Having been around in the O.U universe for almost 10yrs, I have come across two distinct sets of students. There are those that see TMA's as a necessary evil; just one more thing to make you pull your hair out, when the deadline looms and you have the other pressures of life, competing for your time. But there is also the second set (to which I belong), that started out as TMA haters, but after completing a few of them, realised just how much learning actually comes from doing some mathematics, that requires you to properly apply what you have tried to learn, in the preceding weeks.
I believe, that TMA's are a vital and indispensable way, of forcing you to delve deeply into the mathematics, for a level of understanding that you just don't get from practising a few example questions. Now, you may have read the forum posts or looked at the course student reviews, and seen comments such as 'TMA's are formulaic', 'the TMA's were not really challenging', or even, 'the TMA's were a pain in the backside'.
But, reading these comments, you could easily be misled.
From my own perspective, as part of my experiment to learn maths and physics through distance learning and self-study; I have discovered, that no matter how much I apply myself to a particular area of study; I do not seem to obtain such a thorough understanding of it, unless it is tested via a TMA or other piece of coursework.
Exams, are different. I mean, they tend to be the 'lite' version of a TMA; lots of lighter questions to test general understanding and recall of methods and mathematical concepts. But, by its very nature, an exam can't dwell too much on one particular topic and in any great depth. Otherwise, they would have to be more than 3hrs long.
It is TMA's and other marked pieces of coursework, that quite often force you to re-read a unit. Back and forth, dipping in and out of pages, over many hours. Checking and re-checking answers. 'Did I calculate that accurately?', 'Why doesn't the answer look right?'. Sometimes going over a paragraph in a Unit, line by line, word by word.
It is this type of study, that allows you to have those 'aha!' moments, when you finally come face to face with what the mathematics is trying to say. Having said that; the only way to have this type of learning experience when completing a TMA, is to leave yourself the time to do it justice. I have, on previous courses, sometimes left myself with too little time for completing a TMA; only to resent its completion and gain no learning or pleasure from it, whatever.
It is therefore very important, to leave plenty of time for completing a TMA. I often try to allocate the whole 16 - 20hrs of one week, dedicated to its completion. I also often find, that if I am short of study time and my reading of a unit has fallen behind; it is often a better use of time, to stop trying to catch up with the unit and actually start the TMA. You can then catch up with the reading, as part of your research into formulating your answers on the relevant TMA questions.
I 'heart' TMA's; although I know there are those that would disagree!
Friday, 27 January 2012
Tuesday, 24 January 2012
M208, TMA01 Part 1, Completed.
Having had a good head start on the study materials of M208, I have now managed to complete the first part of the TMA01. It comprises of a relatively (deceptively?) straight forward exercise in sketching graphs.
This TMA covers the first intro book, and with the Unit book exercises possibly being more complex than what was required for the TMA, it hasn't quite scared me off from M208, just yet.
This is both good and bad. Good, because it is a bit of a confidence booster, before heading into group theory. Bad, because it only scratches the surface of some of the more complex graph sketching (combination and hyperbolic functions: I'm looking at you!), that is contained within the first unit.
I am not complaining though. After a week of struggling with equivalence classes, it made a change to actually have a vague idea of what I am doing.
All that it about to change, as part 2 of TMA01, hits all the difficult bits of the intro units. I plan to start that TMA, tomorrow. I am not sending my first TMA off to my tutor, just yet. I plan to attend the day school which is themed (graph sketching); as I don't want to drop any clangers.
From bitter experience, I know that tutors have their own styles of marking and their own vision of what they like to see, in each TMA. Once I get a feel for what my tutor wants in each TMA; I'll check that my first effort ticks all those boxes, before sending it in (about the 5th Feb should do it).
This TMA covers the first intro book, and with the Unit book exercises possibly being more complex than what was required for the TMA, it hasn't quite scared me off from M208, just yet.
This is both good and bad. Good, because it is a bit of a confidence booster, before heading into group theory. Bad, because it only scratches the surface of some of the more complex graph sketching (combination and hyperbolic functions: I'm looking at you!), that is contained within the first unit.
I am not complaining though. After a week of struggling with equivalence classes, it made a change to actually have a vague idea of what I am doing.
All that it about to change, as part 2 of TMA01, hits all the difficult bits of the intro units. I plan to start that TMA, tomorrow. I am not sending my first TMA off to my tutor, just yet. I plan to attend the day school which is themed (graph sketching); as I don't want to drop any clangers.
From bitter experience, I know that tutors have their own styles of marking and their own vision of what they like to see, in each TMA. Once I get a feel for what my tutor wants in each TMA; I'll check that my first effort ticks all those boxes, before sending it in (about the 5th Feb should do it).
Saturday, 21 January 2012
Rigorous Mathematics: A Disturbance in the Force
I think that it would be very dangerous to underestimate the 'introduction' part of the Open University course M208 Pure Mathematics. The intro consist of 3 books which cover the required knowledge, that you are expected to have under your belt; before embarking on the course.
It covers logic, set theory, functions, complex and modular arithmetic and is a sudden and violent introduction to a level of rigour, that you tend to only get at a Funeral home. I have found, coming straight off of the back of MST121 Using Mathematics, that there are some gaps in my knowledge base. They are little things that the course never really taught; Including the rigour that is required, to answer even the simplest of example questions on M208.
What has been a shock to me, and has been by far the most difficult part of the last 3 weeks of study; has been the way that you are required to explain results, that seem so bloody obvious. You can quickly get confused and muddled, trying to explain something that is ostensibly so simple, in such formal terms.
As an example, I struggled for hours, trying to prove that set A was contained in set B and set B was contained in set A. When I first looked at the question, I instantly knew what the correct answer was, and why it was so. But could I explain it in the convoluted mathematical way, required in the model answer? Could I hell. I have literally had to rote learn the structure of some of those phrases that seem to crop up, including those charming "hence's" and "therefore's".
It reminds me of the time that I learned to speak French. It took forever to get used to the way that a sentence was structured, and it took much practise to learn and then repeat those structures. The only problem is; that I have worked myself silly for the last 3 weeks and yet I am not quite confident,. that I can produce any good, exam style answers, from previously unseen questions.
It has been thoroughly enjoyable so far, but really quite taxing. It feels like I need to do 30hrs a week, not 15-20hrs, before I can gain that confidence, that I am seeking. I do think, though, that once I am used to the rigour; things will settle down and the 'newness' will not be causing such a disturbance within the force.
On the bright side, I now have a tutor and a set of 5hr day schools at Aston University on Saturday mornings. I am hoping that some tutor input, will allow me to shave some fat off my study regime and allow me to revise what I need for the exam, without any superfluous bits added on. This should help me settle down and gain some confidence as the months progress.
It covers logic, set theory, functions, complex and modular arithmetic and is a sudden and violent introduction to a level of rigour, that you tend to only get at a Funeral home. I have found, coming straight off of the back of MST121 Using Mathematics, that there are some gaps in my knowledge base. They are little things that the course never really taught; Including the rigour that is required, to answer even the simplest of example questions on M208.
What has been a shock to me, and has been by far the most difficult part of the last 3 weeks of study; has been the way that you are required to explain results, that seem so bloody obvious. You can quickly get confused and muddled, trying to explain something that is ostensibly so simple, in such formal terms.
As an example, I struggled for hours, trying to prove that set A was contained in set B and set B was contained in set A. When I first looked at the question, I instantly knew what the correct answer was, and why it was so. But could I explain it in the convoluted mathematical way, required in the model answer? Could I hell. I have literally had to rote learn the structure of some of those phrases that seem to crop up, including those charming "hence's" and "therefore's".
It reminds me of the time that I learned to speak French. It took forever to get used to the way that a sentence was structured, and it took much practise to learn and then repeat those structures. The only problem is; that I have worked myself silly for the last 3 weeks and yet I am not quite confident,. that I can produce any good, exam style answers, from previously unseen questions.
It has been thoroughly enjoyable so far, but really quite taxing. It feels like I need to do 30hrs a week, not 15-20hrs, before I can gain that confidence, that I am seeking. I do think, though, that once I am used to the rigour; things will settle down and the 'newness' will not be causing such a disturbance within the force.
On the bright side, I now have a tutor and a set of 5hr day schools at Aston University on Saturday mornings. I am hoping that some tutor input, will allow me to shave some fat off my study regime and allow me to revise what I need for the exam, without any superfluous bits added on. This should help me settle down and gain some confidence as the months progress.
Wednesday, 18 January 2012
Complexity, Clocks and Study Time.
For those familiar with M208, they will probably guess from the title of this post, that I am in the midst of studying I3 (Number systems). Specifically Complex numbers and Modular arithmetic.
It has been an interesting week, as coming off of the back of a good 2 weeks studying of Functions and Graphs and Mathematical language units I1 and I2; I am already starting to try and guess, which parts I will need to know perfectly, to make the exam easier in October.
With these units, there seems to be a theme whereby, the study material starts off with basic concepts, before descending into some crazy depth involving some nasty looking proofs, that will probably be extensively tested in the TMA's, but perhaps not so deeply in the exam. They are the sort of proofs that you can imagine took some poor mathematician, a life's work to figure out. So, I won't be too hard on my self, for not learning the proofs back to front in approximately 15 - 20hrs of weekly study. However, I am taking extra care, to ensure that I can follow the exercises in each sub-unit, that tests the use of such proofs in a practical question.
I did get a little bogged down this week in the middle of the complex numbers sub unit. I got muddled up when trying to work out other arguments of complex numbers, when given just Z^n = a
It's not that I don't understand the maths; I fully understood it at first reading. It is more that, following through a relatively complicated set of processes, to arrive at an answer, contains its own pitfalls when one is studying it late at night, after a busy day at work. I have just about got the hang of doing questions on this topic now; but, it has eaten into nearly 1/2 of my allotted study time this week. That has not left me much time to conquer clock arithmetic and equivalences; or to do another quick revision of I1 and I2.
I have obtained copies of all of the previous M208 exam papers since 2006, with some example solutions as well. It is comforting to see, that they all seem to follow the same pattern, with a high probability of certain questions or topics, being given their own question space. These include, manipulating some complex numbers to find the Argument, drawing some graphs and labelling correctly, some equivalence work and also doing a basic proof based on a logical statement about some numbers.
It does give one a little bit of hope, that the exam almost looks doable and certainly written to be passed by those that put in some work. Fingers crossed.
It has been an interesting week, as coming off of the back of a good 2 weeks studying of Functions and Graphs and Mathematical language units I1 and I2; I am already starting to try and guess, which parts I will need to know perfectly, to make the exam easier in October.
With these units, there seems to be a theme whereby, the study material starts off with basic concepts, before descending into some crazy depth involving some nasty looking proofs, that will probably be extensively tested in the TMA's, but perhaps not so deeply in the exam. They are the sort of proofs that you can imagine took some poor mathematician, a life's work to figure out. So, I won't be too hard on my self, for not learning the proofs back to front in approximately 15 - 20hrs of weekly study. However, I am taking extra care, to ensure that I can follow the exercises in each sub-unit, that tests the use of such proofs in a practical question.
I did get a little bogged down this week in the middle of the complex numbers sub unit. I got muddled up when trying to work out other arguments of complex numbers, when given just Z^n = a
It's not that I don't understand the maths; I fully understood it at first reading. It is more that, following through a relatively complicated set of processes, to arrive at an answer, contains its own pitfalls when one is studying it late at night, after a busy day at work. I have just about got the hang of doing questions on this topic now; but, it has eaten into nearly 1/2 of my allotted study time this week. That has not left me much time to conquer clock arithmetic and equivalences; or to do another quick revision of I1 and I2.
I have obtained copies of all of the previous M208 exam papers since 2006, with some example solutions as well. It is comforting to see, that they all seem to follow the same pattern, with a high probability of certain questions or topics, being given their own question space. These include, manipulating some complex numbers to find the Argument, drawing some graphs and labelling correctly, some equivalence work and also doing a basic proof based on a logical statement about some numbers.
It does give one a little bit of hope, that the exam almost looks doable and certainly written to be passed by those that put in some work. Fingers crossed.
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