Dead Week: Calculus and Trig in Review (Days 175-176)

This is "dead week" -- the week between senior finals and graduation. Senior grades were due yesterday at noon, and so there's nothing for students to do until they graduate next week.

Indeed, several other teachers and I were anticipating low attendance this week (which is why I handed out the graduation good luck cards last week). This was especially the case yesterday for the zero period Advisory class. Attendance is slightly higher today after the principal sends out a parent email -- and also because textbooks are due today. For those students who do attend my classes this week, I play them all the students video projects that were submitted last week.

Sarah Carter -- the famous math teacher-blogger who provided many of my opening week activities -- has her own dead week tradition. She introduces new activities that could possibly serve as opening week activities for the following year. And so I decide to do the same this year. Yesterday in fifth period I showed them Witzzle:

https://mathequalslove.net/witzzle-pro-math-game/

Like Carter, I used the TI to generate the random numbers. I know -- she calls it "Witzzle Wednesday" and I showed it to them yesterday, but hey, at least I'm blogging about it on a Wednesday! The activity I show both Ethnostats classes today is the Mathematical Magic Trick:

https://mathequalslove.net/mathematical-magic-trick/

Anyone familiar with Square One TV's "Nine Nine Nine" song can figure out the trick. By the way, of the four students in my second period, only one chooses Denmark -- two choose Dubai until they remember that it's a city. One of the Dubai students had already selected an iguana for the animal, so he just switched to Djibouti. The other one changed to Dominican Republic. Everyone in fourth period chose Denmark, but one student chose a kiwi (bird) instead of the expected kangaroo.

Today is Fiveday on the Eleven Calendar:

Resolution #5: We stay focused and on task.

But of course there's not much of that during Dead Week. So instead, I'm going to use these Dead Week posts to review the classes I taught this year -- including some tough decisions I had to make, as well as what I'd do if I were to teach this class again.

Although this is a Stats blog, let's start with Calculus, since the AP exam drove many decisions. (We'll save Stats for my next post.) Of course, the key decision was to cover only Chapters 1-3 first semester and Chapters 4-7 second semester. But unfortunately, this backfired when I was left with just one day to introduce free-response questions -- and my students struggled with these on the exam. There should have been enough time to review FRQ's. To see what happened, let's take another look at Semester 2.

The AP exam was on Monday Week 17 of the second semester. Thus I had 16 weeks to cover each of Chapters 4-7 -- that is, four weeks for each chapter. Since we weren't covering all of Chapter 7, I could do it Weeks 13-14 and then review AP questions Weeks 15-16.

But unfortunately, I tested positive for COVID during Week 4 -- just before I was all set to give the Chapter 4 Test on DeltaMath. And although I assigned the test for the sub to give that Thursday, that day the Wi-Fi failed. (If I'd been present in class, I could have come up with an alternative assessment on paper, but I wasn't there.)

With Monday Week 5 being a minimum day (that is, not enough time to give the test), that pushed the test back to Tuesday. And with the Chapter 4 taking up more than half of Week 5, I ended up moving everything back -- Chapter 5 Weeks 6-9, Chapter 6 Weeks 10-13, Chapter 7 Weeks 14-15, leaving me only Week 16 to cover AP questions.

And then Week 16 was itself a troublesome week. Due to a schedule quirk, Calculus class didn't even meet on Monday, and then I was out on Tuesday (interviewing for a job next fall). This left me with only a single day -- the Thursday before the exam -- to discuss FRQ's on the AP. This is why there needs to be two weeks at minimum to review FRQ's -- if things happen one week to interrupt instruction, at least there's another week of review.

And so it means that I absolutely needed to start Chapter 5 on Tuesday Week 5, so that I'd have four full weeks each for Chapters 5-6. If I had to give the sub a short Chapter 4 assessment on the minimum day (which I could have written over the weekend from home and submitted with my lesson plan), then that's what it took. I needed to be done assessing Chapter 4 so that I could start teaching Chapter 5.

Perhaps I should have stuck with my original plan of teaching all of Chapter 1-4 first semester -- or maybe compromise and split Chapter 4 between the semesters. If I do save Chapter 4 for second semester, then I must make sure I stick to the pacing, no matter what happens (like COVID).

Of course, the timing of the minimum days played a huge part in my planning this year -- in particular my drive to give assessments before Monday minimum days so that the minimum day can itself be used for test corrections. And this all goes back to the lack of a coherent plan coming in regarding how (or whether) I should have test corrections as well.

After the Chapter 2 Test on DeltaMath, some students requested test corrections. At first I wasn't going to allow them, but then one girl had been absent on test day and needed a make-up. So then I set it up on DeltaMath so that the make-up and retakes could be done simultaneously. The problem was that the absent girl then asked for a retake herself -- and she was upset when I didn't grant it to her. And then on top of that, the retakes took time away from the main lesson, forcing me to rush the lesson -- and that left everyone confused with the HW assignment.

It was the other math teacher at the school (my partner teacher) who told me about her retakes. There was a minimum day after the Chapter 3 Test, which she said was a perfect day for a retake (so that I could just do the retake with no rushed lesson).

But even then, notice that I've corrupted my partner teacher's retake methods. First of all, she usually gives corrections only on quizzes, in order to prepare for the chapter test. Her quizzes are sometimes on DeltaMath and sometimes on paper. If it's on paper, the students must write down what they did wrong on each missed question, so that they're actually making corrections. And the tests (for which there were no retakes) are always given on paper. (If I'd followed this, the Chapter 4 Test would have been on paper, and so there would've been no problem with COVID and the Wi-Fi.)

Instead of following these details, I just ran away with the minimum day timing -- I wanted as many assessments to be just before minimum day Mondays. This might have been fine except that the minimum days were unpredictable. Two key decisions were tied to minimum days -- first I didn't give a Chapter 4 Quiz after there was no minimum day in January (had I given such a quiz, I might have skipped the Chapter 4 Test in order to start Chapter 5 on Tuesday Week 5), and then I extended Chapter 5 into Week 9, ahead of the minimum day on Monday Week 10 (I was on the fence about extending Chapter 5 until I saw the short day schedule). All minimum days after Week 10 were cancelled.

What should I do about minimum days and retakes in the future? Well, it all depends on the school -- if minimum days are easily predicted, then I can schedule my tests around them, but if a school gives the slightest hint that it will cancel or delay short days, then I should ignore them and just stick to a firm pacing plan. And it will help to follow my partner teacher's ideas more closely -- only give retakes for quizzes, not chapter tests, and have the students write out their quiz corrections.

There's one more thing to consider with my Calculus class -- the homework. The idea of making each assignment be worth three points and attempting to give 67 assignments for a total of 200 points (with one HW on Mondays, two HW's on block days) goes back to the Calc class I attended as a young high school student. It should have been easy to give 67 assignments in the 16 weeks before the AP, but between unexpected COVID absences and schedule changes, I struggled just to get to 60 assignments.

Perhaps it's better to make each assignment be worth four points instead of three. Then I only need to give 50 assignments instead of 67 each the semester. This is compatible with the block schedule at the main high school (even though I won't be teaching there) -- each class meets two regular days (Monday and Friday) and two block days per week. So I can give one assignment per day, for a total of four HW's per week (three during weeks with an assessment or holiday) and reach 50 by Week 16.

Having one assignment per day also makes it easier to prepare for free response on the AP. There were some free response questions on the AP Classroom assignments that I gave during second semester, except that usually FRQ's would be one of the two assignments that I'd give on a block day (and when going over the HW, I'd inevitably go over the assignment that's not FRQ's). With just one assignment per day, on FRQ days I'd be forced to go over them, thus giving the students more practice with FRQ's even before the last two weeks of review.

There's one more thing I want to say about Calculus class -- and it involves one particular student. She's an excellent math student, but she was absent for much of the second semester. I find out that (like many high students during the pandemic) she's had to work long hours after school in order to support her family, sometimes as much as 10-12 hours! You may ask, how does she work long hours after school, get enough sleep, and still make it to school on time? The answer is that she doesn't. Many times she's absent completely -- on some days she arrives after our third period Calculus class ends. Her 18th birthday was right at the start of the second semester -- and that, of course, is when her frequent absences began.

She attended my class only once during the entire month of May -- and it was last week, on the day of senior finals (so she could pass her exams in other classes). In particular, she was absent on the day of the AP exam -- and so she never took it.

Upon hearing this, I start to argue a little -- but the person I'm upset with the most is myself. I felt that I could have done more to remind her and her family of the AP exam -- perhaps during those last two weeks when I should have reviewed the FRQ's, I also could have emailed her family and called her home to remind her that the test was coming up. It's likely that she would have failed the exam anyway after having missed so many lessons -- but instead, I never even gave her a chance.

As for Trig, this class went smoothly for the most part. The idea of switching to the HW system where I give longer, less frequent assignments worth more points was successful. We completed four chapters of the text and reached Section 5.1 on proving identities.

The only real problem was with the final exam -- as I wrote last week, I neglected to put graphs on the test, leaving me with only 20 usable questions instead of the intended 30. Since Chapter 4 was all about graphing, this meant that the final exam essentially covered only Chapters 1-3. Fortunately, I did give several weekly quizzes on Chapter 4 material -- either that or an explicit Chapter 4 Test would make up for the fact that there was no Chapter 4 stuff on the final. (An argument could be made that since the final is all multiple choice, it's better just to omit graphing-heavy questions anyway.)

If I were to teach this class again, I'd like to make it at least one more section -- to 5.2, which is on the addition formulas for sine and cosine. The text has eight chapters, and some important lessons like the Laws of Sines and Cosines don't appear until Chapter 7. Perhaps I should at least try to make it to Chapter 6, but I like the idea of tying the radian lessons in Chapter 3 to Pi Day, which puts me on pace to make it to the middle of Chapter 5 (unless I speed up the lessons after Pi Day).