Children, Parents and Teachers Enjoying Numeracy

Numeracy Hour Success Through Collaboration

Hamish Fraser, Gareth Honeyford

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781134114610
• Edition: 1
• Topic: Education
• Subtopic: Education General

Written for teachers, maths coordinators and parents, this practical text: shows how best to approach written and mental maths work; illustrates the value of maths investigations; outlines the benefits of non-standard methods of calculations; and addresses the role of ICT and numeracy.

CHAPTER 1

Background to the National Numeracy Strategy

The issue of enjoying mathematics will be discussed throughout this book. We believe that it is crucial that all parties concerned with developing children’s mathematical skills should enjoy the process, but in this chapter it will emerge that enjoyment and mathematics are rarely identified together, and this issue must be addressed. This process can begin by considering the factors that affect the teaching of mathematics. The National Numeracy Strategy has a key role, but is not the complete solution. In this book we aim to extend expertise and confidence so that issues that make teachers less confident and less effective in their mathematics teaching are identified and eliminated.

The National Numeracy Project began in 1996 as a government funded research project to develop the teaching of mathematics. Within three years the National Numeracy Strategy emerged as the means to deliver the target of 75 per cent or more Year 6 children achieving level 4 or higher by 2002. Teachers are the agents through whom this goal can be achieved, so the success of the strategy rests with them and the support they receive.

Confidence, understanding and enjoyment

One of the issues facing many primary teachers charged with teaching mathematics is that they do not like mathematics as a subject and do not feel confident teaching it. This is not the case for every teacher but it is true for many. This lack of confidence in teaching mathematics can often be a key factor in reducing effectiveness and much of the pleasure to be had from teaching and learning mathematics. One London teacher provides the following example:

I had been working for a few weeks in London’s East End and, like most teachers early in their experience, I was nervous about my practice. I suspect that there will always be subjects that teachers will feel ill equipped to teach. One of the issues and strengths, however, of the primary school system is that teachers are responsible for the whole curriculum. It is a burden that can at times be weighty. On this occasion, my worry focused on maths. As I walked through the large Victorian school, I passed the classroom of a teacher whose general competence I envied. She was bawling at the top of her voice. A child’s understanding of place value had clearly distressed her. She exhibited a major shortcoming in personal, school and national practice: confusing getting the correct answer with evidence of understanding. She screamed, ‘Just add a nought and don’t worry about it’! This piece of advice speedily allowed the child to answer a range of set questions correctly and finally to escape to the playground. Was an understanding of place value established?

What is most striking is the transformation in this teacher. Clearly you would not envy the practice of somebody whose general demeanour was as described, but this was very out of character. Classrooms can be stressful, frustrating places and teachers can become very upset, but what this incident indicated was an additional stress above that of general classroom pressure. Crucially the point at which she felt least confident of her abilities as a teacher was when she taught mathematics. Equally significant was her frame of reference for teaching mathematics.

The teacher confided later that ‘just adding a nought’ had been how she was taught to cope with multiplication by 10. This is significant because it shows that her own experience of learning mathematics was her frame of reference for teaching mathematics. Other than their own experiences as pupils, teachers’ points of reference have been limited to initial teacher training, teachers’ resources, mathematics courses and in-service education and training (INSET). The National Numeracy Strategy is an opportunity to develop a significant point of reference.

Central to the work of the National Numeracy Strategy is mathematical understanding, and building connections between such understandings. This is important to teachers because the strategy provides a basis from which to locate teaching in developing children’s understandings. We shall make a significant step if our focus becomes children’s understanding and their feel for the number system, rather than the tricks that, with limited understanding, yield correct answers. Indeed, telling children to add a nought teaches them little of place value and is additionally dangerous because, although it works for whole numbers (e.g. 10 × 23 = 230), it is of no use with decimals: 10 × 2·3 does not equal 2·30. Teaching children to add a nought does not teach them that multiplying by 10 creates a number 10 times bigger. They need to know that when writing the new number each digit moves left one place past the decimal point. If there is no decimal then a nought is placed in the units column because the new number has no units. This is a central tenet of place value. It is this understanding that allows a fuller comprehension of decimals and percentages.

Once understanding becomes the goal of mathematics teaching, the ability to calculate effectively and fluently is improved. It is likely that children will still ‘add noughts’, but seeing the reason why this gives a correct answer is the foundation of subsequent understanding. The development of understanding will always be a higher objective than simply securing correct answers.

Research into primary teachers’ understanding of key concepts in science and technology from the Scottish Council for Research in Education (SCRE) (1995) demonstrates that a third of the teachers in the study identified lack of background knowledge as a source of problems. Is this a factor with mathematics? Haylock and Cockburn (1989) identify weaknesses in the mathematical understanding of early years teachers; weaknesses that were diminished as the teachers confronted their shortcomings: ‘The satisfaction expressed by teachers with whom we worked as previously-fuzzy ideas began to fall into place led us confidently to use the material from these discussions as the basis for this book’ (Haylock and Cockburn 1989: x). Haylock and Cockburn also identify mathematical insecurity as common among student teachers. This lack of confidence is a complex issue, stemming from ‘fuzzy ideas’ or personal experience of mathematics, or both. The effect of these experiences is crucial and the National Numeracy Strategy will help tackle them for the benefit of teachers and pupils.

Mathematics in society

In many people’s minds, mathematics is associated with negative feelings. On hearing a colleague mention his wider role in mathematics education during a computer in-service session, one course member declared, ‘I’m no good at maths – I’m artistic’. This exemplifies what Haylock (1995) identifies as the social acceptability of being poor mathematically and, further, the belief that some people cannot be competent mathematically because of their gifts in other areas. This is supported by what the Office for Standards in Education (OFSTED) argues is our culture’s readier acceptance of innumeracy than illiteracy (OFSTED 1997). The same publication also says that if children become anxious about mathematics because of confused or confusing teaching, attitudes to mathematics can become and remain negative, with destructive consequences for future achievement and enjoyment.

We have already examined, as one source of jumbled teaching, a teacher’s own experience of being taught mathematics. However, this cycle could be significant for more than just teachers’ attitudes. Surveys by Sewell (1981) and Cockcroft (1982) demonstrate widespread feelings of inadequacy and anxiety toward mathematics in the British adult population. These conclusions were subsequently confirmed by the work of Briggs and Crook (1991) and it seems evident that Britons generally lack confidence mathematically. This issue is present for most sectors of society. Buxton’s 1981 study of negative emotions toward mathematics in ‘articulate’ and ‘intelligent’ adults demonstrated feelings of distaste, anxiety and incompetence in the face of mathematical problems. Strong negative feelings toward mathematics are prevalent in society and to change this situation for the better teachers need to break away from the negative experiences of their past. Failure to do so will perpetuate similar attitudes in pupils. The National Numeracy Strategy provides a basis from which to make this change.

The teaching of mathematics

Haylock (1995) gives an example showing how the intervention of a senior teacher damaged both the mathematical and social confidence of a young child:

I remember when I was seven I had to do a hundred long divisions. The head-master came in to check on our progress. He picked me up and banged me up and down on my chair saying Why can’t you do it?’ After that I wouldn’t ask if I couldn’t understand something.

(Haylock 1995: 4)

In examining this example several things are amiss. The task is clearly inappropriate for a seven-year-old; the quantity is disturbing; and the method (algorithm) needed to arrive at the correct answer is complex. Further, we have to assume that the head teacher was not in the classroom while the class worked. So we have difficult and inappropriate mathematics simply being used to occupy children. Is this likely to be an enjoyable experience? The damage this does to how mathematics is perceived is difficult to measure!

The National Numeracy Strategy and its structuring of mathematics will engage with such situations in a number of ways. Clearly it cannot deal with the gross professional misconduct demonstrated here, but it can address two matters that are wrong in the scenario. First, it places the responsibility on teachers to teach. When mathematics is taught, the teacher teaches it! Much of the strategy’s structure emphasises this. Secondly, the strategy is explicit on the teaching of written algorithms. There is a great deal of evidence that their premature introduction is damaging to children’s understanding We will examine these issues in Chapter 4. Long division is a classic example of a written algorithm. Written methods or algorithms do not appear in any form in the National Numeracy Strategy until Year 3, and long division not until Year 6.

Teaching a subject that for some individuals has such unpleasant connotations will have an effect on a teacher’s performance. This may make them more determined not to repeat errors they have experienced or it might mean that anxiety affects their own delivery of mathematics. An individual’s subject confidence is central here. Negative experiences need to be tackled. Teachers can often avoid teaching topics they don’t enjoy. Some recent research we have been involved in examines confidence in handling data. Diffident teachers frequently do not teach this topic and probability is hardly ever tackled. When teaching mathematics with the National Numeracy Strategy, avoidance will be harder for teachers. Planning and teaching are structured around a termly plan, which is very prescriptive, ensuring coverage of the breadth of the National Curriculum each year.

A new understanding

Further, there is more to teaching mathematics effectively than knowing lots of mathematics. Here are three examples of mathematics teachers getting things wrong:

‘There were few maths teachers who could grasp the idea of people not being mathematical.’

‘The teacher just didn’t understand why I had problems.’

‘I always tried to avoid asking questions in maths lessons because you were made to feel so stupid if you got it wrong.’

(Haylock 1995: 4–5)

We need to appreciate that some people find mathematics difficult, understand the reasons behind this and deal with the problems sensitively (see Chapter 7). It is important to consider these experiences while reflecting on personal practice. Feelings of stupidity and isolation should not be acceptable in mathematics lessons. With the wider class discussion and interactive class teaching demanded by the National Numeracy Strategy, teachers must be even more determined to prevent pupils feeling like this. A confident teacher, with insight into the isolation which children can feel, is a powerful classroom practitioner. Understanding the feelings brought to mathematics lessons by some children is a first step in developing their confidence in mathematics.

Realising and appreciating the problems that some children have with mathematics is an asset in teaching it effectively. So too is reflecting on personal experiences of being taught mathematics and identifying why these were wanting. For good teaching the mathematical understanding of the teacher needs to be sound. This, however, is only one aspect of effective mathematics teaching. Fraser clearly thinks there are other important areas where expertise is required: Would our children’s mathematics be improved by a greater understanding of maths by teachers at the higher end of the mathematical spectrum or by a deeper understanding of the stages of mathematical progress lower down?’ (Fraser 1998: 22). A far-reaching mathematical ability, of itself, does not equip you to teach mathematics well to young and very young children. Clear mathematical understanding is only one of the forms of understanding needed to teach effectively. Fraser again makes this point: ‘I have trouble seeing a skilled mathematician helping children in difficulty in Year 2’ (Fraser 1998: 22). Subject knowledge is important, but the teachers’ art is more than this.

A feeling of insecurity when it comes to mathematics is common and there are teachers whose mathematics will need further development. This statement may cause alarm and anxiety for some teachers. These feelings stem from personal insecurities about mathematics, which are a feature of our society. In this situation there are three important elements to consider:

•  Teachers tend to belittle the mathematics they know. Identifying the areas that are sound and which specific areas to work on is crucial – and this process need not be a painful or lengthy one.

•  Teachers tend to underestimate the amount of mathematics they know. It is likely that they know more mathematics than they expect to know. The opportunity of a personal review is useful to increase confidence. A confident teacher is a better teacher.

•  The value of the National Numeracy Strategy in identifying clearly when areas of mathematics are to be taught and predicting when such areas will arise enables teachers to be prepared in advance.

Conclusion

It is clear that enjoyment and mathematics are not normally identified together, but there are clear reasons for ensuring that this essential aspect of raising mathematical achievement is developed. What is also clear is that for children to enjoy mathematics, teachers need to enjoy teaching it. The National Numeracy Strategy provides a basis to do this. In subsequent chapters we will explore issues affecting the implementation of the strategy. This book is useful in this process because it emphasises enjoyment of mathematics and critically tackles key issues in the strategy.

Change has been a constant in education for many years and this has had an effect on schools:

The process by which teaching is changing and teachers are changed, I shall show is systemically ironic. Good intentions are persistently and infuriatingly turned on their heads … They threaten the very desire to teach itself. They take the heart out of teaching.

(Hargreaves 1994: 3)

By developing the confidence of teachers, parents and children along productive paths, the teaching of mathematics and the achievement of children in conjunction with the National Numeracy Strategy can be significant. As Hargreaves indicates, however, some implementations do not always have the intended effect. If this happens to the National Numeracy Strategy, it will be a tragedy, as it represents a significant chance to change for the better the way mathematics is taught. This may put some heart back into teaching.

CHAPTER 2

What is Mental Maths?

Mental Maths is the process by which children, through discussion and practice, develop increasingly sophisticated strategies of mental calculation that are built on their increasing understanding of number. This understanding is further developed in Mental Maths sessions as strategies are explained and refined. In this chapter we explain why Mental Maths should be a feature of most mathematics lessons.

Mental Maths is a central component of the National Numeracy Strategy so there has been an increased awareness of it. We will examine why Mental Maths is such a productive tool for mathematical learning through two key issues. This is intended to be of use to all teachers and parents seeking to develop their own and, possibly, their colleagues’ Mental Maths teaching and, so develop children’s learning and enjoyment of mathematics. The issues to be explored are:

• how the Mental Maths of the National Numeracy Strategy differs from a ‘traditional’ understanding of mental arithmetic;

• how Mental Maths develops children’s mathematical thought.

A health warning

The issue of jargon is evident in explanations of Mental Maths. The jargon often employs phrases like ‘Children developing a picture of how numbers work’ or ‘Building a set of connections between numbers’. ...

Table of contents

• Cover
• Title Page
• Copyright Page
• Contents
• Acknowledgements
• Foreword
• Preface
• 1 Background to the National Numeracy Strategy
• 2 What is Mental Maths?
• 3 Teaching Mental Maths
• 4 The ‘new’ written methods
• 5 Information and communications technology and numeracy
• 6 Mathematics investigations
• 7 Dealing with ‘sum stress’
• 8 Developing home–school links
• Appendix 1: Questions and simple activities for use in teaching Mental Maths
• Appendix 2: Hardware resources and suppliers
• Appendix 3: Software titles and distributors
• Appendix 4: Teachers’ notes to accompany investigations
• Appendix 5: The mathematics classroom
• Appendix 6: Sample content for home–school mathematics activities booklet, produced by parents
• Appendix 7: Photocopiable classroom resources
• Epilogue
• Bibliography
• Index