[Advice Column] How I study maths
This is not the type of post that would tell you to open a textbook and absorb the knowledge like a sponge through osmosis, nor make you feel bad for not spending 2-3 hours a day doing maths. If anything, this is simply the way I study maths without too much suffering but still give me pretty decent results.
Find your own kindergarten
More often than not you might think that your teacher isn’t
as good as you want them to be, and then you keep talking about their failures
as a teacher. A better approach would be accepting that they won’t change their
teaching style, so in the mean time, you’re really better off looking for
another source that talks to your level. Doesn’t matter how easy the
society perceives it; if it works for you, it works.
Story time! When I was looking for resources to study
calculus 3, simple YouTube search brought me to Professor Leonard. He’s
straight to the point, but I found his content rather straightforward. It’s
totally understandable for the students he’s teaching, but I’d love to go a
little faster. A couple more google searches led me to Professor Butler. If
you’ve had unfortunately heard me going off about him, that’s because I found
his examples more engaging and challenging than Leonard’s.
But I have a different relationship with coding. I deliberately
chose one of the easiest books for intro Python, as I found the other books too
hard to wrap my head around. I don’t mind easier practice questions. You know
the motivation boost you get when you know you’ve grasped something even though
you barely scratched the surface? Many times, that’s enough motivation to keep
you going because you’re goin somewhere.
Everyone has their own cup of tea – know thyself and pick
the best path. The same thing can be said for choosing textbooks and questions.
I usually draw stuff from several sources with varying level of difficulty, and
depending on the attainment of the student I’d recommend the most appropriate
place, in my opinion, for them to practise.
Diagnose, learn, practise, practise, rinse and repeat
Four steps to success in virtually anything in life.
1) Diagnose
It’s tempting to jump straight into the content every time –
I definitely fell and still fall into this trap. Learning new stuff is exciting.
Revising old stuff, especially realising that you don’t really know your shit,
isn’t. But what’s the point in rushing through the content with a pretty
limited understanding of the course? It wouldn’t be long before you realise you
lack the foundation to even understand what the instructor is saying. As
the old sayin goes, “you can’t build on a shaking foundation”.
The tricky thing though: sometimes your lack of foundation
comes from the pre-high-school-stuff, which sounds sooooooooo far away, and you
don’t even know where to start. If you’re in this category, I highly
recommend talking to your teacher and/or other people who knows what they’re
doing about the next steps before it’s too late.
2) Learn
You really gotta engage with the content if you want it to
stick. Perhaps take notes during (not recommended) or after (good
choice) you read/watch the content. Pause when the person’s doing a second
example (if there are many) and have a shot at it yourself. More often than not
you’re not that far from the solution.
3) Practise
Practise popped up twice; this is intentional.
The first practise is simply practising the concept you’ve just studied.
Dos:
- find a textbook with a variety of question types and do a
couple questions from each type. A fair number of students have difficulties
with exam-style questions because they haven’t been exposed to a similar type
during practice.
- don’t do all the questions in one sitting – spread it over
several days. The forgetting curve at the initial stages is VERY steep, so actively
forcing your brain to recall how to do a question will improve your retrieval
strength.
4) More practise!
When you can get going with the newly acquired stuffs, it’s
time to put it to a test. Do a past paper or a question set that covers many
topics. You have to know when to use a certain method. Many students
complained that they don’t know what to do when they see a question and they
don’t even know how to start; to me it’s just a sign that you haven’t
practised properly. There’s no flashing sign on the exam “this is the product
rule, go get the formula from the booklet and slap it here!”; you have to know
when to and when not to use the method.
I don’t know if this is my original idea or Dr. Loveless’s
(here, I’d say most advice apply to y’all), but taking a quick look at
the paper and making a mental note (you could also write down on a postit note)
of how you’d tackle the question without spending too much time on the
details. If the third step is done right, you should be able to figure out
the details when you sit down and do the paper from cover to cover properly. Is
it the product rule, the quotient rule, the chain rule, implicit
differentiation or all of the above? Even harder when your brain has to keep
switching from stats to calculus to trigonometry to functions then back to some
tricky integrals.
Appendix: for those who are aiming for a 7
A couple months back I wrote a post on how I think grade 4
students should tackle the paper and it could be useful to some people when
they’re stuck at the grade 6/7 borderline.
1) You do not need to get all the marks for a 7.
Ideally, of course, you should shoot for the stars, but
realise that there’s a reasonable number of questions that you could miss.
However, this also means that you absolutely have to get the easy
questions correct, otherwise it’ll eat into the buffer the IB gives you.
2) Be extremely fluent at the basics
You need to have a solid understanding and fluency of all
topics. If you’re spending more than half of the allocated time for the easier
questions (first half of section A, 2/3 even, or most parts of section B), you
need to up your game. Period.
Do more questions until you cannot get it wrong. Keep
practising over and over again. Doesn’t matter if you’re doing the same paper
as long as you’ve had enough time to forget the specifics of the question. The
time you managed to save (without sacrificing accuracy, obviously) will
be handy when you’re solving the most demanding questions on the paper.
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