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I am a new teacher teaching mathematics (College Algebra, Calculus, etc.) in a college. My wife has made an interesting suggestion that I would like to have a discussion here:

Is it appropriate to assign an extra credit homework question on the "next" session?

Say that I am assigning homework questions for Section 3.1; is it appropriate to assign one routine question from Section 3.2, which will be taught in the next class period, to encourage the students to read the materials before the class?

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    $\begingroup$ On short quizzes (which I gave frequently, at the beginning of class, so that I didn't have to deal with homework) I sometimes designed the extra credit problem to be a natural lead-in to what was going to be covered after the quiz. For example, evaluate $\int \cos x \sin x \; dx$ two ways---one way by using $u = \cos x$ and the other way by using $u = \sin x$ (this would be just before a discussion of the effects of $+C),$ or find $y'$ when $y = xy + 5x$ by first solving for $y$ in terms of $x$ and then differentiating (this would be just before beginning implicit differentiation). $\endgroup$ – Dave L Renfro Mar 24 '16 at 19:23
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    $\begingroup$ My first year Calc teacher gave out chocolate fish for this sort of thing, which was enough to motivate the able students, and more fun than extra credit. This also got around the ethical issues of extra credit, which I don't think was permitted at the university. $\endgroup$ – Richard Mar 26 '16 at 2:08
  • $\begingroup$ Sorry to go OT. Chocolate fish? I always thought fish were like gummy bears, never chocolate. I need to go back and reevaluate all my long held beliefs. And buy me a pound of those fish. $\endgroup$ – JTP - Apologise to Monica Mar 26 '16 at 17:26
  • $\begingroup$ An alternative: Each chapter (unit, etc.), give students a problem set that includes problems from the application section of each lesson's exercises in no particular order, and collect one problem of the student's choice each day (week, lesson, etc.). Throughout the unit, students will have to explore the questions to determine which they have and have not been introduced to, many will successfully attempt problems not covered yet , a few will become unnecessarily frustrated ("you haven't taught us this! How are we supposed to know!?) and all will get a very good overview of the unit. $\endgroup$ – Andrew Apr 6 '16 at 14:58
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In general, I'd think that anything that helps students to break out of a tendency to passivity is good. Initiative should be rewarded, looking ahead is good, and so on.

Sure, if there is a pervasive assumption that everything is "curved" in an invidious way, there are even larger problems... but the possibility of "curving" unfairly (don't do it) is not a sufficient reason to try to keep students in lock-step for worry (?) about weaker students being disserved. Simply don't punish the weaker students for the opportunities given to stronger students to entertain themselves, at least.

The "oh, there'll be chances later for the good students to go into things in depth, it's just a first-year course" I think miss the point, that first-year courses are powerful PR about what the course-of-study is. If it's rules and no-looking-ahead, who'd be interested? One does not have to punitively grade weaker students while making important points to better students about the larger/forward picture of the subject.

That is, surely one can keep focused on the goal of education, rather than grading... especially in the degenerate sense of the latter as "filtering" or "gate-keeping". There is no compulsion to make a richer picture of a subject entail more grueling gate-keeping.

It is also worth making the point to students that, in contrast to some remarks, it is rarely wise to "wait to have the material explained", rather than reading to see what will be discussed. A terrible habit to even passively endorse.

So, sure, give people incentive to look ahead a little. At the same time, there's no compulsion to actually punish those who don't take the advice to do so, by distorted "curving". That's a separate issue.

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  • $\begingroup$ I can see that I had made the assumption that significant extra credit necessitating renormalisation. However they are not seperate issues. A course with 10% available for extra credit by definition scales up the grades of students by 10%. This seems to be simply a discussion about which kinds of grade scaling are acceptable. In particular, the effect of scaling grades up for students who finish the same work a week earlier than class schedule. You are making the case that this scaling is good for students to develop study skills. Is this a fair analysis? $\endgroup$ – Richard Mar 29 '16 at 22:34
  • $\begingroup$ @Richard, I think, yes, that translating grades upward is an entirely reasonable reward (such as it is) for students' doing more than they might have naively thought to do. The disquieting seeming-fact is that many students (ok, special case, "many people", but let's not get political... nevermind) do not seem to consistently understand their own best interests, and do not behave rationally... at least under closer scrutiny. Short-term rational, perhaps, but not even six-months-out rational. I'm not trying to "filter/keep-down" undergrads, but ... ironically... help them. $\endgroup$ – paul garrett Mar 29 '16 at 23:00
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No good can come of this. The students who are already at the top of the class will easily grab the points, and those who actually wait for you to lecture on the topic to learn it from you, will resent the steepening of the curve. What do you really hope to gain from this?

Edit - part of my knee-jerk reaction is from my own experience. A freshman class where the teacher tried a similar approach, multiple chances to earn "extra points". As a freshman, I understood the material, felt no need to do extra, and tried to balance my time toward the classes that were a struggle. In this class, a 96 (combined HW grades and exams) resulted in a B. The teacher graded on a curve, and in hindsight, the extra credit was anything but. 35 years later and that experience stuck with me. If you decide to do anything with extra credit, I urge you to spell out how you intend to grade, to make clear the impact of doing that work, vs skipping it. If you are not curving, keep in mind, the result will be a positive shift toward higher grades, and your supervisor may question your grade distribution.

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    $\begingroup$ Keeping the top students engaged, and giving them the opportunity to develop skills other than memorisation? $\endgroup$ – Jessica B Mar 24 '16 at 8:34
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    $\begingroup$ Re: the edit -- The real problem is the grading on a curve, which is a pox on humanity itself. $\endgroup$ – Daniel R. Collins Mar 24 '16 at 17:46
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    $\begingroup$ Always a pleasure to see a DV with no comment or even another answer to this question. $\endgroup$ – JTP - Apologise to Monica Mar 24 '16 at 21:02
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    $\begingroup$ The cowardly, random downvoting has been a discouraging disappointment to me about this site. Some aspects of teaching are inherently subjective, but it's not like a teacher's judgment is unreliable. Sharing experiences is a standard, indeed generous, and valuable way to help each other develop our craft. Of course, one person's experience won't always help everyone else; maybe sometimes it won't even help most others. But it would be kinder and better supportive of the pursuit of good teaching to let upvoting sort out the relative merits of such answers. $\endgroup$ – user1527 Mar 25 '16 at 2:27
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    $\begingroup$ I don't understand the apparent mandate to renormalize... nor several other implicit hypotheses here. If students can be induced to do/learn more things, maybe everyone has earned a good grade. The traditional objection that this "fails to distinguish the best from the less-good students" assumes (among other things) that there are innate distinctions which are merely "detected" by coursework. $\endgroup$ – paul garrett Mar 27 '16 at 16:24
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I would alter the presumption of the question that "extra credit" is the only way to do this. There are several techniques people use to get students to "read the book" ahead of time which involve "regular" credit.

Tommy Ratliff and Matt Boelkins have a nice article about a good method - nowadays your LMS can handle this for you. The short version is that you have a required writing assignment (long or short) where they would do something related to the routine problem you are asking about.

We have found that a binary grading scheme works well for the assignments: a student earns a 1 for sincerely attempting to answer the questions (independent of whether the answers are correct), or receives a 0 if no such attempt is made. In addition, the assignments count for 5% of a student's final grade in the course.

So this isn't "extra credit" in the same sense. In fact, it's very appropriate at the college level to simply expect students to do this. It's also not realistic to expect all students to do it. But the penalty is relatively minimal and proportional to expectations, and it seems realistic to use this as part of a 'participation' grade, if you use that.

(That said, I do think that very straightforward questions, for regular - not extra - credit are also appropriate no matter what the instruction level, assuming that they are completely procedural and you can give instructions as to where to find models. As students mature, they could be less procedural. I rarely get complaints about these as long as I am sure to cover them in class, or you could grade them on completion, not correctness.)

Finally, I won't bother to link to the zillions of people discussing "flipped classrooms" in math, but this is another method that is much more intense for the instructor, but which also gets at "reading ahead".

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    $\begingroup$ "[A] student earns a 1 for sincerely attempting to answer the questions (independent of whether the answers are correct)"... I'll offer that checking for "sincere attempts" at homework was advice I got from my advisor in grad school, and for a long time it was one of the worst, most ambiguous nightmares for me as a math teacher. Dropping that saved my sanity. $\endgroup$ – Daniel R. Collins Apr 5 '16 at 16:55
  • $\begingroup$ I think in this case, since some of the questions they give are fairly open-ended, and since the point is basically checking if they tried reading the book, it might be okay. When I've done a variant of this, in practice it's been very easy to tell what a "sincere attempt" was. But for standard homework I agree that is a much trickier thing. $\endgroup$ – kcrisman Apr 6 '16 at 15:02

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