Style

Hi sir!
I have a small concern…actually a big concern…. having taken 2 exams already for which new lecturers taught this year, I am completely shocked by the change in style of examination from last year to this year, i have read your blog regarding the style of your paper, but wanted to ask to what level will you require us to have knowledge on the applications of techniques, ie will we have to explain what we are doing, or mention a theorem that we are using to apply the knowledge,and will the applications (and proofs) be set out like previous papers?

Could you let me know if you are going to reply to this e-mail on your blog?

Many thanks
Bhavna Patel

Repy:

I believe I’ve put up a number of different posts where a question of this general nature was addressed. Regarding our exam, I have tried my best to minimize the sense of surprise on the part of students. Having said that, I should once again express my own honest feeling about the matter.

Of course the question of how similar any two things are is a difficult one, subject to much interpretation. At a very sophisticated level, an important part of scholarship in science is the ability to see patterns and similarities that are not entirely apparent. For example, a remarkable series of discoveries in the twentieth century science revealed that the pattern occurring in the diffusion of heat is very widespread, including the motion of small particles in liquid and the fluctuation of the stock market. But even at the level of a basic course in mathematics, an uncontroversial fact is

There are very few problem patterns when the material is examined from a knowledgeable viewpoint.

A major goal of any course is to give people the ability to recognize the few patterns that are relevant to the course material. Eventually, we hope that a competent math major will equip people with sufficient ability to recognize analogous patterns occurring even in the practical problems of natural and social science.

I don’t think I myself ever realized how difficult it is for students to really appreciate this point, so perhaps I haven’t done a good enough job of teaching the material in this respect. In any case, you should be aware that you need to build your skills to a level where the illusion of stylistic differences disappears. For example, you should be able to read through the past papers for our course, and see that they are essentially the same.

Let me close with a comment very relevant to this global age where the skills acquired in education from quite distant regions of the world are subject to frequent comparison. I’ve worked in many different universities in the course of my teaching career. One thing I can say with honesty is that the past papers I’ve examined at UCL appear to me at least as similar to each other as the pattern of exams I’ve seen at other universities.

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