What matters most to you in your teaching?
How are you using technology as a tool to achieve your teaching goals?
How have your students responded to your use of technology?
What new goals do you have for using technology in teaching?
How could the University better facilitate the use of technology in instruction?
Focus on the learning process
Learn by doing
Class web site
Communicating Mathematics as Something with Structure and a Process
I think there needs to be a transformation of how we teach math in this country. Professors think of math as a process, and we need to communicate this to our students. The great thing about math is the ideas, not the formulas. If you understand the ideas you can use them to solve problems and understand the world. This is why I became a mathematician.
The teaching of mathematics has a number of peculiar challenges associated with it because we live in a society that is very math-phobic. It’s socially unacceptable for educated people to say they can't or don't like to read, but it’s completely acceptable for people to claim they are bad at math or can't do math, even if they are highly educated. That's a hurdle that I try to overcome in my teaching of mathematics. Along these lines, one of the things that matters most to me in my teaching is getting my students invested. I want to communicate to my students what math can do for them, why it is useful, why it is interesting, how it can come into play in different aspects of the world across many disciplines--even ones they may not have expected. In short, I want to get them to love the subject. The second thing that really matters to me in my teaching is to communicate to my students that math is not just a bunch of formulas or facts, but that it is a process and that is has a very beautiful structure.
I think there needs to be a transformation of how we teach math in this country. A lot of our students come to college thinking you learn math by memorizing formulas and applying them. Professors think of math as a process, and we need to communicate this to our students. The great thing about math is the ideas, not the formulas. If you understand the ideas you can use those to solve problems and understand the world. This is why I became a mathematician. I have a horrible memory. By understanding a few basic ideas, everything else follows. You can derive almost anything from those ideas, and there are no facts to remember.
My courses offer a class web site in the form of a Wiki, but the main way I’m using technology in my teaching is through the use of student blogs. This is highly non-traditional in mathematics! First of all, what is a blog? It’s a web log, an online diary. Every student creates a dedicated online blog, usually at www.blogger.com. My lectures are typically on Mondays, Wednesdays, and Fridays. By midnight before every lecture, students have to post a blog entry consisting of two parts. The first part must answer the question: “What is the most difficult part of the material for the reading assignment for tomorrow’s lecture?” The second part must say something reflective about the material. Students can write about the most interesting part of the material, how the material relates to something else they learned in mathematics, how the material is useful in the real world, etc. The students post their entries online, and then I read them before class. Students must complete the blog entries satisfactorily in order to get full credit for their participation grade in the class.
The blogging that I have my students do is based on the Just-in-Time (JiTT) Teaching model . The premise behind JiTT is that faculty stage various interventions, some during class, some outside of class, designed to gauge students’ conceptual knowledge of the course material. To state more concretely: the blogs serve three purposes. First, they actually get the students to do the reading before class. In mathematics, the culture is not to do the reading. I subscribe to the philosophy that one learns through multiple exposures; the more times students review a concept, the better they understand it. So if students see a concept in the reading, in lecture, on their homework problems and on a quiz that’s a much better way for them to learn. The second purpose of the blogs is to help me target my lecture. Every morning before lecture I read all of the students' blog responses. This typically takes 20-30 minutes (students don’t write long essays—they’re not supposed to). Usually a clear picture emerges detailing the most difficult material. More often than not, students have the same areas of difficulty. Instead of spending fifty minutes talking about material they already understand, I can focus on the ideas that were most challenging. The third purpose is to engage students in metacognition—to get students to think about their own thinking. We really don’t train mathematics students to ask themselves questions like: “What do I understand?”, and “What don’t I understand?”, and “Why don’t I understand this, and what do I need to do about it?” Even if students don’t understand a concept, the fact that the blogs force them to formulate a question about it makes a huge difference. I notice that when students do this type of self-assessment they are much more able and willing to ask questions when they come to class.
It’s very funny--on the first day of class when I explain we will be blogging, some students are visibly surprised. Blogging is the last thing they expect to do in a math class. But that being said, in my unofficial midterm course evaluation and the official end-of-course evaluation, dozens of students invariably respond that the blogging was hard-- but that it really helped them learn the material! As word spreads, I have more students coming into my class knowing we are blogging, and I suspect it is actually drawing people into the class.
In my field there are not a lot of people using technology in instruction. I thnk that it’s not because they are opposed to the idea, but rather because they don’t realize the possibility. For instance, two instructors in the department have heard about what I am doing with blogs and expressed that they would like to use them in their courses. So other people are trying the blogs now. Along these lines, I think that the best thing the University could do to facilitate the use of technology in instruction is not to provide more technical tools, but rather is to publicize what can be done with existing technologies. It’s about finding ways to tell faculty that there are relatively easy things they can do to improve their instruction if they are willing to be open to new ideas.
Oral Interview, April 2006