Sam Shah and other math bloggers have started a challenge to encourage more math-teacher blogging Mission #1: The Power of The Blog | Exploring the MathTwitterBlogosphere:
You are going to write a blog post on one of the following two prompts:
- What is one of your favorite open-ended/rich problems? How do you use it in your classroom? (If you have a problem you have been wanting to try, but haven’t had the courage or opportunity to try it out yet, write about how you would or will use the problem in your classroom.)
- What is one thing that happens in your classroom that makes it distinctly yours? It can be something you do that is unique in your school… It can be something more amorphous… However you want to interpret the question! Whatever!
I’m not a math teacher blogger—looking back over my posts for the past couple of years, I only see a few that are really about math education:
I use math all the time in my classes (complex numbers, trigonometry, and calculus in the Applied Circuits class; probability and Bayesian statistics in the bioinformatics classes), and I do reteach the math the students need, as I find that few students have retained working knowledge of the math that they need. But it has been quite a while since I taught a class in which math education was the primary goal (Applied Discrete Math, in winter 1998).
So I fell a little like an imposter participating in this blogging exercise with the math teacher bloggers.
I don’t have any “favorite” open-ended or rich problems. Most of the problems that I given in my classes have a heavy engineering design component, in either the circuits course or the bioinformatics courses. Any good engineering design problem is an open-ended, rich problem. If I had to pick a favorite right now, it would be from my circuits class: either the EKG lab (look for many posts about the design of that lab in the Circuits Course Table of Contents) or the class-D power amplifier (see Class-D power amp lab went smoothly and other posts). But these are not the sort of “open-ended” problems that the MathTwitterBlogosphere seem to be interested in—the engineering design constraints that make the problems interesting are too restrictive for them, and a lot of them prefer videos to text (for reasons that seem to me to be based mainly on assumptions of the functional illiteracy of their students, though a few times a sounder justification is given). In any event, I doubt that any of the problems that I give to students would be appealing to math teachers, so they are not really germane to the MathTwitterBlogosphere challenge that Sam Shah put out.
It is hard to say what I do as a teacher that is “unique”. It is not a goal for me to be a unique teacher—I’d like to see more teachers doing some of the things I do, like reading student work closely and providing detailed feedback, or designing engineering courses around doing engineering design.
I may be unique in the School of Engineering in how much emphasis I put on students writing well, and how much effort I put into trying to get them to do so. I created a tech writing course for the computer engineers and scientists back in 1987 and taught it until 2000. More recently, I have provided many bioengineering students feedback on their senior theses, reading and giving detailed feedback on five drafts from each student in 10 weeks. In my bioinformatics classes, I read the students’ programs very closely, commenting on programming style and the details of the in-program documentation—these things matter, but students get very little feedback on them in other classes. In the circuits course, I require detailed design reports for each of the 10 weekly assignments (though I encourage students to work in pairs for the labs and reports). I evaluate the students almost as much on their writing as on their designs—engineers who can’t write up their design decisions clearly is pretty useless in the real world.
I’ve not done much about math writing, though a good class on mathematical writing (using Halmos’s How to Write Mathematics) would be a great thing for the university to teach. I have blogged before about writing in math classes, in my post Out In Left Field: Two ways to ensure learning, which is a response to a post by Katherine Beals: Two ways to ensure learning. In my post, I distinguished between writing mathematics and the sort of mushy writing about mathematics that many high school teachers favor these days.
Centering engineering courses on doing engineering design is a very important thing, but it is not a unique contribution—I’m not the only professor in the School of Engineering who puts the lab experience at the center of a course design. Gabriel Elkaim’s Mechatronics course is a good example, as are most (all?) of the lab courses that Steve Petersen teaches. In think that, in general, the Computer Engineering department does a good job of highlighting design in their courses, as does the Game Design major. I just wish that more of the engineering classes did—especially those where it is much easier just to teach the underlying science and hope that students pick up the engineering later.
At the end of this post, I’m feeling the lack of a good conclusion—I don’t have any open-ended problems to share with math teachers, and I don’t have anything really unique about my teaching that will make math teachers want to emulate me. I just hope that even a weak contribution to “Mission 1” is useful, if only to make other participants feel better about their contributions.