I've got a reputation for moving a bit more slowly than my colleagues through the same course material, and this semester's proving to be no exception. While one of my fellow Calc I instructor's classes is already pounding away at trig derivatives (judging from the terminals bits of his lecture I was able to catch before following his act with my own in the classroom we hold in common), students in my class are just now starting to get a feel for limits and an understanding of how they might be useful.

Why the slow pace? While student-centered learning makes for meaningful learning opportunities, it's certainly lacking in celerity.

Sure, I could have lectured our way through the multistep radioactive decay problem in five minutes, but I'm pretty darned sure my students got more out of it by working through the difficulties themselves, one small but crucial point at a time...even if it took twenty-five minutes to work through the same example that could have been done in 20% of the time in a "traditional" fashion. Evidence for the exercise's success was immediate and evident, and right away I took note and pointed it out to the students in my first section.

"You know what I just noticed, three minutes ago?" I asked them, as we drew near to the exercise's end. "I saw thirty-two pencils scribbling away, without pause, on thirty-two sheets of paper, not a single one in sight at a standstill. Every one of you was busily working away at a solution, because as far as I could tell, every one of you understood what you needed to do to calculate the half-life we're now looking for.

"Compare this with the situation at the outset of the exercise, at which time most of you were staring blankly at your papers, wondering timorously what first step to take. Something happened between then and now: you gained confidence, you gained understanding. Something happened."

I was very happy with the exercise. There'll be more like it tomorrow.

## Wednesday, September 02, 2009

### Signs of student learning, or, twenty-five minutes of time well-used

Posted by DocTurtle at 11:47 PM

Labels: Calculus I, MATH 191

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## 2 comments:

Your teaching style is far superior to a lot of the more "efficient" teachers at UNCA who rely on lecturing alone. In other math classes, it's more like teachers are just

doingthe math and letting us watch, but in your classes, it really feels like you'reteachingthe math and making sure we understand. The interactive nature of the worksheets/notes outlines in your classes make it a lot easier to follow what gets said and written on the board, and your style of speaking to a class is really personal and engaging.There are few things that inspire more despair in a student than feeling totally lost as a teacher breezes through some complicated equation so quickly that the student can't even figure out what questions to ask to make it clearer. You do a great job of eliminating that despair for the students in your classes.

I once observed a calculus class dealing with one of the more difficult integration techniques. The instructor gave the students a list of five such problems and had the students work as a group to solve the first one, while he took notes on their solution on the board. This took 25 minutes or so.

I thought to myself as I watched this, "At this rate, he'll never get through all five problems." However, the students had grappled sufficiently with the first problem that the second, solved in the same manner with the students suggesting ideas and the instructor taking notes on the board, only took 10 minutes.

The third problem took 5 minutes, and for the last two problems, the students didn't even need to solve them all the way. They were able to identify the key difficulties in each and set them up (without solving) appropriately in a matter of minutes.

The whole class was a thing of beauty. The students all left with a deep understanding of the material. They no doubt had no problems with similar problems in the homework.

DocTurtle, you may well find something similar happening with your students this semester. You may be trailing behind your colleagues in terms of the syllabus now, but it's quite possible that the foundation you're laying now will enable your students to speed through later material--while understanding it, too!

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