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Post by Judy on Aug 24, 2020 9:32:01 GMT
A slightly different one this week. Can you work out the error(s) that this child has made?
16 + 27 = 61
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Post by clairemartin on Aug 24, 2020 9:56:37 GMT
I think so!
Have they done it using a formal written method and written 31 instead of 13 when they have added the 6 and 7
Can I pose an error I came across? A teaching assistant on a course I was leading found a child making these errors and she wondered what they were doing-it was only when she asked them to explain their thinking that she found out!
2 + 5 = 9
4 + 7 = 15
6 + 2 = 14
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Becky
New Member
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Post by Becky on Aug 24, 2020 10:07:06 GMT
16 and 27. Have they added the 1 and 6 to make 7 and then added the 2 and 7 to make 9. Then added them together to make 16 and reversed the digits?
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Jenny
Junior Member
Posts: 50
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Post by Jenny on Aug 24, 2020 10:34:07 GMT
Have they added the ones (6+7=13) but written the 1 in the ones column of the answer and carried the 3 over to add into the tens column (1+2+3=6)?
Still thinking about Claire's problem.
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sami
New Member
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Post by sami on Aug 24, 2020 11:35:49 GMT
Applying algorithms without understanding does seem to be the issue.
Claire - it seems they doubled the first number and then added the second. Did the student give any explanation for why?
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Linda
New Member
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Post by Linda on Aug 24, 2020 11:51:28 GMT
Agree with Claire and Jenny.
Re: Claire's query - double first number before adding to second as Sami mentions.
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Post by clairemartin on Aug 24, 2020 12:19:00 GMT
That's correct. The child explained and showed using fingers:
2 + 5 = 9 because...
I put up 2 fingers and then I put up 5 fingers. Then I put the first number in my head and count on so 2 in my head...3,4...5,6,7,8,9 so 2 + 5 = 9 so they were counting the first number twice.
We concluded that the child had not understood that the 2 that they were 'putting in their head' was the first number and so it was already used and didn't need to be counted again.
We discussed how following a process or procedure such as 'put the first number in your head and count on' has the potential to cause confusion/misunderstandings/misconceptions/errors if the child doesn't understand what is happening or why they are doing it.
It was a really good discussion with the group of TAs and I was really pleased that she had spotted the errors the child was making and investigated further, rather than simply marking the questions incorrect. This gave her the chance to address this misunderstanding.
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Post by Judy on Aug 24, 2020 13:54:35 GMT
I think so! Have they done it using a formal written method and written 31 instead of 13 when they have added the 6 and 7 Can I pose an error I came across? A teaching assistant on a course I was leading found a child making these errors and she wondered what they were doing-it was only when she asked them to explain their thinking that she found out! 2 + 5 = 9 4 + 7 = 15 6 + 2 = 14 Hi Claire Yes, that's what I thought! Not sure what's happening with your example- that's much more intriguing than mine.... :)Are they doubling the first number and then adding eg 4 +5 then 8 + 7 but why?? |
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Post by Judy on Aug 24, 2020 13:55:19 GMT
That's correct. The child explained and showed using fingers: 2 + 5 = 9 because... I put up 2 fingers and then I put up 5 fingers. Then I put the first number in my head and count on so 2 in my head...3,4...5,6,7,8,9 so 2 + 5 = 9 so they were counting the first number twice. We concluded that the child had not understood that the 2 that they were 'putting in their head' was the first number and so it was already used and didn't need to be counted again. We discussed how following a process or procedure such as 'put the first number in your head and count on' has the potential to cause confusion/misunderstandings/misconceptions/errors if the child doesn't understand what is happening or why they are doing it. It was a really good discussion with the group of TAs and I was really pleased that she had spotted the errors the child was making and investigated further, rather than simply marking the questions incorrect. This gave her the chance to address this misunderstanding. Fascinating! |
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Post by Judy on Aug 24, 2020 13:55:59 GMT
This is fun- has anyone got any more examples?
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Post by Steve on Aug 27, 2020 8:45:54 GMT
What a great discussion! Thank you. I sort of love/hate expressions like 'put it in your head'. They seem so harmless and benign and probably less daunting than talking about working and short term memories.
And I believe that asking students to tell you how they worked it out can lead to wonderful discoveries about learning (and is much cheaper than all this neuro-imaging-type stuff).
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Post by Cath Wright on Aug 27, 2020 9:45:08 GMT
Thank you for the problem, It is amazing the things student come up with. Yes, I always ask them to explain their working, especially with any word-based problems so you can see where they are going wrong and can support them more effectively.
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Post by peterwhitehead on Aug 29, 2020 12:37:27 GMT
This is a great discussion. I really wish I'd collected some of the "staff room" examples now.
I like Claire's example as it illustrates important points of practise:
1) we absolutely have to be talking to individual students in class at the time to find out what their thinking has been (not paper marking work after class);
2) we then need to work out why that student has that particular misconception; in this instance was this a process error or was it a cognitive load error?;
3) how can we then help that student rebuild or add to their schema going forward.
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