The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

Author(s): The Open University

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector a = a 1 i + a 2 j, what are its magnitude |a| and direction θ?

The first part of this question is dealt with using Pythagoras’ Theorem: the magnitude of a v
Author(s): The Open University

On completion of this unit you should be able to:

• convert a vector from geometric form (in terms of magnitude and direction) to component form;

• convert a vector from component form to geometric form;

• understand the use of bearings to describe direction;

• understand the difference between velocity and speed;

• find resultant displacements and velocities in geometric form, via the use of components.

Author(s): The Open University

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

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

Author(s): The Open University

Hart, K., Kerslake, D., Brown, M., Ruddock, G., Kuchemann, D. and McCartney, M. (eds) (1981) Children's Understanding of Mathematics 11-16, London, John Murray.
McCague, W. (2003) 'A mathematical look at a medieval cathedral', Math Horizons, April, pp.11-15 and p.31. See also http://www.maa.org.
Phill
Author(s): The Open University

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
Author(s): The Open University

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

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

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

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

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

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

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

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

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

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

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.

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

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