8:30 -- First period arrives. This is the first of two Math III classes.
Today is the second day of a review of exponential functions in preparation for logarithms. This time, I decide to bring out "dry erase packets," first introduced by Sarah Carter and other MTBoS teachers. I had out the packets and have the students practice drawing several exponential functions. The emphasis here is on exponential decay, so I show the students f (x) = 2^-x -- the same as f (x) = (1/2)^x -- as well as simple translations of that function.
Then I perform the song of the day, "U-N-I-T Rate! Rate! Rate!" as explained in yesterday's post, except that I return to the verse on exponents as these are relevant to the Math III lesson. Afterward, we do the activity that the Math III teachers agreed to show our classes after the district Benchmarks (for the same reason that Math I classes are doing the Line Art Project this week).
This activity involves a question on transformation of functions where students struggled to explain how to transform a certain function f (x) = a|x + b| + c to another function g(x). For this question, they are given a Google Form that shows the responses given by ten of their fellow students, and they must act as the teacher, deciding whether to give each respondent 2 points (full marks), 1 point, or no points as they match their answer to the rubric. It's a way to show them how to give complete answers to free-response questions like these. Most of these students are juniors who will soon have to take the SBAC, which asks this sort of question.
9:55 -- First period leaves for nutrition.
10:15 -- Second period arrives. This is the first Math I class.
We continue working on the Line Art Project. First of all, on Tuesday some groups had trouble coming up with a drawing containing 16 lines, so I just drew a picture of a house and handed it to everyone. Then the students could stop agonizing over what to draw and begin the math part of the project.
I pass out four worksheets to each group -- each worksheet asks about four of the 16 lines required for the project, corresponding to the categories vertical/horizontal, positive slope, negative slope, and fractional slope (as mentioned in Tuesday's "Linear Art" song). For each line segment, the students must find an equation given its two endpoints, the domain, and its x- and y-intercepts.
11:00 -- In these monthly blogposts, I originally wanted to discuss how I'm making connections to my students, but it quickly changed to how to avoid arguments in the classroom. (After all, it's hard to make connections if I'm arguing with them.)
I believe that I've been making some improvements lately regarding the avoidance of arguments. But unfortunately, at around 11:00, I find myself raising my voice -- and I consider it to have crossed the line into an argument. So since I want to use these points to discuss arguments, let's look at the details here, and see what I could have done to avoid the conflict.
The problem is that too many students are still having trouble finding the equations of lines. So my worksheets provided extra scaffolding to help them out. Still, I try to demonstrate how to fill them out by showing them an example of one line, and then having them do the next line. In the end, it would mean that I've done half of the work of the project, in hopes that the groups will complete the other half.
Here's when the argument occurs: we are on the worksheet on vertical/horizontal lines. Here is what the worksheet looks like, with the part I complete and the part I'm expecting students to complete:
Start: (-10, -11)
End: (-10, 6)
Equation: x = -10
Range: -11 < y < 6
x-intercept: x = -10
Start: (10, -11)
End: (10, 6)
Equation: x = ____
Range: ____ < y < ____
x-intercept: x = ____
This corresponds to the left and right walls of the house. So I randomly call on Group #6 to show me the equation for the right wall, but this part of their page is blank. I ask them why they haven't filled out the equation yet. Then someone from Group #5 (not 6) replies that I haven't shown them how to find it yet -- even though I've already demonstrated how to find the equation for the left wall! And this is supposed to be one of the easier equations to find -- the positively and negatively sloped lines would be trickier, the fractionally sloped lines even more so.
In other words, I'd have to show them how to do this line as well -- and at this rate, I'll end up doing at least three-fourths (that is, three lines on each page) of the work for them on a project for which I'll be giving them 100 points.
At the start of the period, I've declared it to be Tech 55, with no phones out. My thinking is that during my explanations, the kids have their phones out and are ignoring me, so that when I call on them, they still don't know how to do it. But while I do catch someone in Group #6 with a phone out, no one in Group #5 (the group that complains) has a phone. So the issues must be much deeper than simply having phones out during the lesson.
And this is when the argument begins. I get upset that I have to do so much of the work for them on a project that (as I explained earlier on the blog) is supposed to help raise their grades. I knew going in that they would struggle, but I didn't expect them to be this helpless.
So is there anything I could have done to avoid this argument? Much can be said about the project itself, as well as the lessons I previously taught leading up to the project -- a better-designed project and deeper previous lessons might have prevented any conflict. But for this post, I wish to focus only on today and how to avoid this argument.
Perhaps by this point, I should have simply realized -- after having to draw the house for them and provide this much scaffolding -- that the kids simply aren't ready to do this much work for each line. In other words, short of going back in time to change the project or lessons, there's nothing I can do to increase the amount of work the students do on their own without my help. The meager part that they do manage to get on their own is the most work I can extract from them without an argument.
And thus the 100 points become a compliance grade -- I deduct five points each time a group member violates Tech 55, but other than that they get the full points no matter how little they do. Any work that the students do get on their own is icing on the cake. We end up getting through vertical/horizontal and positively sloped lines with the students copying most of my work from the board.
At any rate, this class is definitely not motivated to work after the extended argument. Group #6 spends the rest of the period tearing up little scraps of paper and throwing them at each other onto the ground, and many other students start talking loudly and avoiding the project altogether.
11:40 -- Second period leaves and fifth period begins. This is the second of two Math III classes. (That is right -- I don't have third period conference on Thursdays. With no break and my toughest classes all meeting, it's no wonder that I often end up arguing on Thursdays.)
This class goes much like first period. But with the second period argument still on my mind, I'm more careful to make sure that the students understand the exponential lesson before switching off to the Google Form. I keep on checking the dry erase packets and give many examples until I'm satisfied that most of them understand what I'm doing. The last thing I want is to be in a situation where it's almost test day, and yet almost no one can graph an exponential function (just as almost no one in Math I can find the equation of a line on project day).
1:15 -- Fifth period leaves for lunch.
2:05 -- Sixth period arrives. This is the last Math I class.
Due to the eccentricities of the block schedule, sixth period goes differently from second period. In fact, after I saw second (and fourth) period fail to complete their drawings on Tuesday, I already handed out the house worksheets to sixth period yesterday, their first block day of the week. (There's no purpose, after seeing Periods 2/4 waste a day, to have sixth period waste a day to "just to keep it all equal.") So yesterday's sixth was like today's second -- these kids have already done vertical/horizontal/positive lines and are ready to move on to negative/fractional lines.
As expected, I do at least three-fourths of the work. The students figure out the slope of one or two lines and some of the other information, but not the x-intercept.
And of course, they struggled even more when we reached fractional slopes. I start to raise my voice when I see that I'd have to do all the work on this page -- and then stopped. There's no way that I want another argument after second period. I'm forced to apologize, and then I sigh and do all the rest of the work for the kids, since this is how far I can't get with them without arguing.
3:30 -- Sixth period leaves, thus completing my school day.
Believe it or not, this is still not my last blogpost of the week. Tomorrow is the special day "last day before Thanksgiving break," and so there will be another "A Day in the Life" post. What I hope, of course, is that there won't be another argument tomorrow.
We are now officially in the "holiday stretch" of the year. First noted by traditionalist blogger Darren Miller, the "holiday stretch" goes from Veterans Day to Presidents' Day.
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