Thursday, December 23, 2010

We can do this the easy way or the hard way

There's an obscure change that was made in Office 2007, which I only noticed because of a chance experience. They changed the terminology from labeling the X and Y axes of a chart to labeling the horizontal and vertical axes. What's the difference, you might ask? The horizontal axis is the X axis, so who cares?

I'll get to that, but first how I even became aware of this issue. I happened to be helping a student who wanted help getting ready for a retake of a test on Excel. She missed part of the chart, because she mixed up the X and Y axis labels. As we were looking at what she had done, it was very obvious that the labels did not match. I don't remember the exact topic, but it would have been analogous to having a label that said "States" next to the axis with a range of numbers and a label that said "Population" next to the axis with the names of several states. You look at it and have to wonder if something is messed up, but then again, I have written before about how students will consciously choose to answer a question incorrectly with the idea in their heads that our tests were constructed by idiots and therefore the wrong answer will likely be scored as correct.

I showed her how the labels obviously didn't match, and I opened her spreadsheet file, and showed her how the box labeled X-axis had the text she was supposed to put in the Y-axis box and vice versa. The problem? I have to admit there was some logic to her decision to switch them, albeit based on a possible problem in our educational system, which is where I'm headed with this.

Among the various chart types in Excel are the bar chart and the column chart. I don't want to get into the difference between the types of charts, where you'd use a histogram vs a bar chart vs a line chart, etc. Perhaps another post. Suffice it to say that Excel doesn't really do a histogram without a lot of work on your part, and it's beyond the scope of this post.

So a column chart and a bar chart in Excel are actually both bar charts, with Excel's bar chart rotated 90 degrees. What ends up as the vertical axis, since it is rotated, is actually the X-axis. The reason it is the X-axis is because it is the independent variable. The dependent variable is the Y. I still remember in middle school missing a quiz question, because I hadn't read the chapter for that day and had to guess whether it was the X or Y that was vertical and horizontal. It turns out, that while convention does generally put the X horizontally, it doesn't have to be that way. There is a greater law. Unfortunately, we are taught the simplistic version of the law. If we were to take the advice of some and teach more statistics rather than calculus in school, perhaps there would be some importance of knowing the difference between a dependent and independent variable and thus we might be taught the greater law.

So, what the girl had done based on this "fact" that had been so ingrained in her throughout years of math classes was specifically decide to put the labels in the wrong boxes just so the X label would be on the horizontal axis, even if that meant having the X label in the properties box labeled Y and next to data that didn't make sense. After mistakes like this and others by a multitude of students, I started putting notes like "if something looks wrong, it probably is" on most test versions that I would write.

Apparently, Microsoft must have gotten some feedback from other people getting confused, and so rather than leave it as technically correct but difficult to understand, they punted. They just changed the labels to be called the horizontal and vertical axis labels in Office 2007. Now there is no question. And the three people per year that had a problem with this now don't learn anything, because it never comes up. In case you're wondering, OpenOffice still labels the vertical axis on the bar chart as the X-axis, because that's what it is.

So at what point do we switch from teaching the easy rule to teaching the more complicated but correct rule? Is there ever a reason to teach the easy rule? Wouldn't we perhaps see fewer line charts that should actually be histograms, etc. if we taught people assuming they were capable of understanding an advanced concept? Is this an advanced concept?

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