Teaching Secondary Mathematics as if the Planet Matters

Alf Coles, Richard Barwell, Tony Cotton, Jan Winter, Laurinda Brown

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781136597855
• Edition: 1
• Topic: Pedagogía
• Subtopic: Educación general

'This book moves us beyond a theoretical pondering of the issues and makes concrete suggestions for teachers and students for how things can be different in mathematics classrooms. This is long overdue.'

Peter Gates, University of Nottingham

Teaching Mathematics as if the Planet Matters explores how Mathematics teachers can develop approaches to curriculum and learning which help students understand the nature of the contemporary world. It sets out a model for teaching and learning that allows teachers to examine existing approaches to teaching and draw upon the insights of mathematics as a discipline to help students relate classroom mathematics to global issues such as climate change, the economy, food supplies, biodiversity, human rights, and social justice.

Including practical examples, suggestions for teaching activities and detailed further reading sections, the book covers:

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• the mathematics of description in the measuring, recording and statistical analysis that informs our knowledge of climate change, consumption and sustainability;

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• the mathematics of prediction in the modelling used by governments, scientists and businesses to plan roads, power stations and food supplies and their effects;

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• the mathematics of communication in the news reports, blogs and environmental campaigns, incomplete without graphs, charts and statistics.

The true worth of a school subject is revealed in how far it can account for and respond to the major issues of the time. The issue of the environment cuts across subject boundaries and requires an interdisciplinary response. Mathematics teachers are part of that response and they have a crucial role in helping students to respond to environmental issues and representations.

Part I

A critical stance on global issues

Chapter
1
	The role of mathematics in shaping our world Richard Barwell

There are seven billion human beings on the planet Earth. This fact is simultaneously about sustainability and mathematics. First, sustainability: how can our planet support seven billion people? How much do seven billion people consume? What effect does this consumption have on the planet, on its forests, deserts, oceans and air? What will happen when the population reaches eight or nine or ten billion? What will happen if consumption continues to increase? These are primarily questions of sustainability: they are questions about the changing nature of the planetary ecosystem. A planet with seven billion people seems to be different from a planet with many fewer people. If you are reading this book, you may think some of these differences, including pollution, species loss and climate change, are cause for concern.

Now, mathematics: how many is seven billion? Can you visualise seven billion people? Or seven billion anythings? Where does this figure come from? How is it calculated? How is the population of the planet changing? How many people can the Earth sustain? How much do seven billion people consume? Think about seven billion breakfasts or toothbrushes or pairs of shoes. To make sense of a statement as innocuous as ‘there are seven billion human beings on the planet Earth’ involves a good deal of mathematics and of mathematical literacy.

These questions illustrate how sustainability and mathematics are inseparably linked. Of course, sustainability is about much more than global population: it is about finding a way for us all to ‘tread lightly’ on the Earth; a way for us to live without, perhaps, destroying much of the ecosystem that supports us. Much of what we know about the Earth and the changes that are happening to it is, however, based on mathematics, including counting, measuring, estimating and modelling. While mathematics is not the only way to learn about the Earth, it is an important and widespread one. Mathematics certainly provides a powerful way to understand the Earth on a planetary scale, beyond the range of individual perception. Mathematics, however, is more than simply a way to understand the world: It also shapes our world, particularly through technology. We have written this book because we want our students to learn mathematics so that they may better understand our Earth, our technological society and the impact of those seven billion people. We argue that mathematics teachers can address issues of sustainability in their teaching and we suggest some ways in which this could be achieved. This book, then, is about teaching mathematics as if the planet matters.

The purpose of this chapter is to introduce some general concepts that inform the rest of the book. These concepts are based on an approach called critical mathematics education. They are about the role that mathematics plays in modern society, how this role relates to sustainability and the way mathematics teaching can prepare students to be active citizens, able to both use and critique mathematics for a more sustainable future. To begin, however, I look first at what we mean by sustainability, and then at how mathematics is used to understand different aspects of sustainability.

What is sustainability?

The history of humanity’s relationship with the natural environment, at least in the West, can be summarised in one word: domination. The natural environment has been seen as a source of food and raw materials all to be placed in the service of human projects. Where the natural environment gets in the way of such projects, we simply blast our way through, rather like the blasting of a cutting or a tunnel through a hill that has the misfortune to lie in the path of a new motorway. The trouble is, there are now so many of us, and our tools are so powerful, that we are no longer simply blasting a few holes in the natural environment; we are changing the whole fabric of the complex ecosystem of which, in the end, we are just one part.

Rachael Carson was one of the first to see human activity as problematic for the natural environment and to call for a change in the relationship:

The history of life on earth has been a history of interaction between living things and their surroundings. To a large extent, the physical form and the habits of the earth’s vegetation and its animal life have been molded by the environment. Considering the whole span of earthly time, the opposite effect, in which life actually modifies its surroundings, has been relatively slight. Only within the moment of time represented by the present [twenieth] century has one species – man – acquired significant power to alter the nature of his world.

(Carson 2002, p. 5)

Her book Silent Spring, originally published in 1962, tells the story of how a chemical (DDT) used to control insects like mosquitos had entered the food chain, leading to catastrophic unforeseen effects on other forms of life, including birds. The then widespread and rather indiscriminate use of DDT is a good example of humans working in ‘domination’ mode.

Silent Spring was one of the catalysts for a spreading awareness of and concern for the natural environment. Twenty-five years later, this concern prompted the establishment of a UN World Commission on Environment and Development (known as the Brundtland Commission, after its Chair, Gro Harlem Brundtland). Its report, Our Common Future, defines sustainable development as follows:

Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs.

(United Nations 1987, Chapter 2, para. 1)

At a minimum, sustainable development must not endanger the natural systems that support life on Earth: the atmosphere, the waters, the soils, and the living beings.

(United Nations 1987, Chapter 2, para. 9)

The report also underlines the inseparable link that sustainability requires between the natural environment, economic development and social justice. For example, economic growth is often cited as essential for the elimination of poverty. But a good deal of poverty could be eliminated through a more equitable distribution of existing resources, rather than through growth per se. Similarly, environmental concerns are sometimes seen as a luxury that can be afforded once a certain level of economic development is reached. This kind of view overlooks the dependency of economic growth on the natural environment. For just one example, consider the depletion of fish stocks in many parts of the world: the massive (economic) growth in large-scale mechanised fishing has led to a reduction in fish that may never be recovered. Once the fish are gone, there will not be much ‘growth’ in the fishing industry (see Chapter 5 for more discussion of this issue).

Clearly, then, sustainability is important and it is also complex. But why should mathematics teachers be interested? Well, mathematics is both an important tool in understanding sustainability issues, and is implicated in the causes of environmental degradation, as discussed in the rest of this chapter. As mathematics teachers, we have an opportunity to introduce sustainability issues, and the related role of mathematics, to our students.

The mathematics of sustainability

Mathematics is central to our understanding of human society and the planetary ecosystem. Without mathematics, it would be difficult to go beyond specific local observations to build a bigger picture. We might observe changes in our locality – a river seems to have fewer fish, for example – but it would be difficult to know if these changes were happening elsewhere or if they were part of broader trends. In some cases, it is only through mathematics that most of us have any knowledge of the issue at all. The widespread concern about the Antarctic ozone hole, for example, was prompted by the publication of measurements made by satellites; it could not have been prompted by direct personal experience, since no one can actually see the ozone hole.

In general, mathematics is used to understand the world in three ways: description, prediction and communication. The mathematics of description includes measurement and statistics. Consider human population as an example. To understand the human population of the planet, it first needs to be described. Individual countries conduct censuses, which lead to reasonably accurate counts of the number of people for that country. These counts can then be combined to come up with a global total (see Table 1.1), although, since population is constantly changing, such totals are always approximate. In many cases, averages are used and population data might include, for example, the proportion of the population in different age groups. As this proportion varies from place to place, the proportion is an average.

Table 1.1 Estimated mid-year population by major area and region, 2009 and 2010 (population in thousands)

	2009	2010
World	6,817,737	6,895,889
Africa	999,045	1,022,234
Eastern Africa	315,865	324,044
Middle Africa	123,452	126,689
Northern Africa	205,920	209,459
Southern Africa	57,293	57,780
Western Africa	296,515	304,261
Asia	4,120,815	4,164,252
Eastern Asia	1,567,045	1,573,970
South-central Asia	1,740,110	1,764,872
South-eastern Asia	586,803	593,415
Western Asia	226,856	231,995
Europe	736,855	738,199
Eastern Europe	295,241	294,771
Northern Europe	98,619	99,205
Southern Europe	154,364	155,171
Western Europe	188,630	189,052
Latin America and the Caribbean	583,547	590,082
Caribbean	41,362	41,646
Central America	153,746	155,881
South America	388,440	392,555
Northern America	341,490	344,529
Oceania	35,984	36,593
Australia/New Zealand	26,225	26,637
Melanesia	8,560	8,748
Micronesia	532	536
Polynesia	667	673

Source: United Nations, Department of Economic and Social Affairs, Population Division (2011)

The mathematics of prediction is often more complex, involving the identification of trends and the construction and use of mathematical models. Various models are available, for example, to predict how the population of the planet will change over the coming decades. These models are based, in part, on analysis of past changes, as well as current information about things like birth rates and death rates. The models include certain assumptions. In the c...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of figures
• List of tables
• Preface
• Part I: A critical stance on global issues
• Part II: Into the classroom as if the planet matters
• Index