| Why do pupils find understanding fractions difficult? |
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Research taster
Many of the mistakes that pupils make when working with fractions stem from assumptions they make about fractions that are based on the way natural (ordinary) numbers work.  For example, pupils sometimes believe that one third of a cake is smaller than one fifth of a cake because 3 is smaller than 5. Or, when asked to add two fractions, they may add the denominators. Pupils need to realise that fractions are different from natural numbers. One way in which fractions differ from natural numbers is that fractions are ‘relative’ in nature. The same fraction may refer to different quantities – for example, half of six and half of ten are different. This concept, that fractions involve relations between quantities, is an important one that pupils in years 4 and 5 often find difficult to grasp. For pupils to develop a good understanding of fractions, they need to experience working with them in a variety of contexts.
Your evidence
You might like to find out more about the contexts in which specific pupils have encountered and explored fractions. You could do this by selecting three pupils (perhaps pupils with high, average and low levels of attainment in maths) and reviewing their exercise books and/or portfolios of work. If you make a list of the different aspects of fractions pupils might have encountered over a period of time, such as half a term, you can then check which aspects of fractions each pupil actually covered and the range of contexts. If there are gaps, where are they? Moving forwards Having noted where pupils’ experience of specific aspects of fractions is relatively thin, you could plan how you might begin to help them fill the gaps. Would sharing this analysis with a colleague help to highlight any additional areas or contexts worth exploring in more detail? Find out more  Nunes et al (2006) Fractions: difficult but crucial in mathematics learning Teaching and Learning Research Programme Research Briefing no.13. Available at: http://www.tlrp.org/pub/documents/no13_nunes.pdf The full project is The role of awareness in the teaching and learning of literacy and Numeracy in Key Stage 2 (2001 – 2004) by Prof. Terezina Nunes, Prof. Peter Bryant and Dr. Jane Hurry. The project website is at: http://www.tlrp.org/proj/phase11/phase2h.html |
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