Setting Problem Sheets

Post date: Mar 3, 2017 5:07:54 PM

After nearly two months of silence, I've found time to write my second post. :-)

In my last post, I talked about how we could try to get students to work with definitions, to the point of internalizing them. With this in mind, I tried to implement a solution by redesigning the problem sheets handed out in my course this term. The non-assessed problem sheets were separated into three parts:

• Part A: Questions to get students to think about the new definitions and theorems they have seen
• Part B: Problems they should be able to solve if they had understood the current material in the course (and the only part they had to hand in)
• Part C: A mixture of questions linking this course to other courses, questions to get the students to think about the direction of the course and harder questions in general

The reasoning was that through part A, the students could internalise the definitions of the course, and engage more with the theorems. How did I implement this in practise? During the first few weeks of the course, the student is more or less bombarded with definitions (or recalling definitions from previous courses). So for the first sheet, it was not hard to think of questions along the lines of

• Is this an example of this definition?
• Can you think of an example with satisfies definition X but not definition Y?
• For each of these objects find X, Y and Z (linked to definition X, Y and Z).

In fact, at the beginning, the hardest problem is to make sure there are not too many questions. One could argue that since Section A was not compulsory, there is no reason to restrict the number of questions asked, as students don't have to do them. But I think from a psychological point of view, if a student sees too many questions they are less likely to do any of them. Although I still want to investigate if this is the case.

As the term moves on, there are less and less definitions introduced, so the emphasis moves towards theorems. The problem that arises there is that anything important enough should be included in part B (so that the student know it was important). Hence the only questions I included in part A were questions of this type:

• Is there a counterexample to Theorem A if we drop assumption B?
• Theorem A states "P implies Q", can you think of a counterexample to "Q implies P"?
• Explore how Theorem B is a generalisation of Theorem A (or Theorem A is a special case of Theorem B).

What I need to explore next is whether students used this resource or not, and if they benefited from it. As it stand, the six type of questions above seem to be good questions to engage students with definitions and theorems, yet I am on the lookout for any other type of questions that could also help.