Wednesday remains Trainings and Meetings day around here, and as such I did not have any interaction with my students beyond responding to emails. What I did have was a very depressing Math team meeting where we looked at some data, reflected on the fact that the mid-year test had been (rightfully, mind you) cancelled and so we therefore weren’t going to get any updates on that data anytime soon, reflected further upon the fact that this particular assessment tool demonstrates that our students, by and large, appear to know nothing at all, and had a brief discussion wherein we were all forced to admit that none of us had the slightest idea what we might be able to do under the current circumstances to fix the problem.
(Nor can we be sure that the data captures the issue accurately, since the test was administered while the students were home, and we have no way of ensuring that it was taken seriously.)
One of the more entertaining fights in comments that I have had over the life of this blog was a post where I was complaining about my students performing poorly on a test about slope. Well, it is now several years later and I can confidently report that despite attempting to teach slope in a variety of different ways and with a variety of different strategies since then, my 8th graders still do not really appear to understand slope, and attempting to teach it virtually during a pandemic is … suboptimal.
Allow me, if I may, to further elucidate.
I have not yet actually introduced the formula for slope, which is complicated enough that I can’t reproduce it in WordPress’ text editor and would have to copy and paste an image. Instead, I’ve started beginning the unit with simply counting. Count the rise, or the vertical distance between points A and B, remembering (hopefully) that if you go down from A to B your “rise” is negative (this is confusing, because no one naturally thinks of something called “rise” as negative, and I wish the word was different) and then count the “run,” which is the horizontal distance between A and B and is always positive.
You will note on the above image that the slope of that line is -4, because you count down 4 squares to go from A to B and one square for the run, and -4/1 is equal to -4. I’m breaking this down in such a granular fashion that today was the first day we actually talked about negative slopes. Also, the reason there are no numbers anywhere on that image is that I discovered that some of my kids were simply writing down the number nearest to one of the points as (chosen randomly) the rise or the run, with no actual counting taking place. So I removed them on today’s assignment.
I have discovered that many of my students genuinely believe that there are five squares between A and B, because rather than starting from 0 they are counting the line A is actually on as 1 and going from there.
I have discovered– this is not surprising, but remains depressing– that a number of them do not include “left” and “right” among the concepts that are salient to them, and thus I must frequently remember to say “from A to B” rather than “from left to right.”
And I had a genuinely bewildering conversation with one of my kids, a kid who generally does well in class and has one of the highest scores in his grade on the test we were discussing earlier, absolutely cannot wrap his head around the words “uphill” and “downhill,” a set of terms I was using to distinguish positive slope (uphill, from left to right) and negative slope (downhill, from left to right) while I was talking. He consistently reported that any line was both going uphill and downhill at the same time, even when I made it clear which direction I was moving in. I eventually ended up creating this diagram:
He is color-blind, by the way, a disability that I have somehow never had to worry about in 17 years of teaching, so I have to make sure that color is never salient information in any diagram I do for an assignment, which is why one of the lines here is dotted. This can occasionally be trickier than it ought to be.
Anyway, I pulled this diagram together, still trying to work on this uphill/downhill thing, and asked him, gesturing with my mouse while talking, which of the two lines was going uphill when I moved from left to right. I even said “We’re moving from A to B on the dotted line, and C to D on the solid line. Which is going uphill?”
“Both,” he replied. And I swear to you, he wasn’t fucking with me. I tried a stairs metaphor. Which of these lines looks like you’re standing at the bottom of a flight of stairs, looking up to the top? Both. You’re sure you understand the “left to right” thing we’re doing here? You’re telling me C to D and A to B both look like walking upstairs?
Yes. Yes, he was.
This kid’s not stupid. Not at all. And he wasn’t fucking with me; I could hear the frustration in his voice. He was trying to get this, as opposed to the dozens of my students for whom no set of directions can be short or clear enough that they can be expected to read or follow them. But I don’t have the slightest Goddamned idea where the hell the disconnect was happening.
Today was not a good day.