...and perhaps other subjects too.
Many students who take intermediate microeconomics believe the course title a misnomer, with a more correct title something like "graphs, more graphs, and still more graphs." They may be correct in that perception. Since many students struggle with reading a graph or get completely turned off when extensive amounts of content are provided in this manner (the formal word for this seems to be disidentification) a challenge is presented to the intermediate micro instructor - how to engage the students? One possibility is to move away entirely from the math/graphing approach and make the course more discursive, talking through complex issues rather than focusing on rather simple mathematical models, taking a history of thought approach to the subject, and/or trying especially hard to build connections students might have to the subject matter. I intend to do a bit of all of this in the class I teach next spring. Another possibility, however, is to utilize technology in a way that should make the graphs more penetrable and assist the students in uncovering what is going on with the mathematics. I intend to do more than a bit of this as well, utilizing my favorite tool for the purpose, Excel. Below is a movie about one of the tabs from a workbook on demand elasticity.
I want to discuss the benefits of using technology that can do math for such a presentation, but before I do I'd like to make the following observation. If one goes to the YouTube site for the video below and looks at the suggested videos in the right sidebar, there are many videos on the same subject. After all, demand elasticity is a core topic in microeconomics, and the technology is readily available to make short movies of presentations on this topic. The bulk of these videos are for hand drawn presentations. Though their might be a whiteboard instead of a blackboard, the presentation itself is remarkably traditional. The novelty is that the presentation is in YouTube. There are a couple of clips from Wolfram Research that use Mathematica. One might ask whether Mathematica is superior to Excel for this purpose. I don't know the answer to this, because I don't know Mathematica. Below I will argue where Excel is especially helpful.
1) Numbers or algebra. When I was a junior faculty member I thought everything presented to the student should be done with an algebraic presentation and that using numbers was babying the students. Perhaps true. Nonetheless, if the students don't understand what is going on then perhaps using numbers to illustrate the concepts is a good thing. Excel allows both. Numbers are displayed overtly in the cells and in the graphs, but formulas are readily available by clicking on a cell and looking at the formula bar. Students might have to translate the Excel formula to a hand written algebraic formula. I think such translation is a good thing for them to do. It will facilitate their understanding.
2) Comparative statics with the spin button. I should mention that in addition to not being able to read graphs, many students also have an inability to apply Calculus concepts to the economics, although they've all had the pre-requisite Calculus course. They simply don't get enough other practice elsewhere to internalize the ability to apply the Calculus. Excel offers a very nice way to visualize the comparative statics by using a button to control the value in a particular cell. Once the mouse is on the button, a student can click on it while focusing on the graph or on other cells in the spreadsheet. (With the spin button, holding the button down changes values in the cell but doesn't change the graph until the button is let go. You can get more or less a continuous change in the graph via rapid clicking on the button. With the activex alternative tool, the spinner, the graph changes continuously with the button held down, but as far as I know that tool is not in Mac versions of Excel.) This is far superior to an algebraic approach. When there are multiple buttons for controlling different aspects of the graph, the student can perform "little experiments" by first varying a parameter with one button and then seeing how things look changing another button. If seeing is believing, which I think is certainly true for learning this stuff, we now have much better way for the phobic students to penetrate the graphs.
3) Reverse engineering the spreadsheet. I don't know if all students will do this, but the mathematically inclined are certainly apt to do this and perhaps other conscientious students will do so as well. I have a colleague who believes when teaching this stuff it is important to do constructions in front of the students, building the graphs from scratch and talking one's way through that rather than using a PowerPoint slide where the graph is pre-drawn, so the students can understand the logic of the construction. On this, de-construction of a finished product may actually be a superior approach, because the students will have to supply their own narrative to the deconstruction activity, rather than rely on an instructor supplied narrative. Here is a little video explaining how to use the Excel tools, the graph itself and the spin buttons, to initiate such a deconstruction.
Let me close with a few comments about designing such a spreadsheet for presentation. There are quite a few tips and tricks in doing this, many of which can be uncovered by reverse engineering. So here I will note just a few. First, scrolling down in the worksheet one can see all the data that is plotted in the graphs and the labels with the data are used for the labels in the graph to make ready identification. Nothing is hidden. I've come to conclude that having it all out in the open is better, because it encourages students to do quick checks rather than have to go through a laborious process to reverse engineer. Second, the graph is relatively clean with little in the way of extraneous information to distract the student and not that complex. The goal is to make things as transparent as possible. Complexity is handled by having multiple worksheets, where frequently a subsequent worksheet builds on its predecessor. Last concerns the time entailed in such a construction. It took about a day of work to build the entire workbook, though I had been stewing about this content for months, wondering if I'd do something even more interactive. As the spring semester neared, I opted for what was do-able in relatively short order. Nevertheless, it does take longer to building something like this than to do a PowerPoint. So if it is one and done, maybe this isn't a worthwhile approach. But if the content can be re-used, then a good argument can be made that it's the better way to go.
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