Monday, February 04, 2008

How to deal with uninteresterd maths undergraduates?

This post is going to consist of two parts. The first part (much to everyone's relief) will be about the post title and the second about where the title came from. (i.e. some strange happenings of the day). Note the second part is going to be posted tomorrow!

Indeed, it can be seen that there exists a large number of undergraduate mathematics students, who are really just "students". They come to university with a commercial idea of university life, and try their utmost best to not be disappointed with regards to this impression. In instances like this it is hard not to generalise, but I will be looking at two subsets of the maths undergraduates: maths students and ¬ maths students. (i.e. "not" maths students!)

Is it wrong of me to create such a harsh division? Should students who have no interest whatsoever in their course material, be allowed to be called mathematic students? I am not asking about competent and able students here, for it is obvious that in many instances, being good at something doesn't necessarily mean you enjoy it. Also you could enjoy something and not be very good at it. (I can think of many examples in my case for this, namely enjoying applied maths and not being very good at it.).

This debate breaks into smaller chunks, and each contribute to why studying no longer happens. It firstly starts with the image of knowledge and learning. We can no longer do anything about the nasty image associated with university life, and I will live in my cloud, that once upon a time there existed a place where universities were a place to study. That is the way I see my university: an institute for education. A place with teachers, who provide us with a basis of knowledge to explore maths further. The word education comes first and every other "plus" comes next. (Although I am still scratching my head about these other pluses...) Sadly though, the advertising campaign for universities being there for "studying" has long disappeared.

Before we even get to university, there is the question of what motivates someone to apply for a maths degree. Everyone can't be expected to know what they want to do in life, and so some people apply to do maths by process of elimination. Their reasoning could possibly be influenced by the positive outcomes of doing a maths degree (in terms of transferable skills etc. and job prospects). So this type of student will most likely be mechanic, unless of course they find inspiration from the course material. A student with exceptional mathematics ability might be in this situation and will probably go on to graduate with a top degree, and go on to a good career. All the time not having actively been interested in maths, but studying mathematics as a means to an end.

What about those students whose ability is not quite like the one mentioned above? What happens to them during their maths degree? Do they go on to graduate, albeit it being a struggle?

Behind ability, there is a thing called hard work and struggle. We struggle at different times of our life which influences what we find easy when we do. I don't see any reason as to why those students without "exceptional ability" shouldn't graduate. We all have to put in hard work at some stage of our lives.

My next question is, how can we "convert" these students to see the beauty of mathematics and what a maths degree is about, to help them? I believe that if a student understood the beauty of their subject, they are half way done.

I'm going in circles at the minute, so please bare with me.

The issue I'm trying to address is not of the ability of maths students, but of their motivation to study maths, and why they do so. Some enjoyed maths at college whilst others loved it; and some felt that maths was the only degree they could stand for three years. (I've already mentioned job prospect motivation).

What did they enjoy about maths at college, you ask them? "There is always a correct answer, and you know if you've done something wrong"; "I hate English and can't write essays if my life depended on it, so maths it is."; "Because I was good at it."; "I had brilliant teachers who showed me what a cool subject it was."; "I knew what mark I got after an exam."

And on and on these replies go.

What I failed to mention last week, was that I had an interview. During this interview I was asked something along the lines about how I would go about teaching maths, and what's my take on the current situation. My reply was something along the following lines (with lots of repetition and a lot of erms and "you know"!)

In college and schools the creativity of mathematics is suffocated and drowned. When the word "creative writing" is mentioned, everyone thinks about section B of their English paper. You would be a fool to mention maths and creativity in one sentence in them institutes. What lies are told to maths students is unbelievable. Some teachers find it neccessary to persuade students to like mathematics because there is a right and wrong answer. There is no grey matter, as is ever present in English. If you've done something wrong, keep working at it Chuck, you'll get the right answer soon.

Codswallop. That is the biggest mistake that is happening in our schools. Teachers should impart the creativity of mathematics to students. Not it's finality. Understandably in most instances you either get a question right or wrong; but the most important aspect in answering a maths question is your thought process, and how you arrived at the answer. There is your CREATIVITY. Why do schools scare students who hate the fact of there being only one correct answer? Can't we keep all students interested in maths?

There is a freedom in maths, quite like in English, where one can explore and discover many fascinating things. Students should be taught how to be fearless in this exploration. Indeed what should be developed is their creative mathematical thinking, and what questions they can ask to explore further. Not about how many right or wrong answers they obtained. The process of obtaining all correct answers is a funny one. Some students stumble at the first hurdle and because they got an answer wrong they lose hope. What they fail to understand is, that by getting the answer wrong they've created another route for their adventures.

Whoops. I'm getting all ranty now, but imagine if the motivation for students to study maths at university was the creativity of the subject? Would mathematics departments be different then? The root of this problem then seems to be secondary schools (and possibly college).

I won't ever forget my C3 teacher telling us that there is no point in her teaching us the section on proofs, for we would only lose a few marks if such a question appeared. There are so many constraints on institutes such as colleges and schools, that passing exams is given more importance than understanding material. The teacher was probably given the instructions "everyone must pass" and indeed she always aimed to get everyone get more than 40%. Her job dictated that she do this, and I can't blame her for it. However who does this dictating? I feel a sense of frustration when I see schools and colleges disregarding individual pupils and their needs, but instead seeing grades only.

Colleges and schools impart the systematic nature of mathematics to students, and students believing this, decide to study maths at university. There they fall with a loud bang, grimacing in pain and in shock. They enter a completely different universe. Obviously you have to adapt to the university system when you first start, but many students are left wondering, why was what they had previously been taught called "mathematics"? \hyperbole.

At university though, some students still cling to what they believe used to be maths. How can they be faulted for this, for during the past 7 years of their life they had been told something else, and now their university lecturers are making ridiculous claims about mathematics. These are the students of who I speak of. They demand solutions and resent the notion of having to do more work than they were used to. Obviously since these students have a plan to succeed, they do, however they still cling on to their belief of what maths used to be.

I would say that a majority of students, seemed to have been scared of by the initial difficulties that they faced in their first ever semester. They don't see how they have progressed from them dark days, but they keep on wondering whether it is too late to escape. All week I have been hearing students telling me that they have chosen certain stats options and the history of maths course, because they are easy. They make me feel bad for doing 6 hard pure courses, and not choosing any "easy" ones. These students will graduate happily for once again they feel comfortable, and a medium where what they used to call maths exists.

My first ever semester was dark (but not like the previous semester, for that was demoralising!) I tried to cling onto what I thought maths was, but thanks (mainly) to Dr. Coleman I was cured. Then in my second semester this blog and other inspirational lecturers (erm... all but one!) opened my eyes to what mathematics is all about. I felt that creativity, and my desire to have wings was fulfilled.

Everyone is unique, and not everyone needs motivational teachers. So what do we do of the students who never let go of this "college maths" idea? How can we get the undergraduates to see the beauty and creativity of mathematics? My friends once argued with me, that I seem to have an expectation of people to enjoy maths in the way I do. I disagreed (obviously) and replied that I won't stop being enthusiastic about maths, just because it irks others. (As I once did probably).

Having (positive) second or third year mentors is one thing that can be done; but otherwise, my mind draws blanks on how we can persuade and coax students into thinking creatively, and not looking at and demanding solutions straight away. It took me one semester to come out of that practice (yes, I confess to looking at the back of my reasoning book for some answers due to hating the course material and various other college antics).

I don't know how long I've gone on for, but I'm not going to stop just yet! The "college maths" students are the majority, but you do have some in between, and others who were shown the creativity at a young age. For these students it is important for them to be allowed to work in a positive environment, as opposed to the negative one of the other group. They shouldn't be made to "hide" their love of maths and indeed, they should be able to express it somehow.

This is where The Galois Group comes in, and I'm mightily relieved that some students are actually enjoying the lectures. (An email was sent the other day and I stupidly forgot to write the room number on it. This resulted in a few replies enquiring about the room which made me happy! Yes, small things please me.) One student even asked me about the lectures (even though I wasn't able to persuade him to volunteer, which has become my second aim in life!). My intentions, when having found the motivation to create The Galois Group (TGG), was that it would cater for this small community and I see this happening. I am slowly going to introduce the idea of the magazine for I sometimes see it being a success. Maybe through that we can also work on trying to help the uninterested students?

The idea for TGG further went on to claim, that maybe the larger community can be influenced by the smaller one. Still a long shot, but every little counts! Why does this bother me so much? Apart from being unable to understand how people can spend three years doing something they don't enjoy, their attitude towards maths has changed. There degree is a chore, one which they can't escape from. We should help them though and make this chore as easy as possible.

FINALLY: I will probably be the first person to say that exams are good, for then at least I try to rigorously understand course material, rather than having an artificial understanding of it. But I feel that exams are suffocating as well. I confess that my petty reason for not studying applied maths this semester is due to my fear of failing them. There is no guarantee that I will pass my other modules (geometry scares me), but doing applied maths is a bigger risk (and then what would I drop?) I feel ashamed of my reasoning, which is why I am hoping to attend the fluid dynamics lectures, even though I'm not taking the course. Exams dictate so much of what is thrown at us, which is unfortunate in one sense, for students then forget the beauty of knowledge. The beauty of education and of learning is lost.

Is there any positive answers to the question being asked? Indeed, a healthy mathematical culture at the university can't do any harm, but how to impart it... Ponder on this I will, and I am open to any thoughts on this matter.

*Note: generalisations can be annoying sometimes, so apologies for causing any eyes to twitch!


Anatoly said...

Excellent post.
It is indeed very depressing when you see people who study math but don't understand and even worse don't want to understand what it is all about...

Hope you will manage to change this attitude of the people around you.

Beans said...

Hi Anatoly,

Thanks. The "not wanting to understand" is much worse; or they just want to be able to answer questions (correctly) without thinking too much about the theory or motivation involved.

Thanks again. For a second I was going to write that it's not possible to change people's attitude, but I myself contradict that statement, for my attitude took a drastic change!

Anonymous said...

Good post. I agree with everything you said.

On a different point, why are TGG lectures so "pure"? Everyone knows all the interesting stuff is at the applied end of the range!

Beans said...

Hi anonymous,

Thank you, but would you by any chance have suggestions on what can be done? (I'm still thinking about this you see).

I take it you're an applied mathematician then! If I recall correctly our first lecture wasn't very "pure". Last semester we had one pure, one applied and two to do with history.

Everyone? Does that mean I'm not included then?!

Nevertheless, if you're at Manchester and are so disheartened to see this, please do volunteer to do a lecture which is more "applied"! (And if you're not from Manchester and still interested in doing a lecture, do get in touch).

(I see what you mean though, for a majority of the lectures this semester seemed to be "pure".) I don't think we have many applied lecturers attending, but I'll see if I can get any to volunteer for the future.