Introduction

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour
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Acknowledgements

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

All materials included in this unit are derived from content originated at the Open University.


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1.2 Audio files

The following files accompany the exercise in Section 4.2

Clicking on 'View document' below opens an extract from Section 4.2 of the unit (PDF, 1.7 MB) which accompanies the audio clips, also below. Listen to each of them in turn with the extracted pages open (you may like to print them out). Work on the problems at the appropriate places – you'll find the answers at the foot of this page.

Learning outcomes

After studying this unit you should:

  • be able to perform basic algebraic manipulation with complex numbers;

  • understand the geometric interpretation of complex numbers;

  • know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.


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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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1.6.2 Alerts

Online bookshops and some of the major search engines offer ‘Alerts’ services. These work by allowing you to set up a profile once you have registered on their site, and when there are items meeting your criteria you receive an email. The good thing about alerts is that you don’t have to do anything once you have set up your profile. The downside, particularly with alerts services from the search engines, is that given the extent to which internet traffic is on the increase whether new
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1.6.1 Introduction

The process of keeping up-to-date in your chosen subject area is useful for your studies and afterwards, for your own personal satisfaction, or perhaps in your career as part of your continuing professional development.

There are a great many tools available that make it quite easy to keep yourself up to date. You can set them up so that the information comes to you, rather than you having to go out on the web looking for it. Over the next few pages, you will be experimenting with some
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1.5.4The 5 Ds

If you don’t use a system at all, then you could suffer from the effects of information overload:

  • losing important information

  • wasting time on trying to find things

  • ending up with piles of physical and virtual stuff everywhere

One technique you might like to apply to your files (be they paper or electronic) is the 5Ds. Try applying these and see if you can reduce your information overload.


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1.5.3 Desktop search tools

Finding your paperwork or electronic files can be a problem. You may find that even if you do have some sort of filing system, your structure soon gets quite large with files in multiple locations, which can be hard to navigate. You may find yourself making arbitrary decisions about which folder to place a document in. It may make sense now but in the future, when you look where you think it should be, it’s not there.

At times like this you may resort to the search command from the Wi
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1.5.1 Why is it important to be organised?

  • 87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY

  • The world is producing nearly two exabytes of new and unique information every year – an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)

  • More new information has been produc
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1.4.8 Summary

In this section we have introduced you to the PROMPT checklist as a useful tool for assessing the quality of any piece of information. If you use it regularly you will find that you develop the ability to scan information quickly and identify strengths and weaknesses. As a closing exercise you might like to pick one of the websites below or any of your own choice and try to evaluate it using the PROMPT criteria. To make it easier for you we have provided a printable checklist (see below).


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1.4.6 P is for Provenance

The provenance of a piece of information (i.e. who produced it? where did it come from?) may provide another useful clue to its reliability. It represents the 'credentials' of a piece of information that support its status and perceived value. It is therefore very important to be able to identify the author, sponsoring body or source of your information.

Why is this important?

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1.4.2 P is for Presentation

By presentation, we mean, the way in which the information is communicated. You might want to ask yourself:

  • Is the language clear and easy to understand?

  • Is the information clearly laid out so that it is easy to read?

  • Are the fonts large enough and clear?

  • Are the colours effective? (e.g. white or yellow on black can be difficult to read)

  • If there are graphics or photos, do they help
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4.3.3 Pipe dreams?

The idea underlying complementary currencies – that there is a great well of social capital waiting to be drawn upon to make society more sustainable – is an idea that is becoming quietly influential. ‘Social capital’ is a term frequently used by those mainstream politicians and civil servants tasked with addressing the widening gap between rich and poor people within societies throughout the world. Indeed, investing in and enhancing social capital is now the starting point in
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4.3.2 Complementary currencies

Complementary currencies also demand a rethink of our economy, but have a more imaginative and radical edge. Because of the difficulties with conventional monetary systems, various alternatives are being tried. These are usually restricted to a particular group of people, and so are called ‘local’ or ‘complementary’ currencies. They are generally based in a local community and enable people to exchange goods and services without resorting to ‘traditional’ currency. Some are
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4.3 Green from the grassroots up

People who demand a radical break with the business-dominated path of economic globalisation believe that the claims of the mainstream business community are at best hopelessly inadequate, and at worst deceitful. However, they know they have to come up with some answers of their own. This section outlines ideas that seek to underpin a transition to green economies owned and run at grassroots level. Sounds ambitious? Author(s): The Open University

4.2.3 Business needs sustainability

The second argument is more profound: long-term profitability, and the existence of business itself, is threatened if companies can't transform themselves. This assumes that although the costs of environmental and social impacts can be ignored for a period, in the context of globalisation of environmental, social and political processes, they will come back to haunt businesses, and ultimately threaten their survival. There are several communications and management tools that have been develop
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4.2.1 Eco-efficiency = money in the bank

Business can profit from taking the environment into account (generally called eco-efficiency). Poor environmental performance is seen as a reflection of poor business practice in general. Eco-efficiency promotes the economic benefits of energy and materials savings, at the same time being first to market with new technologies or products. Since business sustainability lobbies promoted eco-efficiency in the early 1990s, the creed has gained rapid acceptance, and with good cause. There
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3.3.3 Obligations to trees?

Citizenship is generally held to be based on a contractual view, where rights and obligations are balanced. In other words, you get various rights in return for your commitment to live by your society's rules and expectations. Political philosopher Andrew Dobson suggests that ecological citizenship is based in a non-reciprocal sense of justice or compassion. The discussion of our relationships with past and future generations in Section 5.2 establishes that our obligations to future generatio
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3.3.1 Too late for the nation state?

Nation states have long been thought of as comprising citizens who ‘share the same fate’. For a long time it made sense to think in terms of the shared fate of members of a nation state (although different social classes would generally have experienced different versions of this fate). However, the global economic, political and social flows described in this chapter, and the global environmental changes charted throughout this book, make it much more difficult to think in terms of clear
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