Two-Envelope Paradox

The Two-Envelope Paradox is an interesting puzzle about probability. You can read more about it at wikipedia, or join the discussion.

In short, there are two envelopes, A and B, and one contains twice as much money as the other. You're holding envelope A in your hands. Before looking in either envelopes A or B, does it make sense to switch to envelope B?

On the face of it, it seems that it doesn't matter whether you switch or not. However a "paradox" arises if you choose to think of the contents of envelope B as containing half or double that of A. Meaning you have even odds of doubling or halving your money. Under this assumption, it makes sense to switch, as you stand to gain more than you risk losing!

My explanation of the "paradox" is below if you're interested:

Popsicle Shticks 1.02 - Bug Fix

One of my students recently notices that she always seemed to be the last person on the group list. Since the class has 22 students in it, that meant that she ways always the odd woman out when we had groups of 3. A quick investigation showed that this was a bug!

I tracked down the source to a poor assumption about how Random.Next(lower, upper) worked. It turns out that it does not include the upper-bound as I had thought, meaning the group generator wasn't considering the last person on the class list until they were they were the last person to be randomly sorted into a group.

Anyway, you can download the updated version of Popsicle Shticks here. Source code here. Original Post here.

Creating Video Resources for Students

A colleague of mine tipped me off to a great tool called Screencast-O-Matic

Screencast-O-Matic is a no-hassle, online tool you can use to quickly create instructional videos for your students. I've been using it to create video solutions to some of my test questions. I open my calculator's emulator software and a copy of the test in OneNote side by side and Screencast-O-Matic will record the audio and video of my solution as I go through the problem.

Layout of a Math Problem Video Solution

What Screencast-O-Matic is doing is just creating a video of whatever is on my screen. You could use it to create videos of any digital content in your classroom. In my math class, I'd like to use it to build up a bank of example questions that students can refer to at home. Some of my colleagues have been getting their students to create instructional videos of their own.

What I love about Screencast-O-Matic as opposed to other similar software is:

1. It's free to create videos shorter than 15 minutes
2. You don't have to mess around with complicated settings like video codecs. You just click record and go.
3. There's a cursor highlight feature so that your students can follow your pen like the bouncing ball in a sing along as you show working or operate the calculator

At some point, I may find that I need some more advanced features found in programs like Camtasia, but for the time-being Screencast-O-Matic is the right balance of simplicity and features for my needs.