In an earlier post, I thought to make my teaching more public, and then subsequently shared some reflections on how my calculus I course looks overall. In this post I’ll give an overview of how a typical week is structured, and in the near future reflect on how a prior class day.
As of Monday, September 9, my class will have met 6 times for 50 minutes, and, inside and outside of class, students will have worked through the vast majority of the ideas and activities in Sections 1.1-1.3 of Active Calculus. That is, we’ll have discussed average and instantaneous velocity, the notion of limit, and the definition of the derivative at a point. This is representative of my goal for the semester: to proceed through Active Calculus at a pace of about two sections per week, or 1 section every two class meetings. With four meetings a week for 14 weeks, that’s 56 meetings: 4 get given to exams, and I leave 2 relatively open and unplanned for flexibility, so that leaves us 50 meetings to consider the 25 sections in Chapters 1-4.
My class meets MWF in a “regular” classroom, and once more on Tuesdays in a dedicated computer lab. The computer lab meetings are, on balance, devoted to self-directed computer-based explorations and activities that are designed to strengthen students’ understanding of calculus. We’ll be using Geogebra as our principal software tool, including its marvelous spreadsheet view.
Here’s what I have planned for next week — week 3 of the semester, September 9-13, which looks pretty typical. For Monday, students will prepare by reading the start of Section 1.4, completing the Preview Activity for that section, and watching some of the great screencasts being produced by Robert Talbert and Marcia Frobish. They are directed and assessed in these tasks in the Daily Prep Assignment for Monday, 9/9. Having started to encounter the derivative as function, in class we will have a short debriefing time, a bit of all-class discussion, and then devote the preponderance of class to Activity 1.10, an exercise on graphing the respective derivatives of various given functions.
On Tuesday, class will be primarily devoted to a graded computer lab activity that focuses on using the limit definition of the derivative to find a formula for f ‘(x) and using a graphical perspective to check the correctness of the resulting formula. This work will parallel Activity 1.11 and essentially complete our study of Section 1.4.
Wednesday, we’ll transition to Section 1.5 where the focus is interpreting the derivative in applied contexts. Similar to Monday, students will complete a daily prep assignment and come prepared to debrief and discuss ideas such as the units associated with the value of the derivative. Our class meeting will involve debriefing on the daily prep, 25-30 minutes devoted to work in small groups on Activities 1.12 and 1.13, and then some closing all-class discussion of the activities. So far, my students are doing a very good job of working actively in class and asking good questions. We’ll look to continue that habit in all upcoming meetings, but particularly on days like this one where the majority of class time is devoted to work in small groups with support from me.
As the week rounds out on Friday, we’ll take some time at the start of class to consider* students’ questions on assigned homework (WeBWorK) exercises or problems of the week they are working on, do a short recap of what we’ve learned so far about the derivative function, and then spend the remainder of class on Activity 1.14, which regards a problem where you really, really have to think about the units on the derivative, since the independent variable itself is a rate of change. Friday will be a rare MWF in that there’s not a daily prep assignment to complete.
While the material will change and there will be some adjustments to the schedule around exams, Week 3 is representative of life in my calculus class this semester. In the near future, rather than looking forward to a particular week of class, I’ll look back and reflect on a recent class meeting.
* One note about how I manage student questions on homework: I typically only spend about 15 minutes of class time each week discussing homework exercises, and students have to make their requests in advance of class via email in response to a message I send them. I’ve done this for the past 7 or 8 years now, and it has greatly improved my efficiency in use of class time. (A) Students have to let me know in advance, so they ask more focused and meaningful questions; (B) I know when I enter the room what the main homework questions are, and I can respond to them more democratically — homework discussion is based on a range of voices, not just whomever is most vocal in class; (C) I’m much more efficient in how I allocate class time to the questions of students. In particular, I’ve found that I can write all the problem statements down in advance, possibly along with a couple hints or key points, and then use the document camera in the classroom to display the problems on the board. In 15 minutes, we can consider 5 or 6 problems; previously, where I’d take questions on the fly, I’d be lucky to consider 3 questions in 15 minutes.