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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Acknowledgements

The content acknowledged below is Proprietary (see made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence  and conditions) and is

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

1. Joi
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Learning outcomes

After studying this unit, you should:

  • understand some current issues in mathematics education, such as the relationship of mathematics content to mathematics processes.

  • understand a variety of approaches to the teaching of mathematics such as 'do-talk-record'

  • be able to approach mathematical problems and tasks in a flexible way.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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:

    Author(s): The Open University

    License information
    Related content

    Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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
    Author(s): The Open University

    License information
    Related content

    Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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.

Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

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?


    Author(s): The Open University

    License information
    Related content

    Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share