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.