Today is a minimum day, and so this counts as my monthly MTBoS blogging day for November. I will be describing today in "A Day in the Life" format:
9:00 -- I arrive on campus. On this minimum day, only certain teachers have meeting before school. There is an all-staff meeting after school, of course.
The big thing that's on my mind right now are the district Benchmark Tests. Once again, it almost seems as if Math 7 and Math 8 are separate departments. The math department head, who teaches Math 7, has decided that we will at least start the Benchmarks this week. But the eighth grade teachers might come up with a different plan. And so I decide to email the most senior Math 8 teacher (the so-called "head of the Math 8 department) to see what her plans are.
9:25 -- The Math 8 leader responds. She tells me that since there's some Unit 4 material on these tests, we will wait until after Thanksgiving to give them. (Notice that there's also some Unit 4 material on the seventh grade tests, yet the department head still wants to start Benchmarks with them this week.)
9:45 -- First period begins. This is the first of two eighth grade classes on this all-distance learning day.
We begin Lesson 4.1.1 in APEX, which is on solving linear equations. The lesson begins with one-step equations before moving on to two-step equations. Since it's a minimum day, there's not enough time for the entire lesson. So I break the lesson off after one-step equations -- a natural stopping point.
It takes about 20 minutes to reach this point. For the last ten minutes of class, I direct the students to go to Canvas and click on the two Edpuzzle links. One assignment is on one-step equations (which is another reason why I stopped the lesson at this point) and the other is on combining like terms. These assignments are officially due today.
While the students begin their Edpuzzle assignments, I inform them that I worked on their third quaver progress reports over the weekend, and unfortunately, ten students will be receiving them -- just about a third of the class. After last week's Wi-Fi outage, I was afraid that the Tuesday cohort would use it as an excuse to slack off, neglect to work on the test, and then get a progress report. But to my surprise, the majority of the progress reports are earned by the Wednesday cohort (which met Monday last week).
10:20 -- First period ends and second period begins. This is the first of two seventh grade classes, and the first class with the co-teacher.
Today is the special lesson to prepare the students for the Benchmarks. And the topic for today's lesson is two-step equations. That's right -- I teach one-step equations to the eighth graders and then two-step equations to the seventh graders. How does this happen?
Well, let's look at the relevant Common Core standards:
CCSS.MATH.CONTENT.7.EE.B.4.A
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
CCSS.MATH.CONTENT.8.EE.C.7.B
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
From these, we conclude that the most advanced equations that seventh graders are expected to solve are two-step, while eighth graders must solve multi-step equations. But APEX, in Math 8, builds up to multi-step by starting with one- and two-step problems, while the Benchmarks in Math 7 jump directly into two-step problems. Thus the seventh graders get a more difficult lesson only because we've chosen to give them the Benchmarks sooner.
For today, the students watch three Khan Academy videos, which take up most of the period. Since these videos are on YouTube, there's no harm in my posting these videos here:
10:55 -- Second period ends and third period begins. This is the second of two seventh grade classes.
As in all of the other classes, I warn the students who might receive progress reports. There are two such students in each seventh grade class (although one girl in this third period class makes up her missing test later this evening, just before the date/time of this post, to avoid the unsat).
11:30 -- Third period ends for the short five-minute break.
11:35 -- Fourth period begins. This is the second of two eighth grade classes, and the second class with the co-teacher.
In this class, nine students might receive a progress report. While this is fewer than first period, it's a larger part of this later class, with nearly half getting the report.
12:10 -- Fourth period ends and fifth period begins. This is the Math Skills class.
In this class, three students will receive progress reports -- in a class where the only assignment is to log in 60 minutes on ST Math or Dreambox each week. One guy has a D+ and is just five minutes away from avoiding the progress report (but it's too late now, as ST Math will count any new minutes for this week rather than last week).
Another girl has a D-, but just when I'm about to warn her that she will receive the progress report, she logs out of the Google Meet, having attended only 2-3 minutes of class (even though she attends all of my third period class). At this point, I realize that I need to crack down on slackers in this class -- there's actually no reason why anyone should have a D or F in this class. So in attendance, I mark her as "X" for non-participating -- and I plan on doing the same for those who aren't logging in minutes to ST Math or Dreambox the rest of the week.
12:45 -- Fifth period ends, and the day is over for the students -- but not nearly for us teachers.
1:00 -- The all-staff meeting begins. The first thing the principal mentions is that Orange County has indeed fallen back into the purple coronavirus tier. But as of now, Governor Newsom's rule is that if a county opens schools in the red tier, then those schools can remain open even if the county returns to the purple tier. Thus we will still have hybrid learning tomorrow and the rest of this week. (On the other hand, LA County schools remain distance-only because the county never reached the red tier.)
The main topic for today's meeting is the sharp rise in the number of D and F students since the start of the pandemic. (I assume that this is a problem everywhere, not just at our school.) And so all teachers must work hard to reduce the D's and F's in the second quarter and beyond.
To this end, the students will attend tutorial in fifth period everyday this week. We teachers must specifically help the students who have one or two D/F grades on the first quarter report card. Those with three or more low grades will report directly to a counselor, who will give them extensive help on raising their grades.
In our mailboxes, we receive a list of our fifth period students with D/F grades. Three-quarters of the 16 students in my fifth period have at least one low grade -- this isn't surprising, since the fifth period Math Skills class is for low-achieving students. The worst offender earned one D and all F's in the rest of his classes for first quarter. And I know for a fact that his lone D- is in Math Skills itself -- the only reason he didn't fail my class is because he never received a first quaver progress report (as the regular teacher didn't bother to give them to that class), and so I wasn't allowed to fail him. He had logged only 22 minutes combined the entire first quarter. Fortunately, he's starting to work harder now in the second quarter and actually has a B so far, easily avoiding the third quaver progress report.
2:15 -- The all-staff meeting ends, but the principal tells us to have a department meeting as well. The head of our department is hungry, so she tells us to have a half-hour for lunch before the meeting.
2:45 -- The math department meeting begins. We discuss the Benchmarks, and we confirm that Math 7 will start the Benchmarks this week while Math 8 will wait until after Thanksgiving. The Math 8 leader tells me that another teacher in the district has created a worksheet to prepare the eighth graders for the Benchmark Tests, and so we'll assign this to the students on the day they return from the break.
3:15 -- The department meeting ends, and so does my day, finally.
These reflection posts are the only ones where I'll mention the old charter school and comparisons. And recall that there were also Benchmark Tests in November 2016 at that school. Thus we can make an apples-to-apples comparison -- what I'm teaching this year before the Benchmarks is what I should have covered at the old school before the Benchmarks four years ago. In seventh grade this takes us up to EE3 and in eighth grade up to EE6. (Recall that in reality, I started out with RP in seventh grade and NS in eighth, and then jumped around depending on the STEM projects.)
The 2016 Benchmarks -- based on the Illinois State text -- were a mess. There were both online and written components, and it took several days to give them. And standards assessed on the written test were illogically selected -- one standard was chosen from each strand, including SP. I hadn't covered any SP standard yet, nor should I have done so, but there they were on the test. I quickly teach one of the easiest (and hence fastest to learn) standards as soon as the Benchmarks were announced -- for eighth grade I chose F1 (introduction to functions) and for seventh grade NS1 (introduction to positive and negative numbers).
By contrast, this year's Benchmarks are more logically organized. But they still aren't without problems, since they test Unit 4 material when we've only made it to Unit 3. The district specifies today's date, November 16th, as the first day to teach Unit 4 and the day that the Benchmark window opens, so it's not as if we fell behind the district pacing guide (and started Unit 4 earlier).
The Illinois State text teaches each Common Core Standard in isolation, while APEX is more like a traditional text. For example, we see that APEX reviews one- and two-step equations before teaching the actual eighth grade standard on multi-step equations. Illinois State, on the other hand, leapt directly into multi-step questions, since that's what the standard says. (Recall that I did eventually reach these EE standards -- albeit in February -- and the students were confused by multi-step equations.)
Yet even APEX seems to be too devoted to a naive reading of the Standards, just like Illinois State. For example, the department head tells me that APEX starts both Math 6 and Math 7 with RP standards -- and she thinks this is too difficult as a starting unit. But we know that Illinois State does the same -- and the reason is because RP appears first in the Common Core.
The department head also laments that an equation like 2(x + 3) = 4 is solved in APEX Math 7 by dividing first by 2, rather than distributing. I now suspect that this is due to Common Core again -- look above at the mention of p(x + q) = r above. And we just saw how APEX Math 8 confuses students by forcing them to compare graphed functions to those represented by equations. I suspected that this is due to an overly literal rendering of the Core -- and sure enough, my suspicion is easily confirmed:
CCSS.MATH.CONTENT.8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Recall that I never actually reached slope at the old charter school. So instead, I think all the way back to the Algebra I classes that I taught as a student teacher and again for BTSA. In general, the most difficult parts of an Algebra I class are the polynomial units taught in the second semester. But restricted to the first semester, the toughest unit is the one on linear functions and graphing. And since Common Core Math 8 and first semester Algebra I are similar, it's no surprise that my eighth graders would also struggle with this unit.
I've been thinking about how to teach linear functions more effectively. I've glanced at two old texts that I've purchased in recent years -- the U of Chicago Algebra I text and a McDougal Littell text based on the pre-Core California Standards for Grade 7 (back when the expected Grade 8 math course in California was Algebra I). Both of these texts are easier to understand than APEX, if only because neither requires students to "compare" functions as mentioned in Standard EE5 above.
In past posts on this blog, I wrote the main idea is for the students to be able to taste success early in the unit, in order to motivate them to proceed. My students struggled even to identify m and b in a linear equation already written in slope-intercept form. Then again, the only questions on APEX that require students to identify m and b are those where they must compare the function to a second function from graph or a word problem -- and this function requires more effort to find m and b. And so they never get to taste the success of finding m and b in the simpler equation.
And so, if I had to rewrite APEX Lessons 3.1.1, 3.2.1, and 3.3.1, perhaps I'd begin in 3.1.1 by focusing on the equations only. Students will be asked to find m and b from the equation -- and as soon as they find them, they are done (as opposed to using that m and b to compare it to another function). Then they can learn how to find m and b in equations where one or both are negative, and proceed to learn other names for m (such as "rate," "slope") and b (starting value, y-intercept). By the way, APEX also uses the term "initial value," but we should just use "starting value" instead. (Recall the summer Shapelore project -- the Anglish word "starting" is preferred to the Latin word "initial.")
In my Lesson 3.2.1, students would see graphs for the first time. This is the best time to introduce slope as the ratio of the rise to the run, so that they can determine slope by counting on the graph. Then in my Lesson 3.3.1, we introduce the slope formula and use real-world descriptions. Only then would we start comparing functions in different formats as stated in EE5 (though we might have them compare equations to graphs in 3.2.1).
As I think about the week ahead, I wonder what song I should perform for the students. Recall that I wrote a "Solving Equations" song at the old charter school, and this fits with the Math 8 lesson -- and for my eighth week at this school, I do wish to sing an eighth grade song. But the Math 7 task will be to take the Benchmarks -- and I also have a "Benchmark Tests" song.
It's easy to argue that, while Math 7 will also solve equations this week, Math 8 won't take Benchmarks until later, and so "Solving Equations" fits both grades in a way that "Benchmark Tests" doesn't. But I might not be able to resist singing "Benchmark Tests," especially considering that the magical word "Benchmark" is used by the district to describe the tests. (Suppose that the district had simply called them "district periodic assessments" like many other districts. Then I'd probably would have just sung "Solving Equations," since "district periodic assessments" doesn't sound catchy in a tune -- and I wouldn't be in this dilemma.)
Well, I'll make that decision by tomorrow, and so I'll announce it in tomorrow's post.
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