Hello Rui,
I wanted to know what you would do if you were on the verge of losing hope in getting better at maths. I've never experienced amazing success in maths so my persistence and motivation for the subject has become lower.
What do you believe would be a great way to make myself become more interested in the subject?
If you have any advice then please let me know 
Thanks,
Kind Regards
JerryMouse2019
Hey
The thing about maths is that success is generally highly influenced by how interested you are in it. And this seems to be a common problem across Australia as a whole really. For me, perhaps the two main things that saved me were:
- Having teachers that genuinely tried their hardest to look after the students.
- Enjoying patterns as a whole, which is pretty much the backbone of mathematics.
And very likely more. But these two seemed to stand out a lot.
The main things I feel that would detriment 'success' in maths are the following.
- Unfilled gaps from earlier work in maths.
- Ineffective teachers; inability to communicate the content well for reasons beyond that of the new QCE system. Or could also be because of inadequate attempt in making the subject area sufficiently interesting.
- Treating it as memorisation instead of problem solving.
- Not asking, or being given enough about the "why this works" or "why we do this" issues.
- Haven't seen enough real world applications of maths.
- Not enjoying problem solving/creative thinking as a whole. (Perfectly justifiable reason honestly, but still needs to be addressed.)
And in all honesty, there could be more reasons than this. But whatever they are, it's about identifying what has probably struck you the most. (Hint hint: That does mean you should take the time to think about it! Totally fine to not actually say out loud what they are if you feel uncomfortable about it, but at the very least think to yourself about it!)
See, no matter how hard you try, it's practically impossible to break out of the issue of demotivation without finding the cause. And without finding the cause, what can be done?
At the very least I'll expand on the above 6, and even then what I say for a completely unrelated point could still be of value anyhow. They're just things that I would advise as a starting point.
Unfilled gaps in learning are detrimental because they cascade. You can think of maths as building a brick wall. You miss one brick, you can no longer build onto it. That leaves 2 bricks that can't be placed on the next level up. Now build the next level. There are now 3 bricks missing. And the gaps just grow more and more over time.
Which means, perhaps unfortunately hurtfully (I mean, I'd be hurt by this), it's time to rewind. The foundations need to be solidified before continuing on. Earlier work will always transition into assumed knowledge the further you go along, and you need to be comfortable with it at the end of the day.
This is by no means an easy task, because at school they're only gonna give you more content. Which is why the only way this issue can be addressed is to be prompt. It requires jumping straight into the boring year 7 textbooks (and I'm not kidding when I say this, but further back if necessary), flipping through the pages, and asking myself "do I actually understand this concept very easily?" I'd argue that with the exception of Year 10, this would also involve worded problems as well, where you have to apply what you know to more practical scenarios.
The potential issue of ineffective teachers is perhaps the biggest misfortune ever, because it's not your own fault. But the idea is to overcome it.
My main suggestion: rely on a different learning source. If you learn well off reading, perhaps your textbooks might show you more. If you learn well off videos, there are educational videos on YouTube all over the place. (Just be careful when searching!) If you still want to be taught in person, honestly provided you can find an effective tutor, the money invested will be worth it. (A good tutor will stimulate the students' love for learning much more!) If you like self-paced interactive activity, you could consider websites that offer these services, say brilliant.org for example.
Make sure that the foundation is in place first. All of the above options will give at least the foundation (although success in tutoring would help later on with more in-depth problem solving questions as well though).
Also, this video series on "What's Worthwhile" may offer up some advice with tutoring schemes. (It doesn't seem to work on the atarnotes website, but you can click into the actual video on YouTube.) You'll find it hard using a lot of options to develop that stronger level mathematical thinking the examiners wish to see, but step by step really matters a lot.
When combating memorisation, I really try to divert my focus onto 'finding patterns' over ingraining formulas. It's a lot linked to the next issue, but I find it far more aesthetic viewing maths as knowing, using and manipulating
patterns in objects of a specific form. I carry this through even later on in schooling life for more convoluted mathematical techniques, like calculus in optimisation. When applied, yes it feels like a boring old systematic process. But at least behind the scenes, I get to appreciate why something works.
So yep, onto the "why". Let's start with this question that makes people hate maths in year 7 - why are we dealing with letters like \(x\) in mathematics? At that early point in life it
is hard to appreciate to be fair, but the whole point is to model with something that is (at least, at present)
unknown. In the real world, we just don't know what certain quantities will be, until some event happens, or we accumulate more information. But we still need to model the relationships
somehow, so that we can have all the useful conclusions we require in advance!
Time skip, now let's say I'm currently in General maths and fitting a least squares regression line. At the very least, I would be asking myself "why" is this line even called that and what makes it so useful? Now let's say I'm currently in Maths methods and doing the optimisation problem. At the very least, I would be asking myself "why" my techniques in calculus gives me the best value for a certain problem.
Doing this keeps the curiosity inside me. It
invites me into asking more about why this this that that holds. (Of course, some questions just aren't answered, due to the limitations of expected mathematical ability at the time. No worries - the curiosity funnels me into finding out at university.)
But that's only one side of the "why" puzzle. The other side is connecting "why" certain techniques work to the problems in hand. Sometimes, they are by definition - that's cool, definitions are the foundations we lay on mathematics so we take it for granted. Other times, a handy-dandy formula/theorem comes into play. In all cases, before jumping into using some mathematical result, I intentionally spend time understanding what was so special about this problem (or in a long problem, where I am currently at right now) that lead me to hitting it with this result in the first place.
What about when I'm stuck? I ask the same question, but instead I turn to the
solutions and ask why
they used a certain technique. (Of course, you might not always have solutions available - this is why people ask for help, for example on this forum!)
That way, the memorisation is no longer forced. It becomes a more natural procedure.
Some people zone out thinking that maths is too abstract once algebra becomes a thing. Look, fair enough, because techniques do make up a lot of the stuff in high school maths. (In fact, on the other hand some students
like maths for the technique manipulation.)
Connecting maths to the real world takes time, and perhaps even investigation. It's more of a concept that needs to be discovered. Inevitably, high school mathematics is still mostly aimed at introducing the tools that lead into the so-called 'common sense' aspects of mathematics at university. Though not
everything will be used (varies from person to person) at uni, many are still surprised by how much mathematics just randomly appears in their studies anyway!
(Personal note: I also found that understanding maths helped make more real-world like concepts make a lot more intuitive sense.)
And lastly, the issue of problem solving generally stems from difficulty in developing patience at the start. Which was me a lot, especially due to stereotypical Asian-cultures with maths. But problem solving is not a one-step procedure.
- Identifying the key components of each problem. This includes listing out exactly what you're given (for example variables, equations, relationships) and so on. It also includes actually breaking the problem down.
- Identifying the objective. What is the problem trying to make me do?
- Use the techniques that I know, on the key components to develop some new information.
- If required, break down the problem AGAIN!
- Continuously use what I know now to head in the direction of the objective.
Obviously the last two steps are harder, but the first two are actually extremely important. Without knowing what's going on, how can you solve the problem? And even then, the last two steps is time consuming.
That's the point. Problem solving is not meant to be something done quickly. It's
supposed to take a lot of time at the start. You need to have physically done enough problems multiple times for your brain to have been used to this kind of situation.
(And it also includes having actually written it down, which slows people down more. But without writing, a lot of the retention is lost.)
So clearly it's not something that comes naturally! Acceptance of this fact is also important in finding the will to actually be consistent again.
Regardless, it's not easy. I'll give you that.
And in all honesty, nobody else knows better what you require, so in the worst case scenario I still haven't even answered your question. But hopefully it serves as a starting point!
P.S. If wanting to be stimulated by maths yourself is something you'd be interested in, over the summer break I would consider checking out this book by one of NSW's leading teachers Mr. Eddie Woo 
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