New Videos in Math SL and Physics HL Extension

I've been on vacation this week so I got off my butt and made a pair of videos on two topics that I find interesting.

First we have acceleration of a rocket with changing mass. In Physics HL we only ever deal with changing accelerations by looking at graphs but I wanted to go through the calculus to find the exact (well kinda) answer. In the end, probably due to some of the assumptions I made, I was off by a factor of 2.

In this video, I attempt to find the top speed of the Saturn V rocket if it were already free from earth's gravity and fully fueled.

Second we create an interesting shape by cutting into the side of a cylinder. Almost 10 years ago when I was still a university student on an internship, one of the drafters asked me what the volume of a circular cut out of the side of a cylinder would be. He already knew the answer, but I guess he wanted confirmation. I wasn't so great at calculus at the time and I didn't have any 3D software to help me visualize the shape so it took me three days to arrive at the answer. In the end I was surprised at how easy it was when you looked at the shape the right way.

Unit Circle Snypa

I find that my students always seem to have difficulty with the unit circle. In class, we work on understanding the symmetry in the circle, and what the meaning of the values are. However at the end of the day they need to be able to reproduce the major angles and that skill comes from practice.

To help them, I made a unit circle flash card program, Unit Circle Snypa.

Download Unit Circle Snypa for Free

The upper button cycles to the next question, the lower button suggests hits (right-hand side)

It randomly quizzes the user on sine, cosine, tangent, and the inverse trigonometric functions. You can also just quiz angles in radians or degrees.

You can quiz any combination of these functions.
Alternatively,  de-select all the functions and just work on angles alone

Unit Circle Snypa can also offer progressive levels of hints to the students if they get stuck.

Hints are offered progressively. Students can get a hand, without getting the whole answer.

I gave the program to my students for practice at home, but I'll also run the program in class if we finish the lesson five minutes early. I find that it works well side-by-side with my random student selector, Popsicle Shticks. My students have been getting better but we'll still need more practice.

You can download Unit Circle Snypa for free, here. The source code is also available, here. I hope you find it helpful!

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.

Etymology of Popsicle Shticks

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.

To download Popsicle Shticks, click here.

Generate Random Student Group with Popsicle Shticks v1.01

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:

Download Popsicle Shticks