Do you think A Level Maths has enough proof in it?

I'm in year 12 and doing both A level maths and further maths (Edexcel), but most of the topics mainly involve following a method to answer a certain type of question.

There are also quite a few occasions where formulas without proof are given and you just have to substitute things in or rearrange equations to get the result given in the question.

I don't think there is enough focus on actually proving things since most proofs fall into one of the following categories:

•

Simple algebraic proofs that rely on odd and even numbers being written as 2n+1 and 2n

•

Proofs that are in the textbook and need to be learnt and written down in the exam

•

Showing that an expression can be written as a quadratic expression and then having to solve it

Does anyone else think there isn't enough proof in A level maths, or do you think it's fine as it is?

Reply 1

dasda

15

it's definitely fine. I hate proofs.

Reply 2

dasda

15

I am in year 12 and hate proofs and just do single maths.

Reply 3

Morcatic

7

I do see your point. It is unsatisfying (?) when you are given a formula without knowing where it comes from and are told to use it. Derivations are quite fun.

Reply 4

dasda

15

Original post by Morcatic

I do see your point. It is unsatisfying (?) when you are given a formula without knowing where it comes from and are told to use it. Derivations are quite fun.

That's true. Deriving formulas in mechanics is fun especially the constant acceleration formulae

Reply 5

GreenCub

OP

20

Original post by Morcatic

I do see your point. It is unsatisfying (?) when you are given a formula without knowing where it comes from and are told to use it. Derivations are quite fun.

In Further Maths we recently did a topic about series which was not very difficult. It was about finding sums of natural numbers, squares and cubes and they gave the formulas without any proof, so we just had to substitute expressions into the formulas and rearrange them to match the form given in the question.

There are some proof questions where you have to show that two trigonometric expressions are the same, but it hardly feels like you're actually deriving something new, rather than following the steps that the examiner intended you to follow.

Original post by dasda

it's definitely fine. I hate proofs.

What do you hate about them?

you have to prove de moivres theorem by induction, vectors has a bit of proof too and with matrices you can be asked to prove things, apart from that tho not much else

Reply 7

dasda

15

Original post by GreenCub

In Further Maths we recently did a topic about series which was not very difficult. It was about finding sums of natural numbers, squares and cubes and they gave the formulas without any proof, so we just had to substitute expressions into the formulas and rearrange them to match the form given in the question.

There are some proof questions where you have to show that two trigonometric expressions are the same, but it hardly feels like you're actually deriving something new, rather than following the steps that the examiner intended you to follow.

What do you hate about them?

It requires a different way of thinking compared to solving equations for x. I have never been good at proofs even though I pick up other things relatively fast.But that's my opinion.

Reply 8

K_mck

3

What is maths and further maths like at A level? (yr 11 taking both in college and starting GCSEs in a couple weeks). I haven't found anyone that does both and I'm a bit worried it'll be awful.

In further maths there is "unseen" induction now, meaning you might be expected to prove, eg. inequalities by induction. You are not expected to know how to do it, you're instead expected to adapt what you know which I think is a good thing.

Original post by Gent2324

you have to prove de moivres theorem by induction, vectors has a bit of proof too and with matrices you can be asked to prove things, apart from that tho not much else

---------

Original post by GreenCub

I'm in year 12 and doing both A level maths and further maths (Edexcel), but most of the topics mainly involve following a method to answer a certain type of question.

There are also quite a few occasions where formulas without proof are given and you just have to substitute things in or rearrange equations to get the result given in the question.

I don't think there is enough focus on actually proving things since most proofs fall into one of the following categories:

•

Simple algebraic proofs that rely on odd and even numbers being written as 2n+1 and 2n

•

Proofs that are in the textbook and need to be learnt and written down in the exam

•

Showing that an expression can be written as a quadratic expression and then having to solve it

Does anyone else think there isn't enough proof in A level maths, or do you think it's fine as it is?

The above may be interesting to you. I would agree with you. The problem is that some teachers take a very disparaging attitude towards proofs, seem as either some distraction or something that has to be learnt and repeated. Really students should appreciate the need for proof, and being able to prove things on your feet. Luckily, if you're interested, practically nothing (except limits) in A-level maths will be beyond your reach proof-wise, and very little in further maths. Further reading will help with, for example, STEP and the gap between sixth form and university.

Reply 10

dasda

15

I'm doing first year a level maths. Going relatively smooth compared to chemistry and biology. As maths isn't difficult. Makes me wonder why I got a 7 in gcse maths

Reply 11

K_mck

3

What letter grade is that equivalent to? My school still won't give us number grades.

Original post by dasda

I'm doing first year a level maths. Going relatively smooth compared to chemistry and biology. As maths isn't difficult. Makes me wonder why I got a 7 in gcse maths

Original post by K_mck

What letter grade is that equivalent to? My school still won't give us number grades.

bizarre attitude considering that 9-1 isn't that new anymore. a 7 is the same as an A, an 8 a high A/low A*, (but it is treated as the equivalent to an old A*) and a 9 is above that.

Reply 13

K_mck

3

Yep, none of us will actually know what our results mean on results day. :/

Original post by _gcx

bizarre attitude considering that 9-1 isn't that new anymore. a 7 is the same as an A, an 8 a high A/low A*, (but it is treated as the equivalent to an old A*) and a 9 is above that.

Reply 14

absolutelysprout

21

enough proof for me, there was this horrible 5 marker on proof on my last assessment which didn't actually turn out to be bad once we went through the paper with the teacher :colonhash:

Reply 15

IQuitTSR

21

Original post by GreenCub

I'm in year 12 and doing both A level maths and further maths (Edexcel), but most of the topics mainly involve following a method to answer a certain type of question.

There are also quite a few occasions where formulas without proof are given and you just have to substitute things in or rearrange equations to get the result given in the question.

I don't think there is enough focus on actually proving things since most proofs fall into one of the following categories:

•

Simple algebraic proofs that rely on odd and even numbers being written as 2n+1 and 2n

•

Proofs that are in the textbook and need to be learnt and written down in the exam

•

Showing that an expression can be written as a quadratic expression and then having to solve it

Does anyone else think there isn't enough proof in A level maths, or do you think it's fine as it is?

It's not fine

there should be A level math for those just needing to us math in uni and for those who are going to need a substantial amount of math (math, physics, and engineering degrees). Kinda like the tiers in GCSE math.

Same thing for physics really. Let them bring back the calculus!!!

Reply 16

Sinnoh

22

I think it's nice that they added in proof by contradiction, but unfortunately the best way to learn that topic is to just memorise the proofs.
That one about proving that there are infinitely many prime numbers - if that comes up in the paper, I expect very few people to actually come up with the proof.

Reply 17

VETF

9

I think it’s fine as it is!

Reply 18

GreenCub

OP

20

Original post by TheTroll73

It's not fine

there should be A level math for those just needing to us math in uni and for those who are going to need a substantial amount of math (math, physics, and engineering degrees). Kinda like the tiers in GCSE math.

Same thing for physics really. Let them bring back the calculus!!!

That sounds like a good idea in theory but the main purpose of A level maths is to facilitate university courses that require more advanced mathematical methods and calculations as opposed to proofs. So it's more useful in preparation for science, engineering, computer science and economics degrees which tend to just require use of methods and calculations.

I do agree that A level physics is very watered down in terms of mathematical content, but it's very difficult to add too much more maths without making it inaccessible to students not taking A level maths. Displacement, velocity and acceleration have everything to do with calculus and successive derivatives but A level physics only gets as far as drawing tangents on graphs and counting squares to approximate the area under a curve. Not to mention virtually all physics concepts are linked to calculus in some way. Nearly all of the equations you learn can be thought of as derivatives or as an integral over time.

In addition, in A level maths many teachers seem to use "proof by many examples" to verify new concepts as opposed to actually proving them.

(edited 4 years ago)

Reply 19

IQuitTSR

21

Original post by GreenCub

That sounds like a good idea in theory but the main purpose of A level maths is to facilitate university courses that require more advanced mathematical methods and calculations as opposed to proofs. So it's more useful in preparation for science, engineering, computer science and economics degrees which tend to just require use of methods and calculations.

I do agree that A level physics is very watered down in terms of mathematical content, but it's very difficult to add too much more maths without making it inaccessible to students not taking A level maths. Displacement, velocity and acceleration have everything to do with calculus and successive derivatives but A level physics only gets as far as drawing tangents on graphs and counting squares to approximate the area under a curve. Not to mention virtually all physics concepts are linked to calculus in some way. Nearly all of the equations you learn can be thought of as derivatives or as an integral over time.

In addition, in A level maths many teachers seem to use "proof by many examples" to verify new concepts as opposed to actually proving them.

I never understood why one would take A level physics without taking A level math as any student wishing to study the sciences, medicine, etc. will be needing to take A level math. Maybe I'm just not seeing any case when students benefit taking A level physics but don't benefit from taking A level math as I'm sure any student who wishes to take a science (so to have a subject that adds breadth) but is not strong mathematically would rather choose biology (or maybe chemistry) at A level, just to avoid having to do too much math.

In the end, I find it ridiculous that universities have to use A level math to judge someone's ability to do math at an undergraduate level as clearly the A level exams tests completely different skills, hence my opinion on the matter. I do think that this causes certain students to be unable to show their potential in a math undergrad and end up in lower ranked universities when they deserved better, which I think is unfair.

Do you think A Level Maths has enough proof in it?

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you