I’m moving.  I’ll now be at whoknows.ca.

So, I had a pretty funny experience today.  When my Math C30 (pre-calculus) students walked in today, one of them held something behind her back and told me she was about to change the way I looked at the world.  I was speechless.  She then produced a comic book.  It’s called “The Add-ventures of MathMan”, and I’m the main character.  They were creating this in their spare for the last month or so.  Unbelievable.  They gave me a nice laminated hard copy, but also threw it up on the web here:

http://mathmanaddventures.wordpress.com/

My favorite bit:
Evil villain Theta: “But how did you escape?”
MathMan: “I shrunk one side of the triangle so the sum of the two smaller sides wasn’t greater than the third side.  The triangle ceased to exist!!”

Sometimes, being a teacher is a lot of fun.

P.S. Whenever you guys read this — thanks.  You made my day.

My foray into using Google Docs in my math classroom was really well received by my students.  Quick summary of the idea: get students to poll classmates on how much time they spend using various media each week (TV, Internet, gaming), then have them use statistics to make guesses regarding the habits of the entire student population.  I revised the orignal assignment slightly. See the final version here. 

Out of my 52 Math B30 students, 49 polled fellow students and entered the results on our online spreadsheet. This made it simple to calculate the mean, standard deviation, et al for the entire set of data (we had 233 students polled, which is close to half of our school population). Check out the final data set here (Note: this is a non-editable copy.  The students had access to a version they could play around with in order to let them perform whatever tests they wanted to).

Although my students could have done this assignment without using an online spreadsheet, attempting to organize all of the results would have been a lot more time intensive. This way, students were able to sort the data and figure out mean and standard deviation of the genders, all within Google Docs.  This led to some really good answers to my last question on the assignment, which was “Is there a difference between males and females in terms of their gaming habits? Explain in as much detail as you can“. A good number of the students came up with exceptionally good answers for this question, supported with the numbers from our spreadsheet.

I will definitely be doing something like this again next year.

Note: We got into a good discussion about whether the data is normally distributed.  It’s not.  It looks pretty bimodal to me, and we came up with reasons why that might be.

In the spirit of sharing, here’s a lesson that I’m using with my Math B30 students right now.  We’re working on Data Analysis (Stats), and in particular, the normal distribution and related probabilities.  I was getting a bit tired of the dated examples in the text, so I thought I’d create my own problem with the students.

Each student will do a poll of other students in the school, with each student getting a minimum of 20 results.  The two questions they are asking are:

• how many hours do you watch TV in an average week?
• how many hours are you on the Internet in an average week (surfing, email, IMing, Facebook, YouTube, etc.)?

Each student will then post their results to a Google Docs spreadsheet I set up (one spreadsheet per class, like this one) that anyone can edit (to eliminate the need for them to log in).  After all of the students have added their results to the Google Docs spreadsheet, they can then use the aggregate data to perform the statistical calculations required (z-scores, what these results mean to a school population that we assume is normally distributed).

The handout that I’m giving the kids is available here.  I’ll let you know how it goes.

Today is the last day of class for the ECI 831 master’s course that I am taking. Alec (the prof) asked students to provide a bit of a reflection on how the course went, so here goes…

What you did:

• schellenbergmath.wikispaces.com
  • created a wiki to house math screencasts created with the math classes I teach (Math 10 – Math C30). Example screencasts are done by me, and students do a bunch in the “Textbook problems” sections of the wiki.
• cs30.wikispaces.com
  
  • a wiki for my Computer Science 30 course, in which all of my students are members of the site, and have full permissions to do anything they want. We had to go this route as opposed to an open wiki, as this was the only way to give the students the ability to change the design of the site.
• drupal.whoknows.ca
  • a last minute addition to the major project, I decided to evaluate Drupal to see whether it was a suitable tool to create and maintain our school website.

What you learned:

Math wiki

• students LOVE having access to instruction on their own terms
• students want to have the same instruction as if they were at class (ie. although my screencasts could be used by any math student, my students particularly enjoy the fact that it is me they are hearing)
• students are excited to show off what they have done — will show friends/parents screencasts that they have created in class
• typesetting math in wikispaces is better than many places on the web, but the lack of inline equations is still frustrating (ie. an equation needs to be on its own line)
• it’s incredibly humbling to capture what you do and throw it up online for all to see (without editing it at all). At first, I would toss out a video if I made a little mistake, or thought that I’d said “um” too many times. Now, something pretty bad has to happen for me to not just fix it up while ‘on camera’. I think there is value in my students seeing me work through technical or mathematical issues, whether in class or in the archived class content online.

CS wiki

• students found the lack of full HTML limiting (one got around it by downloading a backup copy of the website, which allowed him to check which CSS class a certain <div> was accessing. Quite clever)
• students enjoyed personalizing the class wiki — a sense of ownership was developed. Although their personalization resulted in a fairly mediocre looking site, they certainly enjoyed the process. Will try to extend this further to see if it can help with next point.
• organic growth of a wiki resource is hard — and depending on the type of resource, fairly useless (cite Just Google It!)

Drupal

• setting up a Drupal site is quite simple, if you have prerequisite knowledge of how to install MySQL databases, etc on your webserver (can be even easier if your webhost has an auto-install script)
• looks like I’ll be using this to get a production-ready site up for our school
• once the basic site is created, editing it should be a cinch — may need to train one other person at school in the complexities of Drupal, but it should be fairly simple…

Barriers

• Jing is slow; makes my low end machine at school fairly unresponsive
• Wikispaces lack of full HTML editing was irritating for the CS wiki — might look for another wiki that allows for it.
• teach support at school can be… interesting. For example, IT wouldn’t let me use an Ubuntu LiveCD, as I’d have to change the BIOS settings, so instead the IT department spent about 25 manhours getting VMware server and an Ubuntu image on the machines, only to find that they actually need more RAM due to the fact that you are then running two operating systems simultaneously. The RAM comes this Friday. More manhours to follow.)

In conclusion, I’d have to say that my digital project was a resounding success. My students have thanked me many times over for the math wiki, and the CS students are finding their wiki useful as well. (Total tangent — check out the progression in what this student knows about web design by checking out his assignments one after another. This is why I love teaching CS.) I am more and more convinced that the idea of “small tools, loosely joined” is the way to go (this preference is my one hesitation on using Drupal for the school site, incidentally). I’m really pleased with how the combination of Jing and Wikispaces works for my math wiki. For my CS blog, being able to embed del.icio.us links that I tag “CS30″ makes it dead simple for me to share interesting sites with my students.

I’m always on the lookout for new tools that will add some sort of functionality to how I work and how I teach. Most don’t find their way into my classroom, but when they do, it’s pretty powerful.

One difficulty I have had as a math teacher using the internet a lot is that typesetting math is frustrating. This is especially true when students begin typing math, as you have to teach them a whole new math notation; ^ means exponent, ** is also exponent, etc. It’s just messy.

There are a few tools available to make things better. If you are using a word processor, such as Microsoft Word, there is usually a built in math equation editor that allows you to typeset equations quite nicely. If you memorize the shortcut keys (such as Cmd-F for a fraction, Cmd-H for exponent, etc.), you can actually type math at a respectable speed. If you, or your school, are willing to put out some cash (~$60), you can also buy the big brother version of equation editor called MathType. Another option is to use LaTeX, which is a professional typesetting language, though it is a steep learning curve, and more work than it’s worth for many teachers.

It may not be immediately obvious how this relates to typesetting math on the web. As it turns out, some web services allow the use of LaTeX math equations. Here on wikispaces, you can use LaTeX to typeset something that isn’t normally fun to type, like:

Or perhaps a basic fraction, like this:

The LaTeX code for these isn’t a lot of fun — it looks like this:

\lim_{x\to\infty}f(x)=0

and this:

\frac{a+2}{b+4}

Who wants to memorize how to do that, anyhow? (Full disclosure: at one point, I did actually memorize this…) So, rather than writing LaTeX code directly, you have two options:

- if you own MathType, simply change the Export settings to LaTeX. Then, select the part of the equation you’d like to use and copy and paste it into wikispaces. Instead of copying an image, you are now copying the LaTeX code.

- if you don’t own MathType, and are working on a Windows machine, you can use TexAide. It’s freeware, from the same company that makes MathType, and it lets you type your math, then simply copy and paste it as LaTeX code. It’s really handy, especially since it uses the same engine as MathType, so all the same keyboard shortcuts work, just like Equation Editor.

If you are on a Mac, the only really nice way I’ve found to easily generate LaTeX code is through the full version of MathType. If anyone knows of a nice, free solution, please do share.

How to embed the math into your website of choice will depend entirely on which site you are using. On Wikispaces, the first equation above is simply surrounded by math tags. It therefore looks like:

[[math]]
\lim_{x\to\infty}f(x)=0
[[math]]

On WordPress.com, you will need to surround the LaTeX code with $ symbols, and declare the code to be LaTeX. The same equation from above would therefore be:

latex \lim_{x\to\infty}f(x)=0  (should have $ on either end of that)

Hopefully someone else finds this useful.

Cross-posted to the T4L wiki at http://t4tl.wikispaces.com/Typesetting+Math+in+Wikispaces

I’ve been trying to sort out how to incorporate the problem based learning model in my teaching (most recently advocated by Chris Lehman during a session for ECI 831).  I find it much easier to do when teaching computer science than when teaching math (just so you know, I teach about 90% senior math, 10% computer science).  I’ve been pondering why that is, and I think a lot of it comes down to the fact that I haven’t been indoctrinated as much in my teaching of CS.

Although I was trained in computer science during my university days (in C++, no less), the vast majority of what I do now has been a result of teaching myself. When trying to sort out what language to teach my students in an introduction course (CS 20), I did a bunch of research and ended up choosing Python.  In the process, however, I tried out a number of languages, enough to become semi-fluent in about 5 or 6.Since I’m a geek, I randomly get the urge to create a program to automate something or solve a problem I’m having.  This lets me keep my skill level up in a variety of languages, as they all have strengths and weaknesses.  All this has contributed to me becoming rather proficient at learning whatever I need to know by researching it on my own.  I want my students to be able to do this.

As I said, this easy for me to do in CS.  I can give the students a few basic nuggets of info, then let them go to it.  For example, we’re using PHP to learn how interactive websites work right now.  I taught them some basics about how PHP works, just enough to get their feet wet, then gave them a few simple assignments.  The students have access to the net (obviously), and can therefore research methods of solving whichever problem I’ve set for them (say, creating a web form and spitting out the submissions to a text file).  I essentially float around, acting as a resource, and occasionally will grab all of their attention by showing them a quick tip or trick on the projector.

In math, I’m at a loss.  This is crazy, as I was a mathematics major at university, and took way more math courses than CS.  However, the curriculum is so much tighter in a math course (it’s a struggle to finish it all), and the pressure to conform to the accepted way of teaching is so great (by students, parents, nearly everyone…), I find problem based learning really hard to implement.  Not only that, but the sequence of high school math courses is such that if I don’t get around to teaching them something, they are completely lost in their next class (which I may or may not be teaching them).

Because of this, I don’t really use PBL in my math classes right now.  What I do, however, is make my students construct the math that they learn on their own.  I’m there, and I ask questions, but it’s rare that I will give an answer without dishing it off to one of them.  So, if you were to visit one of my classes, you’d see me at the front of the room a fair bit, but I’m really conscientious about only writing what the students tell me to write.  I make them put the pieces together.

This takes engaged students, however.  I get them to buy in by being ridiculously excitable about math.  Seriously.  I tell them about Ug the Caveman, who created all of our number systems (some of them actually go for this, believe it or not).   I point and gesture like a madman.  I play random YouTube videos just for the heck of it.  We have fun.  In return, when I ask them a question, I get answers.  Lots of answers.  If it’s right, great.  If it’s wrong, great.  We figure it out together.

The downside is that I don’t ever get to sit down during a class.  The upside is that I’m pretty sure that by the end of our time together, my students are better at thinking than they were at the start.  It just so happens that I use traditional math knowledge to make them better thinkers.  I don’t believe that teaching them to think this way is any less valid than teaching them how computers and the web work, even if the material is esoteric and will be used by only a few of them.  The thinking, I keep telling myself, they can all use.

The CBC (Canadian Broadcasting Corporation) have begun what may become standard in the future — distributing a DRM-free, full quality version of a TV show (Canada’s Next Great Prime Minister) for all to download and view for free.  To make things even better, CBC has chosen to use BitTorrent technology to distribute the file.  This allows a large file such as this TV show to be distributed to a large number of people without costing the CBC exorbitant amounts of hosting fees.  In essence, you share the file while also downloading it, so the more people who are downloading, the faster it becomes (the exact opposite of what you might expect traditionally).

The CBC is the first North American broadcaster to take this step, though not the first in the world.  A Norwegian broadcaster (NRK) took this step earlier this year, with great success.  Eirik Solheim, one of the masterminds of the Norwegian project, was interviewed by a German news site, and the interview is very interesting.  One major problem with distributing shows using this method is third party contracts, which makes adopting BitTorrent distribution something that only new shows are likely to do.

This is exciting news, and I hope the CBC continues to expand on this.  It seems like such a obvious thing for a public broadcaster to distribute shows to their viewers using the cheapest and most convenient method available, but the issue of third party sponsorship will surely cause some difficulty during the initial stages of this concept.

I had the privilege tonight to listen to Stephen Downes present the software that he uses to run his Stephen’s Web site.  Stephen has created a fairly complex system in Perl that allows him to grab, read, remix and post information from a variety of sources/feeds.

In the Q&A time, I asked Stephen whether the vey nature of open source requires a hierarchy.  The motivation behind the question was simply that I have noticed that for every great piece of software I’ve seen, it has begun with some person scratching their personal itch (ie. solving whatever workflow problem they have).  This one person creates a (usually) complex system that allows them to do whatever they need to do.  Then, once the software is usable, others begin to become interested in it, and collaboration begins.  However, the person who started the project has a higher place on the totem pole, by virtue of the duration of their time with the project, as well as their greater familiarity with the code.

Stephen’s response was, if I understood him correctly (I’ll have to go back and listen to the recording again to be sure), was that heirarchy is not required, since a person can simply fork the code (begin their own version of the software) at any point.  While this is true, I am not at all convinced that this removes the heirarchy.  Does it not in fact simply create a second one (one in the original project, and one that begins with the new fork)?  I am terribly intrigued with the collaborative process of open source software, but it seems to me that it must always begin with a “benevolant dictator” (to quote the Python community in reference to its creator, Guido Rossum).

I don’t think that beginning the collaboative, open source process with an individual makes it any less powerful.  I just think it’s important to recognize that all good projects (that I can think of or imagine) must start through an individual, not a collective.  Does anyone have a good example of when this has not been the case?  I’d love to hear of it if it exists.

I just finished watching Howard Rheingold’s TED talk on collaboration.  Rheingold is the author of Smart Mobs, a book that explores the use of internet/mobile communications in organizing social action.  In his TED talk, Rheingold says:

This is all about self-interest that adds up to more… around the world, citizens have self-organized political protests… using mobile devices and SMS.

The basic idea is that there is a new currency of wealth that is being created through collaboration, and that we need to continue to study the impact that this can have on our individual and collective lives.  It’s worth the 20 minutes.  Have a look.