Introduction

This unit focuses on your initial encounters with research. It invites you to think about how perceptions of mathematics have influenced you in your prior learning, your teaching and the attitudes of learners.


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Acknowledgements

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

1. Joi
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Summary

In this unit you have been introduced to the difference between mathematical content and processes. You have worked on the do–talk–record (DTR) framework for learning mathematics.


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1.6 Do, talk and record triad

The do–talk–record triad (DTR) is a description of what is likely to take place in collaborative mathematics classrooms. It is concerned with observable events, and with the learner rather than the teacher, though many teaching insights flow from it. Although the order of the triad suggests that it should be followed in a particular sequence, this is not necessarily the case. Sometimes talking comes before doing or recording before talking. It also takes time for a learner to move
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1.5 Studying the Möbius band

Task 10 The Möbius band

1.3 Designing alternative programmes and curricula

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
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1.1 Experiences of learning mathematics

You will come to this unit with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to record
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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
Author(s): The Open University

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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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