1. Developing a Mathematical Mindset
Promoting Grit, Resilience and Character within
maths/numeracy lessons
Robert McCallum
PT Maths Carrick Academy
Numeracy Development Officer South Ayrshire Council

2. • 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.
Aims

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
Agree a
little
Agree Agree a
lot
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.
1 2 3 4 5 6
3. I like maths best
when it makes me
think hard.
1 2 3 4 5 6
4. How intelligent
you are mostly
determines how
well you do in
maths.
1 2 3 4 5 6
5. Drawing pictures
or making tables
helps me to do
maths.
1 2 3 4 5 6

9. Do you Agree or
Disagree?
Disagree a
lot
Disagree Disagree a
little
Agree a
little
Agree Agree a
lot
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.
1 2 3 4 5 6
8. Maths ability is
mostly genetic; you
either have it or not.
1 2 3 4 5 6
9. You can greatly
change your ability
to do maths.
1 2 3 4 5 6
10. How fast you
can get to an answer
is a good measure of
your maths ability.
1 2 3 4 5 6

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.

12. What is the difference between fixed and growth mindsets?
http://www.trinitytsa.co.uk/wp-content/uploads/2016/07/Growth-Mindset-Animation.mp4
https://www.youcubed.org/four-boosting-math-messages-from-jo-and-her-students/
Day 1 - Mindset

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

14. 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)

15. 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 www.youcubed.org

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

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

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

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

20. 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.

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

23. 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’

24. The power of Yet.
I can’t do this……………….. YET!
I am not capable of solving this problem …….. YET!

25. It took me
17 years and 114 days
to become an
overnight success
-Lionel Messi

26. “People tell me that
I’m born with natural
talent
I’m like . . . uh no!
. . . I just practice.”
- Ed Sheeran

27. Fixed Mindset
Growth
Mindset

28. 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)

29. Activity
How many cubes are in the 10th case?
How many cubes are in the 100th case?

32. Useful Websites
 www.youcubed.org
 www.midsetkit.org
 http://www.glowmathshub.com/
 http://whiterosemathshub.co.uk/maths-everyone-can/
 nrich.maths.org
 http://www.mathematicsmastery.org/

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

34. 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.

37. What is a Number Talk?

38. 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 up, pinky
finger turns
towards the person
Thumb and first
finger up when you
have more than one
solution to the
problem.

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

40. Interventions Number Talks
Rekenreks
http://www.ictgames.com/brilliant_beadstring_with_colour.html
Using Rekenreks

41. Dot Images

43. 1

44. Tens Frames
Tens Frame video

45. First/Second Level Number Talks

46. 39 + 37

47. 151 - 88

48. 8 x 24

49. • 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’’.

50. Number Talks Resources

53. robert.mccallum@south-ayrshire.gov.uk