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:
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.
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:
It's free to create videos shorter than 15 minutes
You don't have to mess around with complicated settings like video codecs. You just click record and go.
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.
In a presentation on differentiation techniques, a co-worker of mine introduced me to a clever method for randomly calling on students. She suggested writing students names on popsicle sticks and keeping them in a cup. You could pull out sticks to call on random students, or pull out groups to sticks to make random teams.
I really liked the idea from a pedagogy perspective:
Calling on random students helps keep them on their toes
Randomizing groups forces students to be social with each other and takes pressure off of socially challenged students. (Although I might not want to do this every time. I think it’s important to give students an opportunity to stretch and make connections on their own.)
If random students answer, then all students must participate instead of just the most engaged
Instead of an echo-chamber effect from the best students answering all the questions, I get a better idea of the comprehension level of the class when random students answer.
Calling on weak students for difficult questions gives them an opportunity to stretch. I just have to be careful to make the students feel comfortable to try and fail and try again. I’ll also have to be ready to scaffold the answer for the student should they need some help.
However, I wasn’t too keen on managing five cups full of popsicle sticks. As a secondary school teacher, I have five different classes in different rooms across the school, so keeping up with 120 sticks in 5 bundles carried hurriedly around every day seemed like a non-starter. However, my tablet PC isn’t far from my arms during most of my lessons, so the solution seemed to be a program that would hold my popsicle sticks for me. I would be able to edit my lists easily, and I would never drop a cup full of sticks on the floor. Hence, “Popsicle”.
The ‘shtick’ in Popsicle Shticks, is not meant to be joke about poor pronunciation. Rather, Shtick is a Yiddish word that refers to an attention getting routine. Much like a comedian might have a Shtick that he relies on, Popsicle Shticks is a routine I use to keep the student’s attention. Hence, “Shtick”.
If you want to know more about Popsicle Shticks, check out the original blog post.
A colleague of suggested using my random student name picking program, Popsicle Shticks, to quickly create random groups of students for group-work. However, because the normal random name generator doesn't pull the names out of the hat once called, it didn't quite work as planned. In addition, students being what they are, will always manage to forget what group they were assigned to when called.
To address these issues I have added a random group generator to Popsicle Shticks. You can use this feature to quickly sort students into teams, or create presentation orders. When the list is made, duplicates of names in the list are removed so if you have quietly added a student twice to make sure they get selected more frequently, their name won't appear on this list twice. However, it does mean that if you have two students with the same name, you'll have to give them slightly different names in your class list. For example "Joey" and "Joey" become "Joey P" and 'Joey Z".
For more information about Popsicle Shticks, a discussion of calling on random students in class and source code, see my original post. You can download the latest version of Popsicle Shticks here:
Popsicle Shticks is a light-weight program I created to help teachers call out student names at random. As a teacher I like the idea of questioning individual students because:
It keeps students attentive and on their toes
It helps prevent know-it-all students from dominating the class dialogue
It gives me feedback on how well students are capturing knowledge
It helps me learn student's names at the start of the year
I prefer this software implementation over names in a hat or picking names "randomly" from my head because:
In my classroom, I have a wireless video connection to the projector so when I'm direct teaching my computer is never far from me.
I don't have to manage half a dozen hats full of cards that need updating every time students enter/leave my class
I can copy/paste my class list from my excel grade book right into Popsicle Shticks
The program automatically draws a new random name whenever it loses program focus, so every time you check the screen it's ready with a new name.
If I feel like some students need to be called on more than others, I can quietly add their name to the class list multiple times.
I have heard the argument that by randomly selecting students, you will occasionally ask difficult questions to students who are not able to answer. However, I argue that in those cases, you are giving that student an opportunity to exceed your expectations; provided that your classroom has a positive environment where students feel comfortable to try and fail and try again. In addition, if you want to ask a truly devious question, you can simply open up the question for anyone to answer rather than selecting a random student.
I've been testing Popsicle Shticks for a few days in my own classrooms and I have found that student response is mixed. Some students are excited by the chance to answer a question when they weren't brave enough to volunteer before. Other students were used to being able to quietly sit back and are not accustomed to having to be engaged all the time. Personally, I'm having trouble remembering to use the program! I usually ask the question, then remember to get a random name. This means that I don't really have that student's attention until after the question is asked. I need to get in the habit of calling on the students before asking the question.
If you're interested in trying Popsicle Shticks in your classroom, you can download the program from this link:
I also made a video tutorial on installing and running the program. The process is pretty straight forward, but there are two things you might need to look out for.
You need .net installed. At least version 2.0. You can download the latest version here if you don't have it already (you probably do if you have windows 7).
You'll want to save the program to its own folder. It creates new files for each class that you have so if you save it to your desktop, you're going to fill your desktop with class lists.
For those of you who need a slight variation to this program, you can download the source here. Apologies for the sloppy code.
