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Post by Judy on Jul 20, 2020 8:17:16 GMT
Hi Everyone
Last week I delivered a webinar on making mistakes in Maths. How do the learners you work with respond to making mistakes. Do they find them demotivating, or all part of the learning process? Or do they feel happy to use their mistakes to help them to understand. Do they spend time trying to figure out why they made a mistake or do they just forget it and move on? Some school celebrate mistakes- how do you feel about that?
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Post by peterwhitehead on Jul 20, 2020 10:55:21 GMT
Most of our students come with a negative mindset towards maths and this includes an expectation that their answers will be wrong. On the whole, I do reasonably well at changing this, although it takes a good while, and that's only the start of the journey! It's not just mistakes, but students not writing anything at all unless they know they can complete a multi-step problem successfully.
Here are some of the things I do:
1) Use Jo Boaler's screwed up paper (they're invited to throw them at me!) in our 16-18 students' induction, and also some exercises on growth mindset.
2) Open about maths anxiety. Teachers are invited to give each other sealed envelopes with problems to solve unseen in front of their classes. This invitation is rarely taken up but the very thought of it is usually enough to remind any of the maths-anxiety-deniers that it's a real "thing"!
3) Some exercises where I show that students have given verbal answers just based on what they've heard others say rather than what they really thought, as well as questions that I think all students will think easy but get wrong.
4) No-one's allowed to laugh at anyone else's answer.
5) We use Barton's "diagnostic questions" a lot and students start to see that they're in the company of enormous numbers of others in having a particular misconception (they prefer the idea of "misconception" rather than "wrong").
6) Students aren't allowed to answer "I don't know" to questions that start "what do you think...?".
7) We share solutions to questions on the visualiser (especially effective in the FS classroom) and students can comment on each other's methods.
8) Goal-free problems.
9) When preparing for examinations, we work on just getting the first mark in multi-mark questions.
As regards assessments, and as far as possible:
10) Low stakes, bite-sized.
11) Ipsative assessment.
12) Qualitative feedback and no marks/grades (if they want to add them up, they can do!).
13) Always explicit "what to do next to improve".
Finally, lots of encouragement, empathy and setting high standards and expectations.
Of course, even when we think we've made significant progress with a student, those latent fears don't just go away and it's not at all uncommon for students to regress dramatically in and around formal examinations.
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Post by Becky on Jul 20, 2020 17:41:16 GMT
I think it all depends on the child and their experiences of learning and failing. I have some children who are not afraid to let every one know that they've made a mistake and will gladly share it, some that will keep quiet about it but will share their experience but more importantly, some who will actively hide away from letting anyone know to the point of changing their answers. I work really hard on making my classroom a safe environment so that the children feel secure enough to not be ridiculed for getting it wrong. We talk a lot about making mistakes and how this creates connections in our brain, resulting in growth and learning. I've read Bounce by Matthew Syed (myself) and This is Awesome with the children to encourage growth mind set. It takes a lot of hard work to convince children that it is ok to get things wrong but this is only successful if it is taken on board by everyone involved with that child.
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Post by Judy on Jul 21, 2020 8:37:53 GMT
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Post by Judy on Jul 21, 2020 8:40:25 GMT
Becky I think you are absolutely right- there has to be a culture in the classroom that everyone has bought into as it were, so that children feel safe to make mistakes. In Singapore they have a saying- we always agree to listen to everyone but we don't always have to agree with them.
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Post by peterwhitehead on Jul 21, 2020 8:56:48 GMT
Thanks Judy, yes we've used some of Brian Bushart's examples and there's some good numberless stuff out of one of the Maths Hubs projects but I can't for the life of me remember which one!
It reminds me that there's one other thing we do with answers that are "wrong". When it's not a maths misconception but (as is so often the case) a reading misconception, S_b is asked what change needs to be made to the wording of the question so that S-a's answer is now correct. Students are generally a bit surprised by this task at first but warm to it (I guess it has the advantage that they don't have to give a mathematical answer as S_a has already done the maths).
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Jenny
Junior Member
Posts: 50
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Post by Jenny on Jul 24, 2020 9:18:24 GMT
My previous school was great at this and the head had a saying, 'only imperfect people are allowed in this school' which was as helpful to the staff as the students.
I'm working as a teaching assistant in my current school, so have fewer chances to influence the ethos in the classrooms, and think this might be a missed opportunity. The constant time pressure means there is a real danger that opportunities to understand, learn from and appreciate mistakes are missed. I think we too often are in a rush to get to the answer so tell the student what and where their mistake is and move on. This has really encouraged me to go back to using those mistakes well and also modelling on the occasions when I make a mistake.
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sami
New Member
Posts: 14
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Post by sami on Jul 24, 2020 11:06:04 GMT
Jo Boaler's work has influenced a lot of my work and I am really interested to see how it fits in as I become more aware of dyscalculia. I have not seen anything where she addresses dyscalculia directly. I'd love to know if she has.
Many of the schools I work in encourage teachers and students to discuss 'great mistakes' as part of their learning culture. Through this misconceptions are openly shared and addressed. If a child answers that 43+67= 100 then their solution rather than being dismissed and marked as an error can be considered in terms of their use of bonds to ten and place value has possibly being used correctly and then how they need to work with the tens and ones to find the answer. They might also be asked to find 40+60 to help them to identify the mistake themselves rather than marking an answer as wrong.
Some teachers also ask pupils to consider generating 'good mistakes' and 'crazy mistakes'. So 9 is a prime number might be a good mistake since it is the first odd (other than one) not to be prime and it is square but 12 would be a crazy mistake. Pupils really like coming up with crazy mistakes as part of discussion and I've seen it work really well as a way of motivating dialogue in maths.
I love this approach but still find that the culture of correctness pervades most classrooms and pupil (and often teacher's and parent's) perception of success in maths is usually determined by how fast and how many right answers they got in a task.
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Post by Judy on Jul 24, 2020 13:10:00 GMT
Hi Sami
I was on her website yesterday and searched for dyscalculia, but it came up with no results , so I don't think it an area that she is looking at at the moment. No problem, though as we are all on the case!
I love your idea of crazy mistakes and good mistakes. It reminds me a bit of the strategy of asking for an example of something, let's say two numbers that add to ten. Invariable the child would say 4 + 6 or something similar. Then you ask for another but a bit stranger than that and then keep asking until you get a really weird one like 9.9999999 + 0.000001 or even 122 + (-112) etc
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Post by Bernadette CS on Aug 15, 2020 13:46:40 GMT
This is a super-interesting topic. Sometimes in the very first 1-1 session with a new learner, I can see that they really don't don't want to answer as they are presuming that (just like perhaps their experience at school before intervention) that they will make a mistake and the answer will be 'wrong'. It's so common to see genuine surprise from children when they get something 'right' that they are not expecting too. It's almost sad. Great to see the pleasure they can take with their own success, but said to see that they are 'surprised' by it. It really needs some very careful unpicking.
I try to use the word 'yet' a lot in response to "I don't know this" - "you don't have to know this yet', 'you won't know this yet because that's what we are doing today ' etc.
I've also recently had a really good response when I've explained to two very different learners that if they don't make any mistakes, then they are not learning anything new at all.
We spoke about what a strange lesson it would be if we sat together, I asked them things, and they immediately answered, represented, demonstrated EVERYTHING correctly! We agreed that they wouldn't have actually learnt anything new at all that day, that I would just have to go home, , that I wouldn't have a job at all, and generally had a really good laugh about this!
We then talked in very simple terms about how when we make an error , and then explore it' and then put that right, we are actually making a brand new neural pathway in the brain. We drew a brain shape and drew some existing 'pathways' with the journey up and down, forwards and back, on the same pathway when they knew all the answers. I can't remember whose work this was on the 'new neural pathways from mistakes" but will look it up again.
We then drew, really slowly, stoping, starting, pushing etc. a NEW pathway, as they worked through something where they didn't automatically just know the answer.
One child aged 9, later said, "I've got new paths in my brain now". The other, aged 10, simply said 'Yup, that makes sense to me".
Nice positive moments in both lessons that we can go back to when we want to lighten the moment or change the mindset too..
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