if it’s life and death… except for disadvantaged children, the clarity of the education they receive is vital to their success in life.

Lack of clarity leads to misconceptions. Misconceptions that are not addressed lead to further barriers and ultimately to disaffected learners. Disadvantaged children are less likely to have misconceptions addressed as they often lack support at home and rely entirely on it being picked up in school, and with the best will in the world sometimes children slip through the net.

Best to avoid misconceptions from occurring in the first place then – which brings us back to scrutinising what we teach and ensuring we have clarity.

I’m currently writing knowledge organisers for every small step from the White Rose Maths planning. It has really made me question some of the vocabulary that we use when teaching maths and the models that we present children with.

I’ll start with one my bugbears – commutativity in multiplication. Imagine presenting 3 x 2 to a child in the early stages of learning how to multiply. I would want them to know that this is 2 lots of 3 not 3 lots of 2.

“Why does it matter? They get the same answer”

Yes, but they’d also get the same answer doing 3 + 3 or 2 + 2 + 2, or even 5 + 1 etc. I want them to know that these all get the same answer, but I also want them to understand how they are different.

3 x 2 = 2 lots of 3

array

Which then becomes an array…

array1

Later a bar model…

bar model

These models or visual representations look different for 2 x 3 (although arrive at the same answer) so we should be modelling that to children – pointing out how they are different yet give you the same answer. Saying it doesn’t matter as you get the same answer is not clear. 2 + 2 + 2 gives you the same answer as 3 x 2 yet they are clearly very different.

What happens when we move onto division? It’s very important that children have a secure knowledge of multiplication and been presented with very clear models. If children been given the message that it doesn’t matter, they are less likely to have those clear models which could cause problems with division.

 

Sharing…

bar model 1                                           bar model 2

 

Grouping…

numberline 1

 

If you present 2 x 3 as being 3 groups of 2 and 3 x 2 as being 2 groups of 3 you make it easier for children to make the link when they move onto grouping. Ambiguity around how many lots or groups of is unhelpful at this stage.

We wouldn’t tell a child ‘rayn’ was correct. If they hadn’t been exposed to /ai/ yet we’d say it was a great try. If they had been exposed to /ai/ we’d show them the correct spelling. They both sound the same but it does matter. It matters particularly later on when children are spelling more complex words. Mathematically, 3 x 2 means 3 multiplied by 2, so 2 lots of 3. It matters.

Clear vocabulary particularly when first teaching a topic, is absolutely vital to a child’s understanding. Whilst writing the knowledge organisers, particularly for other year groups where I’m not so familiar with the curriculum, I’ve really had to consider the impact of vocabulary.

One example is when teaching subtraction for the first time in year 1. The term ‘counting backwards’ is used in the WRM planning yet also in the planning children were presented with backwards number tracks, e.g.

numbertrack

Counting backwards, i.e. left, would mean we were adding rather than subtracting. Of course, children used to reading right to left would not see that but that is a different matter.

I spoke to colleagues, both in school and on Twitter, and some felt it didn’t matter as the children got it. Some felt it did matter (especially colleagues who taught older children) as it could lead to misconceptions. Children might be able to do the trick at a simple level but roll on a few years and they’re expected to have an understanding of ascending and descending and it soon becomes apparent that they don’t have a secure understanding.

I decided against using the term ‘counting backwards’ for the knowledge organisers, as I felt it related more to the direction and less to the process of subtraction. I opted instead for ‘counting back’ – a small but important difference.

This is the crux of the matter – words matter. Being precise with our words matter. Failing to do so may lead to misconceptions. Unaddressed misconceptions lead to failure.

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