We'd looked at a whole bunch of stats, talked about our friend from high school algebra (formula for slope), and started to repurpose the original gradebook I posted. It was like old home week around here. But we're not stopping there. Nope. It's time to develop graphs for this data. So, let's take a look at the reporting tool in the workbook. I've made a couple of changes.
First of all, because the Power Law focuses attention on the most recent score, the way we look at student progress is going to look different. In fact, if you click on the "Scores" part of the workbook, you'll notice that the columns that used to contain the median scores for a grading period have been removed. In the reporting tool, I've added two items and altered a heading to accommodate the changes. I selected the colour blue to represent "student progress," which is a way to describe the scores determined by applying the Power Law. In other words, black shows the assigned score, and blue the adjusted score. I also replaced the bar chart showing process with the trendline representing the Power Law data. Finally, I changed the head of E10 to be "Learning Trend" instead of "Growth from 1st Quarter."
I'm not going to go through how to create the data validation list for the last name or the whole graph build. If you need a refresher on those items, please (re)visit the Beginner's series Part IIa (data validation, INDEX/MATCH) and Part IIb (graphs). I'm just going to show you the new stuff.
Here's the first row (Row 11) for Steve Canyon's performance. In cell C11, I've used the INDEX/MATCH function to report the most recent score (not an average or median) from the report for this standard. Our "All Scores" graph looks the same as in the original Beginner's Gradebook, but in cell E11, we can see the results of the Power Law plotted out for comparison with a Steve's scores. As you can see, this gives us a different view of student performance. His actual scores jump around, but the overall trend is one of moving toward the standard.
Here are a few other examples for your consideration. In these cases, I've plotted both the student's actual scores (in black) and the predicted scores using the Power Law (in blue).
|Gonna Fly Now...|
|Patient flatlining. Clear!|
The Power Law can provide a different sort of summary of performance vs. simple measures of central tendency, and can generate different kinds of discussions with stakeholders. Also notice that the learning curve doesn't always head in a positive direction. In the middle example, there's a student who has met standard, but never improved on the performance. And in the bottom graph, you can see that inconsistent performance leads to no curve at all.
Some commercial gradebooks have a Power Law option. It's certainly a lot simpler to have a built-in formula at your fingertips. However, I don't want you to think that you have to spend a lot of money to get this sort of information. And, I firmly believe that you should be in control of your data. You're the expert about your students. You can download the final version of the Power Law Gradebook, which has all of the report completed to use as a model for your own data sets.
Music clips from The Power by Snap! (c)1990.