Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood.
Read carefully the article below, School Years. As you read, look out for and make a note of any sentences which resonate particularly with your own experience of learning mathematics at school. It may be that you remember similar feelings or situations. Alternatively, Jung's words may spark off much more positive memories for you.
Click on the 'View document' link below to read Carl Jung on 'School Years'
View documentOf course, there is no single right answer to this activity as your response will depend entirely on your memories of your own experience at school.
Some people might have marked the following sentence as one with which they agreed:
The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn't even know what numbers were.
However, one person reading this underlined the word ‘pretended?, and wrote in the margin ‘The teacher wasn't pretending! I expect for him, as for me, algebra did seem a perfectly natural affair.?
Here are some other parts of the article which have particular significance for some people.
Oddly enough my class mates could handle these things …
I finally grasped that what was aimed at was a kind of system of abbreviation, with which many quantities could be put into a short formula.
Equations I could comprehend only by inserting specific numerical values in place of the letters …
I was so intimidated by my incomprehension that I did not dare to ask any questions.
Notice that this was an activity: and so you were expected to be active. You were asked to read and to make notes.
Spend a couple of minutes thinking about your experiences of mathematics at the schools you have attended. Try to picture the classrooms, the teachers, or any of the individual lessons. Are there particular emotions linked to mathematics? Did any of your teachers affect the way you felt about the subject? Do you think you were ‘good at maths??
Summarize your thinking by completing the following sentence: ‘During my school years, I came to see that mathematics was…?.
Again, this activity has no right or wrong answers. You were asked to do two things: some thinking (mainly using your memory) and some writing. You will know whether you responded to both these requests as thoroughly as possible.
In this case you might have found it useful to do the writing on a separate sheet of paper, or perhaps you squeezed it into the margin beside the main text in the unit.
Here are some contrasting ways in which people have completed the sentence: ‘During my school years, I came to see that mathematics was …?
a subject which I found intriguing, challenging and sometimes confusing.
to be avoided as much as possible.
fun!
going to be useful in my work as a nurse.
Outside school, you will have moved on from learning mathematics to using it, perhaps consciously but, probably more frequently, unconsciously. For example, you may have looked at a statistical chart in a newspaper or on TV and subconsciously used mathematics in interpreting the meaning. You may have had to prepare a report which used numerical data. You will certainly have used mathematics when handling money, comparing prices, estimating the length of a journey (both time and distance), doing DIY jobs, following recipes, and so on.
Think back over the last day or two and try to identify as many occasions as possible when you have been using mathematics. How would you describe your level of competence with the mathematics that you were using?
When was the last time you noticed that you were consciously thinking about mathematics? Did you do so with confidence?
In this activity you were not asked to write anything—the activity required here was simply to think. Of course, there is no reason why you should not have made some notes or answered the questions in writing, and indeed this may have helped you to ensure that you really engaged with the questions asked. It is all too easy to give such questions only cursory thought, whereas the discipline of writing ensures that your thinking is active and purposeful.
An alternative way of ensuring that you engage fully is to speak your answers out loud. If there is a friend or member of the family who is willing to listen it can be very helpful, but otherwise many OU students have found that household pets make good listeners! Either way, writing or speaking your answers will certainly help you maintain an active learning style.
One person discussed this activity with their partner and together they came up with the following list of occasions when they had been subconsciously using mathematics during one weekend spent visiting parents.
Estimating what time to leave home in order to arrive in time for lunch.
Comparing petrol prices.
Calculating (roughly) the cost of coffees when they stopped at the service station?did they have enough cash?
Working out how long it had been since we saw a distant member of the family.
Estimating how much water to put in an unfamiliar teapot.
Discussing with parents ways of increasing the interest they get on their savings.
Working out whether there was enough wood of the right size in the garage to put up extra shelves.
Sharing the cost of a meal in a restaurant.
Planning an alternative route home in order to avoid roadworks on the motorway.
Original Copyright © 1996 The Open University. Now made available within the Creative Commons framework under the CC Attribution – Non-commercial licence (see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/).
