# Extra! Extra! (credit)

As the semester winds down, the emails and office hour visits become much more frequent. Sometimes, students want to ask a specific homework question or clarification on some topic covered in class. But in my experience, most end-of-the-semester visits have one theme in common: “How am I doing in the class? What can I do to get the grade I want/need?” And the thing is, by the end of the semester, there is not much anyone can do to change a trend that’s been present all semester. But I do understand that there are many reasons students might under-perform, especially in exams (see a previous post for more of my musings on that topic), and I like to give them a chance to show me what they have learned in a non-test form. And that is why the math Gods (Gauss? Newton?) created extra credit.

There are many ways to give extra credit, but I believe all of them should involve a little bit of extra work. What I mean is I’m not a big fan of just curving the grades, I would like for them to get some extra experience. Usually for me, this has meant assigning tasks that are not too time consuming but require them to think a little bit more about the class and themselves as participants in the class. Here are some things I’ve had students do for end-of-semester extra credit that worked well for me.

The Applications Project: This started while I was still a graduate student after a student came up to me at the end of a particularly “riveting” pre-calculus lecture and simply said “why do I have to know any of this?” After a second of thinking about what ideal example to give her, I realized this was a great question, so great that I had no business trying to answer it. So I said “why don’t you find out?” And this was the beginning of a really fun experiment.

In its first incarnation, I had students decide between summarizing one of the “applications” sections in the book that I hadn’t taught already and interviewing a professor in a major they were interested in about how pre-calculus is useful to them. The latter was much more exciting to read, especially when the professors they interviewed didn’t really know how they used pre-calculus, and the students and professors ended up figuring this out together.

I have modified this project and used it in almost every class I have taught since. In multivariable calculus, for example, I invited people from chemistry, physics, and applied mathematics to talk about applications, and then had students write a short paper about the lecture. The students were involved in selecting the guest speakers.

In some classes I have even made this project mandatory since it seems they really get a lot out of it. In general, I find that the more students can relate what they’re learning to something they like, the more it feels like this experience of taking the class, if not always fun, was really worth their while. I guess this seems a little obvious (I’m not claiming to have reinvented the wheel or anything), but I think we sometimes forget that mathematics doesn’t mean the same to other people as it does to us. So this project is a fun way to give a new meaning and importance to the material. Some of them really enjoy being able to do this, too (or maybe they just tell me that because they think it might boost the extra credit?).

One question that might come to mind is “why not do this the whole semester?” I try for the most part to explain how certain ideas are applicable. You can tell them about carbon dating just when they’re learning about exponentials and their derivatives (and I usually do), but it seems to get lost somewhere. At the end of the semester, when they’re searching for applications and they realize they can understand how old a fossil is by using differential equations and exponential decay, and they write a short paper about this they don’t seem to forget so easily.

If you’re wondering about logistics, I usually tell them to write a two page paper, which doesn’t have to be typed but definitely neatly written, and it’s worth 2% of their final grade. I also tell them that this is what’s going to bump them up to the next letter grade if they’re borderline, and this makes them very happy.

The study guide: This semester was the first time I tried doing this. I had my Intro Stats students write a study guide for the final exam. For each chapter of the book we covered, they had to write a summary of the big ideas and choose and solve two problems they thought would be good practice for the test. At the end of this document, I also asked them to write a personal reflection about which topic they found the most interesting and whether they thought it might be useful in the future.

One surprising thing to me was how many of my students complained about how much time they were spending on it. This made me realize that not very many of them are studying the way I think they would. I mean, that’s what I always did when I studied for a final: write down the important definitions, theorems, formulas, and then practice with a few problems. I’m not saying everyone has to study the same way, but this seems like a pretty standard approach to me, unless you already know all the material. The other surprising thing is that after they turned in the final exam quite a few of them came up to me to say how helpful writing the study guide was! So I guess it was mainly a success, even though it does seem that it takes them a long time and I should probably mention this much more in advance (I gave them a week and a half to do it).

Reading the personal reflections was also a lot of fun. A lot of them mentioned some of the most difficult topics as their favorites. This makes me think that many of them were finding these topics worth doing, which is another good goal for us to have in mind.

Ender’s Game as a motivational tool: This is actually not something I have done, but my friend and fellow math prof Brian Katz has used it to great success in many of his classes. Ender’s Game is a sci-fi novel by Orson Scott Card, about a young boy who is recruited to be a soldier in a space war with evil space bugs (it is actually quite good, if you’re into sci-fi, and if you’re reading my blog, then you probably are). Brian sees himself mirrored in the character of the instructor. This instructor puts all his young recruits through horrible, grueling training, and the kids don’t quite understand why they’re doing what they’re doing until way at the end of the book (and I won’t spoil it for you here).

Brian has his students read the book and then come in to his office and talk about it. He has this great way of asking his students questions that guide them to understand that they’re like Ender, the hero of the book, and that he’s like the instructor in the book. The students seem to have a much better idea of why Brian is doing what he’s doing, but he never has to find the perfect way to explain it. Rather he has them discover, through reading fiction, what his philosophy of teaching and learning is.

As a side note, Brian teaches many of his classes using inquiry-based learning (something I will definitely write about at some point). The main object of this teaching style is to show students to learn by doing, and in that sense it really is like learning a sport, learning to play an instrument, or training for a space war with evil space bugs.

Please share your favorite end-of-semester extra credit activity in the comments! Extra credit projects are wonderful teaching opportunities and a good way of rewarding hard-workers who have perhaps not performed so great in other aspects of the course. But a word of caution: with extra credit comes extra grading.

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## 7 comments on “Extra! Extra! (credit)”

1. Ricardo Teixeira on said:

Great text! I also ask my students to try to find relation between Mathematics and the “civilian”-world. In my classes, it is worth 10% of the final grade. As extra credit, I allow them to create a video, a comics book, a song, or whatever they feel like doing, that some of their peers would enjoy and feel instructive.

I do not like to simply curve the grades, but it was funny when one of my students at University of Texas at Austin “explained” to me that here in the USA curving is very common (side note: I work at University of Houston – Victoria, but I am originally from Brazil).

2. Michelle Manes on said:

I am actually adamantly against end-of-the-semester extra credit. I got so fed up with requests for it that I now put on every syllabus something like the following (in bold, and larger print than the rest), “Extra credit will be assigned occasionally throughout the semester. If a good grade is important to you in this class, take advantage of those opportunities when they arise. Do not ask for extra credit, ever, and especially not at the end of the term.”

My problems with end-of-semester extra credit are many, but among them:

If I’ve written a good syllabus (and I have) and done a reasonable job (and I have), then students know how they are being evaluated. It is not a shock that if homework is 30% of your grade and you skipped half the homework assignments, your grade is not very good. I think the end-of-semester extra credit is way (way way way) too often used to make up for rest-of-the-semester laziness and other priorities, and I’m not OK with that. (And I have other ways to address things like “I don’t take tests well.” A student with a bad grade in my class at the end of term either didn’t put in the time and effort, or was not prepared mathematically. But no one with the proper background who comes to class and does the homework ever fails.)

I really do assign extra credit throughout the semester, when it’s appropriate. I want students engaged in the class as I’m teaching it, not looking for some kind of busy work at the end to “bring up their grade.”

I think students need to learn sometime that there really are some absolute standards of achievement. If you blow off a few months at work, no client will give you “extra credit” to make it up. Do what is required when it is required!

I think it’s unfair that some students have this grade-grubbing mentality, as if the letter grade is what’s important. Other students feel they get the grade they earn and move on. The ones that ask for the extra credit are the former, and it’s not fair that they get this special treatment and higher grades than the ones who just don’t think to ask for “extra credit.”

Finally, seriously… I have to grade a whole bunch of final exams and final projects already. You want me to grade a bunch of extra credit stuff, too? No, thanks.

• Adriana Salerno on said:

I definitely don’t give credit to people who ask for it. If I give someone an opportunity, I give it to everyone, so usually there is some in-class announcement about the opportunity. I agree that it’s important to be fair. And yes, the extra grading is really no fun.

3. Cassie on said:

So, as a grad student I don’t have the freedom to give extra credit. Occasionally I make a quiz worth 13 instead of 10 and ignore that at the end of term, but that’s about it. I feel like my opinion of extra credit falls somewhere between Adriana and Michelle though. I like being able to give some opportunities for extra credit mid-semester, especially surrounding exams. I have in the past given an opportunity for extra credit by doing exam corrections. I feel like it helps the students who may have some test anxiety show that they do know what they’re doing, as well as helping solidify concepts that will come back later in the course. However, I am constantly annoyed with students who don’t seem to realize how to compute their own grades and determine whether they can get the grade they want or not. The words “not mathematically possible” seem to escape some of them, and their requests for end-of-term extra credit make me feel like I’m teaching junior high again.

4. Xamuel on said:

Gonna have to agree with Michelle. It is cold and cruel, but if a student does not demonstrate they have learned the material, then they need to retake the course– they should not be able to get around it by interviewing professors, making posters, writing essays or anything. Well, maybe if they get their essay into a peer-reviewed math journal…

• Adriana Salerno on said:

The type of extra credit I’m talking about would never give a passing grade to someone who doesn’t deserve it. This is why I make it worth 2 or 3% of the final grade. Nobody passes a class just because of the extra credit, but if they got a 69%, this can bump them up to a C-.

5. Cody L. Patterson on said:

Great post, as always. I think my views on extra credit used to be in the same neighborhood as yours, but they are moving more in the direction of Michelle’s. (This is partly due to the fact that I now teach courses for scientists and engineers. I was a little more liberal when teaching elementary ed majors.)

In my calculus class, I use extra credit as an occasional motivational tool, as well as a way to get my students to work on challenging problems without them feeling like their homework grade is getting destroyed. Each week, I give my students about 110 points’ worth of homework (mostly online, but some written), and they are obligated to do 100. Usually, they try to do all 110 points’ worth, and fail badly at one 10-point problem, so things work out about right. The “extra” problem is something that I genuinely consider a bonus problem, something that students will really have to think carefully about in order to get the right answer, so students aren’t getting extra credit for doing routine work.

Occasionally, if I want my students to think about a problem from lecture outside of class, and then come to the next class prepared to discuss it, I put a small, 5-point extra credit “bounty” on the problem. Students are invited to e-mail me their solutions (not just answers), and receive the points if their solutions are clear and correct. I usually do this with problems that are at the periphery of what they can do, which is why I treat these as extra credit and not required.

One of the great things about extra credit is that you can attach a relatively small reward to something, and students will often think it is a king’s ransom of points. There are about 1200 homework points up for grabs in my entire calculus course, and homework is 15% of the grade, so a 5-point bump is worth about 0.07% of the overall course grade. Yet it’s a very effective reward. Of course, there are also psychological rewards for students; I try to make it a point to recognize students in class who have done something particularly well. And when a student achieves something exceptional, that’s good fodder for letters of recommendation down the road.

But a resounding “Yes” on the idea that extra credit needs to be limited, equitable to students who are less inclined to ask/whine for it, and truly “extra” – not extra points for doing things that a C student should be able to do automatically. I try to explain to my students that their grades are based on their performance on the course material; not on what they might want or wish for or need to keep their scholarship, not on my personal opinion of them, not even on their work ethic, which is a precondition for success but not a substitute for it.

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