Mathematics in Early Years Education

Ann Montague-Smith, Tony Cotton, Alice Hansen, Alison Price

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351745116
• Edition: 4
• Topic: Bildung
• Subtopic: Bildung Allgemein

This fourth edition of the bestselling Mathematics in Early Years Education provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics – number and counting, calculation, pattern, shape, measures and data handling – it provides a wide range of practical activities and guidance on how to support young children's mathematical development. There is also guidance on managing the transition to KS1 and a strong emphasis throughout on creating home links and working in partnership with parents.

This new edition has been fully updated to incorporate the latest research and thinking in this area and includes:

• 
  
  

• why mathematics is important as a way of making sense of the world

• 
  
  

• how attitudes to mathematics can influence teaching and learning

• 
  
  

• how children learn mathematics and what they are capable of learning

• 
  
  

• how technology can support maths teaching

• 
  
  

• maths phobia and the impact society has on maths teaching

• 
  
  

• material on sorting, matching and handling data

• 
  
  

• the importance of educating about finance in today's world

• 
  
  

• ideas for observation and questioning to assess children's understanding

• 
  
  

• examples of planned activities

• 
  
  

• suggestions for language development

• 
  
  

• assessment criteria.

This textbook is ideal for those training to be teachers through an undergraduate or PGCE route, those training for Early Years Professional Status and those studying early childhood on foundation or honours degrees, as well as parents looking to explore how their young children learn mathematics. This will be an essential text for any early years practitioner looking to make mathematics interesting, exciting and engaging in their classroom.

1 Learning mathematics in early years settings

■ What is mathematics?

■ Why do people have so many hang-ups about it?

■ How do young children learn mathematics?

■ What mathematics should they learn?

■ How can we best help them?

This chapter sets out to answer some of the questions people ask about mathematics and teaching in the early years and sets the scene for the rest of the book. It is new to this edition since, with the increased focus on training for early years practitioners at foundation degree and early years profession status levels, students may no longer address these issues in a wider study of mathematical learning. The chapter considers what mathematics is, looks at attitudes to learning mathematics from the point of view of both the practitioner and the children they are working with, summarises some of the theoretical perspectives on learning mathematics, considers the range of mathematics young children can learn and draws out the implications for settings.

The chapter is, by nature, theoretical and some readers may wish to skim read it at this stage and come back to it later in their study.

What is mathematics?

One way to view mathematics, like most subjects studied in education, is as a way of looking at and making sense of the world. If we use the example of a tree, we can look at a tree and describe it in words or write poetry about it (language). We can examine it to find out how it grows and produces seeds to create new trees (science). We could explain why it grows in a particular area of the countryside or how it came to be imported into the country (geography). Or we could talk about its shape, measure its size, count how many branches it has, calculate how much it has grown in the past year (mathematics). Mathematics is one way in which we describe and make sense of the world around us – and we do it all the time, even when we are not aware of it. As we will see later in this book, babies start to make sense of the world in mathematical ways from birth: recognising the difference between small numbers of objects and recognising shapes and patterns of familiar objects in the environment around them. No one sets out to teach it to them; it is part of how their brains work. More complex ideas in mathematics, including counting and calculation, build on this initial sense-making and are essentially social constructs: created by human beings over time to enable us to make sense of and to control our environment.

We make sense of the world by looking for patterns: we understand people by patterns of behaviour, we make sense of the natural world through patterns of seasons, cycles of growth etc. Most people, if asked what mathematics is, would think first of arithmetic: number and calculation. But this is only part of a much bigger subject and Devlin (2003) defines mathematics as the study of pattern. These patterns may be patterns in number, in algebra, in shape, in spatial position, etc. One of the reasons that many people find mathematics difficult (see below) is that they have not understood that mathematics has pattern.

It is pattern that helps us to understand and to learn mathematics. Let’s try a little experiment. Read the following list of letters and think about how you will remember it:

M T E A I S A H M T C

Many of you will have looked to see if there was a pattern to help you and probably did not find one. But how about if it is written as:

M T E A I S A H M T C

Perhaps you can now see how the string of letters was produced and could create a rule by which to remember it: from the word ‘mathematics’ take the odd letters in order and then the even letters. This would be easier to remember than learning the original meaningless string of letters. Even better, you could apply the same rule to another word should you be called to do so. This is, of course, a meaningless task but it makes the point. Understanding the pattern makes the learning easier and also makes that learning adaptable to new situations. Skemp (1971) calls this relational or intelligent learning, rather than instrumental or rote learning.

Once we see mathematics as the study of pattern, rather than as complex, symbolic calculations, it is perhaps easier to see how even young children can look for patterns and start to make sense of the world of number, shape, space and measures.

Mathematics: why do people have so many hang-ups about it?

One student teacher, on hearing that mathematics was a way of making sense of the world, exclaimed, ‘So why doesn’t it make sense then?!’ Her experience of learning mathematics was of a series of unrelated facts that made no sense, which must be rote learnt and reproduced on demand. She is not alone. Many people in our society admit to having negative attitudes towards the subject. In England it seems to be acceptable to claim to be poor at mathematics while in other countries people would be ashamed to do so. As the Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools observes: ‘the United Kingdom is still one of the few advanced nations where it is socially acceptable – fashionable, even – to profess an inability to cope with the subject’ (Williams 2008: 3).

Mathematics in school is a high-stakes subject; everyone is expected to learn it and a good grade at GCSE is required for many careers, including teaching. Perhaps as a result, many people define themselves more by the mathematics which they cannot do than that which they can. Students will often say, ‘I am not very good at maths; I was OK until we did “X” and then I totally lost it’. This is not only true of students but of many highly educated adults, including professors in some of our top universities. What ‘X’ is will vary from one person to the next; however, there does seem to be some commonality: column subtraction, multiplication tables, long division and algebra often being cited. What is interesting is that even people who have studied mathematics to A level and beyond can often identify a sticking point. This way of thinking seems to be distinctive to mathematics. No one when talking about reading, for example, will define their ability in this way: ‘I am not very good at reading; I was OK until we did Dickens [or Shakespeare, or whoever] and then I totally lost it.’

We are not born with negative attitudes to mathematics, they are learnt. They may be learnt at home, since some parents will have poor attitudes themselves and have low expectations of their children coloured by their own experiences at school: ‘You’ll not be good at maths, I was always hopeless.’ As the Williams review, cited above, continued: ‘A parent expressing such sentiments can hardly be conducive to a learning environment at home in which mathematics is seen by children as an essential and rewarding part of their everyday lives’ (Williams 2008: 3). Or negative attitudes may be learnt through experiences at school. Martha, now a secondary school teacher, remembers being in Year 4 at school. At the start of every morning the children each had to complete a work card with ten questions on it. When they got them all right they moved on to the next card. She remembers doing the same card over and over again, making a different mistake each time. As the pressure increased, her ability to get the right answers decreased. By the end of the academic year she hated maths and saw herself as hopeless at it; many student teachers have shared similar stories.

Buxton (1981) studied adults who admitted to negative mathematical experiences and attitudes and set out to help them understand mathematics and see it differently. The result is a book entitled Do You Panic about Maths? Coping with Maths Anxiety, where he suggests that the state of panic that people feel when asked to do mathematics, especially under pressure, blocks their ability to reason and therefore to work mathematically. Buxton also found a sharp contrast in the way that people think about mathematics and its learning. People who are anxious about mathematics, like the student teacher quoted at the beginning of this section, see it as fixed, uncreative, unrelated to reality, inaccessible, a collection of rules and facts to be remembered, time-pressured and mostly about calculation, while those who enjoy mathematics see it as exploratory, creative, accessible, a network of relationships, and requiring time for reflection. He observes that it is not easy to exchange one set of beliefs for the other.

Subsequent research into adult attitudes to mathematics, and the effect that attitude has on learning mathematics and on teaching it, has identified that negative attitudes are often developed early in schooling and as a result of poor teaching (Geist 2010; Ashcroft et al. 1998; Leder 1992). Indeed, Ramirez et al. (2013) found that children as young as five exhibit mathematics anxiety, regardless of their attainment, reading ability, or parental income levels. Using brain-imaging technology has enabled researchers to see the effect mathematics anxiety has on children. For example, Young, Wu and Menon (2012) gave 46 7- to 9-year-olds addition and subtraction problems and found that children who ‘felt panicky’ about the tasks had increased activity in brain regions that are associated with fear alongside decreased activity related to problem-solving. Beilock (2011) found that children undertaking timed tests inhibited their ability to quickly recall known facts because of the effect anxiety had on blocking their working memory. This is particularly impactful for children with good levels of working memory because for these children underachieving leads to further anxiety and eventually leads to underachievement in mathematics. Having analysed the effect that timed tests have on second and fourth graders’ anxiety, Jo Boaler (2014) found that regardless of attainment, a significant number of children feel fear, stress and anxiety.

We see that developing positive attitudes in children, alongside teaching them the necessary facts, skills and concepts is crucial. How we see ourselves in relation to mathematics, and our attitude to the subject, will affect how we teach it. A teacher in a mixed reception and Year 1 class was observed teaching mathematics over...