1. Creativity and Mathematics

2. Research Study
The paper that underpins this study module is 'Pre-service primary teachers’ conceptions of creativity in mathematics
It is written by David Bolden, Tony Harries and Douglas Newton of Durham University

3. First Thoughts
Before looking at the ideas of others it is useful to consider your own position.
Write down your own ‘first thoughts’ about creativity and mathematics.

4. 1.Introduction
The introductory section of the paper begins by looking at
The different ways creativity has been defined
What it might mean in the mathematics classroom
What research shows teachers understand by creativity

5. 1.1 Words
The authors provide the words used by other writers in the field to describe the outcomes of creativity such as
new
unpredictable
of value
original
ethical
Were any of these words included in your ‘first thoughts’?
What other words would you add to this list?
What would you not include?
Read page 2 if you want to know more

6. 1.2 Creative opportunities in the mathematics classroom
According to the authors, creative opportunities exist in
- the need for mathematical expression and communication,
- the construction of meaning and development of personal understandings,
- the generation of ways of solving problems,
- hypothesising about mathematical situations and outcomes,
- constructing tests of those hypotheses
- formulating plans for solving complex problems
You can read about this on page 2

7. Your thoughts?
Do you agree with the authors’ list? Think about a mathematics lesson you taught recently and consider how many of these opportunities existed within that particular lesson Do you think you were ‘teaching creatively’ or ‘teaching for creativity’, both or neither? (see pages 4 & 5)

8. 2.Research Method
38 pre service teachers completed a questionnaire at the beginning of their 38 week post graduate course
10 of these volunteers were interviewed towards the end of their course
No specific instruction or support for creativity was provide by the course
Only 1 student had an undergraduate degree in mathematics

9. 3.Results (a) Teachers’ creative use of resources 17
The conceptions held could be categorised as:
Creativity as creative teaching: 27
(a) Teachers’ creative use of resources 17
(b) Teachers apply mathematics to everyday examples 10
Creativity as creative learning: 18
(a) Pupils undertake practical activities and investigations 12
(b) Pupils develop computational flexibility 6

10. 3.2.1 Creativity as creative teaching(a)
BBolden et al found that the concept of creativity being linked to the use of resources was about having fun. TThese pre service teachers did not consider how ‘the resources themselves could be used to represent concepts in different ways and possibly give young learners better access to ideas’ (page 10).
Think about the resources you have used in mathematics lessons this week that the pupils had fun using.
Did the resources allow for better access to ideas?

11. 3.2.1Creativity as creative teaching(b)
‘I think it’s about finding a hook, find something that’s interesting to the children like I had one child who was only interested in fishing so if you could relate anything to fishing he could do it and if you couldn’t, he couldn’t do it, he had a sort of mental block. So I was making up these ridiculous questions about how many carp are there in a pond, just tailoring the question to their interests, using your creativity to interest them’ (page 11).
Bolden et al suggest that it does not have to be a real context such as this student teacher described: it could be a puzzle.
Think of learning situations with pupils where you have needed a ‘hook’.
How well did it work?

12. 3.2.2 Creativity in learning (a)
‘In these activities, there are no set ways of working, and so, young learners are able to develop their own methods for approaching problems and are encouraged to explore ideas rather than just seek an answer’ (page 11).
Measuring data, fractions, and shape and space were suggested by the pre- teachers as providing opportunities for pupil creativity.
Bolden et al ask whether using pizza slices helps to give meaning to calculations with fractions (page 12).
What do you think? Think about the evidence you have to support your position.

13. Creativity in learning (b)
They are encouraging the young learners to see mathematics as more open and that the way in which calculations are performed is at least as interesting as the answer. This orientation suggests that pre-service teachers saw flexibility as a key element of creativity (page 13)
Do you think that mathematics teachers encourage greater flexibility as they become more experienced? Why/why not?

14. 3.2.3 Creativity and assessment
If assessment practices are to be better able to assess creativity, then we need to get creative in the ways we assess. That is, creative assessment is likely to require children to illustrate their mathematical understanding, and this will require very different modes of assessment than we currently have in operation in England (page 14).
What strategies do you currently employ to assess mathematical understanding?

15. 3.2.4 Narrow conceptions of mathematics and its creativity
Beginning of course: Questionnaire response
‘Maths does not seem to be creative. It deals more with numbers, calculations, and problem-solving. Much of maths seems to be based on rules’ (page 15).
End of course: Interview response
‘….I would say that mathematics can be much more creative, it just needs the right person to
make it creative. I saw scope for creativity in maths before but I see much more scope for it now…….’
(page 16)

16. Your thoughts?
Do you think that thinking about creativity has changed your ideas as it did for some of these pre-service teachers? If so how ? Might there be a difference in your approach to teaching mathematics in the future?

17. Ideas on the portal
Mathemapedia has something for every Key Stage

18. If you want to read more
CCraft, A. (2002), Creativity and early years education, London: Continuum NNACCCE (National Advisory Committee on Creative and Cultural Education) (1999), All our futures: Creativity, culture and education, London: DfEE. SSternberg, R. J. (Ed.) (1988), The nature of creativity: Contemporary psychological perspectives, New York: Cambridge University Press