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Creativity and mathematics An NCETM research study module

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

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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.

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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.

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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 143 if you want to know more

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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 144

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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 page 145)

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2. Research methods 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.

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3. Results 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

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3.2.1 Creativity as creative teaching (a) Bolden et al found that the concept of creativity being linked to the use of resources was about having fun. These 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 49). Think about the resources you have use in mathematics lessons this week that the pupils had fun using. Did the resources allow for better access to ideas?

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3.2.1 Creativity 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 150). 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?

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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 150) 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 150). What do you think? Think about the evidence you have to support your position.

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3.2.2 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 151) Do you think that mathematics teachers encourage greater flexibility as they become more experienced? Why/why not?

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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 151) What strategies do you currently employ to assess mathematical understanding?

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3.2.4 Narrow concepts 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 152). 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 153)

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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?

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Ideas on the portal MathemapediaMathemapedia has something for every Key Stage

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If you want to read more Craft, 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. Sternberg, R. J. (Ed.) (1988), The nature of creativity: Contemporary psychological perspectives, New York: Cambridge University Press

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