Victoria's maths curriculum sucks. It really does. Its mid-range year 12 maths course, 'Mathethematical Methods' (MM), also sucks. Big time. I don't mean that in a funny 'I'm referencing the fantastic HHGttG' kind of way. I mean it in an 'it sucks balls' kind of way. It's not that it teaches the wrong material per se - it seems to hit some of the right areas, although there are things (like geometry and linear algebra) which probably deserve more of a mention. It's the focus that sucks - too much emphasis is put on calculation and not enough on deep understanding of ideas.
It's not that this is impossible to test - all of the other subjects manage it, maths at university usually involves a lot of explanations and maths in general is all about expression (more on this later), so it doesn't seem like something that would be that out of place in an exam. It's just that it isn't being tested.
This leads to every single MM textbook (that I am yet to encounter) kowtowing to the needs of this terrible course design - instead of structuring a text to maximise understanding and THEN focussing on exams, most jump straight into 'exam style questions', which leads to problems that I will mention later. Some manage to avoid this particular mire (notably cambridge's text), but fall into other traps like focussing too much on algebraic manipulation over explanation of ideas in their question material. Also problematic. Also will be explained later.
This doesn't mean everything about every text is bad. All it means is that no textbook currently on the market actually has a reasonable structure for the teaching of maths for high school students. Which is ridiculous. There are good reasons for this, which I will undoubtedly outline later, but they are of little importance now.
What is of importance, though, is what's going to change. In response to this lack of quality in the textbook market, I plan to make the Towel. The Towel will be a year 12 MM textbook which aims to avoid these problems. It will be free, electronic, and available to anyone. It will be structured better, and as such it will help people of all ability levels do better. It will give insight into the reasons people actually study maths, and as such it will motivate people to do more maths. It will be awesome.
At least, that's the goal.
Why 'Towel'? For those who haven't read Douglas Adams' 'The Hitchhiker's Guide to the Galaxy, read it. It's fantastic. Anyway, in the book, every good hitchhiker knows where their towel is, with very good reason. Check out a good explanation here (incidentally, Towel Day is coming up on 25/5. Know where your towel is, people!). I reckon that this can and should be seen as a Towel for MM - indispensable for practical and psychological reasons. Or maybe a hitchhiker's guide, with DON'T PANIC on the front. I guess we'll see.
But back to our depressing reality. As a tutor, I am tired of struggling through lessons, having to jump around the textbook in the hope of finding a reasonable (or reasonably placed) diagram, explanation or proof. Most of the time none of these (except maybe a misplaced diagram) are there. I'm tired of the strange question order. I'm tired of a lack of interesting motivating examples. I'm tired of my students being overwhelmed by the vast number of questions without any semblence of a guide for optimal learning given limited time. So I have to remedy this. I have a plan for how exactly a new style of textbook can accomplish this, and I will post detail on that soon.
In the meantime, I want to note the purpose of this blog. From now on, I will be regularly posting what I tutor on here, for all to see. It will therefore be accessible to my students, obviously. The point of the blog is to have my work critiqued. At first the work will probably mainly be theory, but I intend to eventually start putting up questions to prompt further thought and deeper understanding on given bits of material. In essence, I want to make sure the Towel is user-friendly and actually does what it's made to do. But again, more on that later.
So. I will start posting on Saturday, spend a big chunk of my semester break filling in what was missed throughout the first half of this year, and get some semblence of a structure to both this blog and the Towel itself.
I want to have this project complete by the end of the year, for next year's year 12. This is a labour of love - I really see the potential for this to be a useful thing, and as such any help that anyone can give would be really appreciated. Let anyone you know who would be interested in contributing to a better MM text know about this project - tutors and teachers would be great, especially if they have really well-refined ways of teaching this stuff.
One other thing that would be fantastic is a large base of students of all ability and interest levels to critique this as it grows - please let people know about this! The thing is, everyone involved in MM has an interest in being involved in this project - even if you're in year 12 this year, you can benefit in many ways - from simply gaining a better understanding of the ideas through reading the posts to deepening that understanding by figuring out what is missing in my explanations (and of course relaying that on to me so that I can make the explanations more complete).
That's about it for now. Thanks in advanced people! Looking forward to this!
END CHAPTER 1
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