Education ∪ Math ∪ Technology
"If I am to have faults, I would rather they be my own." Vi Hart
Vi Hart is somewhat critical of math teachers in this video, and of systems which prevent exploration into mathematics in their desire to ensure that all students have equal exposure to mathematical ideas. Of course, as she points out, students rarely have exposure to mathematical ideas. Instead, what they usually experience are mathematical procedures to solve problems that aren’t their own.
This is another in a series of posts about how one could find mathematics in the world around us.
My son loves to play with train tracks. A few days ago, while playing with his train tracks, he observed, "Daddy, I can’t turn a train around." I asked him what he meant. "No matter which way I go on this track, I can’t get my train to start facing in the other direction. I’d have to pick it up, but that’s cheating." (Note: I’m paraphrasing here)
Observations like this are mathematical observations about the world. He has abstracted from his train tracks to a property of his train tracks, specifically the direction his train is able to travel. He has then attempted, and I watched him do this, to verify this statement is true by running his trains around the track in every possible comination.
My wife and I spoke about this later, and she came to the observation that in order to be able to turn around his train on the track (without "cheating" by lifting it up), he needs a closed loop with a single entrance and exit point included in his track somewhere, and this entrance and exit point has to connect to the rest of the track in a certain way. So I asked the question, does he have the right track to be able to create a closed loop? If you look at the picture above, you may be able to answer this question yourself.
The area of mathematics that deals with these kinds of issues is called graph theory, and it was invented by Euler for a very different purpose many years ago. It is unfortunately not in most school curriculums, but it is certainly an interesting area of exploration, and one which is accessible to students.
While I was at my mother’s house the phone rang so I picked it up.
"Hello?"
"Hello Sir," said a female voice on the other end of the line, with a slight accent, "We are calling you from an independent computer security company. We want to let you know that we have received numerous reports that your computer has downloaded viruses and malware, and we would like to help you fix your computer." In the background, I could hear the unmistakable background noise of a busy call centre.
"You know that’s impossible, right?" I responded.
"What’s impossible?" she responded.
"You can’t possibly, especialy as an independent computer company, know the phone number associated with a specific computer, even if you were somehow able to scan my mother’s computer remotely without her permission. You are trying to scam her. It won’t work this time. I teach people how to use their computers. I’ve taught my mother about you. You cannot scam my mother. I will record the phone call the next time you call, and forward it to Interpol. Leave my mother alone!" I said firmly. (I doubt Interpol would be able to do much about this scam, but hey, empty threats sometimes work.)
Click.
Warn your parents, your relatives, and anyone you care about who may be taken in by this scam. My mother got caught the first time, but with some help from me, we recovered her money, and I have hopefully helped immunize her from the scammers.
We are introducing 30 iPads to our elementary school next year, and we are currently exploring what apps to put onto them. We have some suggestions as a place to get started, but I’ve been tasked with coming up with a list of useful apps for the iPads. I’m currently looking through my list of resources I’ve bookmarked for the iPad and deciding which of these apps I’ve seen will be most useful in our school’s context. (The screen-shots below are taken from the linked iTunes page).
This app both teaches kids how to use it (through a series of interactive puzzles) and allows students to create their own projects. It is based on the Logo programming language, but written using a sequence of commands chosen from the menu, rather than by typing. It works on the iPhone as well, but unfortunately (due to an issue with the Apple TOC) programs created with it cannot be shared.
This app allows students to build equipment to try and solve puzzles (which are based on physics concepts). I’ve not tried it out myself, but it is free, and so I’m going to at least try it out with the students.
This app allows students to draw and record their voice while drawing, letting them create a voice-over narration. It could be used for student created tutorials, stories, and animations. According to the description of this app, the videos created can be uploaded and shared via the ShowMe.com website.
The series of apps Motion Math makes for the iPhone and iPad are excellent, because they are more than just the typical flash card apps that are all too common in the app store for math. I’ve played with the fraction one myself (so has my son) and enjoyed using it, and seeing how it creates an alternate representation of fractions. This representation is hardly sufficient for students to completely understand fractions, but I’m sure it helps.
I’ve not used this app myself, but it comes recommended from Trever Reeh. From conversations with the mathematics teachers who work with Sketchpad, and from my time spent using Geometer’s Sketchpad a few years ago, I’m pretty sure this app will be useful. On the app description page, they note that they have activities built into it, which is encouraging.
DragonBox is a puzzle-game which tries to teach algebraic reasoning. It replaces algebraic symbols with visual representations (which are still themselves an abstraction of some arithmetic concepts) and then allows students to manipulate the symbols to try and solve the puzzles, which are all equivalent to standard algebra problems. It has a PC version which runs in the browswer and I have tried out as well. This is not a flash app so students can practice algebra – this game will try and teach students.
I’ve not tried this puzzle-game out myself, but I have used the paper and pencil version of the types of puzzles presented in this game with my students, and I found them very useful. Through solving the puzzles, students will have to employ (and learn) algebraic reasoning skills, which are explicitly described on the support page for this game.
This game allows students to type in words, get presented with images that represent those words, and use the images to solve a puzzle presented. The students have an enormous amount of freedom in what words they choose, and what images result. My son has loved playing this game, and spends his time playing it constantly asking us how to spell words, which he seems to be able to (mostly) remember for the next time he wants that particular item.
These are some of the apps I’m looking into. I’d also like further recommendations. I’m looking specifically for iPad apps which: