Teaching Mathematics in the Secondary School

Paul Chambers, Robert Timlin

• Publisher: SAGE Publications Ltd
• Year: 2019
• Print ISBN: 9781473974289, 9781473974272
• eBook ISBN: 9781526415233
• Edition: 3
• Topic: Education
• Subtopic: Teaching Mathematics

This fully updated third edition looks at the fundamentals of mathematics teaching, how to plan lessons and assess learning, and how to promote an inclusive approach in the classroom.

Key new features include: 

• Updated content reflecting: the 2014 National Curriculum in England, the Teachers? Standards and revised requirements for GCSE and A level mathematics
• Updated ?Evidence from research? features, highlighting developments in the field
• An expanded section on mathematical misconceptions
• New coverage on teaching for mastery.

Chapter 1 Teaching Mathematics

This Chapter

• examines the typical motivations and anxieties of mathematics trainee teachers as they begin training
• summarizes the professional demands of training
• discusses different perceptions of the nature of mathematics; whether it is primarily a subject that is interesting in its own right, or whether it is primarily a tool for solving problems
• considers why people think that mathematics is important
• examines the extent to which mathematics is a human construct

Your early days as a trainee teacher

Training to be a teacher is a challenging and demanding task, but one that provides enormous rewards. One of the biggest rewards is that moment when a pupil’s eyes light up with a sense of understanding, and you know that a small piece of learning is down to you. During your training, you will feel the satisfaction of knowing that your professional skills are developing, and will have the opportunity to work alongside teams of dedicated staff, whose energy you will come to admire.

It is common for people embarking on a teacher-training course to have a number of anxieties. One of these anxieties often concerns subject knowledge. Many people starting training have come straight from university, and many come after a break from study of several years. Whichever background you have, you are likely to be ‘rusty’ on some elements of school mathematics, either because of the passage of time, or because the mathematical topics you studied at university were very abstract or specialized and did not require the use of topics from a school curriculum.

You are very likely to meet others like you: maybe other mature students, others whose first degree is not mathematics or others who may never have studied any mechanics. People come from a wide range of backgrounds wanting to become mathematics teachers.

During these early days, you may have some other anxieties, such as whether you will be able to control the class or whether you will cope with the workload. Such worries are common, but they can be answered:

• You will get lots of support from other teachers.
• You will not be given the worst class in the school.
• You will learn techniques of class management.
• Workload will be heavy, but it is manageable.

It is important in the early days to get to know others who are training alongside you: they will provide invaluable support as you progress through your training. Not only will they share with you their highs and lows, they will also be able to share ideas for planning lessons. If, additionally, they are training to teach mathematics, an agreement to share resources can save you time and effort.

As soon as your training begins, you will be asked to focus on the standards by which you will be judged during, and at the end of, the training. These standards are set nationally and are known as the Teachers’ Standards (DfE, 2013). The Standards document is divided into three parts: the Preamble, which explains the purpose of the standards; Part One, which consists of eight standards for teaching with further amplification of each standard; and Part Two, which outlines the standards for personal and professional conduct. In order to qualify as a teacher you will have to provide evidence that your practice is consistent with the principles outlined in the Preamble and that you meet each of the standards listed in Part One. A listing of the Standards is given in the ‘How to use this book’ section at the beginning of this book. Your training is designed to help you meet the standards.

One of the best ways to feel your way into the training is to develop your knowledge of the school mathematics curriculum. Whether directed to or not, it is helpful to get hold of a recent GCSE paper and work through it. The best exercise is for you to work through it as part of a group, discussing the bits that you have forgotten and explaining to others the bits that you can remember. It will not take long for your confidence to return, but make sure you check that the answers that you think are right are indeed the correct ones! Sometimes your confidence may be misplaced, and it is better to discover and correct your own misunderstandings in supportive company than when you are in the classroom.

Professionalism

During your training, high standards of attendance, punctuality and commitment are expected. When you are in school, you need to be aware of the behaviour and standards expected from teachers, and you should exhibit those standards from day one. Although you may not feel like a teacher on your first day, you need to behave like one: the pupils will observe the way that you are and will be forming impressions of you! In addition to the pupils, the teaching staff will be forming impressions of you and, obviously, it is important that you give the right message through the way you work and behave. Here are a few key pointers to acceptable behaviour in school:

• Arrive in plenty of time each morning; be punctual to lessons and meetings.
• Always let the school know if you are going to be absent or late.
• Treat all members of the school staff with respect. You need to demonstrate that you can work well with others.
• Dress smartly. (Play safe on day one, and after that take your cue from other members of the department.)
• Treat the pupils with respect. Show concern for their learning and welfare, but do not become over-friendly (especially when you are new to the school). Begin to build positive relationships, where pupils see you as someone to be trusted, someone who is fair and someone who can help them to achieve well.
• Set a good example to the pupils. This extends beyond your appearance and behaviour, and includes your values and attitudes; you should demonstrate positive attitudes and encourage the same in your pupils.
• Remain in school during the whole of the normal school day. In general, you should not leave the premises except at lunchtime.
• Use productively any non-contact time that you have. Do not be seen wasting time in the staff room; teachers are busy people, and they will expect to see you working as hard as they are. Do not fall into the trap of believing that your working day ends when teaching ends.
• Give positive support to colleagues, especially within the classroom.
• Take care to learn the school rules. Once you are part of the school staff (even as a trainee) you join in the collective responsibility for the implementation of school policies. This professional responsibility supersedes your personal opinion, so you must promote, for example, policies on school uniform, even if you disagree with pupils having to wear a uniform.

In each school where you work, you will be assigned a mentor within the mathematics department. Mentors are key people in your training; they will provide support and advice, and will also make judgements on you. You need to demonstrate your professionalism to all staff, but particularly to your mentor, throughout your time in school. For example, you can show your commitment to team-working through offering any original work you have done to the rest of the department. (Departments are very likely to have facilities for electronic sharing of worksheets, presentations and links.)

Above all, you need to be aware that during your time in schools, it is not only your skills as a teacher that are being assessed, but also your professional attributes. Part Two of the Teachers’ Standards document is devoted to personal and professional conduct. There are three main headings with some further subdivisions giving eight statements which define the expectations. Having positive attitudes yourself helps, but you need to go beyond this; you must make it clear to everyone (pupils, teachers and, on occasions, parents) in all that you say and do, that you have high expectations and are committed to helping pupils to achieve their very best.

Motivations

The motivations for wanting to teach are many and varied. Some of the most common reasons for starting to train as a mathematics teacher are:

• to pass on my enthusiasm for the subject
• to make a positive difference
• to do something worthwhile
• it is something that I expect to enjoy/find rewarding (Chambers, 2007).

Many potential teachers mention their enjoyment of doing mathematics. Sometimes they have a fascination for mathematics, and a curiosity that they wish to share with others; in other cases their love of mathematics is based on little more than a personal experience of success in the subject. Examples of trainees’ motivations are given in the following quotes:

I want to turn children on to mathematics, in the same way that I am.

I had one particular mathematics teacher who I really admired, and she made all the difference to me. I would like to be that inspiring teacher to others.

I love mathematics and yet it has such a negative image. I want to help change that image.

I want to show children that mathematics is a fascinating subject.

Many people give their reason for wanting to teach as a desire to do something worthwhile, to feel that their efforts can make a difference to the lives of young people. Sometimes this follows many years spent working in industry, where the main motivation of the workforce is to make money. In comparison with this, teaching is seen as contributing to the common good and to the benefit of society.

Others mention their desire to work with young people. Many cite an experience that has helped confirm their decision. This experience may involve one or more of the fol...

Table of contents

• Cover
• Half Title
• Acknowledgements
• Title Page
• Copyright Page
• Contents
• About the Authors
• Acknowledgments
• Publisher’s Acknowledgements
• New to this Edition
• How to Use this Book
• Chapter 1 Teaching Mathematics
• Chapter 2 Fundamentals of Teaching Mathematics
• Chapter 3 Planning To Teach A Mathematics Lesson
• Chapter 4 The Elements of A Mathematics Lesson
• Chapter 5 Learning Mathematics
• Chapter 6 Assessment
• Chapter 7 Inclusive Teaching
• Chapter 8 Teaching Different Topics
• Chapter 9 Ict In Mathematics Teaching
• Chapter 10 Continuing Professional Development
• Index