ECI 831 Reflections

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.

Typesetting Math in Wikispaces and WordPress

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

Problem Based Learning in Math and CS

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.

CBC distributing via BitTorrent

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.

Stephen Downes and Open Source

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.

Howard Rheingold on Collaboration

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.

Global Communications Centre

Listening to Clarence Fisher tonight in my ECI 831 class was quite elluminating (private joke).  As indicated in the title of this post, the key concept for me was that our classrooms should be “Global Communications Centres”.  While I think that I’ve been making some strides in terms of students accessing information from around the world while in my classes, interactive communication with people outside the walls of my class has been extremely limited.  I’m brainstorming ways in which I can address this — live Skype calls with former math professors, etc.  Anyone have an idea of how to do this in high school level math courses?  Any idea is greatfully accepted…

Just in case anyone reads this who is interested in collaborating/creating some interactive format for the students to participate in, I am also really interested in teaching more about social justice in my math classroom.

Playing update

Since my previous post regarding the importance of students playing in class, I’ve become ever more conscious of making sure that I really do spend time allowing this to happen.  As much as possible, I try to work from what they are already interested in.

This past week, a number of my computer science students (geeks in the most positive sense of the word) were telling me about a riddle they had been playing.  It’s called Neutral Riddle, and starts off simply enough, only to become devilishly difficult.  The goal is to finish all 71 levels by guessing the URL that contains the next clue.  These kids are spending hours each night trying to get to the next level.  (Warning: If you are a compulsive problem solver, be aware that this could engulf your time.  Only 70-ish people in the world have solved this riddle, none of whom are from Canada.  One of my students is currently at level 38.)

Today in CS class, we worked on the first 2 of levels in the Neutral Riddle together (for about 5-10 minutes).  Then, after they had all figured out the concept of the thing and were addicted (to varying degrees), I suggested we make our own.  So, today’s class was spent with each student creating one level of the riddle that we will collaborate on.  I got them going by showing them how to find images using flickrCC (making sure they follow the Attribution CC license) and getting them talking to each other about ideas of what their riddle might involve.

This fit in perfectly with what we had been doing.  I just finished up teaching a unit on XHTML/CSS (markup languages for the web), and this gives me a great opportunity to stretch out their learning on these topics. Now, as they are having fun creating this riddle, they are also reinforcing their knowledge of XHTML/CSS.  Hopefully by tomorrow I’ll be able to provide a link to the start page for our riddle (we didn’t quite get to that today).

As an aside, I also had fun with my Math C30 students today.  We played a game with trig functions (taken from the Mathematics Teacher, but I forget the author).  Seriously.  Just get them into pairs, then see who can get the answers in the time limit, using only their brains and a pencil.  They actually really got into it, so I had them create their own variations after we were done.  I’ve posted a template up on Google Docs, and the students are going to add in their variations online tomorrow, so I can use them for future classes.

Teaching students that it’s okay to play

Ken Meredith recently wrote a post highlighting what Dean Shareski mentioned in his presentation to our ECI 831 class about early adoption of technology — namely, that educational value may not be easy to spot right away, and that simply playing with technology is quite alright (and often leads to great ideas of how to use it to achieve curricular objectives).

While I completely agree with this idea, I think it’s equally important to give our students the same freedom.  I try to build explicit play (about 20-30 minutes per week) into the courses that I teach.   Now, I can’t always fit it in, and sometimes it takes longer than I anticipated, but it sure makes kids look forward to coming to my classes.

In my math classes, some things that we’ve done are Fun Fridays (in which I play a random YouTube video at the end of class on a Friday), encoding and decoding secret messages (in which I tend to go off on a short history of cryptography and it’s many uses), playing games on the SmartBoard (everything from Countdown, a distinctly math-ee game, to Yellow Out, a parking lot logic game) and anything else that strikes my fancy that week.

In my computer science classes, there’s a lot more flexibility, since all of the students are on computers hooked up to the net.  In general, I try to show them (and give them time to play around with) at least one new tool/website each week.  The sky is the limit here, and I don’t really have any particular category that the site has to fall into, so long as I think it’s neat, I show it.

Now, I know that I am not the first to use play in my math classroom.  However, it’s hard to not feel guilty on occasion when a fellow teacher is walking down the hall and we’re (gasp!) having a great time in my math class… just playing around.

So, I’m curious.  How do you incorporate play/games in your classroom? 

Most enjoyable in-class review session I’ve had

Whenever I can make it work, I like to give my students one class period to review prior to an exam.  As we have an exam on factoring tomorrow, my Math 20 students were working on a review today.  Inspired by some of the discussions around connectivism and collaboration I have been around lately, I decided to do a bit of small scale social learning (just within my own classroom walls).

I gave my students their review handout, as per usual.  They had the first 5 minutes of the class to get themselves going on the review, after which I would randomly call a student to come and do the question on the SmartBoard.  These were all recorded using Jing, and then tossed up to the course wiki.  The compilation of questions is here.

The reaction of the students was quite something.  I had already modeled how to record examples for the wiki in previous classes, so they already knew how it worked.  It was just a  matter of taking some time in class to let them go at it.  Some students were instantly excited, and wanted to record as many questions as possible.  All of the students enjoyed the fact that they had time to work through the question on their own first, and then record how they did the question.  A number of the students were nervous about making a mistake on the recording, and therefore would ask their neighbor/me whether they had done it right prior to recording.  One student was so paralyzed by fear of making a mistake that she asked me quietly if I would not call on her (this was a student with a fairly high average — 75%+).

Speaking of mistakes, I don’t know how to best record examples of them.  I don’t want the student to feel belittled by posting something incorrect and labeling it as such, but there seems to be so much potential learning in taking a mistake and discovering how it can be fixed.  This is easily done in class, but really hard to show on Jing (of particular difficulty is the 5 minute time limit, which doesn’t allow too much exploration of “what went wrong”).  Any ideas?

In the end, this wasn’t too much different than the normal review period.  However, I certainly saw a drastic increase in student engagement, and a bunch of students left talking about how they would be watching themselves/each other online tonight.  Really, if I’m getting them to voluntarily watch math videos, I’ve got to think something’s going right!