I previously wrote about making sure that every class during our unit on differential equations starts with some differential equation they can see or feel in a concrete way.

During the last class, we investigated a draining tank using the video posted by Dan Meyer at his blog.

Today we did something different. I told them that I was doing an experiment with a simple task. They all needed to find the answers to some questions as quickly as possible:

When they found the answers, I wanted them to quickly throw a hand in the air to let me know. I told them to be honest - they didn't know what I was doing with the information yet, so there really wasn't a chance to skew it.

I then showed them the slide with the questions:

I also simultaneously started the following Python program. (UPDATE: Code is posted here.) This let me easily record any time a student raised his/her hand.

I then pasted the data directly into a Geogebra spreadsheet and graphed the data...

...and then fit a logistics curve to the data:

They had seen and heard the concept of learning/performance curves before, but it was really great to be able to develop one on the spot with the class. I was impressed with how good the data turned out. It was then neat to be able to show the differential equation that describes this type of phenomenon and solve it to get this type of function.

As is probably obvious, I only have ten students in this group. It would be really cool to try something like this with a bigger group and see if the data fits as nicely.

Evan,

I really like this and never thought you would have gotten such nice data from such a small dataset. One small suggestion from code thieves like me. Could you put your code in a github gist so that those who want to play with it can use it?

Hey John,

Thanks for the comment - I hadn't heard of gist before, it is perfect for this. I used the image because pasting lost the indents and I didn't have time to fix it, but your solution is better!

I was surprised initially too, but the more I think about it, the more I think that all of the random variables involved make it hard NOT to look like this. Increasing/decreasing the difficulty of the task will scale it horizontally. The type of task does too - I purposely asked two things that would require more than just a quick calculation.

It would be interesting to pose this to students and ask them to choose a task that would skew the curve in a given way.

There's a lot of interesting stuff embedded in this - glad to have happened upon it!