5 Methods for Studying Mathematics

[jamonwindeyer]

Let’s face it, studying for math is much less enjoyable than many other things you’d prefer to be doing on a Wednesday night. And this is even more especially true when you realise, after 3 hours work slaving away under the dim lights of your desk, that absolutely nothing has sunk in. In fact, your pretty sure you just forgot how to subtract anything at all. Bloody fantastic.

Now I love my math, so I was never overly mortified when “STUDY TIME: MATH” popped up in my Reminder List. But I totally get it: Studying for math can suck. It can be discouraging and very boring. If you and maths study have a hate-hate relationship, then obviously, you want to study as little as possible. Maximum gain for minimum pain.

This guide contains my favourite 5 methods for efficient, effective and powerful study of any level of HC Mathematics. They are all very different, and aim to break the repetitiveness of doing questions from a textbook with no end goal. I used them all at one point or another, and I stand by each of them as super useful. Use them in conjunction with a regular dose of good old fashioned practice.

Method 1: The Teacher
Best For: Weekly Revision

As soon as possible after your lesson with a new concept, sit in front of your Webcam (or record your voice on your phone). Record yourself giving a 2-minute explanation of what you have just learned. You can use your notes, but the idea of this exercise is to capitalise on that first couple of hours after a lesson when your like, “Oh I totally understand that.” Capturing that moment has two benefits: 1 – You immediately re-enforce the concepts, and you remember 75% of what you teach! 2- You now have a handy, quick resource to refer to as a refresher.

Method 2: The Race
Best For: Improving Speed

Find yourself a chapter in your textbook (erg, sorry, no more textbook stuff after this I promise) with a lot of very quick, very easy questions. Put 5 minutes on the clock, and race through as many as you can. These should be questions which take 3 lines max and focus on one specific skill: factorisations, surds questions, derivatives, indefinite integrals, simplifications, probabilities, etc. Keep a record of how many you got correct, then come back in a fortnight and try and beat it. This is an awesome way to polish up basic skills pivotal to the course: It’s like the grown up version of repeating your times tables.

Method 3: The Scholar
Best For: Pre-TRIAL/Pre-HSC Study

Find yourself a past Mathematics paper (preferably HSC/Trial papers). You are going to time yourself for 15 minutes, and in this 15 minutes, you have one job. Read the paper thoroughly, and try and roughly do the questions in your head. Not calculations, but the process. Just looking at a paper full of questions and provoking your brain to remember how to tackle them is an extremely beneficial exercise. However, it has an added benefit. Mark questions that you can’t do with a highlighter (be honest with yourself, otherwise this isn’t effective). These questions are your study for the evening. This is awesome because you know you are doing questions which will actually improve your HSC results, because you are specifically addressing your trouble areas.

Method 4: The River
Best For: Formula Memorization

Get it? The river? DE-RIVER? Never mind…

2 Unit students now receive a reference/formula sheet for their exams. I can have an argument about how this is bringing HSC Math even further below the level of University Math on another day, but at the moment my main gripe is this: I bet teachers are going to stop deriving formulas now!

Deriving formulas is, without a doubt, my favourite way to remember them. What better way to remember (and further, understand) Newton’s method than to recreate the logic of the man himself!

To remember tricky formulas, derive them. Seriously, it works a charm. Experiment with definitions and do some rearranging to arrive at the new result. Some are quite difficult, in this case, be sure to jump on the forums and ask for a hand! I’ve said it before, I love derivations.

Method 5: The Scientist
Best For: Problem Solving Practice

This method is primarily useful for topics with real world applications (probability and calculus, but also sequences/series, algebraic techniques, etc)

Take something you see in real life, and try and examine it mathematically. A few examples I actually did at my desk after getting home of an evening:

-   What are the odds of getting a royal flush in a game of Texas Hold Em?
-   How long would it take me to save for a new car with a certain interest rate/deposit amount?
-   How much force would a skydiver hit the ground with after jumping out of a plane (a bit of Physics involved with that one, but you get the point)

You’d be surprised how much easier something sinks in when it has tangible applications to what is in front of you. Further, it gives you practice of essential problem solving skills, super handy for those 5 markers at the end of your paper.
 
So that’s my 5 effective (and different) methods of studying for Math? Do you have any more? Post your favourite methods below (strange names are optional). I've attached my tips in a fancy document below, print it and stick it to your desk!

To post your study method, make an ATAR Notes account here. Happy study! 

[conic curve]

Hey Jamon

Do you think it important to focus on specfic weaknesses in maths and for every question you struggle with, try to understand the underlying theory behind the question (for questions you struggle with)?

[brenden]

Hey Jamon

Do you think it important to focus on specfic weaknesses in maths and for every question you struggle with, try to understand the underlying theory behind the question (for questions you struggle with)?

Hey Conic... From an economics perspective, this is exactly what you should be doing. This is surrounding the concept of 'declining marginal utility' - if you're bad at something, putting in some work can give you good improvements. If you're great at something, the same amount of work won't give you that much improvement... because you're already great at it.

Think of it this way: if you give $50 to someone who is a millionaire, they don't care that much.

If you give $50 to a homeless person who is starving and begging for change in Woolworths, then you will make big changes to his happiness.

In this scenario, the questsion you're bad at = the person in need. $50 = your study. The millionaire = questions you're good at.

It's only natural that giving effort to what you're bad at will have the biggest impact on your final grade.

And, of course, it's almost important to understand the underlying theory behind maths questions if you're struggling with them. - that's what makes it easier

[conic curve]

Hey Conic... From an economics perspective, this is exactly what you should be doing. This is surrounding the concept of 'declining marginal utility' - if you're bad at something, putting in some work can give you good improvements. If you're great at something, the same amount of work won't give you that much improvement... because you're already great at it.

Think of it this way: if you give $50 to someone who is a millionaire, they don't care that much.

If you give $50 to a homeless person who is starving and begging for change in Woolworths, then you will make big changes to his happiness.

In this scenario, the questsion you're bad at = the person in need. $50 = your study. The millionaire = questions you're good at.

It's only natural that giving effort to what you're bad at will have the biggest impact on your final grade.

And, of course, it's almost important to understand the underlying theory behind maths questions if you're struggling with them. - that's what makes it easier

This is such a great explanation. Thanks so much Brendan. You are awesome 

[brenden]

This is such a great explanation. Thanks so much Brendan. You are awesome 

No worries!

[CinnamonTea]

I think I read it somewhere, maybe here from ATAR notes lol, is to create acronyms
SURD-
S for signs
U for units
R for rationalise
D for does it make sense?

[jamonwindeyer]

I think I read it somewhere, maybe here from ATAR notes lol, is to create acronyms
SURD-
S for signs
U for units
R for rationalise
D for does it make sense?

That's my acronym (or at least I'd never seen it written online before I wrote it on here), so I think that's us!! 

[jazza47]

For me, and lots of other people i have talked to, the best way to study for mathematic exams is to do LOTS of practice papers!! Other subjects you can do notes, etc, but for maths especially PRACTICE PAPERS ARE THE ANSWER...

Hope this helps 

[RuiAce]

For me, and lots of other people i have talked to, the best way to study for mathematic exams is to do LOTS of practice papers!! Other subjects you can do notes, etc, but for maths especially PRACTICE PAPERS ARE THE ANSWER...

Hope this helps 

I'm pretty sure 100% of the people on this forum will agree there

Scanning this post I reckon most of what Jamon said relates back to before trials and HSC, i.e. throughout the year

[conic curve]

Personally I think the best way to studying in maths are past papers (obviously). Also  learn from your mistakes and understand the underlying theory behind the questions which you struggled with

Try to focus more on the harder/question and topics (if you're strong with the basics)

[olivercutbill]

>Method 1: The Teacher

This is great actually

[jamonwindeyer]

>Method 1: The Teacher

This is great actually

Glad you like it! My favourite of the list I've fallen out of using it at uni though, I really should try and get back into routine

[lozil]

I have a big problem with stupid mistakes - often losing 10 or 15 marks to them... Any tips on minimising these mistakes? Apart from do lots of practice :p

[jamonwindeyer]

I have a big problem with stupid mistakes - often losing 10 or 15 marks to them... Any tips on minimising these mistakes? Apart from do lots of practice :p

You nail it when you say that practice is your best bet. Method 2 in the list above might be beneficial for you, doing lots of more "basic calculations" like simple derivatives, factorisations, integrals (etc) to really get the hang of the simple things. Besides this, how is your time management in exams? Do you find yourself rushing? That definitely won't help the prevalence of silly errors

[lozil]

You nail it when you say that practice is your best bet. Method 2 in the list above might be beneficial for you, doing lots of more "basic calculations" like simple derivatives, factorisations, integrals (etc) to really get the hang of the simple things. Besides this, how is your time management in exams? Do you find yourself rushing? That definitely won't help the prevalence of silly errors

Yeah, my time management isn't too bad... I think a big thing is maintaining focus for three hours (while kind of rushing because you need to keep on top of time)