Folks:

William Michael Kallfelz of Georgia State University describes an interesting approach he has developed to be more responsive to his students' learning styles. He can be reached at , for further discussion.

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The "Baseline Themes" Approach to Increased Classroom Participation and Interaction

Background

I am a graduate student (ABD) in physics but have been an adjunct faculty member in the Department of Mathematics and Computer Science at Georgia State University (GSU) for almost three years. During this time I have taught an average of 2-3 courses per quarter, in addition to juggling the completion of 4 master's degrees (physics/geophysics/applied mathematics/philosophy) at Georgia Tech and Emory, and work on my thesis topic. I really identified with the comment that class preparation is like a "gas" rather than a "liquid" or "solid." (Tomorrow's-Professor Msg# 8, 3/16/98.) To add to this, GSU is much more of a teaching-based institute than a research-based one, like Georgia Tech, so they run a pretty tight ship and even adjunct faculty are kept pretty much under the microscope. Add to that still, the typical student I deal with is a freshman/sophomore with little or no interest in mathematics, more often than not lacking in basic prerequisites.

I tried to swim upstream by compensating for all these factors through everything short of literal spoon-feeding. My evaluations stank and I still had to fail a lot of students.

The Approach

My job satisfaction, evaluations, and even relations from fellow faculty members have improved when for the sake of necessity like a jazz musician I'd walk into a class with a "baseline theme" (built around some interesting prototypical example(s)) upon which I'd "improvise" based on student reaction and feedback. This enabled me to let the syllabus "breathe" while not at the same time falling behind, and ensuring a greater cross-section of class participation and interaction. Every class is different. ("Same drama, different actors" -Goethe) This "baseline" preparation would for me take as little as 20 minutes even for a two-hour lecture! (As opposed to 2 hours --of course this "improvisation" approach only works if you'd taught reasonably similar material, otherwise it's improvisation comedy.) Perhaps these ideas seem obvious but it was a helpful change of paradigm for me.

The idea is 'to show, not tell." Here is an example from my "Business Calculus" class:

I want to talk about exponential and logarithmic growth/decay,

Problem: Most of my students understand "exp" and "log" as buttons on a calculator, and that's about it.

Solution 1) (standard) Spend a bunch of lectures talking about exp(x) and log(x) as functions, and inverses of one another, assign a bunch of homework no one does, give a quiz everyone flunks.

Solution 2.) ("baseline") I walk in and say: Can we think of quantity Q whose rate of growth is directly proportional to its instantaneous amount? (They've taken derivatives and integrals by now until they're almost blue in the face) They stare blankly. I write: "dQ/dt = kQ" We spend about 5-10 minutes QUALITATIVELY looking at what that sentence MEANS.

In other words we do qualitative feedback/feedfoward analysis on the differential equations which gives them of course a feel for thinking in terms of how the rates couple with quantities. Then depending on how they catch on, I'll go through the tricks which everyone memorizes (but forgot) solving the differential equation to get: Q(t) = Q(0)exp(kt) We graph this and re-do the feedback analysis looking at the slope of the curve at some points. To get them to pay attention. I let Q(0) be my principal $, and we therefore understand continuously compounding interest in this fashion.

I'll do the same thing above for in the case of: rates inversely proportional to amt. We stumble across logarithmic growth.

Inadvertently, they unwittingly learn about exp(t) and log(t) as functions, inverses of each other, as these properties unfold while we go through the graphing procedure. Gradually letting this example unfold (which takes 3 minutes to prepare, 1.5 hours to develop) they not only see exp and log in this rate-based fashion, but inadvertently the basic concepts (no one learned in precalc) like "function," "inverse function" get activated in this dynamic, heuristic approach.

The 'improvisation' aspect specifically arises in that I may have a class who is on average more algebraically predisposed. I let them stop me and we go through the aforementioned formal definitions (of inverse log, exp) within this context. On the other hand I may have a class who on average is more visually predisposed, whereupon I'll do less formal defining and do more drawing graphs until they really understand the domain-Range properties of Log, exp. The review is built into the problem, under a new penumbra everyone grasps. The example is porous enough to take an entire lecture, yet the manner is leisurely, interactive, and the material very salient.