1. Promoting Grit, Resilience and Character within maths lessons
Developing a Mathematical Mindset
Promoting Grit, Resilience and Character within maths lessons
University of the West of Scotland 24th January 2017
Robert McCallum
PT Maths Carrick Academy
Numeracy Development Officer South Ayrshire Council
Chris McKenna
Teacher of Mathematics

2. Aims
To explore your own mindset
To determine what approaches can be adopted within maths lessons
To experience ‘Low floor, high ceiling’ problems
To explore how to promote mathematical
mindsets in your school
To determine how ‘Number Talks’ can
promote mathematical mindsets.

5. Making Maths Count Scotland has a maths problem. Too many of us are
happy to label ourselves as “no good with numbers.”
This attitude is deep-rooted and is holding our country
back educationally and economically.
Transforming public attitudes to maths.
Improving confidence and fluency
in maths for children, young people,
parents and all those who deliver
maths education to raise attainment
and achievement across learning.
Promoting the value of maths as
an essential skill for every career.

6. Have you heard?
Parent
‘He/she is just not a maths person. He/she gets it from
me. I was never very good at maths at school either’
(usually followed by laughter)
Parent/teacher
‘Don’t worry, obviously you don’t have a maths brain.
You are better suited to ………’
Pupil
‘I know I achieved an A last year but I think I will
Feel better going for a B at Higher.’
‘I am never going to get this’

7. How about you?
Complete the survey. Be honest about your own
beliefs towards maths

8. Do you Agree or Disagree? Disagree a lot Disagree Disagree a little
Profile Number
1. Trying a problem I don’t know how to solve is the best way to solve new maths. 1 2 3 4 5 6
2. You have a certain amount of maths ability and you can’t do much to change it.
3. I like maths best when it makes me think hard.
4. How intelligent you are mostly determines how well you do in maths.
5. Drawing pictures or making tables helps me to do maths.

9. Do you Agree or Disagree? Disagree a lot Disagree Disagree a little
Profile Number
6. How well you can memorise determines how well you do in maths. 1 2 3 4 5 6
7. When a new maths concept is hard, it just wants me to work more on it to figure it out.
8. Maths ability is mostly genetic; you either have it or not.
9. You can greatly change your ability to do maths.
10. How fast you can get to an answer is a good measure of your maths ability.

10. 10-20 You strongly believe that your maths ability is fixed – it does not change
much. If you can’t learn something quickly and easily, you would rather
not do it. You think smart people don’t have to work hard and that some
people are naturally good at maths.
21-30 You lean toward thinking that your maths ability does not change much.
You prefer not to make mistakes if you can help it and you also don’t really like to put in a lot of work. You may think that learning should be easy, it makes you feel uncomfortable when other people answer questions quickly.
31-40 You have not really decided for sure whether you can change your ability
to learn maths. You care about how well you do and you want to learn,
but you don’t really want to work too hard for it. Sometimes it may seem that other people have it easy when it comes to learning new maths concepts.

11. 41-50 You believe that your intelligence and maths ability is something that you
can increase. You care about learning and you are willing to work hard to
learn new, complex ideas. You want to do well, but you think it is more important to learn than to always score well.
51-60 You really feel sure that you can increase your ability to do maths by learning and you like a challenge. You believe that the best way to learn is to work hard and you don’t mind making mistakes while you do it. You might try all different kinds of strategies to solve difficult problems and you don’t give up easily.

13. What is the difference between fixed and growth mindsets?
Day 1 - Mindset

14. Key Messages
Everyone can learn maths
Believe in yourself
Mistakes are important
Speed is not important

15. Research findings
High attaining pupils can develop fixed mindsets by always being told they are clever
They eventually do not want to challenge themselves in fear of failure. Praising the
effort and hard work to achieve rather than their ability is much more powerful.
If a mother communicates a negative attitude towards mathematics their
daughter’s attainment in mathematics will decline immediately. Dweck, Boaler (2015)
Encouraging students to use only one method (algorithmic) to solve problems,
they lose some of their capacity for flexible and creative thought.
They become less willing to attempt problems in alternative ways and become
afraid to take risks’ Narode,Board and Devenport (1993)
Many pupils’, parents and even teachers believe that some people have an innate ability
in maths and that people who are good at maths have ‘maths brains’.
There is also a firmly held view that speed and fact recall are the making of a good mathematician.
This has led to a huge problem with maths anxiety in pupils. Dweck, Boaler (2015)

16. How to develop Mathematical Mindsets
Step 1 : Focus on work, effort, struggle and persistence
Realise that hard work is the key to success not natural ability
Step 2 : Choose challenging tasks and focus on strategies rather that end outcome.
Reflect on strategies that work and don’t work
Step 3 : Face setbacks. See mistakes or dead ends as opportunities to learn more.
There is a wealth of resources on

17. Change your Words Change your Mindset.
I am not good at this
How could I get better at this?

18. Change your Words Change your Mindset.
This is too hard
This may take some time and effort but I can do this.

19. Change your Words Change your Mindset.
I give up
I’ll try some strategies I have learned.

20. Change your Words Change your Mindset.
It’s good enough.
Is this really my best effort?

21. Change your Words Change your Mindset.
I’ll never be as smart as them.
I will figure out how they do it and try it myself.

22. Change your Words Change your Mindset.
I made a mistake.
Mistakes help me improve.

24. If you hear………..
‘I am just not a maths person.’
‘You obviously don’t have a maths brain.
You are better suited to ………’
‘I am never going to get this’
‘I can’t do maths’

25. YET! YET! The power of Yet. I can’t do this………………..
I am not capable of achieving National 5 ……..

27. Ed Sheeran

28. Growth Mindset
Fixed Mindset

29. Pupils describing mindsets

30. Activity
How many cubes are in the 100th case?

31. Raindrop
Bowling Alley
Volcano
Parting of Red Sea
Starirway to Heaven, Access Denied
Square Method

32. Recognising and Celebrating Growth Mindset
Celebrating progress in assemblies, names and pictures
of pupils in classrooms and corridors.
Constantly reaffirming that the best students are the ones
who make the most progress not necessarily the pupils with
the best grades.
Using other pupils as models of a growth mindset. (CI)

35. Useful Websites www.youcubed.org www.midsetkit.org
nrich.maths.org

36. Perfect example of growth mindsets
johntomsett.com/2016/09/06/thi…

37. Number Talks and Mathematical Mindsets
A classroom conversation around a purposefully crafted computation problem that is solved mentally.
The problems in a number talk are designed to elicit specific strategies that focus on number relationships and number theory.
Pupils are provided with problems in either a whole class, or small group, setting and are expected to mentally solve them accurately, efficiently and flexibly.
Pupils share and defend their solutions and strategies in a safe environment, they have the opportunity to collectively reason about numbers while building connections to key conceptual ideas in maths.
Mistakes are regarded as opportunities to learn.
It is a stand-alone activity.
Conducted in five to fifteen minutes.

40. What is a Number Talk?
A number talk is a strategy to build flexibility, accuracy and efficiency in mathematical thinking through the articulation of, and sharing of, mental math strategies.

41. Number Talks Hand Signals
Closed fist, held against chest, when thinking of a solution to a problem.
Thumb up, held against chest, when you have one solution.
Thumb and first finger up when you have more than one solution to the problem.
Thumb up, pinky finger turns towards the person you agree with.

42. Number Talk Stems Make thinking visible!
Display and reinforce through regular use.
Share with parents so that they can use this language too.
Make thinking visible!

43. Early Level Number Talks
Rekenreks

44. Dot Images

46. 1

47. Tens Frames
Tens Frame video

48. First/Second Level Number Talks

51. 8 x 24

52. ‘Pupils are saying things like ‘making mistakes makes
Across the authority staff there are extremely positive
about the impact number talks are having in developing
resilience and confidence in pupils approaches to numeracy.
Pupils are enjoying number talks and have said they like
trying to use different ways to answer the question and
getting the chance to explain how they do it.
‘Pupils are saying things like ‘making mistakes makes
your brain grow’’.

53. Number Talks Resources