Maths: Questions & Answers With a Difference

As a former maths teacher I was used to dealing with closed questions that have only one right answer, while as a Clean Language facilitator, the majority of questions I ask are open questions...

One of my clients knew I used to teach maths, and that I now do some dyslexia coaching in the workplace, and asked if I would work with her daughter who has been having trouble with maths at school. I said yes, as long as her daughter wanted to, and the following week, I met Alex, who is a delightful 11-year old with a double whammy of a desired outcome:

“I would like to understand maths better and not panic.”

Obviously if there was going to be any maths teaching involved, the session would not be completely clean, but I would keep it as clean as possible. Here’s what happened…

I started by asking Alex for an example of something she doesn’t understand. She has been using a website called Mathletics, so we logged into this and looked up the topic Alex was studying at the time: factors.

The question on the screen said:

What are the factors of 92….

And the following set of numbers, with ‘fill-in-the-blank’ gaps:

1, 2, ___ , ___ , 46, 92

“What happens when you look at that?” I asked.

 

Alex:

I hear a voice saying, “I don’t get it. I will never be able to do that. It’s like there is a block.”

Marian:

What kind of block?

Alex:

It’s like a brick wall.

Marian:

And is there anything else about that brick wall.

Alex:

No.

Marian:

What happens if you do understand something?

Alex:

I just get on with it and do it. There’s no voice and no panic.

Marian:

So how about we pretend that this is an example of a question that you do understand… ?

Alex:

OK

Marian:

So then how will we go about it?

Alex:

The two empty boxes means I am looking for two numbers, and they must be between 2 and 46.

Using a process of ‘trial and error’ and with a little bit of guidance from me, she gradually got the answer: 4 and 23.

I wrote a few numbers down as we were working, and doing this helped Alex to realize that it helps to write things down and it’s not necessary to do everything in her head.

It also became clear during this time that Alex doesn’t know her 6, 7 or 8 times tables. So we made a list of tasks that she was willing to do:

  • Write out all the times tables 1-12
  • Get someone to check these are correct.
  • Learn and get people to test you – first in order and then random
  • Get a table square and start noticing patterns on it.

I also asked Alex what she can do if she doesn’t understand something…

She told me about a procedure they use at school:

  • Read question out loud and check you have understood it.
    I asked Alex how she can get help with understanding, and she came up with a number of ways:
    • Ask person next to me in school
    • Ask the teacher
    • Look on Mathletics
    • Ask mum or dad
    • There is also the possibility of looking on the Internet, and we acknowledged that this could cause confusion, as it’s not always clear which is the best website.
  • Underline important parts
    e.g. Gerry wants to share her 10 sweets equally between herself and her friend. How many do they get each? Alex said she would underline share 10 between 2
  • Make a list of possible methods
    e.g. divide 10 by 2 or get 10 objects and dish them out one at a time to two piles
  • Choose the best method.

Then we came back to the brick wall…

 

Marian:

Whereabouts is the brick wall?

Alex:

It’s in my mind.

Marian:

And how many bricks are there?

Alex:

10,000 maybe… 100? Lots

Marian:

What colour are they?

Alex:

They’re greyish / brown

Marian:

What pattern are they in?

Alex:

Like normal bricks

I next invited Alex to draw the wall, and when she started to draw the bricks, they were not joined up in a ‘wall-like’ pattern…

 

Marian:

And what kind of pattern is that pattern?

Alex:

It is more like a maths building site.

She then drew a number of bricks and numbers and signs (equals, plus, divide) strewn randomly around the page. She also drew some lines radiating out from the number 1.

 

Marian:

(pointing at lines) Is there anything else about … ?

Alex:

They are sparkles. I know everything about the number 1.

Marian:

Can you draw a picture of what it’s like when you do understand?

Alex drew a row of numbers (1-4) all with sparkles. She said they were all lined up and happy.

 

Marian:

And what happens to ‘signs’?

Alex:

They are in the cupboard.

She then drew a picture of the signs (including a question mark) all lined up in the cupboard.

 

Marian:

So now you know all of that, can you think of a way for the building site to change to lined up, or to have lined up more of the time?

Alex:

Yes I can just line them up…. But there’s another thing… When we do mental maths, and the teacher asks a question which I find hard… we have got several mathematicians in our class and they say things like “Ooo! Seven times eight. That’s hard!” This makes me angry because for me it is hard and then I panic and get distracted, then it is hard to catch up. I want to tell them to go away and stop making comments like that but I can’t.

Marian:

And you want to tell them to go away and stop making comments like that but you can’t. And is there anything else about that?

Alex:

I can’t say anything to them because they are my friends. You shouldn’t say things like that to your friends.

Marian:

And whereabouts is that shouldn’t?

Alex:

It’s in my heart and in my mind.

Marian:

And when it’s in your heart, does it have a size or a shape? 

Alex:

It has an angry face, like Mr Scary from the Mr Men books.

Marian:

And when it’s in your head?

Alex:

That’s like Mr Grumpy.

I suggested Alex did another drawing, and at this point Mr Happy also appeared. Alex drew a vertical line down the middle of her head and Mr Grumpy and Mr Happy had half the head space each.

 

Alex's picture of Mr Happy, Mr Scary and Mr Angry

Marian:

And what would Mr Happy like to have happen?

Alex:

Mr Grumpy and Mr Scary to go away.

Marian:

Where could they go?

Alex:

A long way away – to Antartica. They can be eaten by a polar bear.

Marian:

And then what happens?

Alex:

The polar bear sends Mr Happy a letter to tell them he has eaten them and that they tasted good.

Marian:

And then what happens?

Alex:

Mr Happy is smiling and has the whole head space. The numbers are lined up and sparkling and the signs are in the cupboard.

Marian:

So, let’s play this through… The teacher says. Ok today it’s mental maths. Get ready. What is 7 x 8? A smart mathematician child says “Ooo! 7 x 8… that’s hard!” Mr Grumpy and Mr Scary appear. Mr Happy send them to Antartica and they are eaten by a polar bear, then Mr Happy smiles, numbers are lined up and signs in the cupboard… And what happens while all that happens?

Alex:

The teacher moves onto the next question and I have to catch up…

Marian:

So how could that process speed up?

Alex:

Mr Grumpy and Mr Scary could be magicked away. It would need to be a beginner magician. Because he is a beginner he knows how to magic them away and not how to bring them back.

Marian:

And how does it go then?

Alex:

The teacher says. Ok today it’s mental maths. Get ready. What is 7 x 8? The smart mathematician says “Ooo! 7 x 8… that’s hard!” Mr Grumpy and Mr Scary appear, but are instantly magicked away. I say, “Could you be quiet when we are doing mental maths, because I can’t concentrate?”

Marian:

Then what happens?

Alex:

Then they are quiet. Or if they are not I tell the teacher.

Marian:

And can you tell them to be quiet?

Alex:

Oh yes.

Marian:

And what happens to numbers?

Alex:

Two numbers float out of the line and they make up the answer.

Marian:

So can you do that now then? What is seven times eight?

Alex:

Um, I don’t know.

Marian:

So then it comes back to learning your tables…

Alex agrees this is important.

 

Marian:

So is there anything else you need help with?

Alex:

Yes, it says here (on a note from school) that I need to learn and retain factors, multiples, prime numbers… I am not sure about prime numbers.

We go back on Mathletics and there is an activity where you have to decide whether a particular number is prime or composite. The second question is 21 and Alex is deciding on ‘prime’.

So I make a times tables chart and get coloured pencils and we look for patterns like:

  • All the even numbers
  • Numbers ending in 5 or 0
  • The pattern in the nine times table, where the first digit goes up one each time and the second goes down one

I ask her to think of a big number that is even. She thinks of 1020 and we factorise it, using the ideas we have just spoken about. Then we come back to the ‘prime number vs. composite’ activity. By now it is clear to Alex that if a number is on the times table chart, it cannot be prime. Alex whips through the remainder of the Mathletics questions. Unfortunately she had already clicked ‘prime’ for 21, so scores 9 out of 10.

Alex seemed to enjoy the session a lot and said she found it very useful. And her mum was there the whole time. Afterwards, she said she found it very interesting listening in –

“It was amazing and very illuminating! And I am glad I was here because know I know her metaphors and will be able to remind her of them if she gets in a flap.”

I had a wonderful time combining maths and clean and asked her and her mum if they would be willing for me to write this up as a blog post. (I quickly wrote it up afterwards from my notes and my memory.) Not only were they willing, but they sent me a drawing Alex did afterwards. A few weeks later and the news is that Alex is much calmer and has now done her SATs and her teacher said she had done well in her maths paper.

And if you know anyone who would like a Clean Maths session, please let me know. smile

Tags: marian way, maths, clean language, modelling

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About the author

Marian Way

Company Director & Trainer, Portchester, Fareham
A highly skilled facilitator and trainer, Marian, who founded Clean Learning in 2001, has developed and delivered training across the world. She is the author of Clean Approaches for Coaches, co-author, with James Lawley, of Insights in Space and co-author, with Caitlin Walker, of So you want to be... #DramaFree. Marian is an expert Clean facilitator, an adept modeller, a programme writer and an inspirational trainer. She has a natural ability to model existing structures, find the connections between them and design new ways for people to learn. Marian was a leading innovator within the Weight Watchers organisation, which included developing the “points” strategy, a local idea that went on to become a global innovation. She is a director of both Clean Learning and Training Attention CIC, world leaders in clean applications for corporate, educational and community development. She designs our programmes and workbooks, leads workshops and teaches on all our courses. She's trained people in Great Britain, Russia, Sweden, Germany, Australia, Japan and the USA. Marian is also a recognised Clean Assessor.

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