[Advice Column] An error in recognising errors

Don't tell me you have never done this before: you do a question from the textbook, flip to the page with your ruler bookmarking the page with the final answer, and panic when seeing that what you have in front of you is nowhere close to what is printed on the page. 

A lot of (usually negative) thoughts go through your mind: am I actually useless at this? Why is this making no sense? I don't understand the answer (the most popular one by far!) or just shouting that the textbook is wrong (usually when referring to you-know-what) and storming out of the room to throw the vase at the wall.

Alright kiddos, blow off some steam, sit down and listen up. Not knowing why you make an error is fine, feel free to ask your friendly helpers or your teachers, but after a while you’ll start to notice the difference between arithmetic errors and conceptual errors.

Let’s break each of them down.

Arithmetic errors

You know my favourite identity 3^2 = 9 = 2^3? In other terms, maths at midnight usually never follows normal rational mathematical conventions. Maybe you miscopied the step right above because you couldn’t follow your own logic.

Problem: Both of them show that you’re running out of working memory capacity and there’s nothing much to worry about. (About the latter though, it’ll bite you when you go to uni, so take the time to do it the right way now. Just sayin’.)

Solution: do more questions. Same logic as always: the more questions you do, the more automated the basic steps are to you, the more space you have in your working memory to take care of the non-essential elements (missing a negative between lines, 2^3 = 9 = 3^2, making sure your work is not like a kiddo trying to do his homework on the bus to school) and you should be able to get the correct answer quite easily.

 

Basic mathematical errors

If you find yourself tempting (or actually doing) incorrect algebra or trigonometry, it’s both a problem of overloading your working memory but also of misconceptions still flying in your head.

Examples: sin(2x) = sin2 * sin(x), sin(x + 2) = sin(x) + sin(2), x + 4(x+2) = x^2 + 6x + 8.

This requires immediate attention. Really. Before they start burning all the marks you’ve been revising for. Go back, relearn the content properly and know that you are not allowed to perform illegal algebra and trigonometry. Nothing is more frustrating to markers (and you, by extension) when seeing a perfectly answered question is totally ruined by some basic errors. We’re forced to put a fat line over your work and give a 0. Really hurts from inside because we’re nice people and we want to give you all the marks if you know your shit.

 

Conceptual errors

Now we’re finally here. If you’ve taken a look at your work and realise that the part is messing you up is the content you’re working on, this is the right place. If you have spent some time digesting the examples and the questions are relatively well sequenced, I don’t think you’ll end up in this territory.

 

Problem: you don’t really understand the concept at the level the question is demanding.

Solution: go back to the examples and read them line by line. Ask yourself “why did they do this?” for every single step in the working out, from the first to the last example. The questions in the problem set are designed to be doable with the knowledge you’ve gained from the examples.

Being good at maths is not a coincidence y’all. Like everything, hard, deliberate work is required to be successful. But if you know how to criticise your own piece of work using the method I showed you, you’ll develop the ability to learn new science/maths concepts yourself. Knowing the line between not knowing the concept vs everything in the background will help building your confidence over time.

 

BREAKING NEWS

I know N22s and some strong M23 mathematicians are waiting for this.

Mocks for N22 will take place sometime between the last week of September and the first week of October. Allowing two weeks for marking, this should give you some time to prep for maths after learning from your mistakes on the mock.

M23s, if you have not covered the entire syllabus I’d recommend not taking the mock this season. Save these papers for later, as all mock examinations and MS will be uploaded to the mocks server after the marks are released.

Over the next few weeks, I’ll release the Survival Papers, targeting at grades 3-4 students. They are not the same as the Booster Papers, which are essentially same format as the real exam but slightly easier than the mocks.

 

I hope at least one of you finds what I’m posting useful. C:

 

Have fun revisin’ maths,

 

Andrew