I tried something new this when I taught the Chi squared test.  Instead of focusing on the formal procedure that one must follow in order to use the test correctly, I focused on what we were actually DOING when we were doing the test.  As a result my students understood the test much more easily, and I had far fewer questions about how to actually use the test.

First, we talked about the expected values, starting with the sums of the expected values.  See the following table.  Here the "Yes" and "No" refer to whether or the particular person being surveyed watches the TV show Glee.

Essentially this backwards from where I started normally, with the observed values table, because I wanted students to understand how we construct this table, rather than relying on rote memorization of the formulas for the expected values.  I started with this fact, that we have 50%  males and females in our data.  Hence, I said, if gender is independent of our question about Glee, how many males should we expect to answer Yes to the question about Glee?  Students pretty easily came up with 60 males, reasoning that 50% of 120 is 60.  I focused their attention on how what they did to get this answer, and then we filled in the rest of the table.

I then set up an observed values table, and filled in the table used way different numbers. I made sure students understand that the previous table represented the expected survey results if Gender wasn’t a factor in people choosing to watch Glee, but that the following table represented our actual survey results.

Right away, one of the students said that this second table obviously meant that there was a relationship between Gender and choosing to watch Glee?  The reason he gave, "Well those numbers are way off the expected values."  

I then asked a really important question.  "How much different do they have to be before the results are significantly different than our expected results?"

Students realized that we’d probably want to start by subtracting our two sets of information like so.

I pointed out that we don’t really care if the difference is positive or negative, since either way the results are "way off" if the difference is big.  So we squared the observed minus the expected values to make the answer positive. Note that we haven’t really done much work with absolute value, so I chose to ignore it for this example, which helped make my case for the calculation, but probably needs some discussion.

Next I pointed out that the numbers were too big, and that I wanted to be able to make a comparison between the size of the difference between observed and expected values in one chart with the size of the same type of difference in another chart.  Normalization (which is not a word I used with the students) is a useful way to do this, and hence we want to divide by the expected values.

Someone noticed that this was a bunch of different numbers and that it would be more useful if we had a single number, so I suggested adding up all of these normalized differences.  This number, I labelled as Χ²_calculated and we had our result.  Note that my objective here was not to formalize the calculation, but more to justify the calculation informally, so that the students would feel like the understood what they were doing.

From there the rest of the lesson was relatively easy, we had a discussion about how to compare Χ² results which led to the table of critical values, and with this table I introduced the notion of degrees of freedom.  I didn’t try to explain why the critical values tend to increase with the degrees of freedom or with the significance level, but the students were okay with these additional steps because the initial calculation, and reasons for the calculation made a lot more sense.  I was able to talk about the test at a deeper level than I had before, and when the students came time to actually practicing the calculation themselves, they had a lot fewer difficulties than I had anticipated.

One observation a student had was, "Using those list operations you taught us on the calculator sure would make this a lot easier," and a bunch of the students had an "Aha!" moment as they realized why I bothered to show them how to do the list operations on their calculator.

The essential difference in teaching here was using a conceptual framework versus my old method of rote memorization of the process.  I think I know which way I’ll try in the future, even with something which seems so mechanical in nature.

Check out this quick comic I made using Bitstrips.com.  Maybe we can start  a whole series of comics on education, with our point of view on how education should (or should not in this case) be done using satire and humor to get our point across. (For those of you viewing this on an iPhone or iPad, check it out at Bitstrip.com as an image)

My father passed away a little more than a year ago, but through the internet he still lives on.  I missed him this morning, probably because of some of the environmental stories I was reading (he was a huge environmental and rights activist) and decided to look him up.  

The first page I found when I Googled his name was his obituary which was, as it always is, a tough read. "Tim Wees packed much into his 64 years of life", it starts and the tears start to flow.  It is a bit morbid to read an obituary, but I don’t read it because it reminds me of his death, but more because it reminds me of all he accomplished in life.  I tried and imagine what it would be like before the internet, when I would have had to keep an album of newspaper clippings and photos, and one of these pages might have been his obituary if I was lucky.  Today, I can look it up online whenever I want a reminder.

Next stop is his website, timwees.com, which I am paying to keep up.  No changes happening here, but anytime I want to read something my father wrote, or listen to the sound of his voice, I can.  One of my favourite pieces of his is about Canada, a kind of montage of interesting things to see and remember about our country.  He had put up all of his writing online mostly because he really wanted to share his work.  Contradicting his desire to share his work, he carefully wrapped all of his text up in the proprietary PDF format, locking up his work from being changed ever.

One of his pieces of work is still being discussed on the internet. In the early 90s, my dad lived on the street, and collected some stories of street children.  His work, No Where Was Home was written from the heart.  I wonder now what has happened to those children, but from a discussion I found on Facebook, it looks like they are still connected to each other and discussing his work.  Pieces like his are a record of the parts of our country which are rarely discussed in as much detail on the nightly news.  They are important, and I’m proud of him for having written it.

I can find comments my dad wrote on other people’s stories, and find stories which quote him.  There are hundreds of pages on dozens of websites that my dad contributed to, and I haven’t read all of them.  Still it is an interesting archive of his thoughts and opinions.

One thing I cannot find of my dad is many pictures of him.  I have a few that I’ve found, but my father was behind the lens of the camera too often for me to find photos of him.  Here’s one that I like, which I found after much digging through his website.  Once this particular post I’ve written is indexed by Google, this photo below will show up when I search for my dad.  

Tim Wees and my son Athanasios (April 2007)

The digital record we leave behind on the internet keeps us alive in a way not possible in previous generations.  It is not hard to take an ordinary person’s life, and if they had any presence on the internet in life, find them "present" virtually on the internet.  The current generation of children will grow up in a world where finding a Youtube video of their parents online is straight forward.  They will be able to interact with their parents after they die in ways which are profoundly different than any other previous generation.  Instead of having to rely on carefully guarded (and easily lost) family archives of old family photos and movies, they will be able to Google their parents anytime they like, even after their parents’ deaths.