1. Pappas Page of the Day???
2. An Epiphany About a Special Scholar
3. August 2016: She Is Isolated
4. September 2016: She Loses Her Phone
5. October 2016: She Fails Her Threes
6. November 2016: She Earns Her Grades
7. December 2016: Her Cousin Arrives
8. January 2017: She Misses Science
9. February 2017: She Celebrates Her Birthday
10. Conclusion: New Mersenne Prime and Phi Day of the Century
Pappas Page of the Day???
This is what Theoni Pappas writes on page 67 of her Magic of Mathematics:
(oops)
Oh yeah, that's right -- we're not reading the Pappas book anymore, because it's 2018. This year marks the grand return of her Mathematical Calendar.
I wrote that from now on, I'll only write about Pappas if her calendar has a Geometry problem. Well, lo and behold, today's problem is indeed Geometry:
What is eight less than the number of faces of a truncated parallelopiped?
Well, the word parallelopiped appears in Lesson 9-2 of the U of Chicago text. We've never truly covered Chapter 9 on the blog before, but we will very soon. In fact, we're less than two weeks away from reaching Lesson 9-2. Anyway, here's what that section writes about parallelopipeds:
"If the base of a prism is a parallelogram, then the prism is a parallelopiped. All the faces of a parallelopiped are parallelograms, and opposite faces are congruent. A box is a right parallelopiped whose base is a rectangle. Thus its fancy name is rectangular parallelopiped. In this box the simpler name, box, is usually used."
Students are asked to find the volume of a non-box parallelopiped later on, in Lesson 10-5.
On the other hand, truncated polyhedra don't appear in the text at all, except for a truncated pyramid in Lesson 9-3. But truncated actually means something else in this context.
Loosely, a truncated polyhedron is one obtained by "cutting off the corners" of the polyhedron:
http://mathworld.wolfram.com/Truncation.html
Notice that the first example given at the link above is a truncated cube. Of course, a cube is a parallelopiped (since a square is a parallelogram), and so a truncated cube really is a truncated parallelopiped as well. The most famous truncated polyhedron is the truncated icosahedron -- also known as a soccer ball.
We need to find the number of faces. It's easy to count the number of faces of a truncated polyhedron, as we simply add the number of faces and vertices of the original polyhedron. This is because in truncation, all the original faces remain faces of the truncation polyhedron, while "cutting off the corners" replaces each vertex with a tiny polygon.
Since all parallelopipeds (including the cube) have six faces and eight vertices, the truncated parallelopiped has 14 faces. We are asked to subtract eight from the number of faces, the final answer is 14 - 8 or 6 -- and of course, today's date is the sixth. Yes, it's been a whole year since we've been able to give the date as the answer to a Pappas math question.
Meanwhile, the Pappas calendar may be back this year, but so far there's no sign of any sort of MTBoS Blogging Initiative for 2018. Then again, it's just as well -- I'm sure whether I really wanted to participate this year anyway.
An Epiphany About a Special Scholar
Today, January 6th, is also known as Epiphany. It marks the end of the Twelve Days of Christmas and is celebrated in various cultures in different ways. For example, many of my seventh graders from last year might be celebrating Dia de los Reyes, or Three Kings' Day (as in the Three Magi).
By the way, there is often confusion regarding Gregorian Epiphany and Julian Christmas. In the Gregorian Calendar, Epiphany is January 6th due to the tradition that it took twelve days for the Three Magi to meet the newborn babe. It has nothing to do with Julian Christmas, which is on January 7th because Gregorian January 7th = Julian December 25th. (Over the centuries, the Julian Calendar had 13 additional February 29ths that don't exist in the Gregorian Calendar.)
Indeed, the Julian Calendar has its own Epiphany -- often called "Theophany." It falls twelve days after the Julian Christmas, so it works out to be January 19th. (Part of the confusion stems from the fact that the Armenian Church celebrates only Epiphany, not Christmas -- and then it's in the Julian Calendar on top of that, so that January 19th is the day of celebration in that country. This explains why there are so many dates associated with Christmas, depending on whether it's the Gregorian or Julian calendar as well as whether it's the Nativity or Epiphany that is being observed.)
Of course, an epiphany is also a sudden revelation -- and for me, I've made the realization about why my classroom management failed last year. And so I celebrate Epiphany in this post by writing about this sudden revelation. This also fits the new year -- in my New Year's Eve post, I announced seven resolutions in the hopes that I can fix the defects in my management plan.
Over the summer, I wrote a lengthy post about my management problems from last year. But because I made a brief reference to another teacher job that I ended up not taking, I marked the post for deletion, and ultimately erased it in October (around the time of my milestone 600th post).
Now I'll restore what I wrote in that post. I'm dropping references to phantom teaching jobs and then adding in connections to my seven declared New Year's Resolutions. I discuss the seven months I spent in the classroom, including one huge mistake I made each month. As it turns out, these seven errors correspond roughly to the seven resolutions -- each resolution fixes a huge mistake.
I wrote that there's one student I want to write about in particular. Even though I'm not proud of my interactions with several students, there's this one girl I definitely wish to reflect upon in more detail. Indeed, my interactions with her represent everything that was wrong with my style of management.
She was an eighth grader with special needs. As I mentioned before, she wouldn't want me to go into the specific details here on a public blog, so I won't. And it goes without saying that I won't post her name on the blog.
So how should I refer to her in the post? Instead of "the special ed student," let me say "the special student" since she really was special. Or better yet, let's call her "the special scholar," since our old school regularly referred to students as scholars.
This post gets the "traditionalists" label, since I mention traditionalists a few times in this post.
August 2016: She Is Isolated
When the school year started, I wasn't sure what to do about the seating chart. I knew that if I tried to assign seats, the middle school students would have just disobeyed me and sat next to their own friends instead. This was bad when I was still trying to learn the students' names! So instead, I decided to open the year by letting the students choose which group of four desks to join. That way, they were more likely to be compliant until I learned their names. Then once I knew their names, I could change their seats to separate friends who talked too much.
And there we have it -- that's the first management error I made last year! I was afraid to ask the students to do something -- like sit in the seats of my choosing -- because I was certain that the students wouldn't comply. Of course, I admit it's tricky to handle discipline issues until I learned their names, and I wanted to avoid a vicious cycle -- I can't learn their names unless I'm sure they're in the right seat, but I can't be sure they're in the right seat until I've learned their names. Still, I sent the students a completely wrong message at the start of the year -- if I predict that the students won't follow my direction, then I'll go out of my way to avoid giving that direction in the first place.
Indeed, there was a flaw in this plan when it came to my 13 eighth graders. There were five boys and eight girls in the class. And of those eight girls, five formed a group of friends -- I supposed they'd be best described as a clique. (The girl who would celebrate Kwanzaa was also a member of this eighth grade clique.) So we immediately see the problem -- I was dividing the class into groups of four, yet this was a group of five girls. One girl had to be left out, and that one turned out to be -- you guessed it! -- the special scholar.
The fact that there were five guys in the class didn't cause a problem for seating, because one of them liked hanging out with the girls anyway. So he ended up sitting with the three non-clique girls. Only the special scholar was isolated.
(By the way, this also caused a problem in sixth and seventh grades when dividing the class into groups for Illinois State STEM projects. I'd need to divide into groups of two or three for a project, so I asked the students to divide in order to avoid arguments. But then arguments would occur anyway as four students would try to form one group, while another student is isolated because he or she doesn't get along with any of the four. The problem is that letting the students form friendship groups is that they're rarely all of the correct size.)
In my "Day in the Life" posts, I often write about the special scholar. But as I look back at those old posts, it's often hard for me to determine which student is the special scholar because I was trying hard to conceal the kids' identities. From my August 16th, 2016 post:
11:25 -- My eighth grade class arrives. This is my smallest class, with only 12 students -- but there are only eight students present at the start of class. I begin the class the same way I start all my classes, with a Warm-Up question:
What is 2 * 2 * 2 * 2? (That is, 2 times 2 times 2 times 2.)
Most students answer correctly, although a few tried to add. A student or two is upset that the very first thing we do on the first day of school is multiply. I point out that the answer is 16 -- and that today is the 16th. I always go around to stamp correct papers -- many teachers point out that students enjoy getting stamps, and my students are no exception.
11:35 -- My student support aide arrives -- the English teacher and I are each assigned one. Actually, she arrives with the four missing students, all girls.
First of all, I believe that all four girls who arrived late were clique girls, and that the special scholar was one of them. Apparently, one clique girl arrived on time, but I doubt that she was the special scholar, for then she wouldn't have been isolated (as three others would have joined her).
I wrote that there were only 12 students that day, not 13. I believe that the absent student that day was the guy who liked the girls. This is because I remember trying to get the special scholar to sit with the three non-clique girls, but she refused. She'd rather sit alone than with the three girls she disliked.
And that's the second management mistake I made that day -- I told her to sit with the three girls she didn't like, and she sat alone instead, and I just let her sit there. That's another bad message I sent -- if students don't want to follow directions, they can just refuse to obey without any consequences. I should have, at the very least, compromised and told her that she had to sit with the other three girls only for the one activity that required groups of four (Dan Meyer's Personality Coordinates) and that she could sit by herself as soon as that activity was complete. This would have been better than just letting her disobey me. After all, over the course of the year I would ask her to perform hundreds -- if not thousands -- of tasks that she doesn't want to complete. And yet she would be expects to perform all of those tasks.
I also believe that the special scholar was the student who complained about my first Warm-Up, even though I wrote about it at 11:25 and she didn't come until 11:35. After the tardy students arrived, I assigned them the Warm-Up, and that's when the special scholar arrived. And now we can see why she complained -- having to do that math problem was the insult on top of the injury of having to be separated from her friends!
Now that we've identified the 2 * 2 * 2 * 2 complainer as the special scholar, let's look back at the rest of the August 16th, 2016 post to see how she reacted the rest of the period:
By the way. some students believe that they have a solution to the Konigsberg problem, but actually they are crossing one of the bridges twice (they start on island D, cross the bridge towards C, but then head back to D). I start to explain about Euler and why the problem is impossible -- and as I do so, the student who earlier complained about 2 * 2 * 2 * 2 figures out that the impossibility has to do with there being an odd number of bridges from each land! I'm impressed!
Along the way, I explain that a "dren" is a reverse-nerd -- a nerd is someone who's good at math, and a "dren" is someone who doesn't understand the basics of arithmetic. As it turns out, the student who complained about 2 * 2 * 2 * 2 enjoys this song and looks forward to my next song.
So as we see, the special scholar does some special things during the remainder of the class! Despite our initial stumble, maybe our interactions started off on the right foot after all.
My next "Day in the Life" post was my monthly post -- August 18th, 2016, the third day of school. I didn't write about the special scholar in that post -- the only eighth grade girls I mentioned (playing with a stamp pad) were non-clique girls, and the special scholar was not involved.
But I do remember a few other things about that day. By now the 13th student (the "lover boy") had arrived to sit next to the girls. There was also a 14th student who showed up, another girl. I ended up seating her next to the special scholar. The new girl was neutral among the cliques, and I recall that she was very smart as well.
Oh, and as for the song I sang that day -- Square One TV's "Count on It" -- I remember that the special scholar liked this song very much, even more than "The Dren Song."
The following week, I did get into a few arguments with the special scholar. Sometimes she would try to sit with the rest of her clique by pulling up a fifth chair. When I wouldn't let her, she would at least move to an empty seat on days when one of the other four clique girls was absent. (Again, the idea --that letting the students choose the seating chart would avoid disobedience -- was flawed because it didn't account for their being five friends with groups of four.) But I didn't want any students moving during Benchmark Testing Week.
When the Benchmarks were completed, the special scholar was among the lowest scoring. The top score belonged to the new girl -- the neutral girl.
As I reflect upon my interactions, I wonder what I could have done to improve them. And this leads to my first New Year's Resolution for 2018:
1. Implement a classroom management system based on how students actually think.
This goes back to the original New Year's Resolution for 2016 that, of course, I'd long forgotten by the time August came around. Mathematician Dave Kung recommended that his viewers avoid paradoxical thinking, yet my classroom management was based on paradoxes.
I didn't force the special scholar sit next to the other three girls because I didn't want her to think that I was mean. Instead, she realized that she didn't have to obey my instructions, and so from that point on she seldom followed my directions. As you'll see later in this post, I would end up doing meanER things to her to make her play.
Another paradox occurs when students claim that it's "unfair" of me to make them follow rules. But most of the time, they're just saying this because they don't want to follow rules. Indeed, students who genuinely believe that I'm unfair rarely complain -- instead, they give me the silent treatment.
Thus if I'm to become the ideal classroom manager, I must know that my goal is get the students to stop saying that I'm mean or unfair -- not to get them to stop thinking it. If the students say that a punishment is unfair, punish them anyway. After the first ten times or so that I punish various students, they'll probably stop saying that I'm unfair. They'll follow my instructions grudgingly -- but they'll follow them nonetheless.
And of course rules such as "respect order" (mentioned in a Summer 2016 post) are too vague. I should just tell the students to follow my directions or face consequences.
Let's return to the first day of school and how I treated the special scholar. On that day, I posted that perhaps I should have reversed the order of the activities. Here is the revised order:
1. Warm-Up: If you don't know the answer....
2. Personality Coordinates
3. Music Break
4. Bridges of Konigsberg
5. Exit Pass: What is 2 * 2 * 2 * 2?
Again, I wrote this because the Pappas-like Warm-Up questions would soon be blocked by the Illinois State Daily Assessment Questions. Thus I should have established the Pappas questions as the Exit Pass, not the Warm-Up. And I believe this order would have helped the special scholar.
First, she's not turned off by entering the question and beginning with math right away. Instead, we begin with the scavenger hunt to complete the Warm-Up phrase (...at least know where to find it) -- or perhaps Personality Coordinates would have started, since she did arrive late that first day. With the group assignment earlier in the period, it would have been more obvious to her why she had to sit with the three girls she didn't like. I should give her a "teacher look" if she refuses to sit down.
When the special scholar finally sits down with the group, I should then praise her for following my instruction despite her opposition to sitting there -- and then ask her to tell me her name. This is how I should learn their names -- giving an direction and then praising for following it.
After the group task is complete, I praise her again for completing the assignment and then allow her to sit alone. As it turns out, it would become beneficial to let her sit alone in the long run (when the neutral girl would sit next to her). When she succeeds on the bridges activity, praise her again. I should have strongly praised her for figuring out the solution to the Konigsberg bridge problem on the first day of school. This will put her in a better mood when it's time for the Exit Pass and the dreaded multiplication problem.
I shouldn't have needed the Benchmark Tests to know that the special scholar was one of the lower students -- her reaction to 2 * 2 * 2 * 2 should have been sufficient. I should have known that this student would need extra help -- and started thinking about how to provide it to her.
I could have taken advantage of both her desire to sit with her friends and her enjoyment of "The Dren Song" and "Count on It" and used these as incentives. If, say, she answered the Warm-Up question on her own, then I could sing her one of her favorite songs. Clearly, I enjoy playing music (as you can plainly see by the music mentioned in this and other recent posts), so I should have made better use of music in my class. Any if one of her four friends was absent, then I could allow the special scholar to move as part of the Warm-Up reward.
The only thing was to make sure that she didn't cheat -- it would be so easy for her to copy the answer from the neutral girl, who of course would have the correct answer. It would be better for me to sit down with her and work on the problem together -- and since there was only one other student in her cluster of four, there'd be a place for me to sit. We'd work together, and if she contributed sufficiently to the problem, I'd give her the reward.
But instead, once I removed a song poster from the wall, I wouldn't sing that song. She certainly did not enjoy the song about "Benchmark Tests."
Finally, as I wrote in previous posts, I need to separate bad academics from bad behavior. When she failed to answer 2 * 2 * 2 * 2, this was a case of bad academics -- she needed help, not punishment. I remember one day when I was telling her about how not to be a dren and she asked, "Will you be able to help me then?" I should have responded with a resounding "Yes!" Maybe then she would have understood why her seat had to be isolated -- so that it would be easier for me to help her. And of course the neutral girl was there to assist the special scholar as well.
This is how I show the special scholar that I don't want to be mean to her. This is thinking outside the box -- but first there must be a "box," the basic set of rules to be followed. And I establish this via the first New Year's Resolution:
1. Implement a classroom management system based on how students actually think.
September 2016: She Loses Her Phone
After lunch was computer practice on IXL. The eighth graders were scheduled to have IXL on Mondays and Thursdays, while the sixth graders had it on Tuesdays and Fridays. Notice that the seventh graders didn't have IXL, while no one had it on Common Planning Wednesdays.
Let me take the time to describe how IXL works. (I hinted at this in my last post, but let me write it out now.) Students select a grade-level standard that would be assigned a letter and a number. Here are some of the eighth grade standards:
I.1 Find the constant of proportionality from a table
K.8 Multi-step problems with percents
DD.5 Quartiles
Let's say that I assigned my students Standard I.1. The computer then begins each student with a score of zero. Correct answers gain points for the students, and wrong answers lose points. Just like the SBAC, the practice is computer-adaptive, so higher scores lead to more difficult questions. The student is considered to attain mastery by reaching a score of 100.
I've noticed that the number of points gained for a correct answer depends on the current score. If the current score is in the single digits, then a correct answer is then points. If the current score is between 10 and 19, then a correct answer is nine points. If the current score is in the 20's, then a correct answer is eight points. The Challenge Zone is the 90's, where a correct answer is one point.
According to this pattern, a student must answer at least 28 questions to reach a score of 100. Here is the running score if all 28 questions are answered correctly:
10-19-28-36-43-49-55-60-64-68-72-75-78-81-83-85-87-89-91-92-93-94-95-96-97-98-99-100
I'm not quite sure how many points are deducted for wrong answers. I think the intention is for the deduction to be one point from a current score of 1-10, two points from a current score of 11-20, three points from a current score of 21-30, and so on. But I don't think that the deduction in the Challenge Zone is actually a full ten points, but something like eight or nine points.
I believe the intention of this scoring system is that the current score is approximately equal to the percentage of answers that need to be correct to maintain it. If the current score is, say, 55, then correct answers gain five points and wrong answers lose six. So students need to get slightly more than half right (about 55%) to maintain that 55. If the current score instead is 72, then right answers gain three and wrong answers lose eight. So students need to get about 72% correct in order to maintain that 72.
If the current score is 99, then only one more question is needed for mastery. A score of 99 is reached after getting eight challenge questions right (since the Challenge Zone often starts at 91). But if the next answer is wrong, the score drops to something like 91, and then the student goes from being one answer away to being nine answers away -- and I admit that this sometimes frustrates students (since these are, after all, challenge questions). But this is the only way to make the percentages consistent, as the 99 score is surrounded by 17 out of 18 correct answers (which is 94%, not 99%, but it's close).
In previous posts (under the traditionalists label), I've mentioned how the SBAC fails to take full advantage of his computer adaptability. Instead of the reported scores being as simple as 1, 2, 3, or 4, students should receive a three-digit score, where the first digit refers to grade level. This way students can score above or below grade level rather than just 1, 2, 3, or 4.
It may be appealing to use IXL scoring for such a computer-adaptive test. A score of 310 refers to a third-grader just beginning the test with an IXL-like score of 10. If the next question is right, the score rises to 319, and if it's wrong, the score drops to 309. A score of 868 refers to an eighth-grader who is approaching proficiency. If the next question is right, the score rises to 872, and if it's wrong, it drops to 861, and so on.
But this scoring system may be too punitive in the Challenge Zone. A student with a score of 397, just three answers away from the fourth grade questions, may get a challenge word problem wrong and have the score drop to 389. The student may end up stuck in the 390's due to an inability to solve the word problems, yet could answer the simplest fourth grade questions (which could be something like single-digit division) quite easily if only the student could get to 400.
There are two ways to solve this. One way is for the computer to start asking fourth-grade questions in the 390's after, say, three mistakes in the word problems.
The other is to use a reverse-IXL scoring system. In the 310's, instead of either gaining nine or losing two points, students can gain two or lose nine points. In the 390's, students can only lose one point, and instead could jump right into the 400's with one correct answer.
This is closer to how traditionalists might like the test to be set up. The 00's can be reserved for the easiest questions, like one-digit multiplication (in third grade), one-digit division (in fourth grade), and so on. Students should have to answer ten of these right without missing one in order to get out of the 00's and into the 10's. On the other hand, they only need to get one word problem correct. So the emphasis is where it belongs -- on the basics.
I can go on and on about this scoring system, but now I'm straying from my original intention, which was to explain how IXL works and what my sixth and eighth graders went through twice a week. But here's the thing about IXL -- I didn't grade it. So in reality, there was no incentive for the students to answer any questions at all!
Some students were highly motivated to work. This included the neutral girl. Because IXL is highly personalized, I thought it might be a good idea to have her work on Algebra I questions -- especially considering that our school, with only 14 eighth graders, didn't offer Algebra I. I was hoping that if she succeeded, I could write her a letter of recommendation at the end of the year. Of course, that recommendation would be to place her in Geometry for her freshman year at her new high school.
But the neutral girl struggled a little with Algebra I. After all, IXL doesn't actually teach math, but only reviews it. I'd have to teach her the algebra on the side -- and I was usually too busy. Instead, the girl usually stuck to Common Core 8 questions, albeit on more advanced standards than what the rest of the students were doing.
In the end, the girl left our school in mid-September -- in fact, it was right at the end of the Willis Unit (or Wong Unit) marking the start of the year. So in the end, I wouldn't have been able to recommend her for freshman Geometry even if I had taught her Algebra I. I used her leaving as an opportunity to make a seating change, since by now I knew all the students' names. The 13 remaining students were divided into six groups of two, with one student sitting alone in the back.
Now some students were less interested in working on IXL. And you can probably figure out who one of those students was -- the special scholar.
During IXL time, many of the students felt that they needed more help, and I couldn't assist all of them at once. (Recall that my support provider was never in my room during IXL time, as this was when she was preparing for her P.E. class.) Many of those students criticized me for not helping them often enough.
For the special scholar, IXL was a struggle. Sometimes she would make it to the 20's or 30's, and then keep on getting wrong answers. Even though the clique was mostly separate, the special girl was now seated with the clique leader, who was smart but lazy. Sometimes the leader would cheat for the special girl and answer the questions for her. Other times both girls would move seats and meet with a third clique member, who would then answer the questions for both of them.
Clearly, the one time of my day that should have been more organized was IXL time. A stronger classroom manager could simply ask the students to work on the ungraded IXL and they'd obey, but a novice manager like myself needed something tangible to hold the students accountable.
I should have implemented an IXL accountability form. On this form, students would record which standard they practiced, and what the running score was. Since my old school didn't have D grades and required at least a C grade to be passing, it would be a good idea to require a score of 70. If a score of 70 is attained, the student would earn one participation point. A second point could be earned for a mastery score of 100, so that the student wouldn't just stop at 70 and call it a day. On the other hand, if a student didn't earn 70 due to being lazy or off-task, punishments would begin.
For the special scholar, I could work with her one-on-one and double her scores, so that if she were to earn a score of 35, I'd count it as 70 and give her the point. I'd much prefer that she work hard to earn the 35 than just to cheat and earn a 70, or even a 100.
The IXL accountability form would have also been helpful in my sixth grade class. This class was much larger -- unlike eighth grade, there were more sixth graders than laptops. Some students would be left without a laptop -- I had often tried to give them something else to do, but it was always such a struggle to keep the IXL students on task (and often it was because many of them could never remember their IXL password) that I couldn't focus on those without a laptop. So students without laptops end up treating IXL time as free time -- and in fact, some students would intentionally pass their laptops to others in order to get that free time.
With the IXL accountability form, students without laptops must answer questions. We notice that on IXL, a student must correctly answer at least 11 questions to attain a score over 70. Therefore there would be space for eleven answers on the form. I'd write the 11 questions on the board for them to copy and answer, and all of them must be correct or else they must redo them. This should eliminate students intentionally giving away their computers.
There were several special ed students in sixth grade as well. Once again, those students would only need to earn a score of 35 on IXL. If they don't have a laptop, then they only need to answer four questions on the form, since only a minimum of four questions are needed to surpass 35 on IXL.
Finally, one problem during IXL time was keeping the laptops organized. I had noticed that the Monday coding teacher would have the students plug the laptops into the cart in numerical order, and I'd tried to do the same with the IXL laptops. (Notice that the coding Monday laptops are not the same as the IXL laptops.)
But I was made to feel wrong for insisting that the students put the laptops away in order. I had assigned the laptops to the students. These were numbered in order in the 600's (for sixth grade, since that was my official homeroom), but some numbers were skipped. At the end of IXL time, I would call up each number in order, so the students could put the laptops away. The problem would be when the student with laptop 602 would insist that he be given a few more minutes to answer two more questions on IXL, while the student with laptop 620 impatiently leaves the laptop on the desk and starts heading out to P.E. class. And the same students wouldn't complain at all when it's the coding teacher who's telling them to put the laptops anyway in order. They only complained if I was the one telling them to do so -- in other words, they neutered the "laptops in order" rule.
First of all, I should have taped in laptop numbers to the slots on the cart. This way, I could call the groups in order by readiness, rather than insist that student 620 wait for 602 and over a dozen more students to put laptops away first. Second, I should have come up with a punishment for those who don't put the laptops away correctly. I knew, of course, that simply denying the student a laptop the next day isn't an effective punishment and indeed, may be seen as a reward instead. The IXL accountability form would have taken care of that problem.
Two weeks after the neutral girl moved away, I had a heated argument with the special scholar. I've recorded this argument in my September 26th post:
It begins as my eighth graders arrive. Usually, the coding teacher arrives 20-25 minutes after the block begins, so I use that time for a Warm-Up and passing out the homework for the week, and then the students can use the extra time to start on the homework until the coding teacher gets here. I pass out calculators for the Warm-Up, since it is still on square roots and irrational numbers.
But then the students continue to use the calculators on the homework. The questions on the homework (that come from a practice workbook) aren't quite dren-level questions like single-digit multiplication -- indeed, the first question is long division. But still, this is the type of question that some people (like traditionalists, for example), say should be done without a calculator.
Of course, you readers may notice that this is homework, and so there's actually nothing stopping them from using calculators at home to do the homework. Nonetheless, I'll do whatever it takes to stop them from using calculators in front of me on the homework.
So I take the calculators away. And this causes one student -- and she happens to be the lowest student in the class -- to say, "I need the calculator because I'm not smart like you are!"
I know that from a traditionalist perspective, the people who can do long division by hand are actually the normal ones and those who can't divide are on the outs! I don't bring up traditionalists in class anymore, but I do say, "I'm not smart -- I'm normal."
The girl's response is, "I need it because I'm not normal like you are!"
The girl I mentioned in this post is, of course, the special scholar. The reason that I used the word "normal" was to emphasize that long division isn't something that only nerds should be good at, but everyone should know how to do it. But the special scholar was clearly offended by my use of the word "normal," because I had implied that she, who struggled with long division, wasn't normal.
I proceeded to write about "a Math Intervention block" (that is, IXL time) that same day:
Keep this in mind as I discuss what happens when the eighth graders return after lunch -- a Math Intervention block that also used for an online math curriculum. The girl enters the classroom upset because someone has taken her cellphone, and so she disrupts the classroom by telling the other students to empty out their backpacks in search of the phone.
At this point I begin to yell at the students to stop the search immediately and get back to work. The problem, I tell them, is that phones are forbidden in the classroom. In theory, all phones are supposed to be confiscated at the start of the day, to be returned at the end of the day. But you can probably figure out why this is doomed to failure -- a student who turns it in is guaranteed to be without a phone for a full seven hours, while someone who keeps it can probably sneak in even just a few minutes on the phone at some point without being caught.
I tell the students that I can't make them turn in their phones, but I can enforce the rules by at least not granting any class time to search for missing phones. The student begins to cry, thinking about what her mother will say when she finds out that the phone is missing.
Then she tries to ask for a restroom pass -- but the problem is that last week, the principal told me that I can't allow restroom passes anymore either. Formerly I've been allowing students to leave during Music Break, but lately they've been taking advantage and using that time to go places other than the restroom. At this point the girl complains, "I hate this class because you care about the rules so much!"
At this point I tell her that if she leaves, I'll have to give her a detention for using the restroom during class time. (Of course she has no intention of going to the restroom -- she just wants to go out and search for the phone.) She accepts my detention and leaves the room. But then the principal shows up to the classroom, having been called in by the English teacher due to the riot in my class. The principal asks for the girl who first caused the disruption, and upon her return from the "restroom," she is forced to go to the office.
Let's step back now and think about what's happening here. Obviously I was yelling at the special scholar, which is generally a bad idea. I write this in my second New Year's Resolution for 2018:
2. Keep a calm voice instead of yelling at students.
The reason that I enforce the rules is that students who use the restroom only during breaks and puts their education ahead of the entertainment of a cell phone find themselves with lots and lots of A's on their report cards. Given a choice between being bored with an A and entertained with an F, I'd always choose boredom with the A.
I've already written about the problems associated with talking about A's all the time. And so this interaction with the special scholar was one of my worst. In that post, I wrote that I continued the argument with sports analogies -- which, of course, don't work with girls uninterested in sports.
Of course, this also goes back to the first resolution. My management was unfortunately not based on how students think. The special scholar asked why she had to follow a certain rule, and I told her it was so she could learn more and earn higher grades. I wrongly assumed that I could convince her to follow the rules by telling her the benefits of learning.
Instead, I should have answered, "Because I said so!" I knew that students don't like this response, but they hate endless discussions about A's even more. Students obey teachers because they want to avoid punishment -- learning more and earning higher grades are, at best, a side effect of trying to avoid punishment.
And indeed, this is how I avoid yelling. I yelled at students when I really needed them to follow an instruction and I knew that they'd ignored me if I merely told them the instruction. Instead, if I follow the first resolution, the students are more likely to comply because they'd know that a punishment is coming, and so I can give the students instructions without needing to yell.
I believe that it was on that day when the special scholar really started to hate me -- before that, I was just another teacher who was annoying sometimes. Indeed, she had liked most of my songs up to and including my last song before the incident, Square One TV's "Nine Nine Nine." But starting with my next song, "Unit Rates," she didn't like most of them.
I ended that September 26th, 2016 post by writing:
So far, I've seen that endless stories about traditionalists, A's, and their futures doesn't work. And of course, yelling at her as I did today doesn't work at all. Of course, there is no simple answer -- otherwise we'd all be excellent math teachers.
Well, now I understand what I should have done about the cell phone incident -- I should have just called the office. Even though the ideal manager tries to avoid calling the office to send a student out of the room, a distraction such as this one merits an office call. Then the administrators in the office could help the special scholar find her phone and I could get the rest of the class working on IXL.
Meanwhile, I know now what to do to avoid both stories about A's and yelling in general situations (other than a missing phone). I simply let the students know that I'm enforcing the rules, and that I'm enforcing them "because I say so." Teacher tone and teacher look may be helpful to avoid arguments, and live up to the second New Year's Resolution.
2. Keep a calm voice instead of yelling at students.
I should have avoided her attempts to neuter the rules. I should have recognized that a student with a weakness for math would have made cheap attempts to avoid learning it. Once she realized that I would enforce the rules, she would have respected my authority, and I wouldn't have felt so helpless that I'd need to yell just to make her hear me.
October 2016: She Fails Her Threes
I've said several times that I won't talk about A's so often. But I still plan on continuing my campaign against "drens." In my October 20th, 2016 post -- one of my most extensive posts on "drens" -- I write about my Dren Quiz schedule:
First, with Quizzes now at only 20% of the grade, I'm giving three Dren Quizzes each trimester rather than four. This dramatically alters the way these quizzes work. When I was going to have four Dren Quizzes per trimester and eleven of them the whole year, I started with 10's and then had the students work their way from 2's to 9's. The two extra quizzes meant that if a student fails (which means anything less than an A, or 45/50), that quiz is repeated, while the other students move on.
But now I'm only giving nine Dren Quizzes the whole year. This means that everyone, pass or fail, will be taking the same quiz. Today is the third quiz, so they will work on their 3's. But my "drop the lowest grade" policy applies to Dren Quizzes -- only two of them actually count. This isn't important now with the students working on 10's, 2's, and 3's. But in the third trimester, when the students work on the difficult 7's, 8's, and 9's, this will make a difference.
Indeed, students who fail their 8's quiz -- the most challenging, according to vjlomocso's chart -- can make it up by passing the 9's quiz.
I proceed by discussing the results of the 3's Dren Quiz:
Of course most of my students pass their 3's Dren Quiz today, but unfortunately, three students (two sixth graders and one eighth grader) ended up failing. There are issues with all three students that, due to their sensitive nature, I choose not to post here on the blog.
And of course, you can figure out which eighth grader failed the 3's Dren Quiz -- the special scholar. I didn't want to reveal the "sensitive nature" of the three students being special ed students. And I still don't want to write much about the issue now. All that matters here is that the special scholar failed it.
By the way, she had no problem with her 10's and 2's earlier -- and due to the grading system that I explained earlier, the 3's Dren Quiz failure had no effect on her trimester grade.
But I believe that the 3's failure motivated her to work harder. At the time of the Dren Quiz, the students were learning about roots of perfect squares and cubes. Just like the Dren Quiz itself, the general quiz required the students to memorize, in this case the square and cube roots.
Meanwhile, it was around October when it became obvious that in my students' eyes, I was below my support staff member on the totem pole. By this, I mean that often students would talk throughout my lessons, and then stop talking only when she arrived. To them, directions from me didn't count -- they only mattered if the support aide or someone else was giving the directions.
This happened one day during a lesson on exponents -- the class was talking during my lesson and stopped only when the support aide arrived. I was upset -- I knew that the students would never learn anything from me if they believed that only her directions counted. And so I called the students out on it and asked, "How come you can't be this quiet when I am teaching?"
The special scholar's replies went something like, "Well, we're quiet now!" and "Why are you wasting time instead of teaching the lesson?"
The third New Year's Resolution for 2018 address the mistake I made with this interaction:
3. Move on from past incidents instead of bringing them up with students.
In this case, once my support aide arrived, the talking was in the past. Bringing it up again did nothing to the solve the problem.
Obviously, my concern wasn't about the past but about the future -- I knew that the next time my support aide left the room, the students would start talking again.
Because of this, my interactions should have dealt with the present and future. Here is what I could have said that would be more in line with the third resolution:
"Good job! The class is now silent. This is what I want the class to sound like the next time our support aide leaves the room."
At this point, I can test the students on this. I can send my support aide on an errand for any random reason -- it could be just to photocopy more Warm-Up sheets. Now I expect the students to start talking again the instant she leaves the room -- indeed, I reckon the first bold student will talk as soon as soon as she opens the door, even before she's actually left. So before she leaves, I say:
"This counts as a warning to the entire class. Anyone who talks will receive a punishment."
When my support aide opens the door to leave and the inevitable occurs, I give the punishment. Then I ignore any protests that the punishment is mean or unfair, since I do make it clear what noise level I desire (namely silence) and what will happen if anyone talks (a punishment).
The third resolution reflects back on the first two resolutions. I don't yell at the student who talks (second resolution), but stick to a solid management plan (first resolution).
Of course, since I didn't do this, in the end the students struggle with exponents. Fortunately, an easier lesson was around the corner -- memorizing basic squares, cubes, and roots.
I gave the general quiz a week after the Dren Quiz, on October 27th. But I didn't write about the results of the quiz until November 1st:
After the final Exit Pass, my support staff member bought a pizza for the eighth grade class. This is to celebrate the scores on their most recent Quiz #3 -- of the thirteen students, ten students received A's and the other three earned C's. The square and cube roots were fairly easy to memorize -- let's see whether they'll be able to maintain their success as we move on to more difficult topics.
And the special scholar was one of the three who earned C's. After the disappointing Dren Quiz, a C on the general quiz was great! I gave the students, in addition to my support staff member's pizza, some Halloween candy as a reward. Each student with an A earned four Tootsie roll pops. Usually the C students earn no candy, but I gave the special scholar one Tootsie roll pop anyway because I knew that she'd worked hard to learn the square and cube roots.
By the way, going back to old posts again, one of my earliest uses of the word "dren" on the blog was back in January 2015:
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.
This is still how I want to use the word "dren" in my classes. I want my students to know that they are too smart to be drens -- including the special scholar. I want to use the word to make them feel smarter, not less smart. So far, my use of the word really did motivate the special scholar to do well on the roots quiz.
Then again, maybe she and the rest of the class would have fared better on the previous exponents quiz if I'd formulated and followed the third New Year's Resolution:
3. Move on from past incidents instead of bringing them up with students.
November 2016: She Earns Her Grades
I never mentioned this on the blog, but when the first trimester ended in November and the students were about to get their report cards, I decided to reveal my own middle school grades. I actually still my old report cards from those grades. Naturally, I showed the sixth graders my Grade 6 report card, the seventh graders my Grade 7 report card, and the eighth graders my Grade 8 report card. My old school graded using quarters, not trimesters -- but that's okay, since I've saved only three report cards from each year anyway. For Grade 7, these were my second quarter grades (since I don't have the first quarter grades), while for the other two years, these were my first quarter grades.
Here are the grades that I revealed:
6th Grade:
Language Arts -- A
Spelling -- A
Math -- A
Social Studies -- A
Multi-Cultural Arts -- A
7th Grade:
Art/Shop -- B
Success -- A
P.E. -- A-
Algebra I -- A+
English -- A
History -- A
8th Grade:
Science -- C
History -- B+
P.E. -- B+
French I -- A
English -- B+
Geometry -- A+
(Yes, I took French in school, which is how I know what "Au Clair de la Lune" means!)
My original intention was to show the students my second quarter marks at the end of the second trimester in March, and then my final marks at the end of the year. But of course, I didn't quite make it to the end of the second trimester.
Regarding the grades that I revealed, of course I liked my sixth grade marks, but I was deeply ashamed of that C that I earned in eighth grade science. This became worse once I was supposed to teach the 8th grade science class! It's not right for the teacher to earn a C in the class being taught.
In my November 10th, 2016 post, I wrote about how my eighth graders fared that first trimester:
Of course, the end of the trimester means giving out grades. As it turns out, none of my eighth graders is failing this first trimester. There were a number of easier topics this first trimester -- and I've said before that I like the idea of giving the students grades before the hard topics come up. This way, students can feel good about themselves and believe that they can succeed in the new trimester on the more difficult topics.
The lowest student in the class managed to scrape barely with a C (recall that there are no D's). I know that she worked hard to pass the last quiz on exponents -- I'm so proud of her! Meanwhile, one guy has emerged as the new top student in the class, and so he easily earned an A this trimester.
I don't quite remember who the "new top student in the class" was. It might have been the eventual valedictorian, but it could have been one of the other guys in the class.
But we can easily figure who "the lowest student" was -- the special scholar. As we see, that last quiz allowed her to pass the class with a C. Recall that at this point, I hadn't taught much science yet. The grade I assigned the students appeared on the report cards as a "STEM" grade -- meaning that both math and science were included in the grade.
So just as we could say that she was a C student in eighth grade math, she was also a C student in eighth grade science -- just as I was a C student in eighth grade science. She pointed out that she had received the same science grade as her science teacher -- and technically, she was correct! And I let her claim the moral victory of having the same grade as the teacher.
By this time, the Pappas-style Warm-Ups had fallen apart, and Illinois State Daily Assessments were now the norm. Since the answers weren't always the date, these computer questions that I projected on the board were more challenging -- especially when I clicked on "hide multiple choice answers."
Many students entered my classroom talking -- and this included the special scholar, who by now was sitting next to one of her friends (the leader of their clique -- the other clique girls had been moved to other groups). Each day the the special scholar and the clique girl would enter the room without ending the conversation they were having. This meant that when it was time to give Warm-Up stamps, the two girls had blank Warm-Up sheets.
Of course, when I didn't give them a stamp, the girls would complain that I was mean and unfair -- that I wasn't giving them the stamp because I didn't "like " them. And then they would hold up the class until I relented and give them the stamp. Other students in the class -- sometimes even other members of their clique -- were upset that I was taking too long with the Warm-Up, which after all the arguing was now spanning 10-15 minutes.
This incident was what I had in mind when I formulated the fourth New Year's Resolution for 2018:
4. Begin the lesson quickly instead of having lengthy warm-ups.
Here is what I should have done with the Warm-Ups. First of all, Pappas-style questions whose answer is the date are to be reserved for Exit Passes -- that is, I should have established the Illinois State Warm-Ups from the very start. Illinois State recommends that the Daily Assessments take about five minutes. Now when I first introduce the Warm-Ups, I give the following reminders:
-- Let's begin the Warm-Up. You have five minutes.
-- There are four minutes to go, yet some of you don't even have a pencil out.
-- There are three minutes to go, yet some of your Warm-Up sheets are still blank.
-- There are two minutes to go, yet some of you have barely started.
-- There is one minute to go. Double-check becayse only correct answers get stamped.
Now the special scholar and her friend receive sufficient warning that they should stop talking and start writing. There's less room for them to complain that I didn't give them enough time.
Of course, that's not what happened. The special scholar concluded that I wasn't stamping her paper because I didn't "like" her, and so she just completely refused to do her Warm-Ups from that day on.
Unfortunately, I got into more arguments with her that week. I mentioned this back in my November 18th "Day in the Life" post. It goes without saying that the girl in this post was the special scholar:
-- On Monday, an eighth grader complained about the Parent Conference week schedule. Nutrition is at 11:05 everyday, but this is after two periods on regular days and three on shortened days. (Other middle schools often do the same -- they have break after 2nd period most days, but after 3rd period on shortened days.) She insisted that it was break and that I couldn't tell time, so I yelled at her.
-- On Thursday, the eighth graders were doing a science lesson with my Bruin Corps member (again, see yesterday's "Day in the Life" post). This was a life science lesson, but it appeared in the eighth grade standards according to our online software. One girl (yes, the same girl from Monday) correctly noted that she learned this lesson in seventh grade (under the old pre-NGSS standards) and therefore she'd refuse to work on the lesson. I was about to login to our website and show her the standards, but she continued to complain before I could get to the site, so I yelled at her again.
Later in that post, I wrote about how I should have avoided the Monday argument (and uphold the eventual second resolution, "no yelling"):
Let's look at, for example, Monday's argument and how I could have avoided yelling at the eighth grade girl:
Me: After this class you will go to English class.
Girl: No, we have nutrition now.
Me: For a participation point, who can read me the schedule written on the board?
Another Student: After this class we go to English.
Me: Thank you. You get a point.
That ends the argument, since now it's no longer me against the girl, but me and another against the original student. The other student is given an incentive -- the participation point -- to side with me and the correct schedule instead of the girl saying the wrong schedule.A similar trick could have worked with the same girl on Thursday. I ignore her when she says that she won't do the science lesson and have another student read the standards from the website. It's even possible that the original girl wouldn't have contradicted me on Thursday -- she might have shown me more respect, because I'd have shown her respect by not yelling at her on Monday!
In subsequent posts (after I learned more about the California Science Test), I wrote that I probably should have focused on physical science (the old standards) with the eighth graders. Likewise, I could have taught life science (the old standards) to the seventh graders. Only to the sixth graders could I have taught the new NGSS standards.
This solves the problem and avoids the Thursday argument. But as I wrote in that post, instead of gaining her respect on Monday, I had lost it. The special scholar would never respect me again from that day on. She might have respected me more if I had kept the fourth resolution:
4. Begin the lesson quickly instead of having lengthy warm-ups.
December 2016: Her Cousin Arrives
In the last section, I wrote that the top student at the end of the first trimester wasn't necessarily the eventual valedictorian. Indeed, several boys in the class could have emerged as the valedictorian. But unfortunately, there weren't as many girls with top grades -- especially not the clique girls.
Actually, there were two girls who had valedictorian potential in the class -- the only problem was that neither one attended our school for the entire year. One of those was the neutral girl who attended our school the first four weeks of the year.
The other was a new student who joined the class right after Thanksgiving. She quickly became one of the top students in the class. She told me that at her old school, she was in an Algebra I class, and so she'd already learned everything that I was teaching.
As soon as I met her, of course I thought back to the neutral girl. I'd wanted to teach her Algebra I during the year and recommend her for Geometry for next year. But she'd left the school so quickly that I never had time to teach her any algebra at all.
But I really wanted to make sure that the new girl could get into Geometry next year. After all, she'd been already enrolled in an Algebra I class at the start of the year. I didn't think it would be fair for her to have to repeat Algebra I as a freshman just because she attended our school. I wanted to do for her what I couldn't do for the neutral girl -- actually teach her Algebra I during IXL time, so she could do well and I could prepare her for Geometry. But I had to wait until the administrators added her name to the IXL roster. After all, IXL accounts weren't free, and thus there were strict controls on who could have an account.
Unfortunately, my interactions with the new girl weren't positive at all. Her seat was right next to the special scholar, who told her all about how I was a bad teacher. And so the new girl didn't like me because of how I had treated the special scholar -- especially the way I'd argued and yelled at her.
Why did the new girl care about the special scholar so much? That's easy -- the girls were cousins.
Notice that it's rare for two siblings to be in the same grade level or same class. Of course, twins are usually in the same grade. It's possible for two non-twin siblings to be born 11 months apart and wind up in the same grade -- and I observed this occurring once, when I was a substitute teacher. But in general, siblings who aren't twins are aged too far apart to be placed in the same grade.
On the other hand, cousins are more likely to be of the same age and grade level. Indeed, several girls in the seventh grade class were cousins. None of these cousins are related to the eighth grade duo, the focus of this post.
By the way, the cousin is not the only relative of the special scholar who attended our school. The special scholar also had a younger sister. I never knew the sister's grade level, but it was definitely one of the elementary grades. In fact, I believe that the sister attended not our charter school, but the district school co-located with us instead. But still, I would see the special scholar walk her little sister, hand-in-hand, to school each morning.
This shows how I could have improved interactions with the special scholar. Each morning, I could have waved to the special sister ("special sister" = "special scholar's sister"), and perhaps even said "Hello," addressing her by name. As a teacher with dozens of students, I can't be expected to know the siblings of all of my students, but I could have at least gotten to know the special sister, especially since I saw the two girls walking to school every morning.
I could tell that the little girl looked up to her big sister -- and I should have said this directly to the special scholar. This might have motivated her to work harder in my class: "Don't do it for me -- do it for your sister." Of course, I shouldn't rub this in her face. I must avoid saying "Do it for your sister" more than once a week -- once a month is more like it.
But let's return to the special scholar and the special cousin. The two cousins were seated together, along with the girl who was the leader of the clique.
Oh, and speaking of cousins, this is something that traditionalists might want to heed. Traditionalists like to point out that teachers don't spend enough time thinking about the top students, instead focusing on the weaker students. They say that it's much better for teachers to satisfy the needs of the top students, even if it means ignoring the weaker students. After all, the top students are the future "heroes" who will make our lives better.
This situation reveals a flaw in the argument. Suppose the top and bottom students are cousins. Then the top student wouldn't want me to ignore the bottom student, her cousin, just to help herself!
Incidentally, the traditionalists will like that the special cousin did ask me why there weren't separate Common Core 8 and Algebra I classes. (The answer, of course, is that there only 14 eighth graders, and we'd hire a science teacher before a second math teacher.) The top student asked me this, even though she knew that if there were two math classes, she'd surely be separated from her cousin, the special scholar.
The week after the new student arrived, I gave a test on volumes of cones and cylinders. I wrote about how the students fared on this test in my December 12th, 2016 post:
Then right after the holiday was the first test of the trimester, and I had to give even more zeros for talking and cheating. Here's how I caught two of my eighth graders -- do you recall the eighth grade test on volume? The problem was that many of my CASIO calculators would convert decimals like 3.14 to fractions, while others would keep them decimals. In fact, one CASIO did neither of these -- instead, it gave answers as mixed numbers. There was only one such calculator, and I knew exactly who had it -- yet three students tried to turn in tests with mixed number solutions!
As it happened, the student with the mixed number CASIO was the special cousin -- and I knew that she was smart, so she didn't need to copy from anyone. One of the cheaters was the girl sitting next to her -- the special scholar. The other cheater was one of the other clique girls who sat at the next table, yet was close enough to copy the answers.
At the time of the test, I had heard sounds from that direction and assumed that the clique leader was the talker. I told her that she was getting a zero, and she responded by ripping up her paper. But after seeing the tests, I knew that it was the special cousin telling the answers to the special scholar. I realized that the clique leader was innocent, and I would have reinstated and graded her test, except that she obviously never turned it in.
Meanwhile, the other student who sat with the second cheater was yet another clique girl. She had left much of her test blank and told me that she didn't get it. Of course, since the answers were blank, she hadn't been involved in the cheating. I didn't like the idea of giving her a score of 50 while the cheaters had copied enough answers to score a 60. So I had to give both cheaters -- including the special scholar -- a score of zero.
Let me post a German word now -- Schadenfreude. It comes from, "misfortune" and "joy." Whenever something bad happens to one person and another person laughs, that qualifies as Schadenfreude.
When I grew up, I developed some bad Schadenfreude habits. Many exhibit Schadenfreude from time to time, but it's not good for a teacher to exhibit it when a student struggles. I'm so afraid of showing anything that looks like Schadenfreude that I try to stop myself from laughing at all in class.
So when I caught the two cheaters, I was proud of the way I had deduced that they were cheating (by spotting the mixed numbers). I almost started to laugh -- but I knew that it would be considered Schadenfreude if I laughed while two students were earning zeros. So I stopped myself.
The special scholar spotted me. She saw me struggling not to laugh -- and it suddenly became a new game for her and some of the other clique girls. They would start saying random things or looking at me weird. I'd start to laugh, and then they'd reply, "I see you laughing!"
It's understandable that the special scholar would struggle with the volume test, but I believe the other girl should have fared better without resorting to cheating. This could be because of how I taught the lesson -- which leads to the fifth New Year's Resolution for 2018:
5. Engage the students in the learning process instead of lecturing excessively.
Here's what happened -- on the day of the traditional lesson, I would ask the students to listen and answer questions, but they talk and do very little work. Then just before the test, there would be a "review" day. I asked the students to solve a volume problem -- but since no one had paid attention, they didn't know how to do the first strp. Desperate to see 14 hands writing something down, I'd just do the entire problem on the board and ask them to copy. This is what "lecturing excessively" refers to here -- having the students copy entire problems on so-called "review" days.
The real problem, of course, is that by "review" day, it's too late to teach the material. Engaging the students to make them participate needs to occur on lesson day, not review day. Lesson day is when I should make sure that everyone is participating.
Of course, some students might still be hesitant to participate. I should have used Sarah Carter's and Christie Bradshaw's dry erase packets in order to help the students learn the material. This would have helped the other students immensely, including that clique girl who gave up with a 50, and the other clique girl who cheated. This would have freed up time for me to assist the special scholar.
One December day during IXL time, some eighth graders started playing with the lights -- and a few seventh graders who had come in to borrow laptops for English class joined them. I knew that I had to punish the students who were involved, and I ended up yelling at one of them. It ended up being -- who else -- the special scholar. Even though she really was involved with the lights, there was no reason to single her out in this situation.
I remember that the special girl cried, and she told her friends that for some reason, many teachers had singled her out for no reason -- I wasn't the only one. I became so upset that I decided to buy her a bag of her favorite candy -- Jolly Ranchers.
I wrote about this incident in my Kwanzaa post. In that post, I suggested that I should have had the students put the laptops away and answer written questions "because I said so." This keeps the third resolution ("no talking about the past"), since the last question would be about not playing with lights in the future, not who was playing with the lights in the past. And of course this all hearkens back to the first resolution ("better classroom management").
The momentum the special scholar once had when she passed the October quiz was gone. But if it's any consolation, she at least passed her 4's Dren Quiz in December. The history teacher had given me the idea of cutting the Dren Quiz in half for struggling students. This worked, since she did very well on the reduced 4's Dren Quiz. And this is despite the 4's being much more difficult than the 3's, according to vjlomocso's chart from earlier.
Some of the other clique girls wondered why the special scholar had a shorter Dren Quiz. Of course I didn't want to explain, and I didn't want them making fun of her. And so I distracted them by intentionally giggling so that they could "catch me laughing" again. In this case, I'd much prefer that they made fun of me and not the special scholar.
The history teacher had planned on giving the students a party on the last day before winter break, but he cancelled the party as punishment for playing with the lights. (This would have been the day of the Kwanzaa Karamu.) But the special scholar claimed that the party wasn't cancelled, and shared a bag of chips with me -- which I ate, which "proved" (from her perspective) that it really was a "party" after all. The special cousin contributed to the "party" by playing some rap music on my laptop.
This ended a rocky December -- and it all started with the problems I had with the volume lesson. In order for students to learn more effectively, I must keep the fifth resolution in mind:
5. Engage the students in the learning process instead of lecturing excessively.
January 2017: She Misses Science
Both the special scholar and special cousin tried to neuter more of my rules. In this case, the special cousin was actually worse than the special scholar! The special cousin really wanted to neuter the "no cell phone" rule, and she accomplished it. First, she told me I was wrong to make her sit in her assigned seat, and so she should be allowed to sit in my support staff member's seat (on a day when my support staff member was not present). There she covered herself with a blanket and started texting on her phone. And of course, if I told her to put the phone anyway, she'd claim that since she was hidden, I couldn't prove that she actually had a phone.
(Yes, I described this incident in yesterday's post.)
Of course I yelled at the special cousin. She then replied, "Stop yelling at me!" and "Stay away from me!" It was a moot point because she still hadn't been added to IXL yet, but at this point she didn't appear to be open to one-on-one Algebra I lessons with me. She was afraid that if I sat close to her, I'd just yell at her.
Is there anything I could have done so that the special cousin would've been happy to follow rules and show me how smart she was at math instead of just outsmarting me with the rules? The answer is simple -- I should have treated her cousin, the special scholar, better before her arrival. Then there would have been less reason for the special cousin to dislike me from the start.
With all of these management problems mounting, I was assigned an instructional aide. This didn't necessarily work, though. The special scholar was one of the students who claimed that the aide's suggestions were "juvenile," and would say so the instant the aide left the room.
One day I tried to give a science lesson. I wrote about it in my January 13th, 2017 post:
But first, let me provide some explanation. My small charter school has no middle school science teacher -- instead, I, as the math teacher, must include some science into the lesson. Notice that some STEM projects, like the ones I gave sixth and seventh, already contain some science. But I want to be sure that the eighth graders receive sufficient science content since this is a tested subject here in California.
And so I go to our online software that we use for science, and download a worksheet based on questions that they may see on the state test. The hope is that next week, they can go to the online program itself and answer the questions correctly. The lesson is on the environment, because there is an upcoming science unit that will begin next month. It is called Green Team, and the students will be learning about energy and water conservation.
But then one girl -- the top student in math -- begins to complain. She argues that at the very least, science should be project-based, and so she wants to have some project rather than a worksheet. I assume that she had her hopes up all week when she saw that we'd be doing science, only to be disappointed when she sees the worksheet today. She says that she enjoys the science projects that she performed at her old school, before she transferred to our school over a month ago.
The "top student in math" refers to the special cousin.
Many of the students, especially the two cousins, become oppositional -- by which I mean that if I think something is a good idea, they immediately oppose it. When I told them about the Green Team, they replied that they wouldn't like it. Most likely, they might have enjoyed the Green Team because it would include the type of project that they were looking forward to. But they didn't like it just because I was the one telling them about it, and they didn't like me.
Similarly, they weren't looking forward to the Hidden Figures movie (which was released last year on Epiphany, by the way), just because I was the one recommending it to them. They told me that they planned on texting during the entire movie (even though that's against theater rules). Anything I liked, they would hate.
The sixth New Year's Resolution for 2018 states how I should have handled the science problem:
6. If there is a project-based curriculum such as Illinois State, then implement all components of it.
After all, Illinois State provided an online science curriculum in addition to math. I've spent several posts discussing other ways I could have taught science better -- most notably searching for the LAUSD pacing plan to handle the transition to the Next Generation Science Standards. Bruin Corps and Green Team were not substitutes for the true science curriculum in the Illinois State text.
Implementing all parts of the Illinois State curriculum also referred to the use of the Illinois State Daily Assessment (fourth resolution), Learning Centers, DIDAX manipulatives, and die-cut art. January 2017 was the month when the administrators held several meetings to ensure that we teachers were implementing all of Illinois State. Over Summer 2016, I made several misconceptions about what the Illinois State curriculum entails (and blogged about them), and those misconceptions ossified to the point that I didn't implement them correctly. It is possible that the special scholar might have enjoyed some of these activities.A few days after the movie field trip, it was time for the 5's Dren Quiz. This time, I would give everyone, including the special scholar, the full quiz, since I knew that even she would be able to handle the easy 5's.
Leading up to the Dren Quiz, I sang a new song called "No Drens," a parody of TLC's "No Scrubs." I set up the song by explain that both "drens" and "scrubs" are losers who don't have enough basic skills to be hired for jobs.
The special scholar was clearly offended by this statement. She started telling me about an older cousin who was a doctor. "She can't read small print, but she's got a better job than you!" It's obvious what was going on -- even though I didn't give any names, the special scholar saw herself in my statement about people who lacked basic skills, which is why she was so offended. And of course, it goes without saying that I shouldn't respond to her comment by yelling at her (second resolution).
Notice that chances are, her doctor cousin could easily multiply by 5 -- after all, this was the setup to the 5's Dren Quiz. Furthermore, the special scholar herself passed her 4's Dren Quiz, and I knew that she'd be able to pass her 5's Dren Quiz (and in the end, of course she passed it). So when I was talking about "drens," I was actually not talking about the special scholar.
Instead of arguing, I just started singing the "No Drens" song. In the end, the song was one of the special scholar's favorites -- one of the first songs she liked since September.
But again, I start thinking about whether talking about "drens" is a good idea. I think that from now on, I should emphasize that a "dren" is someone who is too lazy to learn basic math. The special scholar was not too lazy to learn basic math -- therefore she was not a dren. I should emphasize that my students are not drens because there are no drens in my classes. And besides, the students seem to like my anti-dren songs anyway!
Again, to make sure that my students have a chance to learn everything in the curriculum, I must keep the sixth New Year's Resolution in mind:
6. If there is a project-based curriculum such as Illinois State, then implement all components of it.
February 2017: She Celebrates Her Birthday
In my February 18th, 2017 post, I wrote the following reflection:
3) We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.
This week was Valentine's Day -- a day strongly associated with relationships. Lately I fear that I've been criticizing certain students too often.
In fact, one eighth grader has had enough of all of this. I got upset at her this week when I passed out Valentine's pencils and she decided to take two pencils for no reason. She eventually apologized, but she rejected my own apology for lashing out at her -- probably because she correctly notes that I'll end up yelling at her again at some point. At least I acted like the adult I should be by accepting the girl's apology. But her actions show that it's too late to repair my relationship with this student.
By this point, do I even need to identify the eighth grader in this incident? It goes without saying that the girl mentioned in this post is the special scholar. And it was right after her birthday, to boot -- her special day fell on the weekend, and this incident occurred on a Monday.
When I told her that she couldn't have a second pencil, she reacted by giving back both pencils and telling me that she didn't want any pencil at all -- and that was after she'd made a big deal about wanting a pencil!
In reality, the special scholar was just being oppositional. I wanted her to have exactly one pencil -- so she preferred to have either zero or two pencils, anything other than the exact number that I desired for her to have. Anything I wanted, she didn't want.
In the end, she accepted my one pencil -- only because she proceeded to steal a second pencil from another student (which I'd given to him the previous week).
The final Dren Quiz that I gave before I left the school was the 6's. According to the chart, this was the most difficult row of the table among those that I quizzed on. Yet the special scholar passed her 6's as well, despite having failed her 3's. I think she was so embarrassed after failing the 3's that she worked hard to ensure that she'd pass the bigger numbers.
As it turned out, the special cousin moved away from the school just before I left there myself. She could have been named the valedictorian had she not departed. Her name was never entered into IXL, and so I never did teach her Algebra I. I hope that for her sake that she moved to a middle school that offered Algebra I, and that she's preparing to start Geometry as a freshman next month.
But before she left, the special cousin told me that I was a good singer -- after a music break. I recognized this as the back-handed compliment that it was. She was really saying that I should have been a singer instead of a teacher, because I wasn't a great teacher. I didn't say this out loud, though, since I'd have gained nothing good from saying so.
Unfortunately I never did repair my relationship with the special scholar -- indeed, by the time I left, it was irreparable. In one of my last interactions with her, she told me that she couldn't see what I was writing on the board -- not even if I wrote it darker or larger. It seemed as if she was just trying to avoid listening to me, and of course I yelled at her.
It was a Wednesday, and the students had a SBAC Prep lesson. There were many "review" questions on exponents, and some students -- including the special scholar -- complained that they don't "remember" how to solve the exponent problems. But as I wrote earlier in the October section of this post, they never truly learned exponents in the first place.
That day I didn't really keep any of what would eventually be my resolutions. Since no one knew how to solve the problems, I resorted to writing them all out on the board (fifth resolution -- avoid excessive copying). I kept bringing up how students always complained that they can't see what was on the board as an excuse to avoid writing (third resolution -- bringing up the past). And it was all because of my weak management system (first resolution).
But there is one more resolution to mention here -- the seventh New Year's Resolution of 2018:
7. If there is an official assignment to review for state testing, then implement it fully.
In reality, the students shouldn't have been answering my questions in the first place. Instead, they needed to take out the laptops and try the practice problems directly from the SBAC website.
At first I thought that the site wasn't working. It wasn't until after school on the day of the above confrontation with the special scholar did I notice that a "Secure Browser" had been installed on all the laptops -- the "Secure Browser" to be used to access the SBAC website.
Even after I finally had the students try the practice tests, I didn't realize, for example, that some of the questions forbade a calculator while others allowed it. This would have been a great time to figure out how to use the embedded calculator (powered by Desmos).
In the end, I should have switched each week between written and online questions. The students practice, say, exponent questions one week. Then the following week, they go to the website and answer the exponents questions -- with which they should feel more comfortable after having reviewed them one week -- rather than four months -- earlier. (Sixth and seventh graders had SBAC Prep four times a week. This means that I could alternate between written and online question days -- and this fit the plans of the English teacher, who needed to borrow some of my laptops on the days that I wasn't using them.)
By the way, I never did look up my old school's released SBAC scores, and so I decided to do so in time to write this post. The scores are difficult to decipher for two reasons:
-- Our charter school's results are combined with our sister charter's results. So it's difficult to tell which scores belong to my students and which scores belong to students I never taught.
-- Our charter school is so small that many categories end up being hidden by asterisks (fewer than ten scores reported) to protect student privacy.
For example, our sister charter had no eighth graders, so it's safe to conclude that all eighth grade scores came from our campus. But only 11 eighth graders took the English test -- and all it took was one of those students to be absent on the day of the math test for an asterisk to block it. (The same thing had happened to this cohort the previous year -- 12 seventh graders took the English test, but at least two of them were absent for the math test.)
And so this is frustrating -- I know only the English results for the eighth graders, but not their scores for math -- the subject I taught. And for sixth and seventh graders, I have their math scores -- but many of those scores belong to sister charter students.
As it turns out, our sister charter school is almost 100% black (yes, another vacation post mentioning race), while our school has a few Hispanic students. Therefore I can use "Hispanic/Latino" as a proxy for "was taught by me rather than the sister charter."
The only grade with enough Hispanic students not to be blocked by an asterisk was seventh grade (as I mentioned in previous posts). Here are the math scores -- there were 13 students. One earned a 4 (the highest score -- only PARCC goes up to 5), two earned 3, two earned 2, and the rest had 1. By the way, I have a good feeling as to which student earned the 4.
Comparing all the sixth and seventh grade scores to the previous year, the scores were mostly flat. I see a very slight increase -- but it can be attributable to a single high scorer being added to each cohort, a 3 scorer in sixth grade and the aforementioned 4 scorer in seventh grade. (If the 3 scorer was at our charter, then I think I know who it is. But on November 8th, 2016, when I visited the other campus, I remember a smart sixth grader who might also be the 3 scorer.) Of course, since my students were talking and not learning, my successor teacher should get the credit for keeping the scores flat (since math scores tend to decrease as students get older). I might be able to claim credit for maintaining or even raising the scores had I followed the seventh resolution:
7. If there is an official assignment to review for state testing, then implement it fully.
There is better news in the score report for our English teacher. The highest increase in average ELA scores was for the seventh grade. Even though there were seventh graders at the sister campus, this group was small, so most of the credit goes to our English teacher. The seventh graders might have driven her crazy, but they learned a lot from her too.
In my March 20th, 2017 post, I wrote the following reflection:
Along with the pizza, I'd left a personalized "Good Luck" card for each student. I'd originally planned on giving each student such a card on the last day of school, but due to the circumstances I decided to hand out the cards right then on Pi Day.
And this is what I wrote on the special scholar's "Good Luck" card:
"You are not a dren. You never were, and you never will be. Keep this in mind, and you'll be successful in math from now on. Good luck in high school!"
When I'd first met the special scholar at the start of the year, I was hoping to be the math teacher that she'd remember in a good way. Perhaps five or ten years from now, she could have said something like the following:
I was never good in math until I took Mr. Walker's class. He made me work hard, but I learned a lot in his class. I'm much better at math because of him.
Of course, she'll never say that now, because it never happened. Instead of inspiring her to learn math more, I did the exact opposite.
Is there anything I could have done in order to have become the inspirational teacher that she would have remembered for years after taking my class? Well, what I told her on the "Good Luck" card is what I should have told her everyday in the class. She wasn't a "dren," because a dren is someone who's too lazy to learn math. As long as she worked hard everyday, she would avoid being a dren. I should have developed a rapport with her. Then she might have begun to show some real enthusiasm for learning math.
Ever since I left the school, I missed being there for my students. But the one student I thought about more than any other was the special scholar. I believe that if I had built a better relationship with the special scholar, I would have done better with the other students -- and then I would never have had to leave the school.
If I ever return to the classroom, I will always remember the special scholar -- and I'll make sure to work harder to earn the respect of the special scholars in my new class. And to do so, I must keep all seven New Year's Resolutions for 2018:
1. Implement a classroom management system based on how students actually think.
2. Keep a calm voice instead of yelling at students.
3. Move on from past incidents instead of bringing them up with students.
4. Begin the lesson quickly instead of having lengthy warm-ups
5. Engage the students in the learning process instead of lecturing excessively.
6. If there is a project-based curriculum such as Illinois State, then implement all components of it.
7. If there is an official assignment to review for state testing, then implement it fully.Conclusion: New Mersenne Prime and Phi Day of the Century
This week, a new Mersenne prime has been announced: 2^77232917-1:
https://www.mersenne.org/primes/press/M77232917.html
The discoverer is Jonathan Pace, an electrical engineer from Tennessee. The new prime has over 23 million digits. His computer actually made the discovery the day after Christmas, but it takes a week for a second computer to verify it before it's announced.
Last January I played a Numberphile video for my sixth grade class on Mersenne primes, based on the previous record-breaker 2^74207281-1. I might as well post that video again:
I showed it to my class in January because that was when the sixth graders reached the unit on prime numbers, but as it turns out, January is a a great month for Mersenne primes. The last three Mersenne primes were either discovered or announced in January.
I played this video after a short activity on guessing large primes. As usual, students were talking continuously throughout the activity and video, and so the lesson didn't have as much impact as it would have had in a silence-dominated class. (For once, the special scholar and her clique had nothing to do with the talking, since this was sixth grade, not eighth grade.)
Meanwhile, not only is today Epiphany, but some sources cite today as "Phi Day." Just as Pi Day is March 14th (as in 3.14), since Phi is 1.618033988..., we'd expect Phi Day to be January 61st. But since no month has 61 days, only one digit after the decimal is considered, so Phi Day is January 6th.
Most of the time, Phi Day is ignored. But some people have noticed that since the next two digits are 18, we can take 1/6/18 to be "Phi Day of the Century," just as 3/14/15 was Pi Day of the Century. So if we're going to observe a Phi Day in any year, then at least let's do it this year. (Also, the next digits, 03:39, can be used as the time for a special "Phi Moment," just as 9:26 was the Pi Moment on Pi Day of the Century.)
Unfortunately, not only is Phi Day of the Century a Saturday, but it's winter break -- many students haven't seen the inside of a classroom in weeks, and they won't return until Monday. Indeed, the century Pi and Phi Days were both Saturdays, But hey -- e is 2.7182818, so we can have an "e Day of the Century" on 2/7/18, which is Wednesday, February 7th. So teachers -- especially Algebra II and above -- should prepare a special celebration for e Day of the Century. (Indeed, the earliest date LAUSD students can ever return to class after winter break is January 7th -- they are guaranteed to have the entire stretch from winter solstice to Epiphany off.)
Returning to Phi, let's look at some Phi Day music. Michael Blake, who set pi to music, also did the same for Phi. Here is "What Phi (the golden ratio) Sounds Like":
I was going to wait until Pi Day for some more coding in Mocha, but since I learned about the special Phi and e Days this year, we might as well do the same for Phi today.
Oh, and I was going to code Square One TV's "Triangle Song" today, but yes, that has also fallen by the wayside. Besides, "Triangle Song" fits my scale but contains so many notes to code, while a Phi song can be either long or short depending only on how many digits of Phi we use. (The special scholar liked some of our Square One TV songs, especially "Count on It" and "Nine, Nine, Nine." I don't recall her reaction to the "Triangle Song," especially since the triangle lesson was geared more towards the seventh graders, not the eighth graders.)
We'll use 38 digits (39 including the initial 1), since this is how many Blake uses in his song:
http://www.haplessgenius.com/mocha/
Let's start with the major scale, since this is what Blake uses in his song. In our version, every song will be a quarter note, so we only need to code the digits for the notes, not the lengths:
10 DIM S(9)
20 FOR X=0 TO 9
30 READ S(X)
40 NEXT X
50 DATA 72,180,160,144,135
60 DATA 120,108,96,90,80
70 N=1
80 FOR X=1 TO 39
90 READ A
100 SOUND 261-N*S(A),4
110 NEXT X
120 DATA 1,6,1,8,0,3,3,9,8,8
130 DATA 7,4,8,8,9,4,8,4,8,2
140 DATA 0,4,5,8,6,8,3,4,3,6
150 DATA 5,6,3,8,1,1,7,7,2
Notice that whereas we can avoid the zero problem in pi, zero appears early in Phi. Blake uses a rest for the zero in his song, but I decided to use a major tenth for zero instead, since the 0 key is to the right of 9 on the keyboard.
Once we have completed the song for the major song, there's not much effort needed to change the song to make it fit the minor scale:
50 DATA 30,72,64,60,54
60 DATA 48,45,40,36,32
or the New 7-Limit Scale:
50 DATA 54,105,96,90,84
60 DATA 81,72,70,63,60
or the Bohlen-Pierce Lambda Scale:
50 DATA 21,63,53,49,45
60 DATA 38,35,29,27,23
This is why my New 7-Limit Scale contains ten notes -- I had digit songs like the Phi song in mind when I created it.
Thinking back to continued fractions from my Kwanzaa post, it turns out that Phi has a particularly memorable continued fraction:
Phi = (1+sqrt(5))/2 = [1; 1, 1, 1, 1, 1, ...]
And the convergents to Phi are merely the ratios of consecutive Fibonacci numbers:
1/1, 2/1, 3/2, 5/3, 8/5, ....
Because of this, the Fibonacci songs from my Black Friday post are also great songs to play on a day such as Phi Day.
Sometimes Phi also appears in microtonal music as well. According to the following video, this is called the "Golden Interval" (as in the Golden Ratio):
The convergents of Phi tell us that the perfect fifth (3/2), the major sixth (5/3), the minor sixth (8/5), the tridecimal neutral sixth (13/8), and so on, are all approximations of the Golden Interval.
We can approximate Golden Intervals in Mocha by putting Fibonacci numbers in the DATA lines, but unfortunately we can use only eight notes instead of ten (with degrees from 8, the sixth Fibonacci number to 233, the thirteenth Fibonacci number). I'm not sure how many Golden Intervals are needed for the song that Izzy Water plays in the video, though.
Let's not forget our other celebration today -- the 50th Mersenne Prime. We wouldn't want to program 23 million digits in a song. So we could just code the first few digits (just as we do for infinite real numbers), or we can just choose a smaller Mersenne prime. For example, the twelfth Mersenne prime 2^127-1 has 39 digits, the same number of digits that Blake uses for Phi:
120 DATA 1,7,0,1,4,1,1,8,3,4
130 DATA 8,3,4,6,0,4,6,9,2,3
140 DATA 1,7,3,1,6,8,7,3,0,3
150 DATA 8,8,4,1,0,5,7,2,7
I like coding 2^127-1 on Mocha, because this is the highest number she can handle:
PRINT 1.70141183E+38 (works)
PRINT 1.70141184E+38 (gives an ?OV ERROR for overflow)
(That's right -- she. "Mocha" is most likely a girl's name since it ends in "a," and considering that the emulator can play more soprano octaves than bass octaves, the pronoun "she" is appropriate here.)
Notice that this song ends on 7, while both our Phi song and Blake's end on 2. If you prefer a song that ends on 1 (the tonic), try 2^89-1 instead -- it ends in three 1's. The next Mersenne prime 2^521-1 also ends on 1, but the number of digits jumps to 157. (Except for the first Mersenne prime 2^2-1 = 3, all Mersenne primes end in either 1 or 7.)
This concludes my final winter break post. School resumes on Monday. On that day we'll begin our second semester with Lesson 8-4 of the U of Chicago text.
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