"Additional units can be added to shared walls later as the need arises. Design possibilities can be very exciting with courtyards or alcoves left open for light and exterior access."
This is the final page of the section on 21st century architecture. Indeed, Pappas wraps up this section on this note:
"Now, as in the past, the feasibility of a structure is dictated by the laws of mathematics and physics -- which act as both tools and measuring rods."
There are two pictures on this page of possible 21st century designs. The first is captioned:
"Plane-filling Penrose tiles & space-filling truncated octahedra"
I mentioned Penrose two weeks ago as part of our Chapter 0 lesson on Op Art. "Penrose tiles" are tiles that tessellate the plane, yet without a translation mapping the tessellation to itself. However, there do exist other Common Core transformations mapping the tessellation to itself -- including reflections, rotations, and even dilations. This deserves a link to Wolfram Mathworld:
http://mathworld.wolfram.com/PenroseTiles.html
Here is the second caption:
"The left illustration shows how these pentagons, tessellating a plane, can be adapted to pentagonal prisms that become module space filling units. At the right is a structure formed by modifying the shape of a cube."
It goes without saying that these pentagons aren't regular, as regular pentagons don't tessellate.
Today is my second day of subbing in the science class at the continuation school. Let's see how that went, in "Day in the Life" format again:
8:00 -- I arrive at the continuation school. As it turns out, the "Orientation to High School" classes have some sort of intern teaching special lessons on Wednesdays. She teaches the students about anger management, and shows the students clips from movies where different characters become angry and eventually learn to apologize.
8:55 -- Second period should have been easy, since it was another "Orientation" class with the intern taking over again. But in fact, several incidents occur in this class.
First of all, I have some "Sub Notes" written on the board. I think it's only fair for the students to know who is on the list of names I gave the regular teacher yesterday (and it may even lead them to improve their behavior today), yet I know that kids who see their names might start arguing. So I decide to compromise by writing down only the first initial rather than the full names.
Now one guy sees the initial M. on the board (listed as someone who wrote fewer than 100 words yesterday), thinks that it refers to him, and complains. As it turns out, I intended a different M. -- but he doesn't realize this. Recall that after all, I determined the list of names yesterday by collecting the laptops and seeing which names are logged in, so I never tell the students that they are written on the list until they see it on the board today.
And right afterward, M. engages me in a second argument. When the regular teacher doesn't specify a cell phone policy, I make up my own. My standard policy is, cell phones may not be used for taking photos or watching videos (the two most distracting activities), but other uses (single-player games, texting) are permitted (as long as it doesn't take away from doing work). Well, this student decided to log in to Snapchat, which involves both (snapping) photos and (chatting) texts. He claims that he should be allowed to Snapchat since it's texting, but I only see the camera image on the screen and count it as taking photos.
After the two arguments, M. makes a mistake on the worksheet that he's completing for the intern, and so he asks for a new copy. I start to hand him one, but then he insists that I lay it on another desk, and then he snatches the paper angrily. These are the actions of a student who genuinely feels that he is being treated unfairly. (Recall that cries of "Unfair!" are not considered genuine.) And it's all because I wrote his first initial (actually someone else's first initial) on the board.
As it happens, another event involving student names occurs. A counselor phones me and tells me that she is to observe a student without his knowledge. She's hoping that I can point out which student it is, but of course, I don't know who it is. (Actually, he is another student on my fewer than 100 words list -- his initial is I. -- but again, I got his name from the laptop and so I never associated the name with a face.)
Unfortunately, the intern can't identify him either -- today is only her second day with the students, so she knows the students as little as I do. (In fact, she likely knows them even less than I do -- her first day with them was a full week ago, while I should still remember some of them from yesterday.) So she does something clever -- after the counselor calls but before she arrives, the intern calls out the name and asks him a question. She then whispers his hat color to me, and then I turn around and inform the counselor of the same.
After the counselor completes her observation, she asks me right outside the door whether there's a second student with the I. name. I reassure her that there isn't -- but later on, I discover that there is a student whose middle name is the same as the target student's first name. I sure hope that there is no confusion and that the correct student is observed.
But I'm still thinking about the M. student. I don't like treating students unfairly, yet M. doesn't like the way I speak to him today. I wonder whether there's something I can say to him -- after all, since many of the things I say to him are negative, maybe there's something positive I can tell him.
At the end of class, I get the chance for a positive interaction. The intern asks for two students to volunteer to perform a short skit in front of the class. In first period, no one volunteers and the intern must choose two students at random. But in second period, two students volunteer -- and they are none other than M. and I.!
And so after the performance, I tell them how funny I find their skit. M. promptly apologizes for the earlier argument, and asks whether I can remove I. from the list. I told both guys that I could not, since the regular teacher has already seen the list. But I promised them that I'd inform the teacher how they are the only volunteers to perform the skit for the intent.
Notice that instead of engaging M. in the argument, I use wait time and the power of positivity. In fact, these are principles the intern mentions in her anger management lesson! So I end up learning as much about anger management as my students -- and I'm able to take it to the bank immediately. I've never thought of it this way, but anger management can be seen as a part of classroom management.
9:45 -- The intern leaves, and students go out to nutrition.
10:00 -- The first science class arrives. The students have an assignment in Google Classroom. These students are learning more about populations and the effects of group behavior in organisms. Some vocabulary words on today's worksheet are Communities, Organization of an Environment, Biome, and Ecosystem. In the end, this class is the best behaved of the day -- both students on yesterday's list end up completing their assignments.
10:55 -- It is fourth period, and the second science class arrives. Of the two students on yesterday's list, one completes his work while the other doesn't.
11:45 -- The AM students go home, while the PM students arrive. I use the long break to prepare for the seventh period class again.
2:10 -- Several problems occur in this class. First of all, one student attends the class who isn't on the roster -- and in fact is an AM student who shouldn't even be on campus. Eventually, I kick him out of the room -- but on his way out, he asks, "Is it because I'm Mexican?"
I try to avoid discussing race and politics during school year posts on the blog. If I must discuss race, I save it for posts labeled as "traditionalists" (since the traditionalists often mention race in their posts) or in discussions of racially relevant topics, such as the movie Hidden Figures. (Technically, this post does have the label "traditionalists," but for a different reason.) Unfortunately, I'm going to post about the controversy today since the race card is pulled today.
Recall that earlier in this post, I wrote that students who truly feel that I'm treating them unfairly are more likely to give me the silent treatment (like M. earlier) than say that I'm unfair. I include claims of unequal treatment due to demographics (such as race or gender) -- for example, those girls from last year who believed I was unfair didn't call me "sexist" -- they gave me the silent treatment. And so I expect students who genuinely think I'm unfair to a race to do the same.
Moreover, it seems strange that a student would think I'm treating Mexicans differently, since nearly every student in this class is Hispanic. The one student who isn't is white -- and in fact, he is perhaps the worst-behaved student in the class. (The regular teacher warned me about him yesterday.)
This lone student (let's stop referring to him by his race, which is a red herring and irrelevant to the issues, and call him by the initial C. instead) was absent yesterday. Indeed, much of the reason I had a good seventh period yesterday was due to C.'s absence.
I tell the students that they must complete at least one side of the worksheet. C. does so quickly -- and I reckon that he just fills in random answers in order to proclaim "I'm done!" Then he starts changing seats -- contradicting the regular teacher's requirement that the students remain in their seats. Later on, a second student changes his seat as well.
One factor in the misbehavior of seventh period is the first question on the back of the worksheet:
"What is the hunting style of the lynx?"
One student sitting behind C. asks me what a "hunting style" is. The problem is that I don't know -- and it's not obvious at all what the intended answer is. Sometimes in this situation, I check the worksheets of the third and fourth period students, but there is no consensus as to the correct answer.
The other students, especially C., use this as an excuse not to work. "How can I do the other side if I don't know what a hunting style is?"
This is similar to what happened last year when I tried to teach middle school science. In each case, I lack confidence because I don't have command of the material myself. I can tell that the students are thinking, "Why should I learn science if the teacher doesn't understand science himself?" Notice that this is understandable since I'm a sub who must cover subjects that aren't my strength. On the other hand, this was unacceptable last year when I was officially the science teacher. This is what I meant when I wrote that my problems with science led to problems with classroom management -- and it happened again today.
Furthermore, when the students are talking, it's difficult for me to concentrate on teaching, even if the subject is my strength, math. The notes on which this assignment is based are on Google Classroom, which I can't access without a password. But if I had inspected the worksheet in detail, I might have been able to deduce the answers anyway!
Many students just gave up after seeing the first question on the back. But the third question on the back side is:
"What happens to the prey (food) of the lynx when the population (number) of the lynx increases?"
We don't need to know what a "hunting style" is to answer this question, just common sense. When the predator population increases, the prey population must decrease -- after all, the extra lynx would eat more of the prey. Indeed, my math background should actually help here -- predator-prey models are a common application of mathematics. (I mentioned this two years ago on the blog.) There is a graph provided here, but it's hard to read. (It might be easier the see the chart on the screen in Google Classroom than on the worksheet). But again, we don't need a graph to know that more predators equals less prey.
In the AM classes, some students wrote "hare" as the hunting style of the lynx, since according to the graph, the prey of the lynx is the snowshoe hare. But this isn't the intended answer -- in fact, the last question on the page is a dead giveaway as to the possible correct answer:
"What can you say about the benefits (what is good) and drawbacks (what is bad) of group vs. individual hunting styles? EXPLAIN YOUR ANSWER USING THE CHARTS!!!"
Right there in the question, there are two hunting styles listed -- "group" and "individual"! So the answer to the first question is reduced to two choices -- and so is the answer to the second question:
"What is the hunting style of the wolves?"
In fact, I think I know the answer to this question. I've definitely heard of a "pack of wolves," but never a "pack of lynx." In fact, I confirm this on Google quickly -- "pack of wolves" has over half a million hits, while "pack of lynx" has fewer than 40,000 (and the word "rare" appears in the first two hits, while in the next few hits, "Lynx" is a brand name). The answer is likely in Google Classroom, but based on those search results, the answer to the first is "individual" and the second is "group."
I wish that students in third and fourth periods would have asked me for help. We could have figured out the answer together in a much better-behaved class, so that by the time I reached seventh period, I would have known the answers. Of course, I could have looked at the worksheet during the two-hour break and tried to determine the answers then -- again, I would have been at a disadvantage without access to Google Classroom, but look at how much I figured out with common sense and two quick Google searches.
Oh, and some students make lewd sounds on the cell phones again today.
3:10 -- Class ends, and I go home to type up this blog entry.
Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What have you been doing to work toward your goal? How do you feel you are doing?
I like how I use a positive comment to diffuse the problems in second period. I try to employ a teacher look to avoid arguments, and it works -- even in seventh period (albeit temporarily).
But I'm disappointed with how seventh period turns out. Notice that unlike second period, I know the names of the students in seventh period (as I make them follow the seating chart during attendance, and even after they move I can tell who moved). I might have been able to control C.'s behavior if I actually uttered his name aloud. I admit that I become wary of calling students by their names after all the confusion with names in second period.
Moreover, the problems I have with science reminds me of the science class last year. Actually, the situation where a student thinks I'm unfair reminds me of last year's class as well. I'm able to give a positive comment because the student volunteers for the intern. If I'm the only teacher in a class and the student is upset with me, that student probably doesn't volunteer for anything. Last year, my support staff member could have acted as a mediator. A student is upset with me, the support staff member gives her an assignment, she completes the assignment and produces some work for which I can give a positive comment.
After my first two days of subbing, I still have a way to go before I can call myself an ideal manager.
Today is the Chapter 1 Test. This is what I wrote about the test two years ago:
I am now posting my first test. It is actually the Chapter 1 Quiz that I posted last year, but now I'm considering it to be a "test." This is mainly because in my semester plan at the start of the year, I refer to the first day of school up to Labor Day as the first "unit," and then the month starting with Labor Day as the second "unit." Each test that I post corresponds to one of these "units." Still, I don't want to overburden the students with a hard test at the start of the year, so this still has only 10 questions.
Even though my series "How to Fix Common Core" is over, I will often use these quiz and test days to post links to articles about the Common Core debate, including recent traditionalist arguments. I will start by rewriting what I wrote last year about today's test (including my rationale for including the questions that I did), and then link it back to the Common Core debate.
There is a Progress Self-Test included in the book. But even if I threw out the questions based on sections 1-6 through 1-8, there are some questions that I chose not to include.
For example, the first question on the Self-Test asks the students to find AB using a number line. This is very similar to some of the questions that I gave on the Wednesday and Thursday worksheets. But there is one crucial difference -- this one is the first in which both A and B have negative coefficients.
Now I know what the test writers are thinking here. The test writers want to know whether the students understand a concept. There's not enough room on the test to give both easier and harder questions. If a student gets a harder question correct, we can be sure that the student will probably get a much easier question right as well. But if the student only answers an easier question correctly, we can never be sure whether the student understands the more difficult question. Therefore, the test should contain only harder questions, since anyone who gets these right understands the simpler concepts too.
But now let's think about this from the perspective of the test taker, not the test maker. Let's consider the following sequence of hypothetical conversations:
Wednesday:
Student: The distance between 4 and 5 is 9.
Teacher: Wrong. You're supposed to subtract the coordinates, not add them. The distance is 5 - 4 = 1.
Student: Oh.
Thursday:
Student: The distance between -4 and 2 is 2.
Teacher: Wrong. When subtracting, change the sign. The distance is 2 - (-4) = 6.
Student: Oh.
Friday:
Student: The distance between -8 and -4 is 12.
Teacher: Wrong. You forgot the negative in front of the 4. The distance is -4 - (-8) = 4.
Student: Oh.
And we can see the problem here. The teacher wants the student to be able to find the distance no matter what the sign of the coordinates are -- not just when they're positive. But the problem is that the instant that a student finally understands how to solve the first problem, the teacher suddenly makes the problem slightly harder, and the student becomes confused.
Of course, you might be asking, why only give one problem on Wednesday? Why can't we give more problems to check for student understanding of the all-positive case, then move on to negatives? But you see, I'm imagining the above hypothetical conversations as occurring during, say, a warm-up given during the first few minutes of class -- and warm-ups typically contain no more than one or two questions. The student is never allowed to taste success, because each day a little something is added to the problem (like a negative sign) that's preventing the student's answer from being completely correct. The student never hears the words "You're right." And that's just with negative signs -- the U of Chicago text includes questions with decimals as well. I immediately threw all decimals out of my problems -- since decimals confuse the students even more, most notably when we draw number lines and mark only the integers.
Well, I don't want this to happen, especially not on the quiz or test where most of the points are earned. I want the student to taste success -- and this includes the student who's coming off of a tough second semester of Algebra I and is now in Geometry. Sure, if you feel that some students need to be challenged, then challenge them with all the negatives and decimals you want. But I don't want to dangle the carrot of success in front of a student (making them think that they've understood a concept and will get the next test question right), only to jerk it away at the last moment (by adding extra negative signs that will make the student get the next test question wrong), all in the name of challenging the students.
And so my test questions are basically review questions rewritten with different numbers. My rule of thumb is that the test contains exactly the same number of negative signs as the review. Some teachers may see this as spoon-feeding, but I see it as setting the students up for success. Any student who works hard to prepare for the test by studying the review will get the corresponding questions correct on the test.
Of course, some questions about the properties are hard to rewrite. I considered using the question from the U of Chicago text, to get from "3x > 11" to "3x + 6 > 17." But notice that the correct answer -- Addition Property of Inequality -- is difficult to remember and will result in many students getting it wrong. So even here I changed it to the Addition Property of Equality. After all, the whole point of learning the properties is to be able to use them in proofs. The Addition Property of Equality is much more likely to appear than the corresponding Property of Inequality. All including Inequality on the test accomplishes is increasing student frustration over a property that rarely even appears in proofs.
Returning to 2017, let me link to a more recent traditionalist post, Barry Garelick:
https://traditionalmath.wordpress.com/2017/09/11/the-reviews-just-dont-stop-coming-dept/
Here Garelick doesn't link to an article, but just a review from another author, Sinal Singh:
“Barry Garelick is a surly sycophant for all things anachronistic.”
and then he links to his three books on Amazon. So I assume that Singh is an Amazon reviewer. We see that what Garelick considers "traditional," Singh considers it to be an "anachronism."
There's not much to add here. So instead, let me link to another poster, California high school teacher Darren Miller, aka "Right on the Left Coast":
http://rightontheleftcoast.blogspot.com/2017/08/teaching-from-my-head-or-from-book.html
Dang it -- first I mentioned race in this post, and now I'm referring to politics (since "right" in this case means "right-wing"). Earlier, I referred to Miller as a teacher at a rare California school that has a February break (which is more common in places like New York). But in this post, he actually refers to the traditionalist debate:
So at the end of class I asked my students a question. I told them that I'm not fishing for compliments or anything, that I genuinely want to know what works best for them. Do they prefer that I follow the book, where they only have to write some of the things due to the text's fill-in-the-blank style, or do they prefer when I go rogue and teach my way? I wasn't even done asking the question before the chorus arose, loudly and forcefully, "your way."
...that is, the traditional way. I can only imagine what non-traditional method the text uses -- so let's back it up a little:
Yesterday I needed to cover the section about transformation of functions (stretch, reflect, and translate), and today I needed to cover the section about inverses and composition of functions. Looking at how the book covered the material, I just couldn't do it. It's one thing to present in-depth instruction that makes kids think, it's another thing entirely to present the material in such an obtuse way as to allow someone to pretend that the material is in-depth. The textbook authors charted the latter course. Thus, my dilemma.
This is an Integrated Math course (and Miller, like many traditionalists, begins his post with a complaint about Integrated Math), but this lesson is also an Algebra II lesson. The most confusing part is probably the fact that the graph of f (x + h) is the same as that of f (x) translated h units to the left instead of the right.
I recall once teaching this lesson by having students write their name on a index card and pass it one student to the left -- so now each student is holding the card of the student to the right. This is sort of the reason why f (x + h) is f (x) translated to the left instead of right.
I suspect that the text does something similar. The traditional method would be just to tell the students by fiat that f (x + h) and f (x - h) translate the opposite way from what one might expect. So this is how Miller teaches the lesson, and he claims success.
He states that the students did well on the homework. Only problem I have is, what about the students who didn't do the homework? Would they have preferred the textbook's nontraditional methods? At this point, I don't know.
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