Should I go out of my way and give non-interested students a rigorous understanding of the subject?

Question

I will be working as a TA in Calculus 1 this semester. In Norway, this means leading a study group with about 20 people (most of the days, I guess around five or six will show up), writing up the exercise-numbers on the blackboard, and answer any questions they have about them. More than likely, I will get students without an interest in mathematics (biology students, chemistry, geology etc.)

If the students have no interest in learning the rigorous and (subjectively) interesting parts of the subject, should I still force these concepts upon them? Many of them will be forced into taking more advanced subjects later (Linear Algebra, Calc 2). However, the nature of Calc 1 allows you to get a C, or maybe even a B, by simply cramming methods. I am having a hard time making up my mind about this, because it is very likely that my students wishes (and maybe what's best for them in terms of grades) will be in strict conflict with my philosophy as someone who hopes to become a good expositor of mathematics.

(The best example may be the formal definition of the limit. This can be taught well, as in, "this is why it works", or by simply reducing it to a humanized algorithm, which will often give you a correct value of delta.)

Answer 1

This is a very narrow answer, but I feel that if you construct the questions cleverly, you can teach the neat concepts conceptually, even to previously "uninterested" students.

For epsilon-delta, I've had some success with questions like:

• Suppose someone is trying to prove that $\lim_{x \to 3} x^2 = 12$, and tries $\epsilon = 8$. Find a value of $\delta$ that works with this $\epsilon$.
• What is an example of an $\epsilon$ that will not work when trying to show that $\lim_{x \to 3} x^2 = 12$?

They almost can't help but gain some understanding of why it works if you ask this kind of question.

Answer 2

I imagine a scenario like this: you see an error and ask them how they arrived at what they have written. They can't explain it. You then ask them whether they want an explanation.

I suppose a student might say "just tell me the answer" but that's treating you like a glorified answer key. How will they get the answer on the class' assessment? But their reasoning may be different, even if they did decide, in some way, to come to a tutor.

I think your focus should be on understanding. But, then, that's my philosophy. When you're a tutor, you're working for someone and they may have different ideas. Your colleagues can support you in your philosophy, but some people are hired (for example) to do test-prep work and would not get rehired if they did not use cramming approaches that are (let's be honest) near useless for understanding.

While someone else may have an insight from their experience that will help you, I'm going to say that this may be very much a personal decision because of the employment ramifications. If I am understanding correctly.

A somewhat analogous situation from public school: a school administration in public school may mandate a certain curriculum pr pedagogy. Teachers very often face philosophical differences. They may well ask "should I follow what my math coordinator and district want me to do, or should I go outside of the acceptable leeway I've been given?" If one is in a situation with personal consequences, then it's a personal decision. Especially after other measures (like petitioning the administration) have already been tried.