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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1.6.5 RSS

RSS (‘Really Simple Syndication’ or ‘Rich Site Summary’) newsfeeds supply headlines, links, and article summaries from various websites. By using RSS ‘feedreader’ software you can gather together a range of feeds and read them in one place: they come to you, rather than you having to go out and look for breaking news. The range of RSS feeds on offer is growing daily. There is probably a feed to cover all aspects of your life where you might need the latest information, and you may
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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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1.4.4 O is for Objectivity

One of the characteristics of ‘good’ information is that it should be balanced and present both sides of an argument or issue. This way the reader is left to weigh up the evidence and make a decision. In reality, we recognise that no information is truly objective.

This means that the onus is on you, the reader, to develop a critical awareness of the positions represented in what you read, and to take account of this when you interpret the information. In some cases, authors may be
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1.4.3 R is for Relevance

Relevance is an important factor to consider when you are evaluating information. It isn’t so much a property of the information itself but of the relationship it has with your question or your ‘information need’. For example, if you are writing an essay about the Consumer Price Index a book or website about how the Ancient Egyptians drew circles would not be relevant. So there are a number of ways in which a piece of information may not be relevant to your query:

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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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1.4.1 PROMPT

There is so much information available on the internet on every topic imaginable. But how do you know if it is any good? And if you find a lot more information than you really need, how do you decide what to keep and who to discard?

In this section we are going to introduce a simple checklist to help you to judge the quality of the information you find. Before we do this, spend a few minutes thinking about what is meant by information quality.

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1.3.9 Summary

There is a lot of information available on maths and statistics via the internet. Try the activities below to start exploring what is available.

Activity

1.3.8 Choosing the right tool for the job

Before searching it is always a good idea to check what the source you have chosen covers to make sure it will unearth information that matches your search need (you will notice that all the resources we’ve covered in this guide have short descriptions to enable you to decide which to use). Some of the decision makers, depending on the context of your search might be:

  • Does it have full text?

  • Does it cover the right subject?


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1.3.7 Internet resources

There are many websites where you will find useful information on maths and statistics. With all information on the internet you need to make a judgement on its reliability.

Royal Statistical Society Information about the Society, its publications, section and groups. Also covers caree
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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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1.3.5 Journals

Journals and articles written by academics or experts are an excellent source of information. Journals are usually published monthly or quarterly, and contain a selection of articles providing details of recent research. Often they will also contain reviews of relevant books. They are usually published more quickly than books, and so are often more up to date.

To access content of journals, most publishers require a subscription. There are, however, some journals which you can freely ac
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1.3.4 Databases

At a basic level, a database is a collection of information which can be searched. It is a way of storing, indexing, organising and retrieving information. You may have created one yourself to keep track of your references – or your friends' names and addresses. They are useful for finding articles on a topic, and can be used to search for many different types of information.

You may find some of the following databases useful for your topic. They contain different types of informatio
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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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1.3.2 Search engines and subject gateways

Although both search engines and subject gateways will help you find the resources that you need, the types of information that you find will differ.

Search engines such as Google and Yahoo! search the internet for keywords or phrases, and then show you the results. These results are not mediated by the search engines, and therefore you need to use your own judgement on the reliability of the results. You may, for example, find websites written by experts, alongside websites written by
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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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1.2.3 Basic principles

Whatever resource you choose to use to find information on the internet, many of the same principles apply. Each source that you use will probably look quite different from the one you tried before, but you'll notice that there are always features that are similar – a box to type your search terms in, for instance, or a clickable help button. Different resources refer to the same functions using different terminology, but the principles behind them are exactly the same. The trick is to chec
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