It's funny, but I noticed this week, that I have discovered some new and surprisingly subtle things about functions and other bits of maths, that I thought I had previously known, very well.
I can't quite put my finger on it, but in the last few days, as I have been working through the first week of M208 unit 1, book 1, repeatedly drawing graphs of different functions and combinations of functions; or just sitting with a pencil and thinking about why the parametric equations are constructed, as they are; I have found my brain making subtle but important connections between bits of maths knowledge, that I had stored away from previous months or years.
The outcome? Well, I am starting to realise that learning and using maths, is not just about learning a stack of techniques and theorems; but it can actually be understood conceptually and at a depth of understanding, that allows one to look at a problem and actually know what it is asking and how to approach an answer, without rote learning.
Why am I having this minor epiphany 3/4 of the way through week one? Well, I think it is because, for the first time ever in my study journey; when I haven't been working, eating or sleeping; I have managed to spend every spare minute of each day this week, pondering or doing mathematics in an almost manic and intense manner.
Why the intensity? I think it is because of the exam at the end of the course and a mild state of panic that is motivating me to do mathematics, rather than read, go to the pub or watch television.
What has surprised me, is that this has actually been one of the most pleasurable experiences in my maths journey, to date.
It hasn't been a slog. It hasn't been a chore. And most importantly, by doing many multiple sessions of 10 - 30 mins of study and exercises, I have been able to take advantage of how the memory seems to retain information best; i.e. little, often and with great intensity.
What could possibly go wrong :-)
You have made an interesting observation.
ReplyDeleteI recently found the Khan Academy and started to study Mathematics again (haven't studied Mathematics for 30 years). The videos are usually about 10 minutes in length, and I find that I can retain a lot of the information. Mathematics was not so interesting or understandable at School...!
I took M208 2 years ago. I also found the attention to theoretical detail very enlightening. It was the first time I had read anywhere in detail what is meant by a function, what is meant by a mapping or what a group is. I liken the experience to 'knowing' what a word means from it's context and then one day reading it's true definition in a dictionary, sometimes the two do not marry precisely and a new more intricate understanding can be forged from the process. Also intense concentration without interruption is for me the best way of deep learning. Especially if you go to bed thinking about the subject. Good luck with your goal, it is mine as well, I start on the M823 this year...
ReplyDeleteI know exactly what you mean Marcus. I don't know about you, but I never thought that I would start to understand maths enough, to see those subtle connections.
ReplyDeleteIs it an Oct 2012 start for you and M823?