whoknows.ca

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.

danschellenberg Education, Math, Technology Google, Math, statistics

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:
$latex \lim_{x\to\infty}f(x)=0&s=3$

Or perhaps a basic fraction, like this:

$latex \frac{a+2}{b+4}&s=3$

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

danschellenberg Math, Technology

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.

danschellenberg Computer Science, Education, Math

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.

danschellenberg Education, Math, Technology

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.

danschellenberg Computer Science, Education, Math, Technology