Chapter 11 Test (Day 120)

Today is many things. According to the blog calendar, today is Day 120. Therefore, it is the end of the second trimester -- at least it would be if this calendar weren't based on a high school district. My new district does have K-8 students -- except in this district, today is only Day 111. Therefore it's actually the end of the fifth quaver at the high schools, not the end of the second trimester in K-8.

Today on her Mathematics Calendar 2019, Theoni Pappas writes:

Find the circumference of a circle with area 196/pi.

Well, we clearly use the two Chapter 8 formulas, A = pi r^2 and C = 2pi r:

A = pi r^2 = 196/pi
r^2 = 196/pi^2
r = 14/pi

C = 2pi r
C = 2pi(14/pi)
C = 28

Therefore the desired circumference is 28 -- and of course, today's date is the 28th.

Today I subbed in a high school Spanish class. This isn't two-way immersion like Tuesday's middle school class -- instead, it's three sections of AP Spanish and two sections of Spanish III.

This is a multi-day assignment, since this teacher has been out since Tuesday. (She's so sick that she's lost her voice -- a huge problem in a foreign language class.) On that first day, both classes had a written assignment, but since then it's been mostly free days. She was hoping to play that movie I've seen in so many previous Spanish classes -- McFarland USA -- but it won't play. (There is no DVD player, so we had to rely on YouTube Movies -- but it doesn't work today.)

During tutorial (i.e., every single class), I help out some students in math. Just as I wrote last week, all classes -- Geometry, Algebra II, and Pre-Calculus -- seem to be in their trig chapters now.

And finally, today is the day of the Chapter 11 Test. All those other things might be fun, but this is a Geometry blog, so I must post the test -- sorry.

Today is a test day -- hence a "traditionalists" post. I don't have much to say due to so many other recent traditionalists' posts, so let me repeat something I wrote last year on the day of the Chapter 11 Test:

On the other hand, I read anecdotes from traditionalist homeschooling parents about how their second grader learned fifth grade math effectively via direct instruction. I don't consider this to be a valid argument that the fifth grade math standards should be written from a purely traditionalist view -- because fifth graders, more than second graders, will start questioning why they have to learn how to compute with fractions. [2018 update: This isn't discussed at the traditionalist link above, but notice that one commenter wrote "homeschool" as the only rational response to progressive pedagogy.]

But this does mean that the traditionalists' favored standard algorithms and memorization of basic math facts are to be taught as soon as possible, and not delayed a year as in Common Core. One common complaint among traditionalists is that students are never made to memorize basic multiplication facts. Questions such as six times nine or seven times eight should be considered very easy questions that take no more than a second to answer. But not only do many people consider such problems to be difficult, but it has become fashionable to consider those who have difficulties with such problems to be normal and those who find such problems easy to be outliers -- nerds.

It's often pointed out that people would feel deeply ashamed to admit that that can't read at a third grade level, yet are proud to admit that they can't do third grade math. Since I've stated that third grade math is something that students should have learned traditionally -- that is, have memorized -- I should do something about it in my classes.

The thought is that, rather than have those who find single-digit multiplication to be easy be outliers who get the label nerd, it's those who can't multiply by the time they reach middle and high school who should be considered outliers -- just as someone who can't read at a third grade level is taken to be an outlier. But of course, it's improper for me, a teacher, to start calling my students derogatory names such as idiot, no matter how low their understanding of math is.

So I need a word that criticizes the student, yet is proper for me to use in a classroom. Well, since I want my word to have the opposite effect of the word nerd, I briefly mentioned at the end of one of my posts a few months back that I made up my own word, by spelling the word nerd backwards, to obtain "dren."

My plan is to use my new word "dren" in such a way to make it sound as if a "dren" is not what a student wants to be. For example, when we reach the unit on area, students will need to multiply the length and width to find the area of a rectangle. So I might say something like, "A dren will have trouble multiplying six inches by nine inches. Luckily you guys are too smart to be drens, so you already know that the area is ...," and so on. Similarly, if a student, say, starts to reach for a calculator to perform the single-digit multiplication. I can say, "You're not a dren. You know how to multiply six times nine ...," and so on.

Notice that in these examples, I don't call anyone a dren directly. But every time I say the word "dren," I want to be annoying enough so that the students will want to do what it takes to avoid my having to say that word.

I coined the word "dren" to be the word nerd spelled backwards. But ironically -- according to my new Simpsons book -- the word nerd is already spelled backwards! Originally, the word was "knurd," which is drunk spelled backwards. The net result is that my word "dren" is basically just an abbreviation of drunk. Of course, the word drunk isn't a word that I should use in the classroom!

Last year, I wrote about I might strengthen my anti-dren crusade. I can tell math classes that there are three types of students -- "smart," "almost smart," and "dren." Now I don't teach drens -- I choose to work at your school because the students are all "smart" or "almost smart." Those who are struggling with a concept are "almost smart" until they master the concept. This extends the idea from three years ago that I don't call any student a "dren" directly. Every student who works hard is at least "almost smart" -- and I regret having never said this to the "special scholar" two years ago.

Here are the answers to today's test.

1. Using the distance formula, two of the sides have the same length, namely sqrt(170). This is how we write the square root of 170 in ASCII. To the nearest hundredth, it is 13.04.

2. The slopes of the four sides are opposite reciprocals, 2 and -1/2. Yes, I included this question as it is specifically mentioned in the Common Core Standards!

3. Using the distance formula, all four sides have length sqrt(a^2 + b^2).

4. Using the distance formula, two of the medians have length sqrt(9a^2 + b^2).

5. 60.

6. From the Midpoint Connector Theorem, ZV | | YW. The result follows from the Corresponding Angles Parallel Consequence.

7. From the Midpoint Connector Theorem, BD | | EF. The result follows by definition of trapezoid.

8. 4.5.

9. (0.6, -0.6). Notice that four of the coordinates add up to zero, so only (3, -3) matters.

10. At its midpoint.

11. 49.5 cm. The new meter stick goes from 2 to 97 cm and we want the midpoint.

12. Using the distance formula, it is sqrt(4.5), or 2.12 km to the nearest hundredth.

13. sqrt(10), or 3.16 to the nearest hundredth.

14. 1 + sqrt(113) + sqrt (130), or 23.03 to the nearest hundredth.

15. sqrt(3925), or 62.65 to the nearest hundredth. (I said length, not slope!)

16. -1/2. (I said slope, not length!)

17. (2a, 2b), (-2a, 2b), (-2a, -2b), (2a, -2b). Hint: look at Question 5 from U of Chicago!

18. (0, 5).

If you want, you can add the following questions, as the equation of a circle is still missing:

In 19-20, determine a. the center, b. the radius, and c. one point on the circle with the given equation.

19. (x - 6)^2 + (y + 3)^2 = 169
20. x^2 + y^2 = 50

Here are the answers:

19. a. (6, -3) b. 13
Possible answers for c: (19, -3), (18, 2), (11, 9), (6, 10), and so on.

20. a. (0, 0) b. 5sqrt(2)
Possible answers for c: (5, 5), (-5, 5), and so on.

Chapter 11 Review (Day 119)

Today on her Mathematics Calendar 2019, Theoni Pappas writes:

Find x.

(Once again, all the info is given in an unlabeled diagram, so let me invent the labels. We see AE and CD intersecting at B. Angle C is right, BAC, BED are congruent. AB = 5, AC = 4, EB = 45, DB = x.)

It's easy to see that Triangles ABC and EBD are similar by AA Similarity. One pair of congruent angles needed for AA~ is given, while the other is the vertical pair ABC and EBD. (This allows us to conclude that D is a right angle -- without AA~, we can't determine whether D is right or not.)

We might try to write a proportion:

DB/CB = EB/AB
x/CB = 45/5

But side CB is unknown. Since ABC is a right triangle, we must use the Pythagorean Theorem:

a^2 + b^2 = c^2
a^2 + 4^2 = 5^2
a^2 + 16 = 25
a^2 = 9
a = 3 = CB

x/3 = 45/5
5x = 135
x = 27

Therefore the desired length is 27 -- and of course, today's date is the 27th.

Notice that we could have used the Pythagorean Theorem first to find ED = 36 and then set up a different proportion. I assume that you'd rather square/find the square root of numbers like 4, 5, 9 rather than 36 or 45 -- and besides, we should be able to recognize the 3-4-5 Pythagorean triple without using the formula.

This is a similarity problem that we could solve in Chapter 12 -- and we still haven't quite reached Chapter 12, although we're tantalizingly close.  (In the Glencoe text, this problem can be solved after Lesson 7-4 on the Pythagorean Theorem.)

But this question underlies the need to avoid writing a proportion before writing a similarity. A student might just say "the triangles are similar because we're in the similarity chapter" and then set up the proportion to find x = 36, when this is actually ED, not DB as desired. Instead, the students should actually write Triangle ABC ~ EBD. Only then will they be more likely to set up a proportion correctly (and see the need for the Pythagorean Theorem.)

Today is the review for the Chapter 11 Test. This is what I wrote last year about today's lesson:

In particular, this test is based on the SPUR objectives for Chapter 11. As usual, I will discuss which items that I have decided to include and exclude, and the rationale for each:

Naturally, I had to exclude Objective G: equations for circles, which I take to be an Algebra II topic, not a Geometry topic. (If this had been an Integrated Math course, I would have delved more into graphing linear equations, as we covered this week.) Actually, equations of circles really is a Common Core topic, so you might want to cover some circle problems of your own. On the other hand, we may still want to leave out three-dimensional coordinates, since I posted the leprechaun graphing worksheet instead.

One major topic that I had to include is coordinate proof, as this appears in Common Core. I did squeeze in some coordinate proofs involving the Distance or Midpoint Formulas, but not slope. So therefore, the coordinate proofs included on this review worksheet all involve either distance or midpoint, not slope. The only proofs involving parallel lines had these lines either both vertical or both horizontal. Once again, a good coordinate proof would often set it up so that the parallel lines that matter are either horizontal or vertical.

What good are coordinate proofs, anyway? Well, a coordinate proof transforms a geometry problem into an algebra problem. Sometimes I can't see how to begin a synthetic geometry proof, so instead I just start labeling the points with coordinates and see what develops.

So coordinate geometry reduces an unknown problem (in geometry) to one whose answer is solved (in algebra, in this case). Mathematicians reduce problems to previously-solved ones all the time -- enough that some people make jokes about it:

http://jokes.siliconindia.com/recent-jokes/Reducing-the-problem-nid-62964158.html

I ended up including six straight problems -- Questions 8 through 13 from U of Chicago. Most of these questions are from Objective C -- the Midpoint Connector Theorem. The text covers this here in Chapter 11, but we actually covered it early, in our Similarity Unit, because we actually used the Midpoint Connector Theorem to start the proof of the basic properties of similarity. Still, this was recent enough to justify including it on the test.

Next are a few center of gravity problems. This is straightforward, since all we have to do is average the coordinates. Afterwards are a few midpoint problems, including two-step questions where one must calculate the distance or slope from one point to the midpoint of another segment.

Then there are a few more coordinate proofs where one has to set up the vertices -- notice that some hints are given in earlier questions.

High School -- Performance Task: Properties of Quadrilaterals, Continued (Day 118)

Today I subbed in a middle school Spanish class. This class is different from the usual Spanish or foreign language classes that I've subbed in. It's called "two-way immersion" -- in other words, there are just as many native Spanish speakers who know very little English as there are native English speakers who know very little Spanish.

The class is taught mostly in Spanish. Fortunately, there are special aides who speak the language, so I don't have to embarrass myself with my lack of Spanish skills. Of course, this also means that there is no "Day in the Life" today, since these aides handle the classroom management.

There are two eighth grade classes and three seventh grade classes. The older students are reading El Principe de la Niebla by Carlos Ruiz-Zafon -- a novel I know nothing about. The younger kids are reading a book that I do know -- House on Mango Street by Sandra Cisneros (in Spanish, of course).

Even in this Spanish class, there are many things that remind me of the old charter school. In the seventh grade classes, the two aides and I divide the students into Learning Centers. The students are sitting in six groups of four. Each aide takes one quartet, leaving the other four quartets to work on their Chromebooks. The groups rotate every ten minutes.

The eighth graders read and answer questions on their own. But during the last ten minutes of class, there is a vocabulary game on Quizlet. First, the aide loads Quizlet on her computer, and it generates a code which we project onto the front screen. The students enter the codes on Chromebooks. After all students have joined the game, Quizlet divides the students into groups of at most four, and gives each group an animal name in Spanish. Then the students play the game. The first group to reach 12 points is the winning team.

Even though I didn't play any such game at the old charter school, this set-up of entering a code and having the students join reminds me of the SBAC portal. During SBAC Prep I had to generate a code for the students to take the practice tests -- and I assume that the same is true for the actual test. But unfortunately, two years ago the SBAC website kept failing, and students kept getting kicked out when they tried to take the practice tests.

There's one more thing today that reminds me of the old charter school. The regular teacher wakes up sick today and so she hasn't prepared a sub lesson plan. And so she ends up emailing lesson plans to the office secretary (who in turn prints them up for me) as well as to her main aide.

Recall that my old classroom at the old charter school had a student support aide. (She was a much better classroom manager than I was, and so students often listened to her instead of me.) Anyway, I almost never communicated with her except face-to-face in my classroom. I think only once did I ever email her (when she was taking some photos of my classroom for me), and I certainly never attempted to phone her or text her. It never even occurred to me to ask for her phone number!

This lack of communication between me and my aide is completely my fault -- yet it wasn't until I subbed in this district when I realized it. Several teachers have much wider lines of communication with their aides than I did. This would have been especially helpful back on the day my car broke down (the day of the election).

Meanwhile, this is the second day of a two-day Performance Task on the blog, so there's no worksheet for me to post today. Hopefully our students can figure out the answer. As a hint, students should first try proving that the figure is a rectangle (which requires four slope calculations). Two distance calculations (length and width) are need to confirm that the rectangle is a square. The Midpoint Formula given on this page is a red herring, as it's not needed.

And so thus ends this rather short (at least by my standards) post!

High School -- Performance Task: Properties of Quadrilaterals (Day 117)

This week the Big March starts in earnest. As I've written before, the first week of the Big March isn't terrible, since at least it's a four-day week. The second week starts the string of five-day weeks -- these are what actually make the Big March the Big March.

Today I subbed in a middle school special ed English class. This is the third time I've visited this class this month -- I most recently described the class in my Valentine's Day post. This time, I won't do "A Day in the Life," but I will discuss some of the things I see today.

The middle school rotation is set up to begin with the co-teaching class today. As she often likes to do, the resident teacher begins with silent reading, even though the official silent reading time isn't until after lunch. Afterward, she starts talking about the district Performance Task.

What, you're now thinking, we're still talking about that darn Performance Task! I thought there'd be no more mention of Performance Tasks after President's Day! Well, this teacher decides to take the Performance Task a step further. First, she gives the seventh graders their scores -- and the rubric specifically states that the scale is based on the SBAC, with 4 as the top score. Then she tells them that this entire week will be for editing the essay and resubmitting it for a higher score.

To accomplish this goal, the teacher divides the class into five groups and assigns each group to a particular station. That's right -- this teacher is implementing Learning Centers. And once again, each time I see Learning Centers implemented, I can't help but think back two years to the old charter school and my failure to do Learning Centers properly.

Since I'm here to co-teach, she assigns me one of the groups. This is the top group, and the goal here is to partner up for peer review and editing. Only one student, a girl, has earned a perfect 4, but there are several scores of 3.5. The lowest score in my group appears to be 2.5. (Hmm -- she claims that these are SBAC scores, but I see no evidence that the SBAC uses half-integer scores like 3.5 or 2.5.)

It appears that the students will rotate through the groups throughout the week. The resident teacher is giving weaker students more help before they rotate into the editing station. This is very different from Learning Centers as envisioned by Illinois State, since students aren't expected to spend the entire week in Learning Centers. Then again, some of my colleagues suggested that, considering all the management problems I had that year, I try implementing a full week of Learning Centers.

(What's worse -- "Big Essay" or "Big March"? That's easy -- continuing to work on the Big Essay during the Big March, as this class is doing.)

After this class, I returned to my own classroom with the special aide. Just as we did on Valentine's Day, there is an assignment where students read two articles on a point/counterpoint, answer ten questions about the articles, and then do a current event on the topic.

This time, the topic is year-round schools. I wrote about year-round schools on the blog before -- about 2.5 years ago, just before I started working at the old charter. Let me reblog a little of what I wrote back then:

Here's how students can attend 3/4 of the year on the Year-Round Calendar -- we divide all students into four tracks, labeled by the first four letters A, B, C, and D. At any point three of the tracks attend school while the fourth track is off. The result is that all students attend school for 3/4 of the year, or 180 days, just like the Traditional Calendar students.

You might think that the A-Track student would take, say, the summer off, B-Track students would take the fall off, C-Trackers the winter, and D-Trackers the spring. But the actual Year-Round calendar in the LAUSD wasn't as simple. Students didn't have a single three-month break -- instead, the break was divided in half, so they had two breaks, each a month-and-a-half, during the year.

In today's class, the students consider the pros and cons of this schedule. On the Year-Round calendar there are more breaks, but the traditional calendar summer break lessens the need for air conditioning.

(Notice that on some tracks, there is no "Big March" since students are off-track in March. But on other tracks, the "Big March" may be even longer than on the traditional calendar!)

The worst period of the day, when I must write two names on my bad list, is second period. A seventh grade boy and girl start tearing each other's papers -- and then when I hand them Scotch tape to repair the papers, they just play with the tape.

As for the troublesome third period students from Valentine's Day -- the ones who were making fun of my raggedy shoes -- the girl is one of the hardest working students today. But the boy, meanwhile, is absent. We suspect that he's ditching, since he's present for homeroom (which has the same kids as third period at this school). It's not raining, so there's no double lunch or two-minute period before the lunch starts.

(Oh, and speaking of V-Day, two girls -- one in each grade -- still have the holiday pencils that I gave them that day!)

You might notice that I've labeled this post as traditionalists. Over the weekend, yes, our favorite traditionalist posted, and yes, our favorite commenter commented.

But let me start with something I saw on Facebook yesterday. One poster wrote that Algebra II should be replaced with a basic finance class. Another user -- a former classmate (which is why I'm able to read her post), agreed and added that all math beyond Geometry should be elective.

I expressed partial agreement in my response. We can all get behind the idea that prospective STEM majors should take Algebra II. On the other hand, non-college bound students shouldn't have to take Algebra II at all -- I have no problem ending with our favorite class, Geometry. The gray area is for future humanities/liberal arts majors. On one hand, I can see why such students shouldn't have to take such a difficult math class, but on the other, if we propose eliminating the Algebra II requirement, traditionalists will complain that we're trying to "water down" a college degree (even for non-STEM).

By the way, my classmate also posted a picture of awards earned by her sixth-grade daughter. One of the awards is for academic achievement in "accelerated math" (which I assume is for middle school students who are headed for eighth grade Algebra I). I assume that this girl will have no problem passing advanced courses in high school such as Algebra II.

Ironically, after responding to my classmate yesterday, I did my taxes -- a task for which that finance class might have been useful.

OK, let's get to the traditionalists. Here is Barry Garelick's post from yesterday -- yes, he wrote this just as my classmate was Facebooking and I was signing my tax return:

https://traditionalmath.wordpress.com/2019/02/24/revisit-of-rote-understanding/

I originally wrote about this in an October 2014 article published in Heartlander.  I re-read it recently and decided it’s still true.  I have reprinted it here with minor updates.

Well, I guess I reblog my old posts all the time, so I can't blame Garelick for reblogging here.

During a course in math teaching methods I took in ed school, I watched a video of a teacher leading his students to do a variety of tasks, ostensibly to teach them about factoring trinomials, such as x2 + 5x + 6. But rather than teaching factoring techniques, as is done in traditionally taught classes, the session was a mélange of algebra tiles (plastic squares and rectangles used to represent algebraic expressions) and a graph of the equation being factored (a parabola).

I have mixed feelings on this. Recall that algebra tiles are one of the manipulatives that I was supposed to use in Learning Centers at the old charter school. I believe that students might be more willing to use the algebra tiles (for factoring, the challenge is to make a rectangle with the tiles) than complete a traditional factoring p-set. On the other hand, I suspect that they'd be less likely to want to graph the function (unless maybe if they're using technology to do the graphing, such as on a graphing calculator or Desmos).

Garelick continues:

I recount the above because of an eighth-grade math course I observed as an instructional assistant (a role which one assumes after doing countless hours of subbing, and is generally the last step before being hired as a teacher). The math course was given just before full-fledged adoption of the Common Core standards in California and was piloting lessons that aligned with Common Core math standards. The teacher was quite good, and I do not hesitate to say she is excellent at what she does. But I also add that one can be very good at implementing things that are horrible. Her sessions were a mixture of letting the students “struggle” with a problem and then providing some explanation through limited direct instruction and questioning. During one session the class was learning about linear equations, graphing and functional form.

Garelick doesn't state whether this class is Common Core Math 8 or Algebra I, since he writes that this class takes place during the transition. Linear equations appear in both Math 8 in Algebra I. But he strongly implies later in this post that this is Math 8, not Algebra I.

Then Garelick links to some pages from the Golden Age of math textbooks, and tells us that these texts also promoted the same kind of understanding that the Common Core encourages. Then he adds on the following:

Those who view the traditional approach as strictly procedural believe it does not result in a “deep understanding.” They believe students do not learn the “why” of a procedure, just how to do it through “meaningless” drills. Yet the teacher I observed was still giving the students instruction after allowing them some time to “struggle.” She also gave them opportunities to practice. The difference was that her exercises included having to explain (orally and in writing) various connections—i.e., how the table of values related to the equation of the line, how the line related to equation, and so forth. The writing was also instructed: she gave them examples of sentences that she would say aloud but with blanks where key words would go.

SteveH's short comment is to express agreement here:

SteveH:
A classic. They are parroting and applying their rote understanding of math education from ed school.

Here Garelick and SteveH highlight what they consider to be ironic. The Common Core wants students to show deep understanding -- but to them, the Golden Age texts lead to understanding, while the Common Core lessons lead to rote learning of what the teacher (and ultimately, what the SBAC) wants them to write.

Once again, my biggest concern isn't a definition of "deep understanding" vs. "rote learning." My concern is that when students are bored, they're likely to leave assignments blank or give complaints such as "When will I use this in real life?" No one gains rote knowledge or deep understanding from assignments that are left blank.

And so I want to promote lessons that students are more likely to do and less likely to leave blank. I believe that algebra tiles (a puzzle that looks like fun) are more likely to be done than traditional factoring (a p-set that doesn't look like fun).

Just today, one eighth grader asks me the question "When will I use this in real life?" -- actually, I think he uses the phrase "adult life." Notice that this isn't even math, but English, so I can only imagine what he thinks about his math classes. Of course, the ability to make a claim and defend that claim using evidence ("I think the traditional school calendar is better than a Year-Round calendar.") is a useful skill in real life. It's probably easier to defend the real-life utility of defending claims than, say, algebraic factoring. But I was unable to convince him of anything.

In the end, the student completes the English assignment quickly, then goes to the restroom. When he returns, he threatens another student -- and the aide ends up giving him a referral. I was almost about to place him on the good list for doing his work, but of course I write him on the bad list instead.

A student who asks "When will I use this?" in math might be a typical math hater, but someone who asks it in a non-math class probably just hates school altogether. His assumption is that nothing he's taught in any class these days will be useful in real life. In other words, he's already learned everything he needs to know, so he should be allowed to graduate and spend all the hours he's awake on entertainment.

I ultimately tell the class that in the old days, we did let students graduate at their age. But they didn't have fun all day -- instead, they were expected to work. This is the idea of Dickens age -- teenagers worked long hours for little pay. And this is still the case in Third World countries today.

I actually say of this to the other students, when the "When will I use this?" boy is in the restroom. I know that if I say it directly to him, it would likely lead to an argument. (Notice that if I'd waited until he is in the office with a referral to talk about this, it might count as continuing to discuss past incidents, hence a violation of the third resolution.) I might as well practice saying all of this, since I know I'll hear "When will I use this?" all the time in my own math class.

But it's the traditionalists like Garelick and SteveH who forget about "When will I use this?" They assume that just because we hand the students a traditional p-set, the students will just do it without any questions. That assumption isn't even true in English, much less math.

Before I leave the traditionalists, I do wish to comment on the latest teacher strike. I won't blog about every teacher strike, but I feel I should mention the Oakland labor dispute since it's in California. (I do point out that Oakland is in Northern California, and thus it's much closer to Garelick's home than my own.)

Unlike the LAUSD strike, the Oakland strike apparently doesn't have "overtesting" as a major point of contention. Once again, we see the impact of standardized testing firsthand in my district. First there's a Performance Task for the actual SBAC. Then the district gives its own Performance Task in order to prepare students for the SBAC.  Then an individual teacher in the district decides that she wants to extend the district assessment to give her students extra practice -- probably in the name of making sure that the students are ready for the SBAC.

(Today's co-teacher is the only teacher I know who is making her students rewrite their essays. In particular, in the main class I subbed for, the students haven't even seen their scores yet -- and as far as I know, there's no plan to have these special ed students edit and resubmit their essays.)

Once again, I have no problem with the idea of different tests at different levels, but this easily leads to overtesting when districts add tests to prepare for the state assessment, and teachers add tests to supplement the district assessment.

This is what I wrote last year about today's lesson -- which is based on something that I found in a math class I subbed in last year:

I also find a copy of a Performance Task, similar to what students may find on the SBAC. There's a hole in my U of Chicago pacing plan since Chapter 11 has only six sections. And I've never posted a Performance Task before, despite this being a Common Core blog.

And so I post this task as an activity for today and tomorrow. Actually, I create my own version of the problem rather than the district copy. This is to block out the name of the district since I don't post identifying information (and to avoid any issues with SBAC, which might mistake this practice question for a real test question). Also, I changed it from one day to two days. On the actual SBAC, students are typically given a two-hour block to complete the Performance Task, so they should have two days to complete it.

The question is about the coordinates of a square. It fits perfectly with Chapter 11 of the U of Chicago text -- and indeed it's similar to the Lesson 11-1 activity from two weeks ago.

In the Glencoe text, the Performance Task fits with Chapter 6, on quadrilaterals. Glencoe Chapter 6 is similar to Chapter 5 in the U of Chicago text (and Chapter 6 in the Third Edition), except that coordinates appear early. Indeed, I lamented three years ago that the Distance Formula appears as early as Chapter 1 in the Glencoe text!

2019 update: So now I'm writing about Performance Tasks in math after blogging so much about the Performance Task in English. I have no idea when this task was actually given in the district. I assume that it was well before winter break, since the English Performance Task is after winter break.

Traditionalists probably won't like the explanation required for Part III of this task. They'd say, just graph the quadrilateral and classify it. There's no need for students to explain anything.

Lesson 11-6: Three-Dimensional Coordinates (Day 116)

Today I subbed in a seventh grade science class. This is my second visit to this class -- I wrote about my first visit back in my September 26th post.

I'm debating with myself whether to do "A Day in the Life" today. On September 26th I didn't do "A Day in the Life" because all classes only watched a Jane Goodall chimpanzee video. (Oh, chimps reminds me of crocodiles. Today's Google Doodle features Australian zookeeper Steve Irwin. If we count Goodall as being science-related, then I suppose we should count Irwin as well.)

Today the students actually have a written assignment, so I could do "A Day in the Life" since classroom management is more relevant today than on that September day. But since all the classes are the same, I'd have to keep writing the same assignment over and over. Yesterday's "Day in the Life" was much more interesting, since I covered both P.E. and health.

This is one of the middle schools where all periods rotate, and today begins with fourth period. The assignment is to read two packets and answer questions on the respective worksheets. Students may choose which assignment to do first.

The only period when I must write down names for the bad list is second period. This class rotates into the after-lunch position, and so the class begins with silent reading (with the usual whispering and student "sound effects"). It's the only period with a tardy student.

I write down two names on the bad list -- a girl and a boy. The girl repeats a common trick -- she's summoned to go to the guidance office, and when she returns, she claims that the remaining half hour or so isn't enough time to do any work (even though the good list students are able to finish both worksheets in less time than that). The boy doesn't even try to come up with an excuse -- he just doesn't do the work.

I name fifth period as the best class of the day. In this class, so many students complete both worksheets that I must use a random number generator to decide which names I should write down on my good list (since too many names would water down the list). The next best class is third period, since this class cleans up the room well at the end of the day.

One of the two articles is all about "fixed mindset" vs. "growth mindset." On that worksheet, the students must correct fixed mindset statements so that they reflect a growth mindset instead. One of the fixed mindset statements is relevant to math -- "I'm not good at solving math problems." (A possible growth mindset correction would be something like "I'll work harder at solving them.")

For some reason, traditionalists dismiss "growth mindset" as just another fad. But I see no reason why growth mindset would be at odds with traditionalism. Students with the fixed mindset "I'm not good at solving math problems" are likely to avoid solving problems on traditional p-sets, while those with a growth mindset will find value in working on them.

OK, so I'm not doing "A Day in the Life" today. But instead, I'm doing what I normally do when I sub in a science class -- lament on my failure to teach science at the old charter school. Since it's February, there's much more evidence of student work on the board and around the room than there was in September.

First of all, there are assignments on the board listed with a "Table of Contents" and page numbers -- evidence of an interactive notebook. I've noticed that besides math, science seems to be the class where interactive notebooks appear. This once again makes me feel guilty about not using interactive notebooks at the old charter school.

I'm not sure how such notebooks would have worked out had I used them two years ago. I could use two-subject notebooks and have the students label one section "math" and the other "science." But such notebooks might be hard for the students to find, and some might buy a one-subject notebook or use this as an excuse not to bring a notebook the entire year. Another idea is to mix the math and science pages but use the "Table of Contents" to indicate which pages are which subject. I could even have a pattern where the left pages are for math and the right pages are for science.

The most recent lab these seventh graders did was on percentage of oxygen in the air. I already know that air is about 20% O2, but I didn't know that it's possible to devise an experiment to find this percentage (that seventh graders are able to complete). Apparently, it involves taking steel wool and letting it rust (that is, react with oxygen). The air is in a tube where the oxygen, after reacting, is replaced with water. So students can measure the water to find out how much O2 was replaced. (Two years ago, I had another project involving steel wool -- one that didn't go well.)

A past project involves creating a model of a cell. No, these weren't edible models (bringing to mind the special scholar's cousin who bragged about the edible cell model lab from her old school).

I assume that science in this district is based on the NGSS standards -- the integrated model -- since I see both life science (cell models) and physical science (oxygen in air) in seventh grade. If I had done science at the old charter, it would have been NGSS for sixth grade only (as these sixth graders are now eighth graders about to take the first real California Science Test). Seventh grade would have done labs found in the life science Illinois State text.

Lesson 11-6 of the U of Chicago text is called "Three-Dimensional Coordinates." In the modern Third Edition of the text, three-dimensional coordinates appear in Lesson 11-9.

I didn't write much about this lesson last year. This was the other day during Chapter 11 last year when I subbed in a math classroom, so I focused on that math class instead.

Today is an activity day. Since what I posted last year from the classroom is an activity anyway, I've decided to keep that activity and add a new Lesson 11-6 worksheet instead.

With this worksheet, today I can truly say that I've posted every U of Chicago lesson (from the Second Edition, that is) at some point. (Lessons 8-3 to 8-5 were posted in past years). Last year I claimed to have covered every lesson, but in reality I didn't post worksheets for Lessons 11-4 or 11-6 until this year.

This is what I wrote last year about today's activity:

And besides -- at least today's "Luck O' the Irish" actually fits in Chapter 11 on coordinate geometry, albeit in only two rather than three dimensions. If you wish, you can pretend parts of the graphs are in different planes and make it into a 3D lesson.

Ordinarily I don't post copyrighted material. But Cartesian Cartoons are so easy to find online that I see no harm in posting yet another copy of it. (And besides, I've posted some of them before during years past.) Some students today do remark that this is a bit early to be doing a St. Patrick's Day assignment, but oh well!

One girl has trouble understanding how to do the graphs. I try to help her a little, but her points are still a bit off. I tell her that she is "almost smart"and that she should work harder to make the graphs look right. I hope my words can motivate her.

[2019 update: Yes, that was the "growth mindset" I enforced that day last year!]

Lesson 11-5: The Midpoint Connector Theorem (Day 115)

Today I subbed in a middle school P.E. class. Normally I wouldn't do "A Day in the Life" for a P.E. class that is non-representative of what I'd like to teach this day. But in addition to eighth grade P.E., this teacher also has seventh grade health in a classroom. Thus it's worth doing "A Day in the Life" -- especially since two students (one in each grade) end up earning referrals.

8:15 -- This is the middle school that begins with homeroom and first period, which happens to be the first eighth grade P.E. class.

It seems as if I've been writing about rain a lot on the blog lately. Actually, it doesn't rain that much this week at all -- but it just so happens that the one day it rains is the one day I sub P.E. this week. In fact, the rain was mostly last night (with a little after school), but it's enough for the other P.E. teachers to cancel outdoor activities on the muddy ground. I actually spoke to the regular teacher on the phone before class. He assumes that there would be outdoor P.E. on the track today, and has no idea that the other teachers would cancel it.

So instead, all students meet in the gym. The activities are similar to the one period of P.E. that I mentioned in my January 18th post -- students can either play Dodgeball or watch a movie. I stay out to watch the Dodgeball game.

9:20 -- And once again, we know that this school has a period rotation after first period. The rotation for Thursday goes 1-5-6-2-3-4. Fifth period is the first of the seventh grade health classes.

These students have an assignment from the health text. They must read the chapter on alcoholism and answer 18 questions in complete sentences. This includes a few fill-in-the-blank problems -- so they must write out the entire sentence with the blank filled in.

10:15 -- Fifth period leaves for snack.

10:30 -- Sixth period arrives. This is the second of the seventh grade health classes.

11:25 -- Sixth period leaves and second period arrives. This is the last seventh grade health class.

12:20 -- Second period leaves for lunch.

1:05 -- Third period arrives. This is the second of the eighth grade P.E. classes.

2:00 -- Third period leaves and fourth period arrives -- that's right, this regular teacher has all six periods without a conference. This is the last of the eighth grade P.E. classes.

This time, I watch the movie instead of Dodgeball. For some reason, the movie is Elf -- and yes, I check the calendar and see that today is February 21st, not December 21st!

Actually, if you watch the whole film and count backwards from Christmas Eve, you'll notice that the part of the movie we watch today takes place on December 21st. (The day begins as Buddy the Elf wakes up in Gimbel's after decorating it for Santa, and it ends when he goes home with his long-lost father and his new family.)

I've long been fascinated with school calendars and whether movies that feature school scenes follow a logical calendar (ever since Frosty the Snowman has kids in school on Christmas Eve). We see that the following day is December 22nd, and a bell rings to mark the end of school for Buddy's newly found stepbrother. The students and I decide that this is a good time to mark the end of school for us, and so I stop the movie at this point. (In case you want to know how I determined the dates, notice that the next day is when Buddy goes out on a date with Jovie -- a Thursday night -- and the next day is Christmas Eve.)

And in case you think my dates are wrong since winter break should have started by the 22nd, recall that the film takes place in New York, where there is school on the 22nd and even the 23rd. The short winter break is made up for with a full week off for President's Day -- and that's this current week in real life. (Yes, so I'm finally talking about February, not December!)

2:55 -- The bell rings, and the students go home (a few minutes after Buddy's stepbrother).

Today's subbing indicates that in this district, middle school health is taught by P.E. teachers. I'm not fully sure how it works in this district -- presumably, one of the units in a P.E. class is health, and so students go to a classroom instead of the P.E. area. We know that seventh graders get health, but I don't know whether eighth graders get a health unit or not.

In the LAUSD, health is part of science class, not P.E. class. It's logical to assume that at my old charter school (which is chartered with LAUSD), health is also taught by science teachers. But hold on a minute -- the year I was at that school, I was the science teacher. This means that logically, I was the one who needed to teach the middle school health classes!

Of course, I had all sorts of problems teaching science -- and now we see that I could have taught health on top of science! But at no point did anyone ever ask me to teach health. The Illinois State text contains a science component, but not a health component.

But health could be considered to fall under the umbrella of life science. In the old days, life science was the seventh grade curriculum, and so I could have taught my seventh graders health. But under the NGSS, life science is integrated into all three middle school years.

The following link is to the LAUSD health curriculum:

http://www.heplausd.net/wp-content/uploads/2018/11/CA-Health-Education-Standards_MS.pdf

But these standards haven't been updated since 2008 -- well before NGSS. So the link doesn't explain how to incorporate health into NGSS science courses.

According to the link above, middle school health includes sex ed. I once subbed for a health class in another district -- it was the last class I subbed in before starting at the old charter. (I never mentioned this on the blog.) I'm not sure whether I would have felt comfortable teaching sex ed. But once again, no one at the charter ever told me that I, as the Science/Health teacher, needed to teach sex ed.

OK, let's finally get to classroom management. Here is our focus resolution for today:

2. Keep a calm voice instead of yelling at students.

I definitely feel like yelling in second period health class. And it all starts even before the tardy bell rings, when I see several students gathered around a broken lamp. It's one of those room lamps that's as tall as a human being. Apparently, someone's backpack knocks it down. But no, it's not the light part that's broken -- it's the base. Thus the lamp can no longer stand on its own.

At this point I panic -- when I'm the sub and something breaks, it looks bad on my part. And so while I believe that my voice stayed below the "yell" level, I do begin the class with a long argument about how the students shouldn't go around playing around and breaking things.

This is the class where I must write my first referral. It's not for the breaker of the lamp -- instead it's for one boy who keeps throwing pencils and other objects. Instead of hitting other students, the projectiles land near the window. I'm afraid that he might break the window after the lamp base in the classroom is already fractured. And so I write the referral and call security to escort him from the room before anything else breaks.

I've said it before and I'll say it again -- I consider any day on which I must write a referral and call security to be a failure. The ideal classroom manager is able to handle the students in the room without outside help.

Is there anything I could have done to prevent this incident? I'm wondering whether I might have provoked this boy and the other students by making a big deal about the lamp. When I first see the broken lamp, I think to myself, "This second period is the class from hell -- they can't even enter the room without breaking things. I must keep my eyes on this class!"

But in reality, this class probably isn't that much worse than the other two health classes. The lamp fell when someone brushes it with a backpack -- not because the class enters the room only to start playing with the lamp. (Indeed, there's even a slight chance that the one who brushes against the lamp to knock it down is a student leaving sixth period, not a student arriving to second period. The first student arrives to second period before the last sixth period student leaves.)

And so I argue with the students fearing that this would be the class from hell when it isn't -- and then this becomes a self-fulfilling prophecy. The students get upset that I assumed malice behind the breaking of the lamp, and so they start disrespecting me. Many students refuse to do the assignment who might have worked if only I'd begun the class with "So the lamp broke -- no big deal!" It's possible that this might even include the eventual pencil thrower!

At the start of this post, I mentioned a second referral. I'm not sure whether there's anything I could have done to prevent this referral. It's during fourth period P.E. class. Two P.E. classes enter the gym with their teachers -- yours truly and a regular teacher. Since she's a P.E. teacher, the regular teacher takes Dodgeball while I go to the side room to watch Elf. Thus students are in either the main gym or side room based on their choice of Dodgeball or Elf, not who their P.E. teacher is.

It's the other P.E. teacher who writes the referral -- so I'm not even the one who writes this kid up. But apparently he isn't in her class, but in my regular teacher's class. Thus it counts as a second referral, since my regular teacher will return tomorrow to find out that two of his students were written up.

(This is why the Elf watchers are eager to leave when the bell in the movie rings. I'm standing by the door waiting for the other teacher to dismiss her students so I know when to let mine leave. But she's likely too busy writing the referral to dismiss them!)

Fifth period is the best health class of the day. First period is the best P.E. class of the day. Both of these classes are loud, but these are much better than the referral classes.

Today on her Mathematics Calendar 2019, Theoni Pappas writes:

7/120 rpm = ____ angular velocity in degrees per minute

Since rpm = revolutions per minute and one revolution is 360 degrees, we use dimensional analysis:

(7 rev/120 min)(360 deg/1 rev) = 21 deg/min

Thus the desired angular velocity is 21 degrees per minute -- and of course, today's date is the 21st.

Some might wonder whether this should even count as a Geometry problem. Well, it does use angles and degrees, and there's no mention of negative angles or angles greater than 360 degrees. And so I decided to post it today.

Lesson 11-5 of the U of Chicago text is called "The Midpoint Connector Theorem." In the modern Third Edition of the text, the Midpoint Connector Theorem appears in Lesson 11-8.

Unlike the rest of Chapter 11, this is a lesson I covered well last year. And so this is what I wrote last year about today's topic:

Lesson 11-5 of the U of Chicago text is on the Midpoint Connector Theorem -- a result that is used to prove both the Glide Reflection Theorem and the Centroid Concurrency Theorem. Last year I only briefly mentioned the Midpoint Connector Theorem on the way to those higher theorems, and then when we actually reached Chapter 11 I only covered it up to Lesson 11-4, as I knew that I'd already incorporated 11-5 into the other lessons. But this year, I'm giving 11-5 its own worksheet.

Midpoint Connector Theorem:
The segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.

As I mentioned last week, our discussion of Lesson 11-5 varies greatly from the way that it's given in the U of Chicago text. The text places this in Chapter 11 -- the chapter on coordinate proof -- and so students are expected to prove Midpoint Connector using coordinates.

It also appears that one could use similar triangles to prove Midpoint Connector -- to that end, this theorem appears to be related to both the Side-Splitting Theorem and its converse. Yet we're going to prove it a third way -- using parallelograms instead. Why is that?

It's because in Dr. Hung-Hsi Wu's lessons, the Midpoint Connector Theorem is used to prove the Fundamental Theorem of Similarity and the properties of coordinates, so in order to avoid circularity, the Midpoint Connector Theorem must be proved first. In many ways, the Midpoint Connector Theorem is case of the Fundamental Theorem of Similarity when the scale factor k = 2. Induction -- just like the induction that we saw last week -- can be used to prove the case k = n for every natural number n, and then Dr. Wu uses other tricks to extend this first to rational k and ultimately to real k.

I've decided that I won't use Wu's Fundamental Theorem of Similarity this year because the proof that he gives is much too complex. Instead, we'll have an extra postulate -- either a Dilation Postulate that gives the properties of dilations, or just one of the main similarity postulates like SAS. I won't make a decision on that until the second semester.

Nonetheless, I still want to give this parallelogram-based proof of the Midpoint Connector Theorem, since this is a proof that students can understand, and we haven't taught them yet about coordinate proofs or similarity.

[2019 update: Some of this old discussion is relevant to last Tuesday's traditionalists' post regarding rigor and the Common Core.]

But even with last year's Lesson 11-5 worksheet, I must make a change. Today is Thursday, and so I must replace last year's activity page with an assignment page.