January 2, 2012, 8:00 am
Happy New Year, and greetings from Boston, where I’m attending the AMS/MAA Joint Meetings. This week’s blog posts will be a mix of reports from the meetings and thoughts I’ve been letting incubate over the holiday break.
One of the biggest things I learned this semester is: Everything in a class should revolve around learning objectives.
When I was preparing my transition-to-proof course (MTH 210, titled Communicating in Mathematics), I was struck by something my colleagues were doing. On assessments, preceding each problem there was a little blurb that said what learning objective the item was addressing. For example, an item on proof by contradiction might be preceded by the statement, “The purpose of this item is to assess your skill at proving conditional statements by contradiction”. So simple — and very helpful for both instructor and student.
I started doing this myself…
October 25, 2011, 7:30 am
I just gave midterm evaluations in my classes, and for the item about “What could we be doing differently to make the class better?”, many students put down: Do more examples at the board. I think I’ve seen that request more often than any other in my classes at midterm. This is a legitimate request (it’s not like they’re asking for free points or an extra day in the weekend), but honestly, I’m hesitant to give in to it. Why? Two reasons.
First, doing more examples at the board means more lecturing, therefore less active learning, and therefore more passivity and dependence by students on authority. That’s bad. Second, we can’t add more time to the meetings, so doing more examples means either going through them in less detail or else using examples that are overly simple. In the first case, we have less time for questions and deep thought, and therefore more passivity and dependence….
April 8, 2010, 8:17 pm
One of these days I’ll get back to blogging about the mathematics courses I teach, which make up the vast majority of my work, but the MATLAB course continues to be the place where I am working the hardest, struggling the most, learning the biggest lessons about teaching, and finally having the greatest sense of reward. This week was particularly rewarding because I think I finally figured out a winning formula for teaching a large portion of this stuff.
This was the last in a three-week series on introduction to programming. We had worked with FOR loops already. I had planned to look at WHILE loops in the same week as FOR loops, then have the students play around with branching structures in week 2, then have them apply it to writing programs to do numerical integration week 3 for use in their Calculus II class in which most of the class is currently enrolled. But the FOR loop stuff we…
January 19, 2010, 9:22 pm
This is probably the last of three articles on how piecewise-linear functions could be used as a helpful on-ramp to the big ideas in calculus. In the first article, we saw how it’s possible to develop some of the main conceptual ideas of the derivative, without much of the technical notation or jargon, by using piecewise-linear functions. In the second article, we saw how to use the piecewise-linear approach to develop an alternative limit-based definition of the derivative of a function at a point. To wrap things up, in this article I’ll discuss how this same sort of approach can help in students’ first contact with integration, again by way of a hypothetical classroom exercise.
When we took this approach with derivatives, we used the travels of three college students from their dorm rooms to the cafeteria. Each student had a different graph showing his position as a (piecewise-linear)…
July 31, 2009, 6:22 am
In my last post, I expressed incredulity at Pat Rogan’s statement that by limiting education degrees to no more than 30 hours of pedagogy courses, the state of Indiana would be “put[ting] educators without essential teaching skills into classrooms”. I brought up the example of one-room schoolhouse teachers and homeschooling parents as examples of people who teach successfully without anywhere near that amount of coursework. Another example I realized this morning was my own profession of college teaching. Most college professors have never had a pedagogy course in their lives, and yet many of those are among the best classroom educators our society has to offer. They certainly have “essential teaching skills”.
Of course there are also many professors whose teaching is atrocious. But there are also high school teachers with 30+ hours of pedagogy courses whose teaching is equally…