How to deepen my understanding of Maths?

Heya I've been doing some MAT questions and although I get the answers right I struggle to convice myself I'm right and struggle to understand the questions.
If you have any resources or ideas let me know :smile:

Or any other interesting maths articles. Thanks!

Reply 1

mqb2766

Original post by shaw867

Or any other interesting maths articles. Thanks!

Probably a bit of a general question to really give specific advice, but the usual way to improve your understanding is to do harder questions (step 1 or some ukmt or ...) and read around the topic a bit so you get the context, proofs, .... So the old "train hard, fight easy". If you want some material, it would help to say what youre using and topics youre interested in.

To validate answers, the usual ways are to practice to guestimate solutions or work backwards or see if you can solve problems in more than one way. Though as before, it depends on the topic and whether youre talking about the multiple choice or longer questions.

Its probably worth noting that the mat is changing a bit so more multiple choice and only 2 longer questions (if I remember correctly).

(edited 2 months ago)

Reply 2

tonyiptony

The litmus test for me is if I could explain, in words and with little mathspeak, what the question is trying to ask and the strategy you've adopted to solve the problem. Which means I often speak out loud to thin air - perhaps a trait of a weirdo, but necessary.

To put it anecdotally, I like to approach understanding maths (or anything, really) as if I'm a storyteller, except the story here is perhaps a bit technical, and your audience is perhaps a smart 5 year old who's quick to understand things but lacking the base knowledge.

Though I should stress that there are always methods that are so mechanical that the ability to execute trumps understanding. For instance, knowing how to apply cosine rule is much more important than understanding why cosine rule works. This can only come from repeatedly doing questions over and over to build up muscle memory. In fact, that's my philosophy when it comes to learning stuff - know how to do the thing first, then comes understanding, then comes storytelling. It's perfectly fine to do stuff that you aren't entirely sure what's happening - give it time.