Cross-Curricular Teaching and Learning in the Secondary School... Mathematics

Robert Ward-Penny, Jonathan Savage

• Publisher: Routledge
• Year: 2010
• ISBN:
  9781136857836
• Edition: 1
• Topic: Education
• Subtopic: Education General

Why is cross-curricular work so valuable in the mathematics classroom?Why can pupils sometimes draw graphs in mathematics but not in science?What might mathematics teachers learn from the performing arts?Cross-curricular approaches have much to offer the modern mathematics classroom. They can help teachers to present mathematics as a growing, relevant discipline that is central to much of modern life, and help learners to make sense of what they are doing and why. New contexts, new technology and new qualifications all make this an exciting time to be a cross-curricular teacher of mathematics.

But cross-curricular approaches are not always straightforward. Skills do not always transfer easily from one subject area to the other, and a number of important decisions have to be made. How should this type of work be planned, or assessed? How might it fit into the wider curriculum? Are all cross-curricular activities equally useful for learners? Does mathematics have something to share with all of the other curriculum areas?This book tackles these issues head on, combining educational theory and contemporary research with practical ideas and suggestions. From the mathematics of molecular geometry, wind turbines and impact craters to mathematical haikus, Babylonian clay tablets and juggling, each chapter is packed with examples for use in the secondary classroom.Key features include: Discussion of key issues and debates
Case studies to show you how others have used cross-curricular approaches
A wide range of examples and practical activities to help you develop your own practice
Example approaches for planning and assessmentPart of the Cross-Curricular Teaching and Learning in the Secondary School series, this book is essential reading for all students on Initial Teacher Training courses and practising teachers looking to holistically introduce cross-curricular themes and practices into their mathematics teaching.

CHAPTER 1
The context for cross-curricular mathematics

Of all of the subjects in the school curriculum, mathematics is one of the most ubiquitous. Skills taught in mathematics lessons are often fundamental to other subjects, and pupils’ progress in other curriculum areas frequently depends on them being fluent in basic mathematical procedures. Many lessons in other subjects can be enhanced and made more meaningful through the use of mathematical methods and ideas, and mathematical thinking and problem solving is a critical skill across the curriculum.

However, mathematics often functions as a ‘chameleon discipline’ (Johnston-Wilder and Lee 2010), fading away against the background of whichever curriculum area it is supporting. Consequently, pupils often leave school without a real awareness of the scale of the power and relevance that mathematics has in modern society, and will continue to have in the future. For many pupils this lack of awareness is coupled with a debilitating lack of experience and confidence in applying mathematics in out of school contexts. A cross-curricular approach to mathematics is therefore both urgent and exciting, offering both teachers and learners a chance to engage with the subject in a way that is both more authentic and more motivating.

The book has three interrelated aims: to justify the importance of a cross-curricular approach to teaching and learning mathematics; to provide a wide range of examples; and to explore both the potential and pitfalls of such an approach. In order to meet these aims it will consider a wide range of issues. Some of these will be largely theoretical, whilst others will be purely practical; however all of them will ask you to reflect on and challenge your own practice. You may find it useful to have some paper and a pen to hand as you read, in order to note down your own thoughts and ideas.

Key objectives

By the end of this chapter, you will have:

Considered what ‘cross-curricular’ teaching and learning might involve, and how it might be recognised in the classroom

Reflected on your own views about, and experiences of, cross-curricular teaching and learning in mathematics

Reviewed some of the recent curriculum changes and new qualifications which contain significant cross-curricular elements

Why is cross-curricular teaching important?

It is undeniable that we live in interesting and turbulent times, and that this century poses a number of challenges which are both complex and controversial. The Millennium Project (2009) identifies 15 global challenges currently facing humanity, including the following:

How can sustainable development be achieved for all while addressing climate change?

How can everyone have sufficient clean water without conflict?

How can population growth and resources be brought into balance?

How can the threat of new and re-emerging diseases and immune micro-organisms be reduced?

How can shared values and new security strategies reduce ethnic conflicts, terrorism and the use of weapons of mass destruction?

How can growing energy demands be met safely and efficiently?

It is clear that each of these questions involves knowledge, skills and understandings from more than one school subject area. For example, the issues surrounding the sourcing and delivery of clean water involve concepts typically located in a host of subjects including geography, biology, chemistry, technology, politics and economics. Each of these questions also draws heavily on techniques, ideas and thinking skills that are found in mathematics. In fact, mathematics is a fundamental element here and elsewhere; it is present wherever there is a call for quantification, measurement, modelling or logical analysis, and in this way it underpins the use of each of the other subjects mentioned. It is impossible to imagine any kind of approach to answering these challenges that would not use mathematics in some form. However, it is just as challenging to think of a way that mathematics could solve any of these problems as a stand-alone subject.

If we are to future-proof our pupils’ developing mathematical facility, there is a need for us to present mathematics in a wider context and promote joined-up thinking between mathematics and other curriculum subjects. It is not only the future which is making this demand; there has already been a shift in the employment market, and new technologies and globalisation trends require flexible mathematical thinking as much as procedural competence (Hoyles et al. 2010). Cross-curricular approaches to teaching mathematics offer a range of ways of enhancing pupils’ mathematical learning so as to address these needs and concerns.

Different organisations are beginning to recognise the need to rethink the way that mathematics is presented and delivered in schools, and at the time of writing there have been a number of significant changes in mathematics qualifications and curricula that involve, either explicitly or implicitly, cross-curricular perspectives on mathematics. Many of these changes are exciting ones that offer a range of new opportunities – and new challenges – to mathematics teachers. However, each has its own perspective on what ‘cross-curricular’ mathematics might entail, and so it is important to start this chapter by considering what you, and others, might mean by ‘cross-curricular’.

What does ‘cross-curricular’ mean?

The term ‘cross-curricular’ is widely used by schools and educational organisations, but it can be quite difficult to formally define. Although ‘cross-curricular’ has an obvious semantic meaning, genuine cross-curricular activity transcends this: you would be unlikely to claim that an English teacher asking their pupils to turn to page 76 would constitute a genuine cross-curricular use of mathematics! So what does ‘cross-curricular’ mean?

Reflective task

Think about the term ‘cross-curricular’ and note down what it means to you. How might you recognise a cross-curricular activity in the mathematics classroom? When you have finished, put your jottings to one side, then review them once you have completed reading this chapter.

One way of answering this question is to suggest that a cross-curricular approach can be recognised not simply through an overlap in content, but through associated changes in both the teacher’s pedagogy and the pupils’ learning experience. It is in this sense that Savage offers the following definition elsewhere in this series:

A cross-curricular approach to teaching is characterised by sensitivity towards, and a synthesis of, knowledge, skills and understandings from various subject areas. These inform an enriched pedagogy which promotes an approach to learning which embraces and explores this wider sensitivity through various methods.

(Savage 2011: 8–9)

This definition moves beyond the immediate meaning of ‘cross-curricular’ to describe an approach that is in some sense interdisciplinary, combining two or more different schools of thought to address a problem. Tasks that fully satisfy this principle tend to be steered primarily by the nature of the problem, requiring new skill sets at different stages and a degree of criticality, self-reflection, and even metacognition on the part of the learner.

Savage’s definition also contains a significant challenge for the mathematics teacher, as it encourages us to move beyond simply using scenarios from other subjects as decontextualised illustrations. For example, when teaching the topic of ratio, a teacher might draw two gears on the board, one with 18 teeth and one with 6 teeth, and ask the class how many turns of the smaller gear would equal one turn of the larger gear. This is a valid link to another subject area, but so far no knowledge, skills or understandings have crossed between subjects. The pupils merely have to extract the numbers and select an appropriate operation. To this end, the activity could be developed by introducing ideas from technology such as ‘velocity ratio’ and ‘torque’, or better still, by presenting pupils with a physically meaningful problem together with a set of gears that they could use to help devise and test a solution.

Another challenge arising from this definition is to separate offour understanding of ‘cross-curricular activities’ from the more prominent curriculum area of using and applying mathematics. Cross-curricular activity often uses skills of application and modelling, but in addition it is always informed (and often steered) by content and skills drawn from other subject areas. ‘Using and applying’ investigations, however, can sometimes be based around abstract mathematics, where enquiry can be steered purely by an interest in the structure and properties of mathematics itself.

Throughout this book you will find examples of many different types of cross-curricular activities, from using mathematics to investigate the effects of natural disasters to integrating performing arts techniques in order to explore the properties of quadrilaterals. Some of these examples could easily take place as a small part of a regular mathematics lesson, whereas others are more extensive, and might require extra resources or a wider level of school participation. In every case, what is important is that the blurring of subject boundaries impacts upon the pupils’ experiences, the teacher’s practice, or both. When these conditions are satisfied, activities can have a substantial impact, ideally developing pupils’ understanding and motivating their study in each of the subject areas involved.

There are other ways in which ‘cross-curricular’ teaching and learning can be considered, and some of these will be touched upon in the discussion below. As you read through this book you will undoubtedly continue to develop your own understanding of the term ‘cro...

Table of contents

• Cross-Curricular Teaching and Learning in …
• Contents
• List of figures
• Acknowledgements
• Abbreviations
• CHAPTER 1 The context for cross-curricular mathematics
• CHAPTER 2 Where does mathematics belong? Placing mathematics in a twenty-first century curriculum
• CHAPTER 3 Application and transfer: mathematics and the science subjects
• CHAPTER 4 Construction and feedback: mathematics and technology
• CHAPTER 5 Critical thought and reasoning: mathematics and English, citizenship and geography
• CHAPTER 6 Different perspectives: mathematics and history, RE and art
• CHAPTER 7 Procedures, symbolism and modelling: mathematics and ICT, business studies and economics
• CHAPTER 8 Pattern and pedagogy: mathematics and dance, drama and music
• CHAPTER 9 Putting it into practice: mathematics, modern foreign languages and PE
• CHAPTER 10 Finding your own context for cross-curricular mathematics
• Bibliography
• Index