How to Create Problems for Students (Part-I)

A question sometimes asked to me is ``How do I create problems for tutorials,  assessments etc.?' Ideally, I would like to go through all of the following  steps for creating a collection of problems  in any topic

• First, I would identify the topics on which the problems are to be  written.
• Then I break up the material for every topic  into small units which  must be understood by a student. Each unit could be, for example, a  definition, or a theorem, or a condition in the statement, or result of  the theorem. This gives me a List  of  Topics and Aspects  to be tested.
• Next I ask myself what do I mean by understanding a given (small) portion of physics of maths. So for example, understanding a statement of a theorem means understanding the conditions under which the theorem holds; which condition are necessary and why? precise statement of the theorem; ability to distinguish from  a similar looking loose, or imprecise, statement;  ability to check if conditions of theorem are met or not.
• There will be a similar aspects which need to be identified to test  understanding any physics or mathematics.
• Then ask myself how I can I test students' understanding of each aspect. I start with most important aspect to be tested. {\it Important may usually  mean something that I want to communicate and want the  students to learn \underline{at any cost. I list them in a  order   of  priority I would test.
• Then I start writing questions and problems in different formats. 

I try to test the same things by putting questions in different formats. For example 

•           Check if the following potentials have a  property X;
•           Give examples of potentials having a  property X;
•           Classify the potentials according to their having  properties X, Y ...
•           Sketch graphs of potentials which have  property X

Depending on external factors, time available and deadlines etc, I continue to write questions, problems.  Usually I start doing this without consulting any other source. 

Then next step is to look at external sources and see what they do; I look for different ways questions can be asked on aspects in the List of Small Topics I have created. When I consult external references aand look at the problems from other sources. I check if they test what is already there in my list?  They test something which I missed, I may take the problem, make variations . While consulting other sources, I also check if I  missed out something  in my  List of Topics to be tested.

I Continue doing this for a few iterations. In this process I would create a good number of problems. It is then time to examine the problems closely and to check if the statements are clear and unambiguous etc. A lot of worthless questions will make to the collection of  the  problems created in the above manner. It is important that such questions be identified and  are  weeded out.

Finally, before putting the a problem in assignment or exam papers, I have to check several things. For example,

• Do I supply any set of numerical constants? 
• Do I supply hints or some formula? 
• Do I give the result as part of the question or not?'' and so on.

It is important that a full solution be written out before the problem is assigned or made part of a question paper.
I am lazy and donot do every time.
Frequently, this has casued problems  and resulted in questions that wrere not framed rpoeprly.

Even with best efforts, some times there will be other requirements which must be taken into account. and these become clear only when you have alreday delivered the questions.  One such important requirement is that the questions be posed in such a way that evaluation of the answers becomes smooth. I will give one example.

•  I gave a question to a class of thirty students a question where there  required to draw their own diagrams and were free to use their own notation.  Their task was  to geometrically interpret  the question in  terms of lengths and angle and find their values and had the freedom to present the answer (several in number) the way they wanted.
• Evaluating this one single question became a very time consuming an difficult job.
• So I had to rewrite the question, defined the notation by freezing the notation for different  expressions, as to  which expression will be called \(\theta\)  and which expression will be called\(\rho\) etc. They were asked to draw diagrams showing  various  angles and  lengths with my notation.       
• This time they were given a table to fill  with  the  numerical values. This made  the job of   evaluation   smooth and   fast. All I  had to do was  to compare  their figures and tables with my figures and  tables.

Finally, one has to check that if the questions and answers are OK. The questions must be OK in the sense that they are to  be handed over to some other  person (let us say, non-expert office staff). Assume that he/she   has  to  conduct  the test/ examination without possibility of seeking any   more     clarifications  from the paper setter. And that the answers sheets    will be     evaluated by a  third party person.

{\it This is a long list of things to do. I did something like this for my book on Complex Variables}.

For reasons of time available, I have not always done all this and at  times it has led to statements of problems not being framed properly.

As I said in the beginning, all the above steps are ideally needed for creation of a good (\tt collection of problems).
For a smaller number of problems, I would see what steps are necessary and what are not essential.

Like everything els, you can get more ideas, and  manuals and material on the internet;  (search on 'question types' for example) on the process of creating the questions.

My own favourite method is to do crowd sourcing. You have to wait for Part-II of this blog.