Chapter 9: What's My Curve? (Day 69)

I'll begin with a description of today, in "A Day in the Life" format. This is a monthly minimum day and so it counts as my monthly "Day in the Life" post, but it also doubles as the special day "last day before Thanksgiving break."

8:00 -- Even though I no longer have a first period, something significant does happen at this time -- a power outage. It lasts throughout first period and continues into second.

8:40 -- Second period arrives. This is the first of two Ethnostats classes.

Going into today, I wasn't quite sure what I wanted to do with this class. I was considering having them wrap up the data collection project from this week, but that's a Google spreadsheet, which they won't be able to access during the power outage. (Even if some of the classroom Chromebooks have juice in them, they won't be able to use the wi-fi.)

Also, I was thinking back five years to the old charter school when I assigned a turkey graph. This was a bad idea, especially for the sixth graders, who have barely learned how to graph in four quadrants. That sort of assignment makes more sense in high schools, not middle schools. Since I'm a high school teacher now, I was on the fence considering doing one this year -- and I might have printed one up during first period, except there was a power outage.

So what do I finally decide to do? As a matter of fact, I do assign the students a turkey graph -- except it's not one about plotting points to get a graph shaped like a turkey. Instead, it's a graph that belongs in Stats class -- a scatterplot showing the number of domestic turkeys in the country over the past century.

Recall that I just barely found out that general Stats class is only one semester, not a year -- and so I want to reach Chapter 10 (on samples) by the end of the semester. Of course, you might point out that this refers only to general Stats -- Ethnostats is still a full year. And besides, it's not so important to keep the two classes aligned -- based on their lengths, general Stats should be well ahead of Ethnostats.

But I've unwittingly already started Chapter 10 in Ethnostats! You see, this week's data collection project comes from the teacher from two years ago. She started Chapter 8 on November 1st and assigned a "Chapter 8 project" -- this data collection project -- later that month, so I did likewise this year. But as it turns out, she must have been using a different Stats text. In her text, Chapter 8 is on samples -- the same as Chapter 10 of our text (after all, they collect data by taking a sample of the student population). Thus I've assigned my students a Chapter 10 project this week -- and so I might as well finish Chapter 10 and teach the class about samples in earnest.

So what does that leave for Chapter 9? Well, Chapter 9 is on nonlinear models, just as the previous chapter was on linear models. The number of turkeys in the country could be represented by a quadratic or exponential model -- there were only three million birds a century ago and a quarter billion now. (But note that I couldn't find any data for the years in between, so I just made them up in order to fit an exponential model -- which is likely, since as animals reproduce, their populations grow exponentially.)

8:45 -- The power comes back on fairly early in second period. The students are able to work on their turkey graphs in the light. They learn how to find nonlinear models on the TI-84.

Notice that today's blogpost is the only one that will be labeled "Chapter 9." After Thanksgiving break, we will proceed directly into Chapter 10.

9:20 -- Second period leaves and third period arrives. This is the AP Calculus class.

I give the students the results of the Chapter 3 Test that they took on Monday. Recall that I was on the fence regarding whether I should allow these students to do test corrections -- the other math teacher at our school (my partner teacher) regularly does them, but the Calc teacher at the main high school doesn't do them. Well, since I'd already written the entire week's schedule on the board and announced the test corrections, I end up doing them.

Three of the six students in the class earned A's on the original test and only have a few corrections that they need to do, so they easily finish them today. Two students who don't do as well need more time, and so they will work on them during Thanksgiving break. This includes one guy who failed the test -- I told him that the district has just approved tutoring hours for all teachers. I ask him which day will be most convenient for him for tutoring, and he chooses Tuesday. The last student was absent on the day of the test. I send her next door so she can avoid hearing the answers until she can make the test up.

By the way, for today's Warm-Up, I give the derivative problem that stumped the Calc BC class at the flagship high school -- d/dx (xe^ln(x^3)). Believe it or not, one girl -- the one who earned the highest score on the test -- figured out the trick right away. And the guy who failed the test -- after the girl and I reveal that there was a big trick -- also figures it out. (Once he realizes that e and ln cancel, all that's left is to differentiate x^4, which he can handle easily.) I tell the girl -- the lone junior in the class -- that she would do well in BC next year, except that our tiny school can't offer BC. (She'd be its only student.)

10:00 -- Third period leaves and fourth period arrives. This is the second of two Ethnostats classes.

This is the larger of the Ethnostats classes, and so as usual, things don't go as smoothly here. It generally takes them more time to do calculator activities, since many of them can't remember which buttons they need to press. I tell the students to try a linear model on the data first and see that it doesn't fit the data as well as a quadratic or exponential model -- but by the time the students have figured out how to perform a linear regression, there are only a few minutes left, and I must rush the nonlinear models (that is, the main idea of Chapter 9) before giving the Exit Pass.

Moreover, there are two students here today who were absent yesterday, and both guys need to work on their data collection projects. One of them has already collected his data and just needs to get it entered onto the Google sheet, but the other hasn't started. (I suggest that he survey students after school -- and since he has nothing else to do while waiting for his parents to pick him up, he does it.) But assisting this pair with their projects gives me less time to go over nonlinear models with the others.

10:40 -- Fourth period leaves and fifth period arrives. This is the general Stats class.

By the way, I ask the students whether they knew that it's a semester course -- and apparently, they weren't aware either.

I give the students the results of the Chapter 8 Test that they took on Monday. Again, I ask the student who earned the lowest score to name a convenient day for tutoring, and she selects Thursday. (The special ed student barely beat her score -- and he already has his one-on-one aide to help him, so he doesn't need my tutoring.)

Since this class definitely needs to learn Chapter 9, I give them the same turkey graph that I did with the Ethnostats classes. Of the four students in this class, one guy is absent, another guy is also enrolled in Ethnostats (and so he already did the turkey graph earlier), and the special ed student is summoned to the counselor's office. Thus I end up doing the activity one-on-one with the lone girl in the class (who, based on her test score, can use the extra help anyway).

11:20 -- Fifth period leaves. Sixth period is my other conference, and so my teaching day ends here.

12:15 -- The monthly after-school teachers' meeting begins. A hodgepodge of topics are covered during this meeting:

• We continue to discuss PBIS from the last meeting, including the HONOR acronym. This will be fully implemented in the second semester.
• We learn more about the website tutor.com -- that's right, it's another opportunity for the students to get tutoring online that's separate from our upcoming tutoring.
• A staff team is selected to work on some project. I don't remember what the project is, and I'm not on that team, so it doesn't matter.

1:00 -- The meeting ends.

I've been following these monthly "Day in the Life" posts with reflection -- and said reflection often involves comparing this position to my previous teaching assignments. Indeed, today's power outage reminds me of a similar outage at the old charter school five years ago (also in November). That outage occurred in the afternoon -- during the time usually reserved for IXL on the computers. Since they couldn't access the Internet, I instead did a (rare!) science lesson that day. Fortunately, today's outage occurs mostly during my conference period, and I had something to do (the turkey graph) that doesn't require students to be on computers.

But ever since this week's visit to the flagship high school, the main comparison in my reflections will now be to the Calculus classes I observed there. After watching a veteran teacher do his craft, I'm still trying to figure out which of his ideas I can implement in my own class.

Indeed, going into today, my partner teacher suggested that I ask the flagship Calc teacher about whether he gives homework over Thanksgiving break. It turns out that his homework policy is completely different from my own -- I give short assignments every day while he gives longer assignments and more time to do them. Thus his Thanksgiving break policy is an extension of his usual policy -- today he assigns this students HW, but it's not due on the Monday they return. Instead, they ask him questions from the homework, and not until after he's gone over all those questions (which takes several days) will the HW be due.

On one hand, I want to implement some of the ideas I witnessed in my own class. On the other hand, I don't necessarily want to change horses midstream. Suddenly springing on the students a completely different homework policy where, instead of 10-question HW's each day, they now see 50 questions on a single assignment each week, would definitely count as changing horses.

But there is a class where adopting the veteran teacher's HW policy will make sense -- in the Trig class second semester. This is a brand-new class, so I wouldn't be changing horses midstream. And it also fits the way the Trig text is organized. The text contains seven chapters, each with five or so sections -- hence these sections are longer than those in the Calculus text. They are on par with the length of the chapters in the Stats text, so it will take several days to complete a section. Meanwhile, all the questions appear at the end of each section (unlike the Stats text where some questions appear in mid-chapter). So it's reasonable to assign those questions and then give the several days to complete them.

(In addition, spending more time answering questions will help certain students in the class -- the special ed guy and the girl who sometimes struggles in Stats.)

I haven't quite decided a pacing guide for the Trig class. One way is to use Pi Day as a guide -- I should try to reach Section 3.2 (on radian measure, where multiples of pi frequently appear) by Pi Day. Since Pi Day is about midway through the semester, finishing two chapters and starting a third by Pi Day puts me on pace to finish Chapter 4 and start Chapter 5 by the end of the semester -- and this was the suggested pacing given by the Trig teacher at the flagship school.

Of course, I don't have to worry about Trig until January. Of more immediate concern is the pacing in Calculus (since I've already decided to complete Chapter 10 by the end of the semester in Stats). My original plan was to complete Chapter 4 by winter break, but the flagship Calc teacher will have finished only Chapter 3 by then.

There are two schools of thought here. When I had my online AP Calc training, the presenter suggested finishing differential calculus (that is, Chapter 4) by the end of the first semester and integral calculus (Chapter 7) by spring break. Then all of the remaining can be devoted to practicing free-response questions that might appear on the May exam. My pacing so far has been influenced by the presenter -- I was on pace to finish Chapter 4 comfortably until last week, when I delayed the Chapter 3 Test.

The other way of thinking is to go more slowly, but incorporate more AP questions throughout. This is how my counterpart at the flagship school does it -- when he assigns 50 problems from the text, the questions in the 40's are often higher-level, AP-like problems. He wants to start out slow and speed up if necessarily just before the exam. After all, if the students don't understand differentiation, then they'll struggle with integration (much of which is just anti-differentiation). It's better for the students to understand a little bit of something than a whole lot of nothing.

Moreover, the veteran teacher tells me that his goal is to prepare the students, not for the AP exam, but for college-level math. Thus he wants to focus more on derivations and proofs. He states that if the students are ready for college math, they'll succeed on the AP anyway.

Right now, I'm not completely sure which way I want to go. Since I haven't delved deeply into AP problems yet, I could continue with Chapter 4 and then return to AP problems in April, just as was my original plan. On the other hand, I can see where the veteran teacher is coming from. I suppose it's not too late to spend December on AP problems (at least those relating to differentiation), begin January with Chapter 4, and then follow his suggested pacing.

Fortunately, I have all of Thanksgiving break to make a final decision. Just as I did on the old blog, I plan on posting twice during the Turkey Day vacation. And as usual, I will write about several topics that I didn't have time to discuss in my school-day posts.