Maths everywhere
Maths everywhere

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Maths everywhere

3.3 Skills in learning mathematics

A great deal has already been said about the study skills that you will be developing as you work. But how might these help you in your future study, in the workplace or in any voluntary work that you do? This is the subject of the second band of the audiotape.

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KAREN REX
You may have thought that in studying MU120 you’d only be learning mathematics, but has it actually turned out like that? I expect you found that you are actually doing many other things as well as mathematics. It’s often the case, isn’t it, that when we embark on a journey we pick up lots of new things, but we also use our own personal skills and experiences to help us along the way. Starting MU120 is like beginning a journey. The main aim, clearly, is to get involved with doing and learning about mathematics, so that you can improve – for whatever reason. But in getting involved in learning mathematics you need to be able to do other things as well. And often, the better you are at doing these, the easier the journey. That’s what we’ll be exploring on this band. We’ll be looking at some of the skills you’ll be using and developing while doing MU120. We’ll be talking about how they can be described and assessed, and how useful they are. So, first of all, let’s try to identify some of these learning skills. In fact you’ve been using them already while working on the course. You’ve certainly had to get things done on time, learn by yourself, grapple with the calculator and wonder what to do when you got stuck – and, of course, sort out all the paper from the OU. Try to make a list of all the different skills you’ve been using since you started the course. Stop while you do this. Track 3 I’ve asked lots of OU students to do a similar exercise, and every time they come up with a long list, and each time it’s slightly different. Here’s some of the skills that other students have included: • time management • numeracy • evaluation of information • presentation • analysis • specialised reading skills • summarising • decision making • discussion • and using and interacting with different media. Now take a look at your list. Do you notice that many of these skills are in fact things you do all the time – at home or at work – in all sorts of situations and not just in studying. In fact, these skills are so useful that employers have identified many of them as being crucial in the world of work. So much so that when companies are recruiting, they’re not just looking for knowledge in a particular area – they need these other things as well. Pick up any paper with job adverts and have a look at them. You’ll find phrases like:
FEMALE EMPLOYER (ROSEMARY HILL)
Good presentation skills a must.
MALE EMPLOYER (JOHN JAWORSKI)
Must be motivated and proactive.
FEMALE EMPLOYER
Must have good numeracy skills.
MALE EMPLOYER
We need someone who has a good balance of interpersonal skills and business skills.
FEMALE EMPLOYER
You will need to organise and make strategic decisions in a changing environment.
MALE EMPLOYER
We are not prescriptive about the subject qualifications, but, be warned, you will need to demonstrate that you have the selfconfidence and communication skills essential for the job.
KAREN REX
There are many ways of describing skills and competencies in the workplace, and ideas of these are becoming more widespread. So, you hear people talking about SNVQs or transferable skills, based on what people actually do in the workplace. I spoke to Dee Burkill, who’s a head of personnel for a Volkswagen subsidiary, about the way that her organisation uses skills and competencies with its staff.
DEE BURKILL
We first started looking at competencies in the early ’90s, mainly because the systems that we were using at that time had fallen into disrepute, because of the recession, because of the limited budgets that we had available for training, for salary increases. So, we introduced a fully fledged competency programme, just over three years ago now, for the whole of the group. So, everybody now within this organisation fits into a job family. The ‘job family’ is the generic term we use for people’s roles, and we very much talk about roles now rather than jobs. Nobody has a job description within the Volkswagen Group now. Nobody at all. We have done away with job descriptions, and I will fight vehemently to the end to maintain that, because I do not want to go back to the days where we spent our lives rewriting these job descriptions every time somebody’s job’s changed. But the thing about our competencies, and the thing about competencies that in most organisations that are different – they are all focused on the softer issues. They’re all focused on the ‘how do you do’ things: ‘how do you behave?’ and ‘how do you go about achieving your objectives?’ So, you will have objectives. You will have performance-related objectives, managerial objectives very, very focused. And, yes, I am concerned about whether or not you have achieved this objective, but I am more concerned about how you’ve gone about doing it. And you will be rewarded for the ‘how you’ve done it’. And if you’ve trampled on people, upset customers, been rude to people or whatever, then you will not have achieved that competence, and you will not get the tick towards it. And, as I say, it does drive our salaries as well. So, without evidence of achieving that competence, you will not get a salary increase, so it does focus the mind somewhat.
KAREN REX
So, when you’re looking for, say, new graduates, what are you looking for from them in terms of communication skills?
DEE BURKILL
We’re looking for people who’ve got a range of experiences. We’re looking for people who are exhibiting, in the early stages, the embryonic competencies, the embryonic skills, communication skills, negotiating skills, ambassadorial skills that we want for the future. We will ask them to tell us about a specific project they were given ownership for, that they were responsible for from beginning to end. We will ask them to describe it to us, and how they evaluated its success. And, in hindsight, what went well, and what could have been done better.
KAREN REX
Private-sector companies like Volkswagen often use a set of competencies that they’ve identified for themselves. Many of these are common across organisations. For example, communication skills and the management of people are often part of this type of approach. These skills are equally sought after in the voluntary sector. Michael Murray, who used to be the Chief Executive of Milton Keynes Borough Council, is now active in a number of voluntary organisations. I first asked him what he looks for in recruiting staff.
MICHAEL MURRAY
Obviously, you’re sometimes looking for a particular professional or other skill – if you’re looking for somebody who has an ability of marketing, for the sake of argument. But, most importantly, I think you are probably looking for people who’ve got an understanding of the community they’re going to be dealing with or the particular area that they’re going to be dealing with – if not understanding, at least an empathy with that, because the ‘not-for-profit sector’, or whatever they call it, is a bit different in many ways to many other areas. There are some changing conceptions about what people are or should be doing in the voluntary sector. And the range of skills, then, that people need to perform those roles is quite varied.
KAREN REX
Can you think of a specific example?
MICHAEL MURRAY
The Living Archive Project. If you take the director who runs that – there’s a very small team, four people or something of that order altogether – and that person has to, one, understand about the issues surrounding an oral archive. He has to understand something about the immediate community in which he lives and the opportunities which that community offers. He needs to understand something about making bids for money. In fact he needs to understand a lot about making bids for money. He needs to, obviously, be able to identify opportunities and respond to them very quickly. And he needs to be an extremely good communicator – extremely good communicator – because he’s dealing with a huge number of audiences.
KAREN REX
So when you say ‘a good communicator’, what sort of things do you mean by that?
MICHAEL MURRAY
First of all, a good communicator about the ideas which the organisation is dealing in. Secondly, the range of people whom he has to deal with is very varied, you know, from kind of politicians and your local council, down to all kinds of fundraisers, to staff you have to manage.
KAREN REX
And what about people who perhaps aren’t volunteering at the board level, who are coming in perhaps to do a couple of hours a week for an organisation in a very practical way …
MICHAEL MURRAY
Yes.
KAREN REX
…What sort of things do you look for there?
MICHAEL MURRAY
I think you’re looking for enthusiasm and understanding what the voluntary organisation is trying to achieve, their part in it, and, because it – often the voluntary sector is quite informally structured, an ability to be able to communicate with others within the organisation, with minimal formal structures around them.
KAREN REX
Both Michael Murray and Dee Burkill have emphasised the need for flexibility and for a range of skills. Now have another look at the list you drew up earlier with the skills you’ve used in MU120 so far. Of all the lists you and I might generate, none are right or wrong. They simply represent different ways of talking about skills. And another thing: no one set of descriptions will give us watertight definitions. There’ll always be seepage from one general descriptional category to another. In my list, for example, note-taking, specialised reading skills and discussion are actually all part of communicating. There’s no single set of descriptions which will work well in all contexts. So one important reason for being able to describe skills in a general sense is being able to be confident that something that you’ve learned in one situation will help you in another, different situation. Just think about what you’ll need to be able to do as you progress from this course. You’ll want to be confident that you can apply mathematical techniques and solve problems using mathematics. But you’ll also want to be sure that you can study independently and meet deadlines. And like most students, I expect that you also want to feel that you’re improving as you go on. There’s some value for us then to be able to identify particular skills. But if these skills are to be recognised and valued by others, whether an employer, a voluntary organisation or university, or for your own use, then it’s not sufficient to say, ‘I can present my work well,’ or, ‘I can use this statistical technique to sort this problem out.’ Other people, and organisations, will want evidence of what your skills are so that they can judge the level at which you’re operating. Demonstrating your skills to an employer is not the end of the story. Using and defining skills are all about helping people to develop and improve, and that includes skills you use in learning. So, finally, I spoke to Les Coupe, who successfully studied MU120 in 1996, and has continued as a student with the OU ever since. I was interested to find out how the skills that he developed on MU120 helped him at the time, and what use they’ve been to him since then. I started out by asking him about his work.
LES COUPE
My job is as a Road Safety Officer. I work for Hampshire County Council. It basically involves education, training and publicity issues for all classes of road users, from very young children all the way through to older road users. It looks a great deal at statistics: accident trends, where we have to identify accident problems, whether they’re going up, or they’re going down; the programmes that we implement, whether they’re successful. So there’s a lot of statistical work involved in that.
KAREN REX
MU120 is slightly unusual in the sense that students tend to expect a course that develops their numeracy skills, and just their numeracy skills. But obviously, as you’re aware, it develops other things as well – communication skills and study skills and reflective learning skills. Can you think of any examples where this has been useful to you in practice?
LES COUPE
Yes. We deal with accident statistics, road accident statistics. But generally we deal with members of the public, county councillors, occasionally politicians, where they will ask questions and you can give ball park figures – you can say, ‘Well, we’ve had an approximately 12 per cent reduction in the number of accidents,’ or similar kinds of things, and you know in your own mind that you’re about right. If anybody does actually challenge you when it comes to writing the thing down on paper, you know that you’re more or less right. And again it is just an overall confidence in what you say will be about right. And it’s really only going through MU120 that it’s given me the confidence to do that.
KAREN REX
Have you found that to be useful elsewhere?
LES COUPE
Well, yes, I can; it was actually during ’96 as I was doing MU120, I witnessed a road accident on the motorway, where a car spun off in front of me. I did of course stop; I spoke to the driver, who was completely unhurt – he was okay – but he told me that a lorry had forced him off the motorway. There were other drivers stopped; I just took his telephone number and said I’ll catch this chap up. I know I was stopped for no longer than three or four minutes. So I zoomed off after this lorry. I did eventually catch him up after fifteen to twenty minutes, something like that, and got the registration number of the lorry and, later the same day, telephoned the chap back. I was somewhat surprised a few weeks later to get a summons by a court to go and give evidence about what I’d seen. And I related my story to the court, and the defence solicitor questioned me; he said there was absolutely no way I could catch this lorry up in the time that I’d stated. And I was actually able to say to him that ‘oh yes, I could quite easily do it,’ and I was able to relate to him, really off the top of my head, that the length of time I was waiting there, which was only three or four minutes, this would put the lorry three to four miles down the road at 56 miles an hour. And, at the speed I was travelling, 70 to 75 miles an hour to catch him up – a speed differential of about 15, 20 miles an hour – that I’d be able to catch him up at about a rate of a mile every four minutes, and therefore 12 to 15 minutes later I would catch him up. And of course, at that speed, would put me 15 miles away from the scene of the accident, which was on the outskirts of Winchester, which was where I said I’d actually caught the chap up. So it gave me the confidence to actually question someone who I saw as an authoritative figure and to actually contradict what he’d said, but, more importantly, be actually right with it as well. Because that was the thing, I do remember quite vividly whilst the court adjourned for a few moments, while they got maps out and checked my figures, I can remember scribbling all these notes down, working these little calculations out to see how right I was. But it was never questioned. My evidence was taken as correct. So, from a communication point of view, it’s improved things tremendously for me.
KAREN REX
The other thing that MU120 does is this idea about getting people to reflect on the way that they’re learning. It takes a little while for people to appreciate how that actually works. Can you think of how it’s made a difference to you in the way that you study?
LES COUPE
I certainly can. You have to lay out a study schedule of the work that you have to do, the timescale that you have to do it in. Now, I’ve been able to use similar kinds of study schedules with subsequent courses, not entirely completely successfully because of work pressures, but generally I’ve found it to help in planning my study time for the OU, because I can say that ‘yes, I’ll have a couple of hours free here or there’ – or whatever, and because I know that from the nature of my work – I don’t do work regular hours – I have to slot study periods in whenever I can. And planning it helps considerably towards that.
KAREN REX
Can you think of a time during MU120 when you suddenly realised perhaps that this was useful?
LES COUPE
I think, if I’m honest, as far as planning my study time is concerned, it was really during the final assessment, and if I were to give any advice to new MU120 students, it would be to say, is: plan your study time.
KAREN REX
As you can see, the skills that you’re developing on MU120 may not be entirely those that you’re expecting. Most of us want to get better at what we’re doing, but often we’re not quite sure which skills to improve, and indeed how to go about it. This is one reason why the course isn’t just about doing mathematics. As you’ve seen, whenever you’re learning and doing new things, you’re using many different skills. MU120 helps you to improve those skills while you’re doing the mathematics. That’s why you’re encouraged to complete a variety of activities, review your progress and keep a record in your learning file.
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Skills in Learning Mathematics
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Activity 18 Identifying skills

Listen to the audi clip above, entitled ‘Skills in learning mathematics’. As you listen you may wish to make some notes, and at one point you will be asked to stop the tape in order to draw up a list of skills that you have been using and developing in the course so far. In the last part of the tape, a former student of mathematics at the Open University speaks about some of the skills that he developed during his course of study and how he has been able to use them since.

Much of this section has involved looking at how you study and making learning more explicit. Many people can improve the effectiveness of their learning if they spend some time focusing not only on the content of what they are trying to learn, but also on the learning process itself. Even if you do not find any particular difficulties with studying, it is important to pause regularly to evaluate how well you are doing and whether you can learn more effectively by changing your approach. To this end, before you finish this course, there is one more study-skills activity to complete.

Activity 19 On reflection

Think about your first course of study and, if you feel it is helpful, briefly note down your thoughts. Consider how many hours you have studied, the pattern of your study periods, and where and when you have studied. Think about how you might like to change the way you work so that your study becomes more effective.

Outcome

Now that you have completed your work on this section, you should have:

  • organized your learning file (Activity 18);

  • reviewed the way that you are studying the course so far and begun to think about improvements (Activities 17 and 19).

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