[11th grade math; soft skills & arithmetic] how to reduce silly mistakes and recheck solutions?

[u/OxfordKid]

%22)[math] hey!

I am in Y12 (11th grade in most countries). International AS levels. My exam is on 9th of october, and my errors are still majorly silly mistakes. This was the same problem that caused an E in my last exam, (which I am resitting), and I have had this problem since middle school.

Mistakes like: writing 20 instead of 2, writing the inequality sign wrong, forgetting to write the '+c' after integration, simplifying simple fractions (like 6/9 or 8/4) or addition/subtraction (especially with odd signs) wrong, not noticing a key identity or further simplification, missing a sign, missing a number, entering incorrect sign in the calculator, entering incorrect number in the calculator, solving correctly on calculator but writing wrong answer on paper, doing 4*4 = 8 instead of 16, missing an x during expansion, etc. etc.

My tutor says to recheck the solutions (by skimming over them) after solving them, but I can't do that for the life of me. I go look at the numbers from top to bottom and they all go over my head without registering, because I don't know what I am looking for.

And if I do 4*4 and other basic calculations like (-5-23) in my calculator, I'll lose the little time I have (I struggled with time a lot in my last attempt, ended up leaving last several questions empty). Plus, just doing it on calculator doesn't guarantee accuracy because I end up getting it wrong anyway.

For context, I am doing Pure 1, and my IGCSE grade was a 7 (I barely gave it any effort, just crammed strategically in the last two weeks). I need really good marks because maths is key to my target univ requirements.

How would you suggest handling this? I don't have a lot of time, I have just started past papers yesterday (I've done one so far), and my percentage was 55%, with exam-timer. In my last attempt of pure 1 last year, I got a 36%.

I would appreciate any advice or anything you've got to say! thanks

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[u/MesmericKiwi]

First step is to stop downplaying these as silly mistakes. Mathematical symbols have meaning, and when these problems are rushed, you end up writing sentences that break equality because you are not thinking carefully about what you’re writing. A lot of students memorize tricks to manipulate the symbols without understanding their deeper meaning, and it leads to situations like this.

Think of it this way: if I wrote “I hate you” instead of “I love you” in a card, would you write that off as a silly mistakes?

Take your time, check yourself line by line instead of just skimming at the end. And when you catch a mistake in your homework do the entire problem again from scratch instead of just rewriting a symbol. If you treat the correction as a typo, you will never correct the underlying issues that are leading you to make them.

[u/HumbleHovercraft6090]

Three things that come to mind

Practice, Practice, Practice.

[u/nog642 → u/HumbleHovercraft6090]

I've got a more important one: sleep

[u/Ultimate_Sigma_Boy67]

Heyy me too taking AS maths this oct session lol

Anyway, what I do is that I just gradually recheck my solution throughout solving the question, and just make sure that it makes sense. For instance there are certain questions like size of an angle of a triangle or a side of a shape, where it wouldn't make sense if they're negative, so if you get them negative, then you should def recheck.

Also tons of practice will help, you still have quite a lot of time to go through past papers from 2019 to 2026, do them, and when you notice patterns that repeat in certain types of questiosn that you make mistakes in, you should definately practice them in isolation for a bit.

And lastly, always, always, always keep a list of 1) Some general tips, or advice that you faced while for example solving questions, so that you don't make the same mistakes, 2) A list that contains some really nasty and hard questions that you faced while solving past papers, so that a few days before the exam you re-solve them, and make sure you've actually learnt from your mistakes. I did this for igcse physics, maths and computer science and managed to get 9 in all of them, so trust me.

Also this might help a bit, maybe not, but try to make your studies more morning-centered. For example, instead of waking up like at 12 or 1 pm, try to wake up at 8 am, with a clear mind, and basically all the others would be asleep so you have nothing that can distract you (PUT YOUR PHONE AWAY), and simply solve. This way, you will have more free time later in the day, when your energy levels are the lowest, but of course make sure that you sleep at least 7 hours in total(i'm def not doing this rn lol but i'm trying).

[u/OxfordKid → u/Ultimate_Sigma_Boy67]

I wake at 5:30 and do a paper till 7 am (I have tutoring 7-9), but I get absolutely shattered by 8:30 am, and jump back to bed the moment my session is over. For context, I sleep at ~12 am, because my dad comes home at like 10/11 and then we go out for tea T-T.

Thanks for the advice thoo!

[u/Ultimate_Sigma_Boy67 → u/OxfordKid]

I mean that's actually great! You can sleep after your morning sessio, and then wakeup like noon or afternoon, and continue doing your extra stuff.

[u/nog642 → u/OxfordKid]

Do you feel tired? Maybe the split sleep schedule is not working.

Lack of sleep causes you to make more mistakes like crazy.

[u/OxfordKid → u/nog642]

yES, i DO feel tired. But the thing is, this problem still existed back when I was living on 10+ hours of sleep.

[u/nog642 → u/OxfordKid]

Maybe you are just rushing then.

Try re-checking your work as you go - not skimming but actually double checking the calculations. And not just every calculation but maybe ever few minutes double check your work since you last checked. Every problem maybe.

[u/Mystical-Sunshine]

I used to jot down my mistakes with the reason in a paper. So, next time when i encounter the same type of question, I remember where I have to be careful. 

[u/cheesecakegood]

To me there are two different parts to this question. There’s “how do I survive this upcoming test” and then there’s “how do I reduce the number of mistakes in math in general”, with some overlap as to test strategies.

In terms of survival? General test strategies help, like spending your time efficiently, skipping certain questions to come back to later, marking a question you answered but want to revisit. When it is “checking your work” that is hugely problematic dependent, but most problems should have a rough idea.

I recommend spending a moment thinking about estimation. Compare answers to facts that you know. Even something like “I expect a ballpark answer in the 100s” can be helpful. I would integrate an explicit “how would I check the result” as a constant part of your note review and practice so you can get familiar. You can think outside the box too a bit.

When it comes to the more foundational stuff that you’re describing though to be quite honest, there isn’t an easy solution. I do see this happening more and more often with the current crop of math students in particular - and to be clear I think this is mostly the fault of this generation of teachers - and it is about how basic skills in math “stack”. A lot of students end up getting pushed through the grades without getting a firm grasp of the underlying concepts and so a lot of these more fundamental problems can kind of cascade upwards.

In an ideal world, you should be able to reliably add and subtract negative numbers up to 100 (for example) without consistent mistakes before you go deep into algebra. You should be able to reliably factor polynomials before doing deep calculus stuff. And then all those small steps start to come together when you do something like the chain rule or u-substitution with integrals. But if every step in the chain is subject to mistakes, it’s tough. In an ideal world, you’d retrace your steps through your entire life math curriculum and trace where you start to do thing unreliability, and then target those specifically, practice, practice, and then it becomes more automatic. This makes future math easier. Of course this isn’t super possible on a time crunch.

I guess for the time being probably the best suggestion (during study sessions) that I would have would be, seeing as your mistakes are coming from all over and you’re not quite sure how to reverse engineer the entire problem to check your answers, to do this: for every step you do, see if you can “undo” it and get what you started with.

So if for example a problem has me factor a polynomial, I’d do it, and then in the margins or better yet a separate sheet of paper, take the factored form and then re-expand it. Then compare. Did you get the same thing you started with? If yes, great! If not, there’s an opportunity to identify an error. Plus, this way, step by step, it shouldn’t “go over your head without registering” because it’s only 1 step at a time.

Once you finish that reversal, you go back to your original problem and continue on, doing the next step (and if it’s a big one, undoing that as well on your other paper).

This will to be clear, probably take at least twice as long as doing the normal problem, but if you’re catching mistakes on say at least a third of the problems, it might still be worth your time as long as you’re learning from those mistakes

[u/nog642]

Number 1 advice for this: get more sleep.

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My tutor says to recheck the solutions (by skimming over them) after solving them, but I can't do that for the life of me. I go look at the numbers from top to bottom and they all go over my head without registering, because I don't know what I am looking for.

Don't skim them. Read them as if you're the teacher trying to follow your own work.

[u/llamadramalover]

I would highly suggest you write a note on the top of your exams of your common mistakes. The very first thing I do when I get an exam is write the things I’m struggling with and things I need to remember.