Does A-level Maths set students up for Higher Education well enough?

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_gcx
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There's a lot of disquiet about the inadequacies of the maths A-level in preparing students for undergraduate maths courses and differentiating between strong students, hence the widespread use of admissions test like the MAT, STEP and TMUA by universities. There's a notable minority of students who are never really happy with the style and nature of university-level maths, with the course perhaps not providing the "natural continuation" of A-level maths that they hoped for.
  • If you've gone on to do a mathematical subject at university, do you think you were adequately prepared by the maths A-levels?
  • Is there anything you'd change about the A-levels to make them better preparation?
  • Do you support the use of admissions tests in distinguishing A/A* candidates? Do you think there's a better way to do this?

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04MR17
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The one point I would make to begin with is that A Level Maths is designed to cater for more people than those who are interested in studying Maths (and associated subjects) at uni. I'm not the hugest fan of the current A Level structure but I do think it is worth adding that caveat in early that no A Level qualification is especially well-adjusted to the same subject as a uni degree.
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(Original post by 04MR17)
The one point I would make to begin with is that A Level Maths is designed to cater for more people than those who are interested in studying Maths (and associated subjects) at uni. I'm not the hugest fan of the current A Level structure but I do think it is worth adding that caveat in early that no A Level qualification is especially well-adjusted to the same subject as a uni degree.
I don't think any other subject is compromised nearly as much, except a-level physics which is held back at least a bit by the requirement that it shouldn't require a-level maths. (calculus is used in a few derivations but these are non-examinable) I do think the purpose of an A-level should be first to prepare someone for university study in that subject and then everything else should be second. Then if that leaves significant gaps, introduce new qualifications to fill in those gaps.

In an ideal world there would be a separate qualification to cater more to people looking to do maths at uni but some teachers seem to struggle enough with the A-level further maths content - I would think very few schools would be able to offer such a thing.
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Baleroc
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(Original post by _gcx)
There's a lot of disquiet about the inadequacies of the maths A-level in preparing students for undergraduate maths courses and differentiating between strong students, hence the widespread use of admissions test like the MAT, STEP and TMUA by universities. There's a notable minority of students who are never really happy with the style and nature of university-level maths, with the course perhaps not providing the "natural continuation" of A-level maths that they hoped for.
  • If you've gone on to do a mathematical subject at university, do you think you were adequately prepared by the maths A-levels?
  • Is there anything you'd change about the A-levels to make them better preparation?
  • Do you support the use of admissions tests in distinguishing A/A* candidates? Do you think there's a better way to do this?

More curriculum conversations like this
This thread is one of a series of Curriculum Conversations happening on :tsr: in July. If you would like to receive notifications for more of these, click here and tick the box.
To answer this question, we first have to examine: what is the goal and intention that A-level mathematics has to fill.

Right now: the goal is to provide the essential mathematical concepts and ideas necessary for all industries of math, including:
- Chemistry, Biology, Physics
- Computer Science, Engineering, Finance, Accounting, Economics.

There are a lot of industries that A-level math has to accommodate. That, is one of the fundamental issues with A-level Math and Further Math. It is too general to accommodate so many different areas, that it cannot focus on topics pertinent to University Mathematics, because it has to provide so much context to other subjects, like Chemistry and Physics, that's it's very difficult to compromise on changing A-level math, without some subject being negatively affected by the topics being removed/added.

Therefore, to change A-level mathematics, I propose that the idea is to change the other A-levels first.
Firstly, ask yourself the question: does it make sense for many degrees to depend on A-level Mathematics more than the A-level subject its self? If I want to study Chemistry, A-level mathematics is more important than Chemistry its self for the degree. If I want to get into a Physics degree, Mathematics is more important than the Physics qualification its self.

That needs to change.

I think that all qualifications that depend on A-level mathematics should have Core and Additional for each subject.
Core focusing on the mathematics for that subject.
Additional focusing on the subject using the mathematics from core.

Then, you can change A-level mathematics to be focused more on University level Mathematics; otherwise, in the current system, it's difficult to change the qualification unless some other subject/field suffers as a consequence.

So, as a concrete example:
A degree in Chemistry requires A-level mathematics. Instead, Chemistry Core A-level should have all the essential math from A-level math/Further Math included in the subject, while Chemistry Additional is all of the content from the current Chemistry A-level.

Then, you can change A-level mathematics, so we no longer need to include some topics of math that are applications of chemistry, or physics, engineering or computing, etc, and we can focus A-level math more on Pure Math, proofs, etc, as a result. That way, A-level math and Further Math, is focused more towards a university level qualification, rather than providing lots of applications of math, which shouldn't be the role of A-level math.

To summarise:
A subject that depends on A-level mathematics as part of its syllabus, should be divided into two A-level subjects:
- Core Subject A-level. Focuses on the math of the subject
- Additional Subject A-level. Uses the math in a theoretical/practical way.

The Core would take all the mathematics from the A-level Mathematics and Further Mathematics qualification, and teach it there. Additional would teach the current A-level for that subject.

For example:
- Core Physics A-level, teaches all the mechanics and mathematics pertinent to Physics from A-level Math and Further Math.
- Additional Physics A-level teaches all the current physics content, using the math from Core.
- Remove the Physics math in A-level Math/Further Math, and have A-level math focus more on Pure Math or university level preparation.

Physics A-level shouldn't depend on A-level mathematics to provide all the math. All the math from A-level mathematics, should be included in a Core Physics A-level, that teaches all the mechanical content of A-level Mathematics, while Additional Physics focuses on the current A-level content.

Personally, it doesn't make sense how a subject completely depends on another, to be considered for a degree. Unless other subjects are changed first, we cannot change A-level mathematics, as changing that subject could potentially remove essential math that is important for other fields, like Physics (Mechanics), computing (discrete math), Economics, Finance (Statistics), etc.

Hope that makes sense
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Baleroc
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(Original post by Baleroc)
Core focusing on the mathematics for that subject.
Additional focusing on the subject using the mathematics from core.
To expand on what was said in the previous post, this will entail the following:

Physics Core A-level will cover all the mechanics from A-level math/further math.
Computer Science Core A-level will cover all the Discrete Math from A-level math/further math.
Statistics A-level will cover all the Statistics from A-level math/further math.
Economics Core A-level will cover the essential math relevant to Economics from the old A-level math/further math.
Chemistry Core A-level will cover the essential math relevant to Chemistry from the old A-level math/further math.
Biology Core A-level will cover the essential math relevant to Biology from the old A-level math/further math.
Mathematics A-level will be reworked to cover only pure mathematics. Good preparation for mathematics at university.
Further Mathematics A-level will be reworked to cover additional pure mathematics. Excellent preparation for mathematics at university

Then, people can take a combination of these qualifications.
Someone could take AS Physics Core, for 180 hours of physics/mechanics.
Someone could take AS Statistics for 180 hours of statistics.
Someone could take AS Computer Science Core for 180 hours of Discrete Math.

That rework will allow A-level math/further math more freedom to focus on university level mathematics, as opposed to being limited by different subjects depending on it.

Finally, one question that may occur is: if the old A-level math/further math, only had, say 80 hours of Discrete Math, and the Core A-level for a particular subject is 360 hours, what do you teach in the remaining hours? In the remaining hours, you would teach the essential math that is important to that field. So for computing, after teaching 80 hours of Discrete math, the remaining 280 hours, would be focused on other important math for computer science, like statistics, linear algebra and calculus. Similarly, with Physics, if the mechanics is 240 hours, then for the remaining 120 hours, it would focus on other topics important to physics that aren't in mechanics, perhaps that's Linear Algebra, or advanced calculus, etc.
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