Sunday, June 10, 2007

A piece of paper and Mathematical Fear.

I have been meaning to blog about this for quite some time, however one can say that I never got the time to previously or I was too lazy. Actually, I consciously left this post till after my exams. There is some discussion happening at Mathematics Under the Microscope about oral exams, and it is the comments there which have reminded me of wanting to blog about this. That and accidentally stumbling across something which I'd bookmarked some time ago!

Before I get started, well started started that is, I was wondering something. How much can we deduce about a persons character, personality etc by reading what they write? I mean I could write in a certain different way and you could possibly think differently of me. Anyway this is not about me (!), I mean in general. When we read other peoples blogs do we really know them? You see in my case I read something by a lecturer at the University of Manchester. I've read quite a few articles by this lecturer and well through his writing I like the lecturer. I mean the person he is but through his writing. I see him on occasions and indeed he is friendly, since he always smiles back! Now is that always the case? Can we judge someone by what they write? Don't know really, but that's just some random thought which went through the empty space in my head!

The piece which I have mind whilst writing this can be found here. However I'm not sure whether you'll be able to access the link. (It is with some difficulty that I found it again!). Anyway, through the University, I believe that I have access to the magazine 'Mathematics Today'. It is an interesting read, and there are obviously things which I don't understand, but these I don't concern myself with. I think more importantly it's about exposure. The magazine isn't just about maths but many other things like the education system present today. I always look out for this magazine, however it seems I'll have to wait till next year to hopefully get my hands on the June issue. (I tend to pick it up from University, since that's the only way I can get it!)

So if you haven't managed to read the editorial then don't worry, for I'm going to be talking about most of it. I quote from the editorial,

'However, for many of them, the thing they are committed to is success itself. They need a piece of paper to say they have passed my course. If I could spend the rest of the semester going through past examination papers until, when faced with any likely question, they could regurgitate a sufficient amount of information to pass, several of them have indicated that they would be happy.'

Now I believe there is a certain truth to these words. However, I don't believe this is entirely the students fault. I'm not sure which part of the fence I sit on, but I think I'm more in the middle. I do fear 'failure' as such, and always aim to pass. However, whenever it comes to revision etc, I always look to enhance my understanding of concepts. I mean it's long and takes me a while, but I really do start from A and go to Z. My problem is that I sometimes stupidly don't go through past papers because I'm dead bent on trying to complete my understanding of things. This is also the reason as to why I panic, since I fear that I haven't properly understand the subject and so won't be able to do the questions.

The editorial also goes on to talk about this 'fear',

'If I had to summarise in a single word the overriding emotion that governs my students, I think that the word would be “fear”. Fear that the next thing that I will tell them will stump them completely, fear of failure. The whole process of their education seems to have had every scintilla of intellectual excitement and joy squeezed from it. We have produced a generation who live in unrelenting fear of examinations.'

This is why I say it may not be the student's fault. I seem to be slightly lucky in the sense that I enjoy what I study, however let me now talk about mathematical fear.

In school, thanks to help from my Dad, I was OK in maths. I mean maths was the one subject which I really did love. Every Friday mornings, in year 11, assemblies always over ran and maths used to be the first lesson. I won't deny that I used to get very agitated by this, and upon the assembly finishing I was the first back to the maths class and I used to tell my friends to get a move on! I mean, maths lessons were the best. This I believe, is obviously due to my maths teacher and the atmosphere in my maths class used to be great as well. (In year 10 a group of us had childishly made names for each other and so we used to refer to each other by this -Trevor McDonald, Marge, Maggy, Chappy, Homer etc to name a few!). I'm sure that maths lesson used to be over so soon.

I have been giving a 'history' of my maths, and I had originally intended to write about this there (yes I'm still writing about year 10 at the moment!). But I think now is a more appropriate time for these comments. In year 11 I had to apply to colleges to study my A Levels. All I knew was that I wanted to do Maths. I eventually only applied to one college, for it was local and well I had wanted to go there as well. At that time I didn't know much about further maths, however during my interview I happened to luckily be interviewed by a maths teacher - Mrs. R, who later went on to teach me. During the interview my choices had been chopped to Maths, further maths, chemistry and law (aaahh!). We did discuss some maths and I happily left the interview with an offer of 5 GCSE passes.

Some time later, they invited students to an open day. Naturally I first went to the maths classroom and there I met Mr. B. However I also came across something else. After he had finished talking to me, I saw some past papers on the table for pure maths. I obviously had a glance through them and it was then that I felt that mathematical fear. I couldn't make sense of anything. Well the first few questions anyway. I didn't manage to look through the whole paper, since this fear caused me to replace the paper and continue browsing through the room. This fear was a new feeling. I really did become worried for a while. However, although my fear made me react this way, my brain said, 'we'll cross that bridge when we come to it, don't worry about it. Concentrate on your GCSEs- you'll do that next year.' This made me normal again. The fear evaporated and I started looking forward to starting college. Tinky Winky had also been doing a maths a level at the time and from what I can remember, after my GCSEs I did have another look through Tinky Winky's work. This time the fear was considerably less. I felt excited. Looking forward to the prospect of being able to understand what that past paper was about.

I joined college and continued my mathematical journey. Year 12 wasn't particularly great in the sense that I wasn't on top of things, however year 13 was much better. I'd rather discuss the ups and downs of college in the posts which I intend to, however a deja vu moment happened. I naturally applied to study maths at university and I was really looking forward to it. I was 'disappointed' when I learnt that Mr. B had taught my further maths class mate extra stuff because she was possibly going to sit the STEP exam (for her Uni offer since I think she applied to Oxbridge). I wanted to know more maths and wanted to be taught extra stuff as well, but I didn't take my disappointment to Mr. B. What I did was to Google STEP papers.

Damn- I shouldn't have done that. They were darn difficult and so once again I felt that fear. This time I had a worse confidence crisis. I felt that how the heck did I imagine that I could do a maths degree when I can't do much of the STEP paper! I possibly spent far too long- breathing in the fear - but it was alive. It was frightening. Eventually I saw sense and decided not to worry about my inability to do the questions, but to concentrate on passing my A levels. However I did sometimes try to do a question here or there- the fear hanging close by. This time round I made plans to do STEP papers during the summer holidays, after my exams. Hence, once again I began feeling slightly positive about things. I had something to look forward to, having banished STEP stuff till the summer holidays.

You see thankfully this mathematical fear, has always in the end turned into positivity for me. For it gives me a hope that one day I'll be able to understand and do certain things. This is what has ultimately been the key. The 'one day' thing has been vital, since it has allowed me to keep the here and now different from the then. I am pretty easily distracted and so throughout my education I believe it was necessary for me to separate things. The editorial mentioned the unrelenting fear of exams which follows us students. I think it's a shame that one has to 'not do' something, because of having to pass exams. Such immense pressure is on us to pass, that it's hard for students to actually think or consider other things. As soon as one feels they're 'straying' they pull themselves back to the here and now.

What do exam results actually tell you about a person? I mean they are an indication to what? I'm not trying to devalue peoples achievements, for I have been delighted at some of my results for it's like scoring a goal. Is that what it should be like? A student may be able to pass an exam without actually having understood the concepts too well. However another student who might have full understanding but poor exam technique doesn't do too well. This is where oral examinations are a plus. I think I'd probably do badly in an oral examination and so I'm cautious of what I'm trying to say. But I think it is indeed sad that in students focus to pass exams they sometimes ignore or cast aside the beauty of their subject. I did that myself, however I thankfully had the hope that after my exams I'll tackle what I didn't. Oral exams benefits have been discussed in the comments to the page I linked. I think oral exams should be (re)introduced for they really do test whether or not someone understands a concept. I mean make it fifty percent written and fifty percent oral, but I think this will make a lot of difference in how much students actually understand. Then last minute revision will be impossible! Maybe not, but oral exams really will be able to determine whether you've learnt stuff or understood it.

I'm trying to say that maybe oral exams might eradicate the 'fear' of passing- the fear of failing.

Before I move along, I felt this mathematical fear for a third time. It was when, after having been offered a place at Manchester, I decided to see what I could do in the holidays to prepare myself for university. I must confess, I see other students nowadays in year 13 who are much more mathematically informed than me. Even during my first year, V had done much more maths than myself and had even heard of books like Fermat's Last Theorem and read them as well! I was pretty damn ignorant of the maths world outside of my A levels. This is my own fault since I tended to banish everything 'hard or un-doable(!)' outside my bubble, in risk of it interfering with my studies. My love for maths was what carried me through, and that hope that one day the complex stuff will be something which I'll be able to understand.

I do sometimes wonder whether or not I should regret not doing much 'reading around the subject'. I mean when I went onto the Manchester site and found course units for first years, and looked at the exam paper I really did worry. I remember it so clearly, since I now understand the stuff which generated so much fear within me at the time. (It was statements!). My initial reaction had been what the heck has that go to do with maths! I had quickly closed the file and once again, the same chain of events came to pass. 'I'll cross that bridge when I come to it' or so I told myself. I concluded that all I could do in preparation for university was to make sure I knew all my A level pure maths stuff. I probably didn't have the right guidance in college, because I really was ignorant to the maths world which I have now discovered. The reason I don't regret my ignorance is because I have learnt a lot from that experience. Had I let my two worlds overlap i.e. the banished one and current one, then I might have lost sight of things. I don't really know. Maybe I would have become too scared of doing a maths degree then, whereas now I enthusiastically look to read more books and learn more about maths.

I have realised that my banished world and current world overlapped in my second semester. This signalled the start of my 'obsession' for maths, and it may have been the reason why I slightly messed up my second semester studies. I wanted to learn about all sorts of other things which I encountered on either other blogs or other maths site. Obviously that's not possible, unless considerable time is devoted. Did I just say time! Yep- maybe I should have spent more time on Linear Algebra, but alas my exams results will answer that question for me.

So, I believe that the mathematical fear helps me- more importantly the way my brain attempts to overcome it helps me. Impossible is nothing, as the Adidas adverts claim! I'm glad that this fear has got me this far. I still do feel it now, when I come across alien things, and I always banish it first, but hopefully I'll be able to balance this overlap. Something about wanting the cookie and the glass of milk springs to mind, but I'll take care to take small bites!

The piece of paper with our results, gives us so much having also destroyed so much. The fear of failure is also a result of expectation as well. What can we achieve without this piece of paper?

EDIT: The editorial also mentioned this,

Despite their higher attainments at GCSE, it turns out that girls are significantly underrepresented in the group that do A-level Mathematics (in the case of Further Mathematics the situation is even worse). I wonder, in a climate where success is all and fear of failure is so strong, could this mismatch between the sexes be accounted for by looking at the different attitudes that males and females might have to risk?

I think the last point is indeed a very interesting point. Looking at one of my school friends, who got great marks in her GCSEs, the one reason she chose not to do a maths a level was because she didn't consider it a safe choice. She knew that she could get, say an A in history, but she wasn't sure about maths. Whereas AJ, he didn't really consider what grade he would get, he just chose it! Food for thought indeed.

*For those who are (hopefully) waiting for pictures of my wall, I'm sorry but am having troubles trying to compress the video. Maybe at 3am I'll be posting them! :o

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