Examples and Non-examples

numeracy leaders teachers Mar 09, 2023

I believe that having an explicit focus on vocabulary in our maths teaching is of critical importance. There are so many words that we use in our descriptions and explorations of maths concepts and more often than not these are words that the students would have never come across in their life. In my PD sessions I always ask teachers if they have ever heard the phrase “place value” being used by students outside of the walls of the classroom.

Unsurprisingly no one ever has!

If the only place students come across these words is in our classroom, there is limited opportunity for them to practice and explore context for their meaning.

I think it is an essential part of the planning process for us to list all the words we are going to use as we teach particular content. Too often as adults we forget that the students we teach will have possibly never heard the words we are using in our maths lesson before (and I’m talking about students who have English as their first language here, EAL/D students have an even more challenging time with maths vocabulary). So taking a few minutes as a team to brainstorm a list of words we want to explicitly address in our teaching is really important.

In the classroom, we want to take time to unpack the words we are using. One of my ways to do this is through the use of a Frayer Model (Frayer,Frederick & Klausmeier. 1969) . A Frayer Model is a graphic organiser that was originally designed for teachers to use in the field of science education. But it is just as useful in our maths lessons.

This is a Frayer model:

You can see that you write the word in the centre (in this case ‘Composite Number’) and then as a class or in small groups, you define the word, include facts/drawings, and finally examples and non-examples.

For me, the most impactful quadrant of the model is the non-examples. Often in our teaching we will use examples. But how often do we include non-examples?

I think one of the most powerful ways to come to understand a word/ idea is to also know what it is not!

Not long ago, my 3 year old saw a large fluffy white dog and said “mum look a polar bear”. As you can imagine I was very shocked to hear that there was a polar bear in a Melbourne street, but as soon as I saw it I knew why he used that description, it was white and fluffy, just like a polar bear.

I said, “actually that looks a bit like a polar bear, but it is a dog, polar bears are a lot taller, taller than me”

At that moment, he had been shown a non-example and had refined his definition of a polar bear… the updated version was: white, fluffy and BIG!

I always say, I dated a few non-examples of “husband material” before I refined my definition and decided upon my “example” (don’t worry I didn’t compete a Frayer model in this process I promise!)

So this week I encourage you to have a think about the vocabulary that your students must comprehend to engage with the content you are teaching, and if you haven’t already, include this as a section on your planner so you can have a consistent approach across your team to vocab (and maybe even give a Frayer model a go!)

P.S I also think this book by Dr Paul Swan and David Dunstan is a fabulous resource for ensuring we have a systematic approach to maths vocabulary- it lists all the words you need to teach and sorts them by year levels. it is a staple in my planning resources.

Want to learn more from Dr Ange Rogers? Click here to find out about her 'Quality Place Value Assessment in Years 3-6 Mini Course'

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