Dear Doctor...An activity for overcoming misconceptions in maths

Thanks to John Dabell for this post which addresses key misconceptions in maths and suggests an effective activity to overcome them. John is a teacher with over 20 years teaching experience across all key stages. He has worked as a national in-service provider and is a trained OfSTED inspector. 

Dear Doctor…maths advice and support

When you are at sixes and sevens with your maths, numbers can take on a whole new shape. They become ugly and intimidating and can make you feel sick - well, they can for some learners. So what can we do?

There are lots of novel ways we can help children get to grip with their maths so it isn’t painful and one way to do it is by using common misconceptions.   

In this activity we ask children to adopt the persona and role of agony aunts/uncles or doctors who reply to letters sent to them about our maths problems – the children become the experts. Even though children might not feel very confident about taking on this role, they aren’t expected to do this on their own. They work together in small groups and discuss what’s what and what’s not before formulating a mathematical response and co-constructing a reply. This draws together their own knowledge and understanding and they use their ‘corporate’ expertise to help each other. This is a valuable strategy to assess the level of sophistication children are working at and it gives you insights into their thinking and how you can plug any holes and build bridges between concepts. 

Dear Doctor or Dear Aunty/Uncle  is a great way of combining maths and literacy so this is a ‘Twofer’ or ‘Two For One’ strategy that can pack in a lot of learning and ‘kill’ two subjects with one stone. It unites talking, listening, reading and writing in mathematics and enables children to explore and evaluate ideas collaboratively.       

What to do:

  • Decide on a theme or common misconception

  • Write a fictitious letter

  • Have children working in small groups discussing the letter

  • Each group offers their ideas to the class

  • Children write a reply

  • Repeat and focus on another misconception…or have children write their own letters

Look at the following examples. Some of them might fit with what you are already doing in class so perhaps try one and see what children say. Can they write a reply and explain their thinking? 

Dear Dr Merryweather,
      I think that my teacher has marked my work wrong! I did 6 -:- ½ and worked out the answer to be 3. She has put ‘see me’ but now it is half-term and I can’t wait that long to ask her. It has to be 3 surely, I mean what else can it be?!
Hope you can help soon,
Dear Doctor Shipshape,
         We have a problem! There is a poster of 2D and 3D shapes in our classroom but I think it is wrong. My friends don’t agree. It shows a picture of a ‘square’ and a picture of a ‘rectangle’ but I thought a square was a type of rectangle so they should both be labelled rectangle shouldn’t they? My friends say that a square can’t be a rectangle because it doesn’t have two long sides and two short sides.
What do you think?!

Yours sincerely,
Dear Doctor Piece,
                A group of friends at school can’t agree on something. We have a homework question and it asked us to add together 3/5 and ½.  I make this 4/10 because you just add the top numbers and the bottom numbers. One of my friends says it is 1 1/10 and another even says that is 11/10 so I’m confused.
Yours, in bits,
Dear Dr Point,
               I’ve been arguing with my sister (Zara aged 10) about angles. I think angles with longer lines are bigger than angles with shorter lines. Zara says the length of the lines don’t matter which I think is silly, of course they do, don’t they. Can you help?
Jacob, 9
Dear Uncle Harry,
          We were measuring the length of different objects for homework but couldn’t agree how to do it. Elliott says you measure from the edge of the ruler. Megan thinks you measure from 0cm and I think you measure from 1cm. We are all measuring the same things but we get different answers.            Can you help us to get things straight?
Thanks you,
Dear Aunty Nina,
         A group of friends can’t agree and we hope you can help? I think 0.275 is bigger than 0.9 but Johnnie disagrees with me. It’s obvious to me that 0.275 is miles bigger because it’s got more digits: I think it is bigger by 266. Johnnie doesn’t seem to get the point. Can you help?
Yours, confidently,
Dear Dr Dear,
           My brother and I had a huge argument in the supermarket yesterday which caused a bit of a scene. You see I saw a box of chocolates priced at £1.5 which I think means one pound and five pence. My brother said it meant one pound and fifty pence. We couldn’t agree so we took it to the checkouts. The man on the till scanned it and it came up £1.50 but I said it was wrong and I said I was only going to pay one pound and five pence. My brother stormed off embarrassed whilst the supervisor called security. Please help me to prove the supermarket wrong and put my brother in his place.
Yours, steaming with rage,
Dear Doctor activities open up many different opportunities for exploring maths misconceptions and for children to come together and share their thinking, e.g. place value errors, rounding, greater than/less than signs, adding with negative numbers, telling the time, multiplying by 10, the relative value of money, reflection, lines of symmetry, properties of triangles, and so on.   

See if you can write a Dear Doctor letter for the following misconceptions:

  • Confusing tenths with hundredths, e.g. writing 0.4 as 4% rather than 40%   

  • Writing 100087 for the value one thousand and eighty-seven

  • Writing 8 – 5 + 2 = 1

Take a Dear Doctorr activity four times a term, mix it up with other strategies and see how you get on. You can always increase the dosage if need be. They are a penetrating formative assessment strategy and they can help children approach maths in a more engaging way. 


Mathematics, Maths

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