Here's an answer key for the test:
1. a. 90 degrees. I could have made this one more difficult by choosing a heptagon, or even a triskaidecagon, but I just stuck with the easy square.
b. Here is the Logo program:
TO SQUARE
REPEAT 4 [FORWARD 13 RIGHT 90]
END
Notice that the side length is 13. I'll still find a way to sneak 13, if possible, into each problem.
2. a. If a person is not a Rhode Islander, then that person doesn't live in the U.S.
b. If a person doesn't live in the U.S., then that person isn't a Rhode Islander.
c. The inverse is false, while the contrapositive is true.
Notice that Rhode Island is the thirteenth state.
3. y = 10.
4. There is a line MN. (M is the thirteenth letter of the alphabet.)
5. Every name in this list is melodious.
6. The equation has no solution. (This question references 13, as 13x appears in the expansion.)
7. a. 13, 11, 9 (descending odds).
b. 13, 17, 19 (increasing primes -- of course, Euclid proved that this sequence is infinite).
8. a = 2, b = 1, c = 3.
9. kite.
10. I discussed this problem earlier this week. It is the same as the problem from the Glencoe text, except that I only drew half of the figure -- the part where a contradiction appears.
Assume that the figure is possible. Then ABC is isosceles, therefore angles A and C are each 40 degrees (as the third angle of the triangle is 100). Then ABO is isosceles (as it has two 40 degree angles), so AO = BO = 3. Then by the Triangle Inequality, 3 + 3 > 8, a contradiction.
11. Through any two points, there is exactly one line. (This is part of the Point-Line-Plane Postulate.)
12. a. KML measures 13 degrees.
b. K measures less than 167 degrees.
c. L measures less than 167 degrees. (This is the TEAI, Exterior Angle Inequality.)
13. a. Law of Ruling Out Possibilities.
b. You forgot to rule out another possibility -- that nothing bad will happen to you today. Hopefully, this will be true for you.
Since it's test day, this is a traditionalists post. None of the major traditionalists have posted this week, except for Ze'ev Wurman. On the Joanne Jacobs site, Wurman wrote the following (sarcastic) comment in response to the Army National Guard dropping its Minuteman logo:
https://www.joannejacobs.com/2019/04/the-minuteman-whos-that-is-history/
Ze'ev Wurman:
We really should have petitioned King George to kindly give us our rights instead of declaring war on him.
Oh, we did that, didn’t we?
I have nothing to say about Wurman's comment here. Instead, I still have more to say about Part I of The Freedom Writers, which I played in class on Monday.
Notice that today's post will not be a racial post. This isn't a vacation post, and I've already had too many racial posts lately. So let's focus on the parts of The Freedom Writers that aren't directly related to race.
For example, on Monday I mentioned the following comment made by a student in the film:
"Why should we respect you, just because you're a teacher?"
Even though this question ultimately leads to a racial argument in the movie, it's possible to look at this question without looking through the lens of race.
It's often said that in past generations, students were expected to -- and did -- respect teachers merely because of their rank. Students who got in trouble with their teachers would find out that they were in twice as much trouble at home. But nowadays, parents of students are more likely to defend their children against the teachers' treatment of them.
This is most noticeable when it comes to grades. Indeed, grade inflation often occurs because when the teachers try to hold the children to high standards, the parents complain -- and the complaints don't go away until the teachers lower their standards.
Thus nowadays teachers don't command respect merely because of their rank. I'm not quite sure when society switched from respect to disrespect as the default attitude to show teachers, but one good estimate is right around the time of The Freedom Writers -- the class of 1998.
Traditionalism, on the other hand, is based on the assumption of respect as the default attitude to show teachers. Traditionalists prefer direct instruction because at the start of a lesson, the teacher knows everything about the lesson and the students know nothing. Only after the traditional lesson does what the students know change from "nothing" to "something."
But if respect isn't the default attitude to show teachers, then students can simply refuse to do any of the traditional assignments, and so they end up learning nothing. Thus traditionalism doesn't work during the current era -- especially when the students are at an age when they are more likely to disrespect teachers.
The question "Why should we respect you, just because you're a teacher?" doesn't mean that teachers should never be respected -- it only means that respect should be earned, not granted. And the one thing teachers can do to earn said respect is to show the students that they care about them -- in short, that the teachers respect the students as well.
Two years ago at the old charter school, there were two things I did that I feared made it appear to the students that I didn't care about them. One involved pencils, the other markers.
I always like to give my students a gift of pencils around the holidays. The problem is that students often didn't come to school prepared and asked me for pencils when the holidays were far away. Not only did I want to teach the students responsibility, but it would water down the holiday pencil gifts if I just gave out pencils to anyone who asked for them throughout the year. What ended up happening was that between the first day of school and the first pencil holiday (Halloween), students came to the conclusion that I didn't give them pencils because I didn't care about them.
In my St. Patrick's Day post, I mentioned at least part of a solution to this problem -- add an extra unofficial pencil holiday about halfway between the first day of school and Halloween. (Depending on the district calendar, some possibilities are the fall equinox and Back to School Night.)
As for the markers, they often dried out and became difficult to see on the whiteboard. My plan was to have about one marker for each student in my largest class (about two dozen) and replace about half of them every time there was a whiteboard lesson (about once a week). I would buy some of the markers at full price and others at the dollar store.
But even this wasn't enough -- some markers dried out before I could replace them. The students complained that I should buy more expensive, better quality markers -- but even the full priced markers often didn't last the week. Once again, the students came to the conclusion that I didn't really care about them -- that I only cared about my wallet and saving money.
There are several things I should have done. I should have made a sharp distinction between student markers to be used for their dry erase lessons and teacher markers that I use on the board. My teacher markers can thus last longer if students aren't borrowing them for their own lessons. The student markers should be purchased by the box, and I should keep them in the box when they aren't used.
Also, if necessary, I could have asked my fellow middle school teachers where they bought markers from -- where I could get markers that last more than a week at a reasonable price. In the case of student dry erase markers that mainly math teachers used, since I was the only math teacher at my school, this is a question I could have asked other math teachers on Twitter.
There were a few other arguments with my students that involved spending money. The English teacher next door had a much better pencil sharpener than I did. Once again, I could have asked her where she had gotten it from. And the support aide even had a small heater -- but during times when she wasn't in the room, students couldn't touch it. The kids assumed that I wouldn't let them touch the heater because I didn't care whether they were warm or not. It's possible I could have asked my support aide where she'd purchased the heater, so I could have bought my own. Then the students could keep warm in my aide's absence.
In The Freedom Writers, Erin Gruwell eventually gains the students' respect when she buys new books for the class -- at her own expense. She must get a second (and even a third!) job just to pay for the books. What does it say about me, then, if Gruwell is willing to make such a huge sacrifice for her class when I couldn't be bothered to get my students pencils.
There are a few other interesting comments at the Jacobs site this week:
https://www.joannejacobs.com/2019/04/what-will-i-earn-what-will-i-owe/
The article is all about college and jobs. One frequent commenter whom I count as a traditionalist is Darren Miller of "Right on the Left Coast" ("right" as in right-wing):
Darren:
Just playing Devil’s Advocate here, but the unspoken thesis seems to be that the role of a college/university is to prepare someone for the working world. In other words, a diploma is a credential, nothing more. Is there to be no learning for learning’s sake? No, we don’t need thousands of Medieval Uzbeki Film Studies majors, but don’t we need one or two just to pass on the cultural knowledge?
And Jacobs, the author of the blog, responds:
Joanne:
Mark Bauerlein argues that humanities professors (except for a few who are pushing retirement) no longer teach history or literature.
Mark Bauerlein -- hmm, where have I heard that name before? That's right -- Mark Bauerlein is the author of The Dumbest Generation, referring to people born between 1978 and 2008.
Bauerlein is the only traditionalist I ever directly mentioned in the classroom. (I did briefly start to talk about something Bill wrote, but I abruptly stopped as it didn't lead to anything.) Two years ago at the old charter school, I wanted my seventh graders to know why I was giving them a Dren Quiz -- and so I told them that it was to challenge Bauerlein's name for their generation. I wanted them to show that they can do basic math without a calculator.
Notice that I first blogged Bauerlein's book a full year before I started at the old charter. But here's the problem -- what's appropriate to give as an answer to a question on a blog might be inappropriate to tell a student.
Here the question I answered was "Why do we have to take Dren Quizzes?" The best answer to almost any "Why?" question in the classroom is "Because I said so!" But my response that day was essentially "Because Mark Bauerlein said so." As I wrote earlier, teachers must work hard to earn the respect of their students. But instead of getting them to respect me, I was more or less trying to get them to respect Mark Bauerlein.
And in the end, the students didn't respect me when I gave that answer. One girl in particular thought that I was personally insulting her, and she told her mother this. (After all, Bauerlein wasn't the one in the classroom talking to her -- I was.) And I just wrote above about how parents strive to protect their children these days.
Jacobs links to Bauerlein's own blog. I notice when I click on his name that he's been blogging at this site for years. Ironically, the article currently at the bottom of the first page of his archive is dated September 2016 -- exactly the month when I invoked his name in my classroom.
The particular Bauerlein article to which Jacobs links mentions race -- and I already promised that this is a race-free post, and so I won't link to the article. In fact, I choose not to link to Bauerlein's website at all, since most of his posts are deeply political.
It's obvious that Bauerlein is a political conservative. I have no problem with quoting or linking to conservative (or for that matter liberal) writers -- after all, I just quoted Darren Miller just above in this post. But many of the things that Bauerlein discusses aren't the sort of things that I want to say in front of students -- he disparages other groups besides a certain generation.
It's notable though that The Freedom Writers were born right at the start of the generation that Bauerlein disparages. Indeed, it's not a coincidence that this is also one of the first cohorts that didn't automatically respect their teachers. I myself graduated a year after The Freedom Writers did, also placing me at the start of Bauerlein's disparaged generation. Bauerlein is an English professor, and so it's when our classes of 1998 and 1999 reached college that he started to notice a change that marked the arrival of his disparaged generation.
Once again, I point out that the definition of "Millennial Generation" often varies, but Bauerlein's disparaged generation covers all definitions of "Millennial." Actually, I'd argue that The Freedom Writers and I are the last members of Generation X, since we graduated in the old millennium. (By my definition, a Millennial was born in the old millennium and graduated in the new millennium.)
But we definitely mark the start of Bauerlein's disparaged generation. An interesting question is, when does his generation end? His main thesis is that technology has ruined the ability of young people to think, so that as long as that technology exists, the generation continues. His disparaged generation could last a century or even longer.
Yet that contradicts any reasonable definition of "generation." To the extent that Bauerlein has labeled my cohort the start of his worst generation because of how we acted once we reached college, he can't react to how my middle school students will act in college because they haven't made it there yet. My declaring 2008 the end of Bauerlein's worst generation simply refers to the year he wrote his book.
Thus it's possible for this generation to be replaced with a new one -- The Smartest Generation. It's possible that my students could be part of this new generation, but only if they work hard. And even if my students weren't part of the new generation, students born after 2008 will very soon reach middle school -- at which point I can no longer claim that both they and I are in a single generation at all, much less Bauerlein's worst generation.
So perhaps this is what I should have done. Instead of declaring both my students and I are in Bauerlein's worst generation, I tell them that I'm in that bad generation, but they won't be, provided that they work hard in my class. They should use technology to gain knowledge, rather than use technology as an excuse not to gain knowledge.
Better yet, I can make this point without mentioning generations at all. Instead, I tell them that my goal is to build The Mathematical Majority. This is a world in which technology has progressed far beyond what it is today. It is a world in which people can enjoy a vacation on the moon or Mars, or enjoy a staycation using virtual reality technology, and so on.
But in order to develop this technology, we need more people to be good in math. Under The Mathematical Majority, a majority will answer "yes" to the question "Are you good at math?" And I will not stop until that majority is achieved.
The last Jacobs link that I'll post today is another article by Jasmine Lane, the English teacher who insists that her students have a strong grasp of grammar:
https://www.joannejacobs.com/2019/04/i-did-well-at-my-level-till-i-failed-in-college/
And indeed, Lane herself leaves comments at this link. Let's start though with Momof4, a frequent commenter at the Jacobs site:
Momof4:
Even assuming they have average intelligence and decent motivation, I don’t understand how that works with kids who are far behind grade level. For example, what about 9th-graders who read at a 4th-grade level (and write below that) and therefore cannot read HS-level English works, history or science textbooks? I understand that is not uncommon in too many schools. How can they “experience success with grade-level materials, writing and discussion”? It sounds nice, but is that possible, let alone scaleable?
As soon as I read this, I immediately think about The Freedom Writers again. These are indeed students who read far below grade level. Furthermore, in the film, the head of Erin Gruwell's department echoes Momof4's concerns -- the students won't be able to read grade-level texts. Gruwell asks the head for some copies of Romeo and Juliet -- and Momof4 even mentions the famous Shakespeare play in her next comment:
Momof4:
It seems to me that giving such kids the kind of instruction you mention to get them to the place where they are able to read, independently, about Romeo and Juliet from a stories from Shakespeare book would be much more useful and desirable. Not everyone needs to do text analysis of classic lit.
At my small-town HS, in the 60s, the two biggest differences between college prep and regular English were the former’s greater focus on text analysis of classic lit and its greater focus on the academic writing that colleges expected – and everyone entered HS with solid literacy, numeracy and general knowledge (thanks to explicit instruction, across all disciplines, from our 1-8 teachers). However, not all were expected or prepared to do college-prep work. Today, if we could get everyone of reasonably average ability to that level at the end of HS, that would be real progress.
In the movie, the head similarly discourages Gruwell from assigning Romeo and Juliet.
Here is Lane's response to Momof4's first comment:
Jasmine Lane:
Hi! I have seen this possible in a number of cases. Namely, the school I student teach at now. Students at a lower reading level need things explained more in depth, which in return actually helps all students learn better. Just because a student cannot read the words fluently does not mean they can’t understand the content– it just means that their cognitive load is tied up in trying to decode, so the content is being lost. Reading is also background knowledge + decoding, so I also make sure to include a lot of knowledge that is necessary to comprehension. I write about that in my latest post in teaching “To Kill a Mockingbird” to classes that have about 3/4th of the class an average of 3 years behind grade level.
To your point, if a students is still in the K-3 reading level, then yes they have a much harder time because they are lacking phonics instruction. This is why we read aloud together, offer audiobooks in addition to the textbook. Additionally, so long as I teach using evidence-based practices with a lot of supports (scaffolds), modeling and guided practice, they should be able to experience success. Will they jump 5 grade levels in one year? No. But I would hope that they get at least 2 yrs of growth if I provide quality by whole-class teaching plus any interventions they are receiving.
Notice that Lane is still a traditionalist -- she explains things in depth, and she also mentions direct instruction in a later comment. On the other hand, Gruwell's students didn't respond well to her traditional grammar lesson. Once again, this could be because Lane's students, unlike Gruwell's (at that point in the film), knew that their teacher cared about them, so they're willing to do more for her.
As for the rest of this long comment thread, there are several racial comments -- once again, I promised you that I won't bring them up in this post.
Some of the non-racial comments involve grading. The concern, once again, is grade inflation -- how does one assign grades in a class were nearly everyone is below grade level? If a freshman starts the year reading at a sixth grade level but ends the year at the eighth grade level, what letter grade should that student receive?
One side of the argument is that giving that student any grade other than "F" makes it seems as if the student is more prepared for college than he/she really is -- a "C" should represent achievement at grade level (ninth) . But the other side argues that in that case, 100% of all students in such a class would see no letter other than "F" on the report card, which is undesirable.
There is no simple solution to this debate. Instead, let's worry about the letter grades that our students will receive on the Chapter 13 Test.
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