MST121, Passed!

I received my final result today, for MST121 Using Mathematics and I am thrilled to be able to say that I have passed.  I received 96% for the final piece of course work TMA04 and 82% for the CMA, giving an overall combined course result of 93%.  I plan a critical review of the course content in MST121, in the next few weeks!

So, now I can start to relax properly into my exam prep for M208 Pure Mathematics.  However, I received some bitter-sweet news yesterday when I found out that the Open University have now confirmed some course changes for the next two years, which affect me greatly.

The first of these, is that they have now postponed presentation of the new course M303 Further Pure Maths until October 2014.

This means that I can no longer realistically take that course, without extending my studies by a redundant year.  Now, the OU have countered this by stating that they will provide an additional presentation of the course M381 Number Theory and Mathematical Logic, which will actually allow me to take that course.

This is pleasing, as I do have a hankering for Godel's Proof which forms part of that course material.  I will now also need to take the separate course M336, Groups and Geometry, again a good course that I am looking forward to studying.  The only downside with these courses is that it will cost slightly more money to do two separate courses and will mean two 3hr exams instead of one.

But the real pain in the backside of all this is M338 Topology.  By not doing M303, I will miss some important Topological material, and the O.U's Topology course is in its last presentation in Feb 2012, which I am not ready to take.  So, It leaves a gap in my studies with the O.U.

I don't know how much of a profile gap that will leave, and whether I can successfully plug it by buying the Topology course and self-studying it.  We will have to see.

More on Dyslexia and Mathematics

I thought I would drop in another quick post about dyslexia and how it affects the assimilation of knowledge, and in this case, mathematics.  I have been researching the most up to date theories on the causes of dyslexia and how it affects learners.

One thing that I have known for a long time, being dyslexic myself, is that there are significant advantages to being dyslexic when carrying out certain tasks or roles.

For example, I find that I am able to work on manipulating 3D abstract objects, in my head; rotating them this way and that.  However, with  linear objects such as 2D graphs or some areas of algebra, I find no such advantage.

The ability to work in 3D can have nice advantages when doing certain elements of group theory and are wonderful when it comes to geometry in 3+ dimensions.  It has also helped the visualisation of the complex plane, when handling 'i', and its 'real' friends.

As part of my research, I have discovered that the latest neuroscience surrounding the root causes of dyslexia, gravitate towards the theory that a primary cause is found in the theories surrounding left and right brained thinking models.

I'll explain.  As children, we used our right-brain more than the left, to begin with.  The right brain area deals more in whole pictures and broad themes, able to get the gist of a subject or concept, but not with much detail.  The left brain, is where the detail is processed and the more linear and analytical side of ones approach to a task or subject, is generated.

As children become adults, the use of the brain hemispheres starts to even up and although most people will end up slightly biased towards either big picture / creative thinking or towards detailed analytical thought; most people will generally have a bit of both.

However, with most dyslexics, the brain doesn't seem to make the transition from right brained to left, all that well as they move towards adolesence.  This means that for a dyslexic, they can cope with the big picture and sometimes see connections where others do not.  They can handle tasks better in 3D, but will perhaps struggle with linear and fine detail tasks and working memory.

So where does maths fit into all of this?  Well, if a dyslexic was to play to their strengths when learning maths, they would firstly aim to learn the broad themes and structures of a unit or topic, then followed by work on the detailed mathematics underneath.  By working in this order, it allows a dyslexic to 'hang' all the detail from the broad branches that have been learned first, and provide structure to aid the retention of detail.

So is it impossible for a dyslexic to learn the finer details of maths sufficiently?  Well, no.  However, it takes a huge amount of effort to rote learn any mathematical facts, proofs or theorems, unless they can be pictured as part of the subject as a whole.

How does one do this?  Well, I am using mind mapping software to lay out the subject, unit by unit, into a large and explorable mind-map.  This is then followed by diligent study of the detail and exercises.  I don't know if such a system of learning would suit a non-dyslexic and I know that there are some of my non-dyslexic peers who prefer to work in algebraic terms rather than geometric pictures or models.

I guess we are all different but I see my dyslexia as an advantage.  I wouldn't quite go as far as one of my dyslexic friends, who described all non-dyslexics as 'Muggles'; but I think I understand where he is coming from, and perhaps for some types of maths, dyslexia is a gift rather than a hindrance.

Sometimes the simplest mathematics, is the most satisfying.

As I prepare for M208, Pure Mathematics, in January; I often take some wonderfully interesting and  short diversions into areas of simple maths skills.  These areas of interest include manipulating fractions or logarithms; messing about with inequalities or complex numbers; or simply factorising polynomials.

It can be very relaxing, something akin to doing Sudoko or crossword puzzles, glass of wine in hand.  However, it all has a serious purpose.  Whilst I suspect that there is less use for basic maths skills, as one approaches the dizzying heights of group theory etc.  I do still find, that being deft at the handling of numbers and formulas, is like having a big fluffy comfort blanket.

Perfect for those dark winter nights!

Mind-Genius and Mathematics

What I am really enjoying about my distance learning journey, is the fact that I am discovering new things about myself all the time.  I have been able to try out and eliminate, any unhelpful learning strategies, that don't help me to achieve my goals.

When I studied maths with the O.U, last academic year; I discovered that whilst I found the details and elements of the actual maths, relatively easy to handle, intellectually; I did find that I would struggle to remember set solution methods to problems and also I would also keep loosing track of how one bit of maths, fitted in with another.

This led to some wasted study time, having to revisit maths I had already examined, because I hadn't gained a holistic view of the subject.

Now, I have dyslexia.  And, the experts say, and I tend to agree with them, that dyslexics need to think in terms of connections, and that they learn more effectively, if they are able to 'hang' details from the branches of the whole subject.  That is, in order to keep track of the details and to learn them completely, we need to know the bigger picture, and how these details slot into that image.

One of the best ways for this to be done, is through the use of mindmaps, as developed by Tony Buzan many years ago.

However, the problem with mindmaps is that they can be a devil to produce.  This tends to mean that the creation of the map, can be a pain in the backside, that gets in the way of your study subject.

However, I have been trialling a piece of software called MindGenius 4, which is an important discovery for me, particularly as it fits my 'dyslexic' way of viewing the world.

I have enclosed a link for info purposes only, as I don't receive money for sending you there.  There are alternative mindmap software's that I have tried, but they aren't as easy to use, as this one.  I would encourage anyone to shop around and find what fits for them.

I won't bore you with the details, as anyone that is intrigued, can download a 30day trial for free and try it out.  But, it basically allows you to create mindmaps, as quick as you can type and press return.  It also collects and orders into mindmaps, any references and research material.  Thus, it is also useful for creating a thesis or essay.

What this has allowed me to do, is to split my study time and study focus, between three aspects.  These are; gaining a holistic view of a study unit, learning the detail and also doing example questions.  I have found that learning the whole before delving into the detail, has meant that by the time I come to do the detail, I have a solid grasp and good memory retention, of the subject matter in hand.

Just as an example to illustrate my method, is my study of M208, Intro block A:

1.  Mindmap created of the main subsection topics, including any definitions of theorems or other equations. (Time taken a very rapid, 1hr).

2.  Entire unit book scan read and all facts and sentences that need to be remembered or studied, are highlighted. (Again, a rapid 2hrs.  The art is not to get bogged down in the text; just keep moving and highlighting!)

3.  Review of the mindmap is now done for 10 minutes before each subsequent study period.

4.  Mindmap review followed by careful revision of the highlighted text (four periods of 2hrs each).

5.  Detailed review of the mindmap (1hr).

6.  Getting to grips with the example questions from the Unit.  The aim is to repeat all the examples until I can achieve 100% accuracy without referring to the answers.

All in all it should take me 14hrs per week, allowing another 2-4hrs for sticking points or units that are more taxing.

Simples!