Tag Archives: Spreadsheet

Spreadsheets vs. online gradebooks

One of the things my students like the most about learning managment systems (LMS’s) such as Blackboard, Angel, or Moodle (I’ve used all of these at some point in my career) is the online gradebook feature. I enter their grades online, and students can check in on the web at any time and see their grades and get the info. These things are useful to be sure. But I’ve been wondering if they are the best implement for managing grades. I’ve been wondering if it wouldn’t be better to simply hand back graded work and then have students keep their grades on their own using a simple spreadsheet. Some reasons why I think this way:

  1. Spreadsheets have functionality. I can enter, view, and edit grades in an online gradebook; students can view them; but nobody can perform any meaningful analysis on the data that have been entered. The gradebook is just a two-dimensional list. But of course in a spreadsheet I can not only store and view data but also manipulate it any way I want and play the many what-if scenarios that profs and students alike play. Of course this is not a big deal because most LMS’s allow you to download gradebook data in some kind of spreadsheet-compatible form, but why not just start with a spreadsheet to begin with?
  2. Spreadsheets allow greater choice of implementation of other LMS features. Online gradebooks are often the only redeeming feature of LMS’s, and profs tend to stick with LMS’s they don’t like just to have the gradebook. This often hurts the students, who have to put up with substandard email clients (see this post for more) and file-sharing systems that LMS’s provide rather than use something easier and better-implemented. Or else, profs end up using only the gradebook feature of an LMS and use other software (class blogs, wikis, Netvibes, etc.) for the remainder of what an LMS does (such as posting files and announcements), which can get confusing for students, who then expect the prof to use the features of the LMS.
  3. Having students keep track of their grades with a spreadsheet encourages them to learn about spreadsheets. If you take the approach of expecting students to manage their own grades, and teach them how to use spreadsheets to do this, my experience is that students will be motivated to learn the basics of spreadsheets simply because they care about their grades and because they can now answer on their own all those questions such as “What do I need on the final to get a B- in the class?” One can learn a lot about spreadsheets just by using it as a personal gradebook for one class in one semester. And since spreadsheets are an increasingly important tool for data management in general both in and after school, the more students can learn about them, and the earlier they can do so, the better for them.
  4. Using spreadsheets encourages students to take responsibility for their learning. One of the detriments of online gradebooks is that it removes an important responsibility of learning — managing the outcomes of your assessments — from the student and makes it the instructor’s job. I don’t mind the work of entering grades into a gradebook, but I do think it would be better for students to learn that responsible record-keeping is important and that they should practice it, and I like the idea of students  being closer to their grade data than they are with instructor-managed online gradebooks.

I don’t know if I’m quite ready to completely give up using an online gradebook for these reasons, but I find them to be pretty compelling. What do you think?

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Spreadsheets and calculus: Proceed with caution

Spreadsheets are one of the  most underrated tools available for doing and learning mathematics, especially calculus. At my college we include spreadsheets as a central tool for our Calculus I course and use them every chance we get. But as with all technology, there is the possibility of encountering a seemingly inexplicable glitch when using them even in a very tame situation.

Here’s one I encountered this week when setting up a spreadsheet to do an average velocity/instantaneous velocity problem. We started with a falling object whose position from the start point at time t is given in the following table:

blog-post-1

The eventual goal is to compute the average velocity from t=2 to t=3, then t=2.5 and t=3, then t=2.9 and t=3, and so on, finally estimating the instantaneous velocity right at t=3. Actually, this is where the glitches started. The “25” in the third cell was supposed to be a “20” because I wanted to position data to be fit, exactly, by the function s = 5t^2, which we were going to use to generate the position data not in the table. I caught this after an initial edit but decided it would be more interesting to proceed with the 25 there, then use my spreadsheet to get a power function trendline through the data, and go from there.

Go from there I did, and here’s the chart with the trendline:

blog-post-2Pretty close to s = 5t^2, right? Well… not exactly. Here’s what we get when we use the trendline formula to generate the position data for value of time approaching t=3 from the left, and then the average velocity from those times to t=3:

blog-post-3What’s supposed to happen is that the position values approach the position attained by the book at t=3, and the average velocities stabilize toward a single number which represents the instantaneous velocity at t=3. But the little deviation in the t=2 position from the original table (25 instead of 20) throws the trendline off so that the position as time approaches 3 overshoots the actual position at t=3, and so we end up with average velocities that are spinning out of control. (-1781 m/sec is roughly 4000 miles per hour, for reference, and the direction is wrong to boot).

But, you say, this is no surprise, because the mistake in the original table had the position off by 5 meters from where you intended. But what’s funny is that if you go back and make the mistake in the original table smaller, even a lot smaller, you encounter the same effect. If you change the 25 in the t=2 cell to 20.1 — that’s just a difference of less than 4 inches from the intended position of 20 meters — the trendline changes to y = 5.0089x^{1.9992}, and here’s what you get as time approaches 3:

blog-post-4

As we close in on t=3, we still get the object rocketing upward!

What we learn here is that if you use a trendline for calculations, you really shouldn’t mix data from the trendline with data from the table which produced the trendline. In fact, the original trendline created using s(2) = 25 would predict s(3) ≈ 46.813, and when that value is used instead of 45 in the average velocity calculations you see the averages stabilize, although slowly, towards something like 31.2 m/sec.

But even then, if you took that trendline formula and found y'(3) using the Power Rule (as we typically end up doing later in the course to tie algebraic diferentiation rules back to table calculations), you get y'(3) \approx 30.634, which is not what the average velocities are approaching in the table.

So spreadsheets are useful tools for learning mathematics, but for the kind of infinitesimal, close-up work that we have to do with calculus, error propagation becomes a viable course topic as the students are learning about limits.

Note: I used Numbers 09 for the charts and trendlines. I think Excel uses the same algorithm to produce power function trendlines as does Numbers, so this isn’t an Apple vs. Microsoft issue.

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Filed under Calculus, Math, Teaching, Technology