Study Topic 16: Mathematics
This study topic considers the nature of mathematics, or ‘maths’, as a subject and its place in the primary
curriculum. For many people, maths stirs up feelings of panic and dread. Yet, the reality is that we ‘do’
maths all the time as we go about our everyday lives.
In this study topic we use the term ‘mathematics’, or ‘maths’ for short, although we recognise that the
term ‘numeracy’ is now frequently used instead. The National Numeracy Strategy, when it was
introduced in England in 1999, conceptualised numeracy as ‘a proficiency which involves confidence and
competence with numbers and measures’ (DfEE, 1999, p. 4). This includes having an understanding of the
number system, computational skills, an inclination and ability to solve number problems, and an
understanding of the practical ways in which information is gathered and presented. More recently in
Wales, numeracy is described as ‘the application of mathematics to solve problems in real-world context’
(Welsh Government, 2020).
We have chosen to use the term ‘mathematics’ because we believe it promotes a broader way to think
about the subject: that is, in terms of the relationships among and between numbers, shapes and
quantities. We also emphasise how developing mathematical thinking across the whole curriculum can
enable children both to draw on their common-sense understanding of maths and to enjoy the beauty of
mathematical patterns and relationships (or what Einstein referred to as the ‘poetry of logical ideas’).
1 Attitudes to maths
For children to enjoy learning mathematics it is essential that they should understand it … not just learn
to reproduce learnt procedures and recipes that are low in meaningfulness and purposefulness.
(Haylock and Manning, 2014, p. 3)
Concerns over standards in maths and particularly children’s numeracy skills seem to surface on a regular
basis – from successive governments, the media, the teaching profession and others. The influential
Cockcroft Report in the 1980s – which followed a governmental inquiry – drew attention to the high
number of educated and intelligent adults who were unable to engage comfortably in everyday activities
because they were ‘hopeless at arithmetic’ (DES, 1982, p. 5).
The 2008 Williams Review found that negative attitudes to maths in early years settings and primary
schools remain commonplace. It noted that ‘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, p. 3). The Williams Review (2008) highlights the detrimental effect that negative
attitudes have on children’s achievement, and how important it is for adults who work with children to
foster positive attitudes to maths.
So, even though maths permeates our everyday lives, it appears that a significant proportion of the
population remain convinced that it is too hard for them to understand. We might speculate that the
kinds of strategy for supporting or scaffolding learning promoted by Rogoff (1990), that you read about in
Study Topic 3, are too rarely applied to maths.
Learning maths goes beyond the content of the curriculum and the skills that are needed to pass exams.
In common with other areas of learning, mathematical achievement also depends on persistence,
confidence, curiosity and a degree of self-belief. Take, for example, Stephen.
Stephen
Stephen had been working as a classroom assistant in a special school. He had completed a part-time
honours degree in early childhood studies, which had involved a great deal of hard work and
commitment. When asked by his tutor about his career, he admitted that he wanted to be a teacher but
,that he couldn’t do maths. His tutor encouraged him to persevere and, within six months, Stephen (with
some hard work and support) had the necessary qualification. Stephen’s motivation to succeed had made
all the difference.
When a group of staff at The Open University were asked to complete the sentence ‘Mathematics is …’,
their responses included words like ‘hard’, ‘complicated’, ‘difficult’, ‘painful’ and ‘boring’. Some described
it as ‘my nightmare’ and, interestingly, as ‘something you do at school’ and ‘something I’ve forgotten!’ A
very few talked of it as ‘fun’, ‘interesting’ or even ‘wonderful’.
2 What counts as maths?
Many adults and some children, when asked about maths, refer to ‘hard sums’. Yet maths
includes much more than calculations and numbers, and schools are required to teach a
wide range of mathematical topics. For example, the Scottish Curriculum for Excellence:
Numeracy and Mathematics (Education Scotland, 2018) highlights:
number, money and measurement
shape, position and movement
information handling.
But a list of topic areas does not identify what is involved in thinking mathematically.
Rather, thinking mathematically covers a wide range of skills, not just the content of maths
(shape, space, measures, numbers, and so on). These are sometimes called ‘process skills’
because they are useful in the mathematical process. They include skills like sequencing and
estimating.
Activity 16.1 Becoming a mathematician
Timing: Allow about 20 minutes
Task 1: Reflect on your own mathematical learning and also think about the topics identified
above.
Task 2: Jot down in the box below some of the process skills you think are needed to think
mathematically.
Activity 16.1 Becoming a mathematician, Your response to Question 1
Solving mathematical problems involves a number of processes and strategies. Sue Fox and
Liz Surtees (2010) suggest that problem-solving includes the following stages:
identifying and understanding the problem
planning ways to solve the problem
monitoring progress as the problem is tackled
reviewing the solution.
Although the authors were writing about mathematical problems, their approach is useful
for all problem-solving and highlights a key point: many of the skills that are important for
mathematical thinking are important in other areas of our lives.
, 3 Maths and life
The role that maths plays in our lives sometimes goes unnoticed. This is highlighted in an
amusing way in Counting on Frank, a children’s story by Rod Clement (1991), in which the
young hero performs mathematical calculations, measurements and estimations as he goes
about his daily life. He finds out, for example, the length of a line that a ballpoint pen will
draw; he calculates the size of the pile of peas that could have accumulated if he had
‘accidentally’ knocked fifteen of the hated vegetables off his plate each night over the
previous eight years; and he works out how long it would take to fill the entire bathroom if
he left both bath taps running at full force.
Of course, most people’s use of maths is probably more down to earth than Frank’s.
However, we do all use maths every day, even though a lot of people think of it as
something they did unsuccessfully at school and may still have bad feelings about it. Even if
the word ‘maths’ for you conjures up negative memories of school, perhaps ‘hard sums’ and
boring lessons, you would have great difficulty in getting through your life if you were not
doing mathematics on a regular basis.
Activity 16.2 Maths at home
Timing: Allow about 1 hour and 20 minutes
Task 1: Think back over the last day or half day and note down in the box below all of the
times when you used aspects of maths as you went about your everyday life. Perhaps your
day involved a journey, for example. How many miles was it? How long did it take? What
time did you need to arrive? What was the best route? Complete the task before revealing
the comment.
Activity 16.2 Maths at home, Your response to Question 1a
Task 2: Try the following problems. In the box below each one, write down your answers
and note down what you did.
1. 1.5 ÷ 0.25 = ?
Activity 16.2 Maths at home, Your response to Question 1b
2. Which of these two fractions is smaller?
99/50
80/35
Activity 16.2 Maths at home, Your response to Question 1c
3. How many 25 pences are there in £1.50?
Activity 16.2 Maths at home, Your response to Question 1d
4. You are in the supermarket buying snacks. Snacko costs 99 pence for 50 grams, and
Nibble costs 80 pence for 35 grams. Snacko and Nibble taste exactly the same. Which is the
better buy?
This study topic considers the nature of mathematics, or ‘maths’, as a subject and its place in the primary
curriculum. For many people, maths stirs up feelings of panic and dread. Yet, the reality is that we ‘do’
maths all the time as we go about our everyday lives.
In this study topic we use the term ‘mathematics’, or ‘maths’ for short, although we recognise that the
term ‘numeracy’ is now frequently used instead. The National Numeracy Strategy, when it was
introduced in England in 1999, conceptualised numeracy as ‘a proficiency which involves confidence and
competence with numbers and measures’ (DfEE, 1999, p. 4). This includes having an understanding of the
number system, computational skills, an inclination and ability to solve number problems, and an
understanding of the practical ways in which information is gathered and presented. More recently in
Wales, numeracy is described as ‘the application of mathematics to solve problems in real-world context’
(Welsh Government, 2020).
We have chosen to use the term ‘mathematics’ because we believe it promotes a broader way to think
about the subject: that is, in terms of the relationships among and between numbers, shapes and
quantities. We also emphasise how developing mathematical thinking across the whole curriculum can
enable children both to draw on their common-sense understanding of maths and to enjoy the beauty of
mathematical patterns and relationships (or what Einstein referred to as the ‘poetry of logical ideas’).
1 Attitudes to maths
For children to enjoy learning mathematics it is essential that they should understand it … not just learn
to reproduce learnt procedures and recipes that are low in meaningfulness and purposefulness.
(Haylock and Manning, 2014, p. 3)
Concerns over standards in maths and particularly children’s numeracy skills seem to surface on a regular
basis – from successive governments, the media, the teaching profession and others. The influential
Cockcroft Report in the 1980s – which followed a governmental inquiry – drew attention to the high
number of educated and intelligent adults who were unable to engage comfortably in everyday activities
because they were ‘hopeless at arithmetic’ (DES, 1982, p. 5).
The 2008 Williams Review found that negative attitudes to maths in early years settings and primary
schools remain commonplace. It noted that ‘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, p. 3). The Williams Review (2008) highlights the detrimental effect that negative
attitudes have on children’s achievement, and how important it is for adults who work with children to
foster positive attitudes to maths.
So, even though maths permeates our everyday lives, it appears that a significant proportion of the
population remain convinced that it is too hard for them to understand. We might speculate that the
kinds of strategy for supporting or scaffolding learning promoted by Rogoff (1990), that you read about in
Study Topic 3, are too rarely applied to maths.
Learning maths goes beyond the content of the curriculum and the skills that are needed to pass exams.
In common with other areas of learning, mathematical achievement also depends on persistence,
confidence, curiosity and a degree of self-belief. Take, for example, Stephen.
Stephen
Stephen had been working as a classroom assistant in a special school. He had completed a part-time
honours degree in early childhood studies, which had involved a great deal of hard work and
commitment. When asked by his tutor about his career, he admitted that he wanted to be a teacher but
,that he couldn’t do maths. His tutor encouraged him to persevere and, within six months, Stephen (with
some hard work and support) had the necessary qualification. Stephen’s motivation to succeed had made
all the difference.
When a group of staff at The Open University were asked to complete the sentence ‘Mathematics is …’,
their responses included words like ‘hard’, ‘complicated’, ‘difficult’, ‘painful’ and ‘boring’. Some described
it as ‘my nightmare’ and, interestingly, as ‘something you do at school’ and ‘something I’ve forgotten!’ A
very few talked of it as ‘fun’, ‘interesting’ or even ‘wonderful’.
2 What counts as maths?
Many adults and some children, when asked about maths, refer to ‘hard sums’. Yet maths
includes much more than calculations and numbers, and schools are required to teach a
wide range of mathematical topics. For example, the Scottish Curriculum for Excellence:
Numeracy and Mathematics (Education Scotland, 2018) highlights:
number, money and measurement
shape, position and movement
information handling.
But a list of topic areas does not identify what is involved in thinking mathematically.
Rather, thinking mathematically covers a wide range of skills, not just the content of maths
(shape, space, measures, numbers, and so on). These are sometimes called ‘process skills’
because they are useful in the mathematical process. They include skills like sequencing and
estimating.
Activity 16.1 Becoming a mathematician
Timing: Allow about 20 minutes
Task 1: Reflect on your own mathematical learning and also think about the topics identified
above.
Task 2: Jot down in the box below some of the process skills you think are needed to think
mathematically.
Activity 16.1 Becoming a mathematician, Your response to Question 1
Solving mathematical problems involves a number of processes and strategies. Sue Fox and
Liz Surtees (2010) suggest that problem-solving includes the following stages:
identifying and understanding the problem
planning ways to solve the problem
monitoring progress as the problem is tackled
reviewing the solution.
Although the authors were writing about mathematical problems, their approach is useful
for all problem-solving and highlights a key point: many of the skills that are important for
mathematical thinking are important in other areas of our lives.
, 3 Maths and life
The role that maths plays in our lives sometimes goes unnoticed. This is highlighted in an
amusing way in Counting on Frank, a children’s story by Rod Clement (1991), in which the
young hero performs mathematical calculations, measurements and estimations as he goes
about his daily life. He finds out, for example, the length of a line that a ballpoint pen will
draw; he calculates the size of the pile of peas that could have accumulated if he had
‘accidentally’ knocked fifteen of the hated vegetables off his plate each night over the
previous eight years; and he works out how long it would take to fill the entire bathroom if
he left both bath taps running at full force.
Of course, most people’s use of maths is probably more down to earth than Frank’s.
However, we do all use maths every day, even though a lot of people think of it as
something they did unsuccessfully at school and may still have bad feelings about it. Even if
the word ‘maths’ for you conjures up negative memories of school, perhaps ‘hard sums’ and
boring lessons, you would have great difficulty in getting through your life if you were not
doing mathematics on a regular basis.
Activity 16.2 Maths at home
Timing: Allow about 1 hour and 20 minutes
Task 1: Think back over the last day or half day and note down in the box below all of the
times when you used aspects of maths as you went about your everyday life. Perhaps your
day involved a journey, for example. How many miles was it? How long did it take? What
time did you need to arrive? What was the best route? Complete the task before revealing
the comment.
Activity 16.2 Maths at home, Your response to Question 1a
Task 2: Try the following problems. In the box below each one, write down your answers
and note down what you did.
1. 1.5 ÷ 0.25 = ?
Activity 16.2 Maths at home, Your response to Question 1b
2. Which of these two fractions is smaller?
99/50
80/35
Activity 16.2 Maths at home, Your response to Question 1c
3. How many 25 pences are there in £1.50?
Activity 16.2 Maths at home, Your response to Question 1d
4. You are in the supermarket buying snacks. Snacko costs 99 pence for 50 grams, and
Nibble costs 80 pence for 35 grams. Snacko and Nibble taste exactly the same. Which is the
better buy?
