2 Reflection on mathematics
2.1 Reflecting on your mathematical history
One of the obstacles that we see to understanding and working with mathematics is that people feel the need to avoid it entirely, because they feel nervous about it. Others don't feel as nervous, but may still avoid mathematical work. In practice, you may well be using more mathematical concepts than you think, as numbers are all around us; for example, when shopping, going out for a drink with friends, paying bills, or planning a budget so that you can take a holiday.
This activity is designed to get you to look at the previous experience you have of mathematics. It will take you between 15 and 20 minutes, and to put your concerns into context, we suggest that you carry it out before you begin work on the rest of the unit.
All through school
Think about your schooldays: nursery or kindergarten, first or primary school, middle or secondary school. Now consider the following questions.
- What were your experiences of mathematics?
- How do you feel about these experiences?
Work and study since school
- How have the jobs you have done since school affected your mathematical thinking? Think about reading newspapers, preparing reports, watching television. For example, when was the last time you noticed that you were thinking about mathematics?
- In your experience of study since school, what more have you learnt about your own use of mathematics? What do you expect of yourself when you approach a mathematical problem: are you confident, worried, or concerned?
Now that you have completed this for yourself, perhaps you could check out the following questions, either on your own or with a fellow student or friend.
- How could past experiences have influenced the way that you feel?
- Can you see why some people don't feel this way? Why could this be?
To help you, we have asked several people to complete this activity and have collected some of their views and feelings under three headings: ‘Feelings about mathematics’, ‘Coping strategies for mathematics’, and ‘Need to learn mathematics’.
Feelings about mathematics
Many people have strong feelings about mathematics, often linked with worry or fear, from a difficult previous experience.
I wouldn't say I have learnt a great deal more since school and regret not having a better grounding in it. When faced with a problem I feel confident if the problem is within the realms of my capability. However, I do know that I end up going the long way round. Or as we say in Guernsey, I go round Sark to get to Herm (two islands off Guernsey).
I am constantly worried about the use of maths – I always presume that I will get simple problems wrong if numbers are involved.
We were mixed-ability taught in all subjects in the first year, but after that we were rigidly grouped according to ability and, as expected, I ended up in one of the lower maths groups, where I remained for the rest of my time at secondary school. Any chance of improving my mathematical skills were also limited by the school deciding we were a lost cause, and being taught by a procession of some of the most eccentric and disinterested teachers I have ever met.
It is possible that you came up with comments that are similar to these. We are not trying to suggest that everyone feels this way about mathematics; some people really enjoy it and others can get by, but feelings of apprehension can often get in the way of learning.
Coping strategies for mathematics
To get round feelings of worry, people have often developed very good coping strategies, and you might recognise some of these. There is nothing wrong with this at all; it's a sensible thing to do.
On reflection I suspect that I have spent most of my working life sidestepping anything vaguely connected with maths and have consequently developed a number of avoidance techniques. These range from ‘I am busy at the moment, I am not sure what you want to know, try to work it out yourself’, through to ‘I haven't got my glasses’ – all very similar to the techniques employed by those who have difficulty in reading.
If I see a pure mathematics problem then I don't attempt it. I tend not to be drawn to articles in newspapers/TV that have a mathematical focus.
I was good at hiding within the class… I usually stay quiet and I would never contemplate a job where I would have to add up in front of others.
I am not terribly confident when presented with certain sets of figures, but, if I work through it carefully, I can usually cope with it.
Need to learn mathematics
How much mathematics do you need to learn to study successfully? Well, that is likely to vary depending on the courses that you take.
I have just started a science course, so I know I will need to improve my skills.
I am aware that presumed difficulties with maths prevent me from attempting certain aspects of the course. Basic skills could help my confidence, though I feel it may be too late to start. (Arts student.)
In my previous course, I was studying German. My ideas about what mathematics meant to me were not even considered and did not develop throughout. My next course (Third World Development) will be different, but I haven't started it yet.
What we have asked you to do here is to look at your experience of mathematics in the context of your experience as a student, as well as in the past. As you can see, other people feel unconfident about their use of mathematics. Now you can move on to considering what to do about it. The final question in the activity asks you to think about what you need to concentrate on now, and we hope that you are now ready to look at the rest of the unit.