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Motivating A-level maths students, and comparison of examination systems
By Jeff Lindsay (T2855) on Thursday, June 22, 2000 - 11:29 pm:

I work at a large college where we take a wide range of students to sudy A-level Maths - from GCSE A* to those with C at intermediate.

One question that I have is 'how do teachers motivate students to work well?' Many students of middle ability seem to drift along, not making the most of class time, not doing all of their homework and so on. They seem to improve at the time they make their application to university but by then some time has already been lost.

It may be that we are doing all that we can - but I'd like to know other people's ideas.

Thanks

By Muthukumar Udayappan (M41) on Thursday, July 6, 2000 - 08:04 pm:

I am a 30-year old bank clerk working in the Middle East and I've got into re-learning Maths after being a not-so-good performer in Maths at school.

For me, the main motivator has been understanding the meaning of mathematics. It is necessary to go behind the symbols and equations and try to visualise what we are trying to achieve. When this is done regularly along side formal classwork, the student invariably realises that maths is just another language and a very precise one at that. Finally, when concepts are applied, the utility of theory and the realisation that pure maths itself is just an abstraction of so many class of problems, make one want to learn more deeply and widely.

You could direct your students to the Nrich site for a start in this kind of a experience.

By Brad Rodgers (P1930) on Thursday, July 6, 2000 - 11:18 pm:

As a student, I have been able to see why some of my peers don't enjoy maths. The first and foremost is that generally maths is taught (at least in my school) as a bunch of formulas. While most average students, losing their zest for "why?" at the age of four, find this method to be easier, they can still refind this inner genius by generally learning just a single proof of why things are. Research has shown that students exposed to the reason behind finding parallelograms area will go on to find the area of other geometric shapes on their own free will. So always explain why formulas exist and encourage questioning the teacher. One of the best ways to teach students reasoning is, as said above, tell them what's behind the symbols.

Also, be sure to teach them the relevance of maths in our everyday life. Few students find maths to be beautiful, so they really see no reason in it.

By Dan Enache (P2704) on Tuesday, July 11, 2000 - 08:17 pm:

I think that students must really be motivated by their own ambitions. They shouldn't rely on a teacher to motivate them. At A-levels you are already, what? 17-18 so there can't be any more mtivating factor than the real world.The world is very harsh on some people.But really there are no limits in where you can go if you do very well in school. I'm at GCSE level, taking exams next year. I don't rely on teachers to write letters home so I can get a bashing from my parents. I guess, what I'm trying to say is just do all the hard work and don't limit yourself on the easiest way out.

Peace, Dan

By Joanna Cheng (P2322) on Saturday, August 12, 2000 - 09:49 am:

Ok before I actually say anything I want to get a few things straight.
what are A levels? And what are GSCEs? Do you have to do them? etc

Anyway, I think many people don't enjoy maths because there is no creativity in it. This is true for nearly all my friends. There isn't really much you can be creative about in maths. no matter what 1+1 is always going to equal 2.

But I agree with Dan; you really have to motivate yourself to do well in anything. If someone does not want to work at something, nothing anyone does or says is going to make much difference.

Anyway I think if you're not going to work hard at something, why do it in the first place? A couple of my friends (who don't really like maths) are doing specialist maths just because it boosts up your ENTER score. I think that's a bit stupid, as it's just going to be a drag.
What do you guys think?

Joee

By Neil Morrison (P1462) on Saturday, August 12, 2000 - 12:12 pm:

A-Levels are an English qualification, which are done in the latter two years of secondary school. GCSE are generally done in the two preceding years. You usually choose between 6 or 9 different subjects in GCSE (although there are restrictions; you probably have to take English and Maths etc). The general choice for A-Level is 3 subjects, although many students take 4 or more. The problem with A-Levels is that you work for two years and it all depends on a month of exams at the end. I think in Australia you just choose a number of subjects, and get an overall diploma thing (HSC?).

In Scotland, where I live, the GCSE equivalent is Standard Grades (fromerly called O-Grades) and there is no direct A-Level equivalent. In Scotland you usually do 3,4,5 or sometimes more Highers, which are a one year qualification in each subject. The bonus is that although they only take one year, you can do them the next year as well. However, many students nowadays going to university stay on for the final school year to do CSYS (Certificate of Sixth Year Studies) which is sort of like A-Level, only again it takes one year, and it is more like a first year uni system.

Hope that wasn't too confusing!

Neil M

By Brad Rodgers (P1930) on Saturday, August 12, 2000 - 08:09 pm:

It is interesting that you should bring up the point that mathematics doesn't involve much creativity. While I tend to disagree with this, I do agree that the way that things are taught in school invokes no creativity. So perhaps it would interest more students if schools would not just hand out formulas or methods and give students values to "plug in", but actually allow them to develop the methods on their own with a little bit of guidance. Surely it would take some creativity to develop nearly any formula, method, or nearly anything in math, but schools seem to be avoiding this aspect of it. Whether most students would find such a style too difficult is another question, though.

Brad

By Sean Hartnoll (Sah40) on Saturday, August 12, 2000 - 08:51 pm:

I agree with Brad here, maths involves loads of creativity, just that it is never presented that way. Even in university you are given a load of finished axioms and theorems, and never a view of how they were discovered, and what was the process that lead to their discovery. This contrasts with, say, physics, where a historical view of the subject is very common. I think that teaching maths in a way in which the pupils themselves come up with the answers would be good.

Sean

By Tom Hardcastle (P2477) on Sunday, August 13, 2000 - 12:07 am:

In many subjects, including maths for several syllabuses, the A level courses are modular; this means that exams are taken over the course of the two years, usually twice in each year. This avoids the month of exams at the end problem Neil raises. I think that statistically, more people pass in modular courses but less people get As, although how valid this is I have no idea.

Tom

By Neil Morrison (P1462) on Sunday, August 13, 2000 - 01:10 pm:

Brad is right. I think the Scottish system tries hard (but still fails) to envoke some creative exciting image, (some of the CSYS questions are quite imaginative) but in A-Level, you are taught how to do a type of question, which will come up with the numbers different. This is not really teaching.

Tom-

I know about the modular system in some places, but doesn't this just mean more exams (with each having a share of the importance)? My CSYS Maths Paper 1 was solely dependant on a 2.5 hour exam (and the SQA competency;) but the point I make is that it was only a one year course, which is supposed to be like uni first year. This is good because people who know they want to go to uni to do a certain subject, can get an impression, while people who aren't sure what they are doing next can take more higher's in different subjects. I've seen people who didn't know what to do get 8 Highers in different subjects. They could have had 10 or more (but usually someone doing 5 in 5th Year would just to SYS next year) Compare this to the standard A-Level 3 courses, and there is a huge imbalance.

By Tom Hardcastle (P2477) on Sunday, August 13, 2000 - 11:13 pm:

Neil

Yes, you do get more exams, it's just that your entire grades don't depend on a month at the end of two years, which is nice. It also makes retakes easier, for those that need them, and gives people an idea of how well they're likely to do; you might really enjoy maths, but if you can't pass exams in it you aren't going to study it at university. It makes the system a lot more flexible, too, allowing students to pull forward modules and so cover more ground; even into their GCSE years. I don't really know much about the Scottish system, but I think you might be being a bit unfair on A levels. In the later modules at least there is more depth to the exam questions. Presumably this is one reason why Cambridge demands Further Maths wherever it is offered. And within the course there is an implication that the ideas behind methods are taught and understood by students; I don't think you'd find any A grade student who didn't understand what they were doing.

Tom

By Sean Hartnoll (Sah40) on Monday, August 14, 2000 - 01:02 am:

Actually, Tom, I think I've got to disagree on the last point. In the first year at Cambridge, I was amazed by the number of people who had As in maths and further maths who didn't know what they were doing (I'm not talking about a majority of people or anything, but a significant minority). This was manifested particularly two ways

(i) in an inability to cope with things that were really quite similar to what they had been done in A-level, only slightly different. And even more difficulty in generalising from previously learnt concepts.

(ii) in an inability to do exam questions at the end of the year, which in many cases were quite similar to A-level questions. In fact, I would say STEP papers are harder than first year exam papers (although I didn't actually do STEP papers, so I may be wrong here)!

So if this is the case for a significant minority of Cambridge students, I dread to think what the general situation in A-level classrooms must be!

Sean

By Joanna Cheng (P2322) on Monday, August 14, 2000 - 07:40 am:

Can someone tell me what further maths involves? Here in Australia, Further maths is for people who are really crap at maths but do it to get into a course at university. Then there is methods, specialist, and MUPHAS. I'm guessing Further maths there = specialist here, but i'm not sure.

By Tom Hardcastle (P2477) on Monday, August 14, 2000 - 01:01 pm:

Sean - Oh well, fair enough. Admittedly I don't spend very much time in A-level classrooms - I'm teaching myself the A levels because my college doesn't offer further maths.

Further maths seems to vary across syllabuses quite a lot. I'm just flicking through some textbooks and finding the chapter headings: we have
complex numbers
conics
hyberbolic functions
vectors and matrices (again, and forever)
limiting processes
multivariable calculus
differential geometry
abstract algebra

Some of these I've come across on NRICH so other people seem to be covering them as well. But others I don't think I've seen. What are other people doing? I'm on the MEI/OCR syllabus, by the way.

By Sarah Berman (P155) on Thursday, January 18, 2001 - 11:20 pm:

Joanna - further maths here basically means doing twice as much maths as you would for normal A-level. You get 2 A levels out of it and it is the best preparation for a maths degree.

I'm not yet on the 'further maths' stuff - we are doing all the modules people normally do in 2 years over one and are then going on to harder things nect year.