In this blog I share my sceme of creating problems and assessment for teaching and evaluation.

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
to be tested.**List of Topics and Aspects** - 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
. I list them in a order of priority I would test.**Important may usually mean something that I want to communicate and want the students to learn \underline{at any cost** - 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.