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What do you look for in a mathematics course

Hi. I'm a lecturer at a UK mathematics department. We are currently revising our curriculum. I'd like to ask you all: what do you look for in a university maths course? What makes a course attractive to you? Why choose one course over another? Is computing important to you? Are projects important? And, if you're already at university: how is your course different or similar to what you expected?
I’ll bump this for you :smile:
Original post by AnonymousMathmo
Hi. I'm a lecturer at a UK mathematics department. We are currently revising our curriculum. I'd like to ask you all: what do you look for in a university maths course? What makes a course attractive to you? Why choose one course over another? Is computing important to you? Are projects important? And, if you're already at university: how is your course different or similar to what you expected?

Variety of modules apart from the standard ones.

Lack of modules in the area of interest of a student will discourage them (at UG at Aberdeen, lack of Stats modules caused people not to go as I observed on open days. This applies to Pure too, as Nottingham are/were getting rid of Galois Theory which I know current students who were really not happy with that, to the extent they were thinking about transferring).

Computing will be important to some and not to others, so the option should always be there. Too many mandatory courses piss people off more than anything else. Freedom of choice is a massive plus.

Solo projects are always off putting to people to start with. However, they are a great way to get people into reading actual papers. Getting people to write mathematics in a clear and concise way and allow them to express themselves. So they should be encouraged. Also for getting people into more niche areas this will be a big boost.

At the end of courses have a lecture about where the specific module leads and explain some big results that have come from the module.

Nothing to do with curriculum but:

A common area where you have tables, chairs, BLACKBOARDS (NOT whiteboards) comfortable seats, etc. So people can do mathematics, talk mathematics or relax, with other mathematicians from first year UG to senior academics. Making the atmosphere of the department better.

Renowned mathematicians who actually teach UG courses is a massive boost.

Tutorials, with time with the lecturer.

Just my thoughts as I had nothing better to do.
(edited 2 years ago)
Thank you, your comments are very interesting. I'm afraid many of the students I teach find it hard to make use of tutorials or small group supervisions. Instead the larger Q&A sessions (online in Covid) we've introduced seem to suit them better. Also we introduced many online quizzes, a bit like the quizzes you might have seen in MOOCs, that have been popular. Any further comments would be very welcome. Your idea of a 'big picture' lecture is great ... but yet again I'm afraid it is very far from the concern of the typical student: I find even our better students treat each course as an indivisible silo, to be remembered for the exam, and then forgotten as quickly as possible. (Moan, moan.)
(edited 2 years ago)
Original post by AnonymousMathmo
Thank you, your comments are very interesting. I'm afraid many of the students I teach find it hard to make use of tutorials or small group supervisions. Instead the larger Q&A sessions (online in Covid) we've introduced seem to suit them better. Also we introduced many online quizzes, a bit like the quizzes you might have seen in MOOCs, that have been popular. Any further comments would be very welcome. Your idea of a 'big picture' lecture is great ... but yet again I'm afraid it is very far from the concern of the typical student: I find even our better students treat each course as an indivisible silo, to be remembered for the exam, and then forgotten as quickly as possible. (Moan, moan.)

You need to take that up with the english education system!
Original post by AnonymousMathmo
Thank you, your comments are very interesting. I'm afraid many of the students I teach find it hard to make use of tutorials or small group supervisions. Instead the larger Q&A sessions (online in Covid) we've introduced seem to suit them better. Also we introduced many online quizzes, a bit like the quizzes you might have seen in MOOCs, that have been popular. Any further comments would be very welcome. Your idea of a 'big picture' lecture is great ... but yet again I'm afraid it is very far from the concern of the typical student: I find even our better students treat each course as an indivisible silo, to be remembered for the exam, and then forgotten as quickly as possible. (Moan, moan.)

I think that is true everywhere, similar to how office hours are virtually never used, sadly. But I think it's still useful to have as an option for people.

I hope to see more comments as I'd like to know what others think makes a difference in maths courses.

Spoiler

I'm at Cambridge, and have had only online supervisions this year. I haven't really found having virtual supervisions to be a barrier to learning in any way - usually the supervisor just writes on a tablet and screen-shares while talking about the problems. The only thing is perhaps people accidentally talking over each other but that's really intrinsic to Zoom itself.
Original post by AnonymousMathmo
Hi. I'm a lecturer at a UK mathematics department. We are currently revising our curriculum. I'd like to ask you all: what do you look for in a university maths course? What makes a course attractive to you? Why choose one course over another? Is computing important to you? Are projects important? And, if you're already at university: how is your course different or similar to what you expected?


•

A broad range of options. I'm generally interested in pure, so if a university's department is quite small and has most of its modules in applied, it probably won't be for me. Equally, people who are into applied should have their interests well served. Granted, this requires your department to be quite large.

•

Depth of options. Again, this really depends how strong your department and its students are. If I'm interested in analysis and the course stops just after complex analysis and has nothing on functional analysis - or I like geometry and there's no differential or algebraic geometry course in the later years, that'll be no good for me and will mean that stronger students get bored and will go elsewhere for further study.

•

Challenging, but not too challenging assignments. Considering the assignments are where the bulk of the actual learning happens, and exams are some contrived ritual, this is a really big part. I appreciate a lot of extension questions, clearly signposted.

•

Opportunities for creativity in the course. Optional projects that really allow you to explore a part of a course more deeply, opportunities to write essays and dissertations.

•

Computing isn't particularly important to me but I think it falls under "very broad range of options".

•

I like Warwick's opportunity to take a reading course https://warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/year4/ma472/ I think this is an excellent idea for any department who can implement it. Prevents students from being tied down by a lack of module choice, and awards advanced knowledge and skill in more specialized areas your curriculum may not cover.

•

I want a strong student culture with a lot of students that are interested in the subject. It's an unfortunate reality that at undergraduate level many students aren't a fan of their degree. Optional seminar series for undergraduates, essay competitions, and so on would be excellent.

•

Personal niggle - I prefer long exams. (at least 2 hours, ideally 3) I don't like time pressure, it's not very useful for examining mathematics and timing is easy for a lecturer to get wrong, so giving an excessive length of time is the way to go imo.

(edited 2 years ago)
My mates at other unis say that their lecturers aim their modules towards the lowest achieving students and as a result they feel unchallenged. Modules should be designed and taught with the interested students in mind, not just so that the dud students can get their 40%.
Original post by WarwickMaths281
My mates at other unis say that their lecturers aim their modules towards the lowest achieving students and as a result they feel unchallenged. Modules should be designed and taught with the interested students in mind, not just so that the dud students can get their 40%.

Thank you. You've summed up in two lines what my department has been agonising about for years: I sometimes think we are the last remaining maths department to take mainly weak students and still try to teach them genuine maths. I fear this is not an unqualified success, either for our students, or for our admissions position.
Original post by AnonymousMathmo
Thank you. You've summed up in two lines what my department has been agonising about for years: I sometimes think we are the last remaining maths department to take mainly weak students and still try to teach them genuine maths. I fear this is not an unqualified success, either for our students, or for our admissions position.

Do you subscribe to the notion that high entry thresholds are an indicator of the quality of graduate that a university turns out? Or do you think it’s a case that if the exit thresholds are met, the entry threshold matters less?
Original post by Turning_A_Corner
Do you subscribe to the notion that high entry thresholds are an indicator of the quality of graduate that a university turns out? Or do you think it’s a case that if the exit thresholds are met, the entry threshold matters less?

Can't both be true? For the first: it's hardly unexpected that high quality students in implies good graduates out (even if maybe little value is added). But in maths the entry threshold obviously matters a lot, because it determines what we can realistically teach. We have to give students something they can do! Sometimes we can achieve this by flattening the learning curve, while still ending with genuine maths. But if the entire cohort is weak, something has to go.
(edited 2 years ago)
Original post by AnonymousMathmo
Can't both be true? For the first: it's hardly unexpected that high quality students in implies good graduates out (even if maybe little value is added). But in maths the entry threshold obviously matters a lot, because it determines what we can realistically teach. We have to give students something they can do! Sometimes we can achieve this by flattening the learning curve, while still ending with genuine maths. But if the entire cohort is weak, something has to go.

That’s the question isn’t it. Do graduates from universities with lower entry thresholds represent less added value because as well as meeting the minimum learning outcomes they have also demonstrated higher capabilities? Is it then the problem that there’s no way of quantifying or measuring the additional value those degrees add?
Original post by AnonymousMathmo
Thank you. You've summed up in two lines what my department has been agonising about for years: I sometimes think we are the last remaining maths department to take mainly weak students and still try to teach them genuine maths. I fear this is not an unqualified success, either for our students, or for our admissions position.

Glad to hear this. Without want to sound snobby (I suspect you'll probably agree though), I've been shocked at the state of some maths degrees, barely covering what would be first, edging into second, year maths at another university, if that, with a lot of focus on (sometimes very tangential) applied maths. It sits weirdly that these degrees are given the same title as degrees elsewhere. I feel we need to make it clearer how degrees can differ not just in module selection but in demand, though I suppose that's an unpopular opinion.
Like others I think a course is attractive when there is a broad range of modules available, including all the areas that potentially interest me (and I was pretty mathematically open-minded when I was a sixth former!). The general environment also matters to me; decent staff-student interaction, and a student body who love the subject. Beware sampling bias I suppose.

I'm a big fan of numerical work, some of my friends were not, and some were indifferent. This is why I liked my university's approach of being able to submit combinations of optional computational projects chosen from a long list covering most fields up to a maximum number of credits. I don't have strong opinions on dissertations.

The main things I really liked about my course were:

1.

Ability to try modules (including non-assessed problem sets) before committing to sit them for examination, and being able to audit courses.

2.

The university provided assistance organising summer research projects in academia and industry.

3.

Longer, terminal, exams.

4.

Student and staff culture.

(edited 2 years ago)
Original post by zetamcfc
Variety of modules apart from the standard ones.

Lack of modules in the area of interest of a student will discourage them (at UG at Aberdeen, lack of Stats modules caused people not to go as I observed on open days. This applies to Pure too, as Nottingham are/were getting rid of Galois Theory which I know current students who were really not happy with that, to the extent they were thinking about transferring).

Computing will be important to some and not to others, so the option should always be there. Too many mandatory courses piss people off more than anything else. Freedom of choice is a massive plus.

Solo projects are always off putting to people to start with. However, they are a great way to get people into reading actual papers. Getting people to write mathematics in a clear and concise way and allow them to express themselves. So they should be encouraged. Also for getting people into more niche areas this will be a big boost.

At the end of courses have a lecture about where the specific module leads and explain some big results that have come from the module.

Nothing to do with curriculum but:

A common area where you have tables, chairs, BLACKBOARDS (NOT whiteboards) comfortable seats, etc. So people can do mathematics, talk mathematics or relax, with other mathematicians from first year UG to senior academics. Making the atmosphere of the department better.

Renowned mathematicians who actually teach UG courses is a massive boost.

Tutorials, with time with the lecturer.

Just my thoughts as I had nothing better to do.

BSc Applied Maths enrollee at Aberdeen University for 2021/22.

What is UoA like for its maths classes?

I heard the programming class is pretty decent for introduce students to Python.

As for the Calculus and Algebra units what method of teaching do they use there?
Reply 16
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Original post by AnonymousMathmo
Hi. I'm a lecturer at a UK mathematics department. We are currently revising our curriculum. I'd like to ask you all: what do you look for in a university maths course? What makes a course attractive to you? Why choose one course over another? Is computing important to you? Are projects important? And, if you're already at university: how is your course different or similar to what you expected?

Former Maths student from U. of Cambridge, failed 2nd year exams and was kicked out.

I enjoyed solving problems. That was the best part of it. Trying problems at example sheets and seeing if I could solve them. That's also why I applied to cambridge, because I wanted to do the STEP papers, it was fun.

What I didn't like was the lectures. They were sometimes hard to follow and there were no handouts/teaching materials for if we missed lectures or couldnt keep up with them, so I mainly used the notes of a past student to study, but that didn't really feel right.
Original post by gesuom1
Former Maths student from U. of Cambridge, failed 2nd year exams and was kicked out.

I enjoyed solving problems. That was the best part of it. Trying problems at example sheets and seeing if I could solve them. That's also why I applied to cambridge, because I wanted to do the STEP papers, it was fun.

What I didn't like was the lectures. They were sometimes hard to follow and there were no handouts/teaching materials for if we missed lectures or couldnt keep up with them, so I mainly used the notes of a past student to study, but that didn't really feel right.

Out of interest how were you doing throughout first and second year academically? Were you expecting to get the result you did or was it surprising?
Reply 18
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gesuom1
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Original post by GreenCub
Out of interest how were you doing throughout first and second year academically? Were you expecting to get the result you did or was it surprising?

I was struggling but I didn't expect to fail. I had depression but I didn't understand why I was depressed. I suspect it may have been because of some drugs I was prescribed.

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