Maths Misconceptions

What’s the one main thing you can’t get your head round with maths?

3d trig for sure - really struggle to visualise stuff. At least not enough to draw a diagram. Thinking about imaginary lines is always tricky

Yup, quite an advanced topic.
Here’s my suggestion, create a large cube with edges only. So essentially a skeleton box.
Then when you complete questions on right angled triangles in 3-D the physical prop can help you visualise the triangle by placing a straw as the hypothenuse (slope).
Let me know if that helps?

3d trig for sure - really struggle to visualise stuff. At least not enough to draw a diagram. Thinking about imaginary lines is always tricky

Is 3d trig not just regular trig but with an extra triangle or 2?

Sort of but I really struggle with the visualising. I'm happy with A2 trig equations and similar but GCSE 3d trig stumps me. Here's an example:
ABCDE is a square-based pyramid. E is the apex of pyramid, directly above the centre of the square base with length 23cm. M is the midpoint of AC. AB = 23 cm and CE = 22cm. Calculate the angle AEC to 1dp.

What’s the one main thing you can’t get your head round with maths?

So its an egyptian pyramid and when you sketch it - maybe try that before looking at the spoiler?
Really the key thing is to think about where you slice the 3D space with a 2D plane as thats pretty much all you need to do. Then its the usual 2d pythagoras/simple trig. Here you want <AEC, so that pretty much defines the plane (3 points) and its along diagonal of the square base AC and includes the apex / pyramidion E. So sketch the 3D pyramid and the corresponding 2D slice (without all the reptilians living in there) and it should be straightforward?

Sort of but I really struggle with the visualising. I'm happy with A2 trig equations and similar but GCSE 3d trig stumps me. Here's an example:
ABCDE is a square-based pyramid. E is the apex of pyramid, directly above the centre of the square base with length 23cm. M is the midpoint of AC. AB = 23 cm and CE = 22cm. Calculate the angle AEC to 1dp.

I'd split it up into two triangles - ABC and EMC - find half the length of AC and then it's just SOHCAHTOA. It's particularly hard without a diagram but I can do that more easily now than ~1 year ago. Not the trig that's the problem - more just visualising it. Though I do have specific diagnosed difficulties that can make this difficult.

I would assume you are a maths teacher, or are knowledgeable in the subject, so maybe you will be able to help me with this problem:
Whenever I take a maths exam, I can do all the questions fine, but I always end up making silly little mistakes like writing a 2 instead of a 1 or a minus instead of a plus, so my question is, how do I stop doing this?
I know what I am doing is obviously wrong and I don't mean to, but it keeps ending up with me losing easy marks and it won't help me out much in my exam next week. Have you ever encountered this problem, and how do I fix it?

Boring answer, but the number one thing is practice. Other advice:
Don't try to do more "in your head" than you're comfortable with. People think "I need to save writing time" but the writing doesn't actually take much time relative to the thinking. It certainly takes less time than getting to the end, finding you've got the wrong answer, and having to go back looking for mistakes.
Check what you're doing as you go along. Often there are "sanity checks" you can do (e.g. the first line equals 23 when x = 0. Is that still true for the second line?).
If you have time, do the question twice (or at least the error prone part of it). I know this kind of sounds overkill, but sometimes you have a bunch of calculations that you can't easily check (e.g. matrix multiplication) - I found it actually easier to just do it twice, quickly, rather than doing it once and second guessing myself every step of the way.

Small bit of concrete advice: draw diagrams, make them large, neat (i.e. use a ruler for straight lines!) and roughly to scale. (There's no need to be exact, but if you have a triangle with sides 5, 12, 13 and you draw it like an equilateral triangle it's going to throw off your intuition).
There's also nothing wrong with miming out the structure in actual 3D if it helps.
You may already be doing this (or not find it terribly helpful).

I guess you can draw the 3d egyptian pyramid and youre pretty much there about the triangles/trig. Though Id still recommend (for this/similar questions) thinking about the 2D plane the angle lies in so passes through lines / edges AE and EC and draw that.
Youre right that you need ABC to work out the base diagonal (half that), though its a square so its 23*sqrt(2) (trivially) Then its just the isosceles triangle AEC which you should have a 2d sketch for. So basically Q2 in
https://mathbitsnotebook.com/Geometry/3DShapes/3DPyramidConePractice.html
and triangle AEC is the pink shaded area which lies in the 2d plane which is the extension of this shaded area. Note Q5 explicitly draws the 2d plane as well the triangle that lies in it and it could easily be done for this question.
For me, Id try and get in the habit of explicitly thinking about / sketching the 2d plane the angle lies in. Without knowing what problem youre referring to, if you cant do that, youll have trouble forming the approach/calculations.

Diagrams are usually the problem and I do try and do this - thanks. Don't see these questions as much in A-Level maths than in GCSE (I lost a total of 6 marks in GCSE maths - 5 of those marks were 3d trig/coordinate geometry).
Ah I see what you mean now by the 2d plane - it's a bit easier to see it in Q2 than Q5. The difficult is with regards to spatial awareness - you probably get the gist.

I would assume you are a maths teacher, or are knowledgeable in the subject, so maybe you will be able to help me with this problem:
Whenever I take a maths exam, I can do all the questions fine, but I always end up making silly little mistakes like writing a 2 instead of a 1 or a minus instead of a plus, so my question is, how do I stop doing this?
I know what I am doing is obviously wrong and I don't mean to, but it keeps ending up with me losing easy marks and it won't help me out much in my exam next week. Have you ever encountered this problem, and how do I fix it?

Hello and yes you’re correct. I’m here because sometimes students need an alternative idea to better access maths.
Well done on your success so far and your tenacity.
Learning maths is about those small mistakes. Overlooking units and so on.
There are a few reasons why students make this sort of mistake.
1) speed - being too hasty to finish question or exam paper
2) 3 fundamental rules. Have you got the correct units. Have you checked over each of your steps. Have you actually answered question or worked out part of the solution
I find it’s the simple mental maths aspect that catches students out more than the actual process.
If you’ve got examples of your work I’d be happy to confirm my thoughts.
Happy to help

Thanks for the advice, I'm usually a high achiever, and I know I sound cocky, but I'd like to achieve the highest out of everyone, and the only thing that stops me from doing so is these mistakes 🥲
I usually make the simplest of errors, like writing a minus instead of a plus, I think the main problem is I'm thinking of the answer while I write my working, which causes me to do something like writing the answer instead of another number, causing me to get the question wrong.
If you have any advice on how I could stop doing this it would be very helpful!

Thanks for the advice, I'm usually a high achiever, and I know I sound cocky, but I'd like to achieve the highest out of everyone, and the only thing that stops me from doing so is these mistakes 🥲
I usually make the simplest of errors, like writing a minus instead of a plus, I think the main problem is I'm thinking of the answer while I write my working, which causes me to do something like writing the answer instead of another number, causing me to get the question wrong.
If you have any advice on how I could stop doing this it would be very helpful!

Hi,
Try one small tip at a time , maybe redo questions / exams you’ve done previously and see how you have improved.
Questions are best answered with a relaxed mind. Do you feel somewhat anxious to get a perfect score if so the perfectionism could be holding you back.