Responding to students' questions that aren't directly relevant to their exams

Question

What would you suggest as the best way to deal with students' questions that seem irrelevant to their upcoming exams?

When I was studying for my university-entrance exam, I came across a couple of university-level integration questions that I couldn't answer. When I asked my school teacher for help, he advised me to ignore them as they are irrelevant to the exam.

In another incident, when approached for help with a question from a Physics textbook, my school teacher said that the question is important but he didn't know how to answer it. I eventually got the answer from the educational service of a state radio channel, then the same question appeared in the following year's physics exam.

I think that in addition to exam-related knowledge, having a healthy curiosity about our teaching subject is important when assisting students with relatively novel issues.

Answer 1

What would you suggest as the best way to deal with students questions which seems like not relevant to standards of exam comparing with past papers?

First, commend the student.

Second, either start the student on an answer, or point them in the right direction, or say "let's figure it out" or .... Here's a story.

A woman I know was a math teacher at Hunter High School in New York City (this is a school for gifted kids). One student in her calculus class asked:

"I know about 2nd derivatives, 3rd derivatives, even -1st derivatives, but what about fractional derivatives?"

My friend didn't know. But they went to the library (this was before the internet) and found a professor in Germany who was an expert in these. The student wrote to the professor and they wound up writing a paper together for some mathematics journal.

And remember what Plutarch said:

A mind is not a vessel to be filled, but a fire to be kindled.

At a minimum, don't be a fire extinguisher.

Answer 2

Here are a few thoughts to assist with responding to student inquiries which address some of the scenarios mentioned with the guiding principle that every question has an appropriate time and place:

• Instructors have limited knowledge just like students, so if a question is raised for which the answer is not obvious, there's nothing wrong with either showing the student how you would figure it out (working it out, asking a colleague, Math SE, etc.) if there are not immediate competing demands on your time. If there are competing demands, you can commit to get back to them and provide a timetable for your response.
• If the answer is obvious but is best answered using some more advanced method outside of the scope of the course, then the most appropriate time to revisit it is after the student has become familiar with that topic. An approach would be to name-drop the topic and course (e.g., interesting integral -- it may be easiest solved using a technique in complex analysis).
• If the answer is obvious and easily answered using methods from the course but there is a limited amount of time (e.g., last in-class review session before the final) and it is not relevant to the exam, I think it is fair to defer the question (e.g., "see me after", send an email) or possibly say that we don't have time to answer that at the moment but make a comment about how you would answer it. If all of the above but no demands on time, I think the instructor should answer because relevant student questions should not be set aside solely based on whether the content will appear on the exam.