Introduction

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section 2, in which you will also work with bearings.

This unit is an adapted extract from the Open University course
Author(s): The Open University

2 Your own mathematics

It is crucial to remember that you are a learner of mathematics as well as a teacher. In this unit you will be asked to undertake some mathematical tasks. The aim of these tasks is not to improve your mathematics, but to give you experience of doing mathematics for yourself—experience that you can reflect upon subsequently. The reflection is used to develop your awareness of the ways that learners deal with mathematical tasks, and how learners' mathematical thinking is influenced by the way
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1 Forces for development

Working in mathematics education involves a sense of both past and future, and how the two combine to influence the present. It may seem that, because the past has already happened, it cannot be altered; however, you can alter how you perceive the past, and what lessons you take from it. Each of us has a personal past in mathematics education—the particular events of our personal lives, who taught us, where, what and how they taught us, and what we took from the experiences. Each of us also
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Learning outcomes

After studying this unit you should:

  • reflect in depth on aspects of mathematics learning, whether you are directly concerned with mathematics teaching or simply interested in issues of mathematics education;

  • examine established views about existing practice in a critical way and engage with research evidence on mathematics and learning.


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1.2.3 Process

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. A list of processes could contain:

  • problem-solving (including investigating);

  • mathematical modelling;

  • reasoning;

  • communicating;

  • making connections (including applying mathematics); and

  • using tools.

Each of the six processes liste
Author(s): The Open University

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1.2.2 Content

School mathematics curricula often focus on lists of content objectives in areas like number, arithmetic, statistics, measurement, geometry, trigonometry, and algebra. A typical list of content objectives might contain over one hundred objectives to be introduced or revisited and learned each year. These can be seen as hierarchical in nature but many textbooks do not attempt to organise the objectives in ways that enable the bigger underpinning ideas to become apparent to the pupils. In addit
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1.6.4 Blogs

Technorati reports that over 100 000 new ‘blogs’ are created each day. Because these online diaries offer instant publishing opportunities, you potentially have access to a wealth of knowledge from commentators and experts (if they blog) in a wide range of fields. Most internet searches will turn up results from blogs, but there are some blog-specific search engines such as: Blogdigger
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1.3.6 Encyclopedias

Encyclopedias can be useful reference texts to use to start your research. There are some available online, such as Wikipedia, which is a freely available collaborative encyclopedia.


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1.3.3 Books and electronic books

Books are a good source of information. The publishing process (where a book is checked by an editor before publishing, and often reviewed by another author) means that books are reliable sources of information, although they may need to be evaluated for bias. A growing number of books can be found online.

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1.3.1 Introduction

You can find a lot of information about the maths and statistics on the internet.

To find this information you might choose to use:

  • search engines and subject gateways;

  • books and electronic books;

  • databases;

  • journals;

  • encyclopedias

  • internet resources


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1.2.1 Planning your search

Your approach to searching will depend to a great extent on what kind of person you are. In an ideal world, when searching for information for a specific purpose, we would all find what exactly we were looking for at the first attempt, especially if we are in a hurry. However, it’s always a good idea to have some kind of plan when you are searching for information, if only to help you plan your time and make sure you find the information you need. If I was starting to search for material on
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1.1.4 Evaluating information

How well does the following statement describe your approach to evaluating the information that you use?

When I come across a new piece of information (e.g. a website, newspaper article) I consider the quality of the information, and based on that I decide whether or not to use it.

  • 5 – This is an excellent match; this is exactly what I do


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Learning outcomes

By the end of this unit you will:

  • Have gained an understanding of the four dimensions of globalisation in relation to climate change;

  • Be able to distinguish between the three approaches to achieve sustainability;

  • Know the difference between ‘government’ and ‘governance’;

  • Identify what makes ecological citizenship distinctive;

  • Understand how the medium of the web can aid transitions to sustainability.


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1.5 ‘Radiative forcing’ as an agent of climate change

Since its first major report in 1990, the IPCC has used the concept of ‘radiative forcing’ as a simple measure of the importance of a potential climate change mechanism. The basic idea is straightforward. Any factor that disturbs the radiation balance at the top of the atmosphere has the potential to ‘force’ the global climate to change: it will either warm up or cool down until a balance is restored. The perturbation to the energy balance of the whole Earth-atmosphere system i
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Learning outcomes

By the end of this unit you should be able to:

  • understand why systems thinking might be useful and know something about how it can be applied in the context of environmental responsibility;

  • describe the significance of environmental pragmatism and cognitive justice as tools for supporting environmental policy and action.


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1.5 Conclusion

Throughout this unit, a major concern has been to show how the demand of the antisweatshop movement that we not only respond to, but take responsibility for, economic injustices, no matter how distant, is an intensely controversial one. Claims by campaigning groups such as Oxfam and Christian Aid that consumer demand for cheap branded goods perpetuates poverty wage levels in the sweatshop industries are countered by claims from the pro-market lobby which point in an altogether differen
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1.3.8 Summary of section

  • During the 1970s and 1980s, countries such as Hong Kong, Singapore and Taiwan benefited from their low-cost advantages in the new global division of labour. Now, however, the gap between rich and poor nations is wider and competition in the world economy greater, prompting campaigning groups to argue that contemporary low-wage economies do not have the options for economic development that their predecessors had.

  • In the face of market fragment
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1.2.9 In praise of cheap offshore labour? continued

Significantly, no one from the pro-market lobby is actually denying that sweatshops exist, or trying to cover up the fact that workers in such places have to endure bad working conditions. But, as the subtitle of Krugman's (1997) article suggests: ‘bad jobs at bad wages are better than no jobs at all’. Low as the wages are in the offshore T-shirt or microwave factories compared with those in more developed economies, they tend to be higher than those of other workers around them. The huma
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5.3 The rebound effect

When individuals or organisations implement energy efficiency improvements, they usually save money as well as saving energy. However, if the money saved is then spent on higher standards of service, or additional energy-consuming activities that would not have otherwise been undertaken, then some or all of the energy savings may be eliminated. This tendency is sometimes known as the ‘rebound effect’. For example, if householders install improved insulation or a more efficient heating boi
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Learning outcomes

By the end of this unit you should be able to:

  • appreciate different connotations and traditions of the terms ‘nature’ and ‘environment’ in the context of environmental responsibility;

  • use conversation as a core metaphor for describing ‘what matters’ in environmental responsibility;

  • identify and compare formal and less formal expressions of environmental responsibility.


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