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I sometimes encounter students who ask questions like 'Why are we learning this if it won't be on the exam?' If there is time to spare I like to teach interesting applications or natural extensions of the material we have covered.

How do you respond to such students?

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    $\begingroup$ How do they know it won't be in the exam? You decide what to include in the exam unless it's a standardized exam. $\endgroup$ – Paracosmiste Dec 29 '18 at 18:00
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    $\begingroup$ Explain to them that acreditation and degrees are not the only goals of studying and learning. Explain to them positively what are some other goals of studying and learning. Some will not accept such explanations, but some will listen, and in general even the most instrumentally motivated students respond positively to an instructor who professes a respect and enthusiasm for learning and studying for their own sake. Also students have a reasonable desire to understand what will be the criteria applied in evaluating them, and part of this entails having an idea what is subject to evaluation. $\endgroup$ – Dan Fox Dec 29 '18 at 18:18
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    $\begingroup$ @DanFox: Perhaps you could convert your comment into an answer? $\endgroup$ – J W Dec 30 '18 at 8:28
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    $\begingroup$ @user683: Perhaps you could convert your comment into an answer? $\endgroup$ – J W Dec 30 '18 at 8:28
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This is really two different questions: (1) applications of the standard material, and (2) additional material that extends the standard material.

For applications, my answer, addressed to my students, would be something like this. We have just learned math topic X, and I've presented a couple of its applications, A and B. These applications will help you to understand X better, will help you to understand why we would care about X in the first place, and may come up in later coursework in your major. You ask whether A and B will be on the exam. Applications on the exam could include A, B and C, where C is some application you've never seen. If you actually understand what the material means, and have seen a couple of applications, then you should also be able to figure out new applications for yourself. If you can't do this, then you don't understand the material.

For additional material, it really depends on what your motivation was. For example, if you're teaching first-year calculus but you want to introduce some vector calculus, the answer is probably that you just shouldn't. If the motivation is that it's super fun, then present it that way. Say, literally, that that's why. In general, make sure you can give a clear answer to the question and then preemptively answer it when you introduce the material.

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Well, for me it would be a big deception if that happened to me, provided that the students didn't actually have reasons to complain. If so, avoid teaching this "extra material":

  1. If the students do not have the required previous knowledge. Make sure they all have it (or at least the big majority). Having been taught before doesn't mean they remember it either.
  2. If the students have so much pressure. Nobody appreciates learning when they've got more urgent things.
  3. If those contents are quite unrelated to the main topic, while other issues are more important. I remember things like "why are you teaching us group theory when we are needing Fourier transforms and nobody's helpping us?". That's very dissapointing.

So, if it is not any of those cases, or similar, then yes, the situation must change. I assume we're talking about lazy / unconcious students who just want to pass, and they don't really care about learning or not.

So here my advice. In short, it is: "okay, you won't need it for my exam, but next year you'll be using this. The teacher won't have time to explain this, and (s)he will go very fast through this, so you better understand it now so that you can follow he class".

But it is important that you must transmit how much one suffers when one gets lost in class. The suffering of being in your seat and ask yourself "what am I doing here?" And you can't leave. That's stressing and agonizing. And not only you have a bad time in class. Then you don't understand anything. Since you don't udnerstand it, lessons go by and you keep at the start point, so you can lose a whole year. Make them imagine and "live" the situation. That's what I'd do.

EDIT: I didn't have much time and I left the answer like this. Now, re-reading it looks quite terrible . Of course, you should also do the opposite: transmit how satisfactoy is to learn something new, which helps people make sense of everything. Connecting concepts is always good. Those times when "suddenly everything makes sense" are enormously satisfying. You must transmit all this as well.

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    $\begingroup$ I don't understand the first sentence of the answer. $\endgroup$ – Ben Crowell Dec 30 '18 at 16:19
  • $\begingroup$ It means I'd be sad if my students asked "why should we be learning this?", as long as they had real reasons to reject that knowledge by the moment. $\endgroup$ – FGSUZ Dec 30 '18 at 20:04
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    $\begingroup$ Why "deception?" $\endgroup$ – Ben Crowell Dec 31 '18 at 1:52
  • $\begingroup$ I meant "dissapointment", "desillusion". $\endgroup$ – FGSUZ Dec 31 '18 at 10:48
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If you're going to teach it, than include it, or a credible threat of it (meaning sometimes on the exam).

Furthermore, if the class is not nailing the regular topics (high percentage of strong grades) than perhaps you shouldn't do extra topics but drill more on the ones that aren't strong yet. Remember drill is more effective than lecture.

It's not about how much you can "get through" but about how well you teach the majority of the students the topics they need to know. It's like sports. Fundamentals rule.

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First, any time students ask "Is this on the test?", it makes me reach for a vomit bag. But my reaction is irrelevant compared to the student experience.

Most students [consider themselves] busy and [in their minds] you've already decided that the material is not important enough to assess for grading. This incentive of grading is, for many students, the one true signal of what is important enough work on. Once students know something isn't graded, they will turn their attention to friends, family, health, other classes, jobs, money, relationships, housing, etc. and other areas of life that they actually perceive as important.

Analogous situations:

  • You call customer service and are told by an automated recording for 2 straight hours, that your call is very important. How much do you care about such claims of importance relative to the fact that the company doesn't hire (incentivize) enough people to work in customer service?

  • Your boss says: "From now on, everyone in the company spends 10am-12pm every Monday, Wednesday, and Friday working on project X, under my direction. You're not going to get paid for those hours but I expect you to show up cheerfully and work as hard as you can anyway. Why? Because we don't just work for pay! We work for many other reasons, such as fun, learning, and natural interest. Come on, guys, be intrinsically motivated! Like me! Project X is cool! As a bonus, some of you might find the experience with project X useful someday. [Edit: Besides, I'm not sure how to measure your productivity at all for X, so there's another reason for me not to pay you for your labor.] Anyone who doesn't want to put in those hours is just lazy and instrumentally motivated and that's a big problem."

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    $\begingroup$ I disagree that deciding material is not on a test says anything about the instructors' view of its importance. There are so many other factors. Is the material testable in a reasonable fashion ? Some things are just easier to test, especially problems which allow some canned solution. In contrast, understanding definitions or inutition are really hard to test but that material is very important. Testability and importance are not the same. Also, our "feeling" as instructors does matter compared to any experience. If we cannot share our feeling, then replace us with robots already! $\endgroup$ – James S. Cook Jan 6 at 23:07
  • $\begingroup$ I apologize for the poor wording. I agree that testing ≠ importance. I MEANT to write that post from a typical student's perspective, which is: "The teacher isn't trying very hard to test this, so why should I try hard to learn it? It must be unimportant because otherwise the teacher would do SOMETHING to grade it..." Whether or not we like that perspective does not change its status as a normative response. Our feelings really are irrelevant to that. $\endgroup$ – WeCanLearnAnything Jan 9 at 1:01
  • $\begingroup$ Also, those things you think are super hard to test - are you sure no other teacher in the world, ever, past, present, or future, has ever found or will ever find a good way to test it? Are you sure it's really so hard? Do you expect their effort to learn it to be greater than your effort to assess it? $\endgroup$ – WeCanLearnAnything Jan 9 at 1:02
  • $\begingroup$ It's not hard the first time. It get's hard as the years go on and the questions become known. It takes a lot of time to come up with good questions. Good teaching takes a lot of time. Unfortunately, many institutions saddle teachers with 4/4 teaching loads and numerous other responsibilities. So, yes, it is hard. Not impossible, but hard to maintain those sort of questions with sincerity. I see your point, but I also think that more responsibility needs to be put on the student these days. The trend we take is not healthy overall. Of course, just my opinion. $\endgroup$ – James S. Cook Jan 9 at 6:43
  • $\begingroup$ Would you like it if your boss said: "Employees these days need to take more responsibility for doing work that is not paid. I'm too busy to figure out how to measure employee productivity, so they should just accept unpaid work responsibilities cheerfully and work really hard anyway." How would you feel about those responsibilities? Probably the same way your students feel about ungraded material. $\endgroup$ – WeCanLearnAnything Jan 13 at 1:08

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