Chapter 8: What's My Line? Continued (Day 61)

Today is a minimum day, when teachers get to go home early due to last week's Parent Conferences. It is not officially a monthly minimum day, and hence this is not "A Day in the Life" post. But something big happened to me this week, and so I write about it in an extended post -- just not "A Day in the Life."

This week I received my second parent complaint. The principal didn't divulge who exactly made the complaint, but the student is in my Calculus class. Based on some of the information she gave me, I think I can figure out who it is, as well as the incident that triggered the complaint.

It all started about three weeks ago, on the day of the second DeltaMath quiz (on Sections 3.1-3.3). Of the six students in my class, four of them earned a C or better, one girl earned a D, and the last girl was absent and didn't take the quiz at all. When she returned to school the following week, she asked to make up the quiz she missed -- and the girl who got a D wanted a retake. I told the D student that normally I don't allow retakes, but since I was giving a makeup for the absent student, I'd let them both take the quiz after school that Wednesday. Well, the retake student raised her grade from a D all the way to 100%, but the absent student failed the quiz.

Now here's where the problems began -- the absent student wanted me to grant her a retake. But recall that the only reason I gave the other student the retake was because I was reopening the quiz for the absent student anyway (namely her) -- ordinarily I don't reopen the quiz just for retakes. The absent girl thought it was unfair that the other student got a retake and she didn't. (It didn't help, of course, that the retake student scored 100% -- seeing how successful a retake could be made her want to improve herself.) She even challenged the syllabus -- arguing that somewhere in that document I stated that all students are entitled to a retake. (I didn't.)

It's easy to see why I'm wary of retakes -- I think back to last year at the long-term middle school. All quizzes were on APEX, which already allowed one retake anyway. Then students would ask me to give them a reset (and hence two more attempts). The Math 7 leader (and department chair) warned me that since all APEX quizzes were multiple choice, a student could ace any quiz by choosing all A's on the first attempt, remembering which A's were correct, then changing the wrong ones to B's next time. By asking for a reset and change any remaining wrong answers to C's on the third attempt and D's the fourth time, so by that point they're guaranteed to score 100% without knowing any math.

Also, the Math 8 leader informed me that she had strict requirements for retakes. The retakes were allowed only at the end of the semester, and the students had to complete a short assignment to show that they really did learn something since their earlier attempts.

Because of this, I decided that I wouldn't allow retakes in general. But because of how DeltaMath (and Illuminate, which I use in Stats) work, I had to reopen the window when an absent student made up a quiz. So I let students retake during the makeup quiz, but at no other time. In particular, I didn't allow absent students making up a quiz to do a retake themselves.

In Stats classes (including Ethnostats), I gave the Chapter 6 Quiz at the same time as the Section 3.1-3.3 Calculus quiz. My second and fifth period classes have four students each, and all the students in these classes have excellent attendance, so I gave no makeup (hence no retake) quizzes. Fourth period was a different story though -- one or two students were absent, and so I gave makeups and retakes. If I recall correctly, three students in this class who earned D's on the first try got A's on the second try (just like the one girl in Calculus).

After the quizzes, we moved on to Chapter 7, on scatterplots and correlation. Some of the examples from the text involved plotting test scores vs. hours studied. I like giving real-life examples, and so I decided to take my Calculus class and plot quiz scores vs. days absent in October. The plot showed a strong negative correlation -- the two students who scored 100% had no absences, the one who had a D (who later improved it) was absent twice, and the two one-absence guys scored in between.

Notice that this was before the girl absent on quiz day itself made up her quiz -- and so she wasn't even included in the data for the plot. And when I showed my Calculus students the plot (to show them the importance of regular attendance), I deliberately hid the scale on the test score axis and only indicated where 100% was.

This is why I believe that the absent girl is the one whose parents sent the complaint letter. Included was a concern that I told their daughter I wouldn't let her retake because she was absent "ten times" (in reality, she'd been absent only twice, and my scatterplot didn't even go up to ten absences).

I've given one more quiz, on Sections 3.1-3.6, since then. There was a problem with this quiz -- due to Parent Conferences, the quiz landed on a minimum day. I assigned eight questions, and DeltaMath gave an estimate of 19 minutes for these questions, so based on this, the minimum day period should have been adequate for the quiz. Unfortunately, it wasn't -- the top students finished only six questions by the end of the period. I decided that I would count six questions as 100%, and then rescale the other quiz scores accordingly.

Using this new scale, some students improved from the previous test. This includes the student whose parents sent the concern letter -- she earned a D on this quiz. But she still isn't satisfied -- first, she told me directly that the reason for her D was that she ran out of time. Notice that even though I rescaled the quiz to take running out of time into account, the whole ordeal sent the wrong message. It would have been much better if I'd assigned only six questions in the first place. Perhaps if I'd given only six questions, she might have paced herself better.

According to the concern letter, I'd belittled some of the struggling students. I'm not quite sure when exactly I did this, but I have some guesses. One possibility was when I was trying to decide which two questions to remove. I threw one of two implicit differentiation questions -- students told me that they were struggling with it, and I replied that if they had figured out the first one, they should've had no trouble with the other since both were in the text (and they're expected to know both for the AP).

Also mentioned in the concern letter was whether I'm teaching effectively -- it was stated that students had to study certain topics independently because I didn't teach them right. This might refer to absent students who miss the lesson and have to figure it out on their own (including one guy, a future engineer, who figured out the derivative of ln x on his absent day), there's one incident in particular that's most likely the source of concern.

I've already mentioned rushing lessons on minimum days on the blog. But there was one block day when I had to move through a lesson quickly -- the day I discussed the Product Rule. The problem was that I ended up giving another makeup/retake that day -- the Chapter 2 Test (on limits). One student had been absent, and several others wanted a retake (including a girl who'd earned a B). Since everyone was testing, I just cut off the Product Rule lesson so that they'd have enough time for the test. But of course, I knew that the students still needed more help on the Product Rule, so I posted some notes for the students to read over the weekend. This is most likely what the concern letter was discussing -- the students having to learn the Product Rule on their own.

Knowing that my students were struggling with the Product Rule, I helped the students with it the next day in class. A Michael Starbird video was scheduled for that day, and so I played the video -- during which I gave one-on-one lessons with each student to make sure they knew the Product Rule. But unfortunately, this was one of the days that the concerned girl was absent, so she never realized that I was finally helping the class with the Product Rule.

One problem any math teacher faces is, if a lesson is ineffective, the students will ask many questions about the homework the next day. Answering those questions takes time away from the new lesson for the day, and so the teacher must rush through it -- leading to less understanding and even more questions asked by the students the next day, and so on. It's a domino effect. If I'd taught Chapter 2 on limits effectively, there wouldn't have been so many students wanting to retake that test -- and so I would've had more time to finish the Product Rule lesson.

So this suggests several solutions to the concerns addressed in the letter:

• Check for understanding. Back when I was in BTSA (to earn a California Clear Credential), my mentor told me that if my lessons are ineffective, the most likely reason is that I'm not checking for proper understanding -- and this remains stuck in my mind.
• Don't just rely on the examples in the book -- ask questions to check for understanding. If I can't think of any good examples, look at the homework I'm going to assign -- if I'm assigning odd problems, then I can use the evens for examples (and vice versa).
• Make sure that the homework corresponds to what was taught. It's possible that even during the best of times, I might have needed to split the Product Rule lesson, because the students needed me to re-explain more than once before the light goes off in their head. In that case, I should reduce the homework -- if it means that I can only assign four or five problems from the book because all the rest require the unreached part of the lesson, then so be it. On the day of that fateful Product Rule lesson, my plan was to assign #1-19 odd. So over the weekend, I "helped" them by posting notes on how to do the even problems online. What effectively happened was that the students were doing #1-19 all, and not understanding most of it. This is the opposite of what I should have done -- instead, I should have cut it down to, say, #1-9 odd (or however far we got in the lesson), and used those even problems as examples in class.
• Make sure that the quiz/test corresponds to what was taught. I believe that with the Chapter 2 Test, I wasn't terrible with the limit lessons. The problem was that the students weren't prepared to answer the questions as they were worded on DeltaMath, as opposed to the text. This is why they were requesting retakes -- on the second attempt, they were better prepared for DeltaMath wording, and so they fared much better.

In fact, this is dramatically exemplified by the quartet of students (one in Calculus, three in Ethnostats) who jumped all the way from D's to A's on the retake. It's not necessarily that they were cheating the second time (as the middle school kids did last year on APEX) -- especially since not all of these questions were multiple choice. Instead, the students knew what to expect the second time. For Calculus, the problems might have looked different in the text and DeltaMath. For Ethnostats, I posted questions from the online test bank onto Illuminate -- in theory the quiz and the text come from the same source, so there should be no problem. But I might have de-emphasized some examples or vocabulary during the lessons that appeared on the quiz.

This leads to another issue -- how exactly am I preparing students for the assessments? So far, I've been handing out the markers and having them answer review questions or whiteboard right before the quiz or test. This is an artefact of what I did back at the old charter school -- it was often the only time that I used the whiteboards, and the students enjoyed it.

When I was subbing just before the pandemic, sometimes the regular teacher would assign a "study guide" on the day before a quiz or test. Often this was done in history or science classes. Notice that last year at the long-term school, I often referred to "study guides" on the blog, but this was what APEX called its regular lessons. Then again, each lesson ended with an APEX quiz, so technically speaking, these study guides also prepared students for quizzes.

Some Ethnostats students told me that their previous math teachers would regularly assign study guides before quizzes and tests -- and they thought that there was something wrong with my class in that I wasn't providing study guides. I finally gave in -- for the second quiz, I gave them a study guide, but still had them answer questions on marker from the guide before the quiz. Since the third quiz was on the minimum day, there was no time for marker -- the study guide became a pure assignment that the students had to complete on Google Classroom.

Meanwhile, I'm continuing to assign even-numbered problems from the end of the chapter in general Stats, and of course Calculus is getting DeltaMath to review for their quizzes there. Sometimes DeltaMath does throw students curveballs -- for example, one guy on a simple Power Rule question was asked to find the derivative of 4pi^3. (That's a constant, so its derivative is 0.) But in general, students know what to expect if the DeltaMath review corresponds to the DeltaMath on the real quiz.

OK, so all of this is nice and dandy, but what does this mean for my Calc class today? Originally, I was going to cover Section 3.9, on linearization and differentials. But after hearing about the concern letter, the last thing I wanted to do was rush yet another lesson on a minimum day. Instead, I did what I should have done with the retake issue in the first place -- allow for quiz corrections. My partner teacher tells me that she regularly allows quiz corrections, and indeed DeltaMath has a test correction feature (though she admits that it's a bit tricky to use). She gives back 75% of the points for corrections -- and I decide that I might as well do the same. The concerned girl has already raised her quiz grade to a C -- and I told her that she can do even more problems over the weekend. So she might even get to a B.

Section 3.9 is the last lesson of the chapter, so originally, I was going to give the Chapter 3 Test on derivatives next week. Instead, doing quiz corrections today ends up pushing the test back to the following Monday (the fifteenth). Of course, giving a test on a Monday is awkward, since many students forget what they learned over the weekend. 

So instead, this upcoming Monday will be the Section 3.9 lesson. (Originally I was going to do another Michael Starbird video that day.) After I told my partner teacher about the complaint, she has agreed to observe my lesson to make sure that I'm being effective -- in particular, she will notice whether I'm checking for understanding. There are only four examples in this section, but I want to be sure that the students understand each one before I move on. How many problems I assign will depend on how many examples we get through -- in fact, I might even prepare four different homework assignments, corresponding to the four possibilities.

Hopefully, the math chair and I will be able to debrief and discuss what I do right and wrong. I also plan on asking her for ideas on how to do the Chapter 3 Test. She's told me that, while she often assigns DeltaMath for short quizzes, she prefers to give major chapter tests on paper. Therefore she might tell me to give a written Chapter 3 Test as well.

I've written so much about Calculus that I've only briefly mentioned Stats, on what is supposed to be a Stats blog. Of course, with the concern letter, it's hard to think about anything else. In all Stats classes today (general and Ethnostats), I have students continue to work with linear regressions on the TI-84.

Oh, and there was one more point of concern mentioned in the letter. According to the principal, the parent was upset that I didn't allow the student to go to the restroom right after lunch. But she didn't make it clear whether this is the same parent or not. For one thing, most of the time Calculus doesn't even meet after lunch. It's possible that this was after nutrition on an all-classes Monday (the only time that Calc meets after a break), but with all the minimum days shifting block days to Mondays lately, it's been nearly a month since we had a regular Monday -- and that was the Product Rule Monday when the concerned girl was absent. Before that, we have to go all the way back to September to the previous Monday with Calc after nutrition.

If it really was a parent upset with my after-lunch restroom policy, then it's more likely to be the parent of a student in a sixth period class I subbed for during conference period (and such students don't know me or expect me to cover their class, so they wouldn't have known to go to the restroom at lunch).

In Calculus, there were more recently problems with tardies instead -- the mixed-up bell schedules (combined with the students walking nonchalantly to class rather than hurriedly) result in several kids arriving after the tardy bell lately. It happens again today, with two girls (including the concerned student) arriving a few seconds late. Just in case this is what the actual parent complaint is about, I decide not to mark these students tardy. (On the other hand, another student doesn't even arrive on campus until third period -- an hour and a half late. So I definitely had to mark her late.)

What should I do about these tardies? I'm not sure, but I do remember something that Fawn Nguyen wrote in her last post:

https://www.fawnnguyen.com/teach/dear-new-teachers

You can measure the students’ enthusiasm for your class quantitatively: time how fast they arrive at your door the next day.

Fawn Nguyen obviously knows how to instill enthusiasm in her students -- she doesn't have to worry about so many tardies to her class. On the other hand, considering how I failed to teach the Product Rule, the students might as well have arrived late that day and spend most of class in the restroom -- they would have learned just as much Calculus.