Tuesday, January 3, 2017

The Year 2016 in Review

Happy New Year! This is the first post of the new year, and as 2017 begins, there are many thoughts racing through my mind. Since this is the third week of winter break, I will take this opportunity to write about some of the thoughts,

Table of Contents

1. My Favorite MTBoS Challenge of 2016
2. Theoni Pappas and the 2017 Mathematical Calendar?
3. Evaluating My 2016 New Year's Resolution
4. 2016 Week 1
5. 2016 Week 2
6. 2016 Week 3
6. 2016 Week 4
7. My Final Subbing Day
8. Alternatives to Yelling
9. Fulfilling My 2016 New Year's Resolution
10. My 2017 New Year's Resolution

My Favorite MTBoS Challenge of 2016

The year 2016 was a huge year for me. Obviously, I became a full-time teacher in 2016, and I also became a full-fledged member of the Math Twitter Blogosphere, or MTBoS.

I participated in a number of MTBoS challenges in the recently completed year. It all began with the MTBoS 2016 Blogging Initiative, and it ended with Tina Cardone's "Day in the Life" challenge -- which of course continues into 2017.

Of these, I'd have to say that Cardone's challenge is my favorite. After all, I'm now a middle school teacher, and for ages, Fawn Nguyen's blog was the only middle school math blog I knew. But as it turns out, many of the other "Day in the Life" participants teach middle school. For introducing me to other middle school math teachers -- recall that I work at a small charter school with no other math teachers -- I consider Cardone's challenge to be my favorite. And besides, unlike the other challenges, Cardone's only requires one or two posts a month -- not 30 in one month, which I can't handle.

On the other hand, the 2016 Blogging Initiative was my first MTBoS challenge, and so it formally introduced me to the math teacher community. Recall that back in January and early February, the Initiative consisted of one post per week, each on a different topic. A different teacher came up with the topic for each week. One of those was Tina Cardone -- and naturally her topic was "Day in the Life," just as with her current challenge.

So far, I've seen no sign of a 2017 Blogging Initiative. I assume if there was going to be one, it would be getting ready to start now. Of course, I don't really need a 2017 Initiative, since I'm already a part of Cardone's project. Then again, if the 2017 Blogging Initiative begins and "Day in the Life" is the Week 1 Topic, that will be easy as I can submit the same post to both challenges!

Theoni Pappas and the 2017 Mathematical Calendar?

The MTBoS Blogging Initiative isn't the only math idea from last year that's missing in 2017. As it turns out, Theoni Pappas will not be publishing her Mathematical Calendar this year. But on Amazon, I notice that there's already an announcement for a 2018 Mathematical Calendar!

Then again, I like setting up math problems in class where the answer is the date -- an idea I took directly from Pappas. The same thing happened in 2013 -- Pappas created calendars for 2012, 2014, and 2015, but not 2013.

So I've decided to post a Pappas-like Mathematical Calendar for 2017 right here on the blog. Each day, my post will begin with a math problem whose answer is the date. I already wrote that I can't handle 30 posts in one month, so I'll only write problems on days I actually post.

If it's a school day, then I'll post an eighth grade math problem. I'm hoping that it will be the actual Warm-Up question from my class, but sometimes I'll assign problems from Illinois State -- and most of the time, the answer won't be the date, When that happens, I'll post a different problem. On the other hand, if it's a vacation day, I'll post a typical Pappas-level problem. Most of these questions will be from high school math.

Here is the first problem:

2.996 rounded off at the hundredth place is ___.

The correct answer is 3.00 or 3 -- and of course, today's date is the third.

Evaluating My 2016 New Year's Resolution

Last year, I mentioned a New Year's Resolution in my first post of the year. It was influenced by David Kung -- a mathematician whose Great Courses lecture I'd received as a gift:

At the end of the lecture, he offers the following challenge to the viewers: "Find something you're wrong about. Find some area of your life, your world, and stop ignoring the cognitive conflict." By resolving the paradoxes inherent in our lives, we can become not only better mathematicians, but better people. To me, nowhere is this more important than in the classroom.

And so I declare this to be my actual New Year's Resolution for 2016. I want to find something wrong about the way I'm teaching and managing my classroom and resolve it, so that I can become a better teacher.

Now that 2016 is over, let's evaluate this resolution to determine whether I've fulfilled it. Recall that Kung's lecture is about paradoxes and the idea that we can hold two beliefs simultaneously, even though they are mutually incompatible. Another word for this is doublethink.

My goal was to become a better teacher. But as I mentioned in my most recent reflection post for "Day in the Life" (December 18th), I'm nowhere close to meeting that goal. There are several classroom management issues that I'm having trouble resolving.

When I first wrote that resolution, I was still a substitute teacher. Still, the idea was that there were several flaws in my classroom management back then. I wanted to develop good teaching habits that I could bring into my own classroom if I were to get one -- and I did get my own classroom. Often, I would try one thing, then keep on doing even though it doesn't work. Or I would see a problem and ignore it even though I knew I should do something about it.

That, in a nutshell, is doublethink! And I didn't do enough to erase this doublethink and begin developing better teaching habits -- and so I brought my bad habits into my new classroom. Since I didn't resolve the cognitive conflict enough to be a better teacher, I must admit that I have broken my 2016 New Year's Resolution.

Of course, many people break their New Year's Resolutions, and by the time we reach August and the first day of school, we've forgotten all about our resolutions. But I have no excuse for ignoring my resolution back in January and early February, when I was still watching Kung's lectures! To see where I went wrong in fulfilling my resolution, I should go back to my subbing assignments from January and early February.

Now most subs can't recall their assignments from a year ago. But I can -- since I faithfully recorded my subbing assignments right here on the blog as part of the 2016 Blogging Initiative! So I can go right back to those posts to find out where I went wrong.

So that you readers can follow along, here are the links to my 2016 Initiative posts, which took place during the stretch from the end of winter break to President's Day:


2016 Week 1

My first subbing job of 2016 was on January 11th. That day, I was at a continuation high school. I didn't write much about the continuation high school here on the blog, since that class was unrepresentative of the classes I usually subbed for or would eventually teach in. It was considered a special ed class, and on sub days, the aides essentially managed and ran the class.

But there is one thing I'd like to day about that class. The aides told me that even though this was a tough class -- some of the students even had their own parole officers -- the students behaved better when I was the sub than when there were other subs.

I believe the reason for this is that each day would begin with a P.E. lesson -- twice a week it was basketball, the rest of the week was weight training. And since I wanted to keep myself in shape, I decided to participate in P.E. along with the students! I even had a Kobe Bryant jersey that I would wear on basketball days. And so I believe that by participating in P.E. along with the students, I had gained their respect. (I never posted it on the blog at the time because it was irrelevant to math.)

At my current school, all middle school students have P.E. at the same time, and we three middle school teachers are required to supervise them while the support staff members run the class. And so, keeping my continuation school experience in mind, I give a high-five to any students who are running their assigned laps. And once in a while, one of the students would challenge me to a short race, and occasionally I'd oblige. Most of the time, the student wins -- even though I ran cross country in high school, as a teacher I'm not dressed for running. My hope is that I can gain my students' respect the same way I did at the continuation school.

Returning to January, let me state that the period from January 14th to February 1st was critical. For during that stretch, I subbed nine times -- all at middle school. In fact, eight of the nine subbing jobs were at the same middle school.

January 15th was the day I chose for the Week 1 "Day in the Life" prompt -- but even in that post, I wrote about the my job on the 14th as well. When I posted, my focus was on the math that I taught that day -- but today, let me focus only on classroom management. Let me cut-and-paste all that I wrote in that post regarding management:

After the teacher leaves for his meeting, I decide to go to the classroom where I subbed the previous day, in order to establish continuity with the second sub for the ELD class. When I was in that class a day earlier, the students were supposed to divide into the three reading groups to which they had previously been assigned. Instead, they'd split into two large groups. One girl had informed me that the others weren't in the correct groups, as well as how to find out what the correct groups were.


I decide to use the seating chart to keep track of the laptops. As each student takes a laptop, I write down the laptop number next to the student's picture. I also use the seating chart for attendance. There are no absences during this period, but one boy is not in the seat listed on the seating chart -- he should be in the second row, but instead he is in the front row in the corner. Naturally, he claims that this is his real seat. I tell him that there's an 80-90% chance that he is lying, and that I'd have to write his name on the board, intending to write it in the note I was leaving the teacher. Sometimes I wonder whether sitting in the wrong seat is worth leaving his name for the teacher, or perhaps he's telling the truth about his seat -- but I know that I must be extra strict with the seating chart on days when there are laptops out or the students are taking a quiz.


When the quiz begins, some students say that they should be allowed to use notes, claiming that the teacher allows them to use notes on a quiz (as opposed to a test, for which no notes may be used). I check this out with the aide, but she's not aware of this rule either. And so the students have to put their notes away. A few students are confused with a quiz question where they are to use the variables x and y to write the explicit formula, and so I decide to help them out on this question only.

Notice that in all three of these examples, the students do something that they're not supposed to be doing -- forming two groups instead of three, going to the wrong seat, or using notes on the quiz. In the case of the groups (which had occurred on the 14th in a reading class), the regular teacher had explicitly stated that there were to be three groups. In the math class, the teacher didn't explicitly say that students should be in the right seats or silent during the quiz -- but he shouldn't have to.

2016 Weeks 2

I didn't sub at all the following week. At the high schools, this was finals week -- so although middle school students didn't take finals, there was a lower demand for subs in the district. But the Week 2 prompt was "My Favorite," and so I wrote about my favorite game as a sub -- "Who Am I?" That day, I wrote a little about how the game went when I played it in classrooms in 2015:

But in early November, I had an opportunity to play my game. Most of the eighth grade math classes were assigned to take notes, but the Math/Computing class had a worksheet to finish. And so I began by asking the students to guess my age, and then my weight. So two of groups already had a point, while the other seven were scoreless.

Then the third question I asked was simply the first question from the worksheet -- namely to graph the equation x + y = 5 using intercepts. Just as I mentioned from my original Conjectures worksheet, every third question was a chance for each and every group to earn a point. I think that only about half of the groups earned the point. Some of the groups drew the graph incorrectly, while others had the correct graph but identified the slope as 1 instead of -1. My fourth question was the second question from the worksheet, x + 2y = 8 -- which, just as planned, allowed for only one group to earn the point.

So we can see that the students weren't in much mood to work. And yet, I believe that there was a game, the allure of earning points motivates them. Many of the students might have just thrown the paper away, or worked on it at a snail's pace and still be on the first graph late into the period. Also, checking every third question keeps those who might have drawn every graph incorrectly or calculated every slope with the wrong sign.

By the way, what exactly was the prize that I gave the winning groups? Actually, all I did was leave their names for the regular teacher with a positive note!

2016 Week 3

The following week, I subbed in a sixth grade class for three straight days -- January 25th-27th. The Week 3 prompt was "Better Questions," and as luck would have it, one of the days was a group project for which students had to ask each other questions.

I also had a chance to play the "Who Am I?" game on one of the three days. With so much math to write about that week, I didn't mention classroom management in that post at all.

2016 Week 4

On February 1st, I subbed at the middle school for the last time, and from February 3rd-10th, I had another multi-day assignment, this time in a high school biology class. But in order to fit the Week 4 prompt, "Teach My Lesson," I wrote about a sixth grade math lesson I taught on January 29th:

This game didn't go well at all. Group 6 was working way ahead of the game and answering most of the questions before I asked them. But Group 4 struggled with almost every question I gave them. I tried to help Group 4 out by letting them know which coordinates they had to keep and which ones they had to change the sign to. But the other groups grew restless, and I had to abide by the rules of the game by declaring Group 4's answers wrong and not awarding a point. This led to Group 4 getting upset, and one girl even started to cry.

This revealed a flaw in the "Who Am I?" game -- especially when I tell the class that the reward for winning is a positive note for the regular teacher and the consequence for losing is a negative note for the teacher. Group 6 was talking throughout the game and Group 4 was quietly working, yet in my note to the teacher, I wrote Group 6 on the "good list" and Group 4 on the "bad list." This is why the sixth grade girl cried -- her teacher would read my note and punish her even though she was quiet, just because she struggled to answer the eighth grade questions (as the students were switching signs in order to reflect the points over an axis)!

This is doublethink on my part at its worst. I simultaneously held two contradictory beliefs -- "the basis for leaving names for the teacher is academics" and "the basis for leaving names for the teacher is behavior." In reality, the sole basis for leaving names ought to be behavior -- the regular teacher can just check the written work upon returning, but can never see the student behavior on the day the sub is there. But the "Who Am I?" game rewards academics over behavior.

In fact, I notice this a lot with many sixth grade classes, including my current class. Some of the top students academically are also the most talkative. So if my current sixth class were one that I were only subbing, I'd have given points for correct answers -- to the most talkative students. And one girl who's very quiet but often has trouble reading would have found herself on the list of bad students for the regular teacher!

On February 12th, my last day before the President's Day holiday, I ended up back in the same class that I was in on January 14th -- a middle school special ed class. This time, I already knew that there were supposed to be three reading groups, and I made sure that the students followed them. But since the classes was still loud, I'd come up with the idea of having a "Noise Meter" where I would mark on the board whether the class was noisy or quiet. Based on how many marks I made, this determined whether I would leave the teacher a good or bad note for the class.

Of course, you readers can see how silly this is -- by the time I create a "Noise Meter," the class is already too loud, so a "Noise Meter" can't convince any student to be quiet at all. In fact, the first time a class I'm subbing for typically begins to talk is during attendance -- the class may be quiet as I'm reading the first name on the roster, but by the time I reach the tenth the class is talking. Yet in another case of doublethink, I kept on using the "Noise Meter" for months before I finally dropped it.

My Final Subbing Day

The last time I subbed in 2016 was -- if you recall -- on November 8th, Election Day. Yes, by then I was in my own classroom -- but that day, my car broke down and I found myself filling in for my counterpart at our sister charter school.

On this day I tried to be a better sub and get through my classes without problems. But, as you know from my November posts (especially the 18th, my reflection day for Cardone's project), that didn't go as well as I hoped.

There were two big problems that day. First, one sixth grader claimed that the teacher allowed them to drink water in class when the regular teacher explicitly wrote down that they can't. (Compare this to the class that divided into two groups when the teacher explicitly wrote down three.) Then later on, a seventh grader claimed that he was done with the science worksheet just so that he could get free non-academic time on the computer. In both cases, I ended up yelling at the students -- and as you already know, I find myself yelling much too often in my regular classroom as well.

In some ways, yelling ends up being an effective management technique. When I yell, often another teacher, such as the history teacher or the fifth grade teacher, hears me yell. That teacher enters the room and starts meting out a punishment to the student who caused me to yell. Then the other students start obeying me because they fear I'm going to yell again and cause the other teachers to enter my room again!

But of course, yelling is not how I want to run the classroom. There are several reasons why it's wrong for me to yell in the classroom:

1. Yelling disturbs classes next door.
2. Often when I yell, water flies out of my mouth, Spitting in the classroom is always wrong.
3. It's not the job of other teachers to control my class. They have their own classes to worry about.
4. It sends the message that I don't matter -- real punishments come only from other teachers.
5. Students need help in math, but they don't ask me because they fear I'll yell at them.
6. I want to be able to give special help to my top students. I've already written about the new girl to whom I'd like to teach Algebra I. She's already told me to stay away from her if I'm yelling -- even if it's at other students and not her.

Therefore, even if yelling appears to work, in reality it never works.

Alternatives to Yelling

Back when I was still a substitute teacher, I almost never yelled. So for example, when that reading class divided into two groups instead of three, I didn't yell at them. Instead, I simply wrote down the names of the offending students for the regular teacher -- in this case, I think I actually listed every student's name in the groups formed that day, so the teacher could compare what groups the students formed versus what groups they were supposed to form,

On the other hand, if my current class were to divide into the wrong number of groups -- and it has happened before, for Illinois State STEM projects -- I would yell at them.

And so I ask myself, is there an alternative to yelling in these situations? Let's think about it. Again, I often played the "Who Am I?" game when subbing. The students would be divided into groups, and I would award points to the various groups.

Well -- there's a solution right there. First of all, I shouldn't have limited "Who Am I?" to math classes -- instead, I should have some sort of point system in every class in which I subbed. And I should have awarded more points for behavior, which would have accomplished two purposes. First, behavior points helps out those students who are quiet but need extra time to work. Second, if I extend the game to non-math classes, sometimes I'd have trouble with the subject myself. I may not know the answer to every question in the literature text (especially if I haven't read the story myself), but I do know what good behavior looks like. And so I give the points to well-behaved students.

I saw the troubles that a purely academic scoring caused -- yet I played the game anyway. Moreover, in my current class, I started an individual participation points system where students can gain or lose points -- where most points were gained for "participating" (i.e., giving right answers) and points were lost for "not participating" (i.e. off-task behavior). I would begin giving out consequences when a student has lost all his or her points.

And there is the problem -- those smart yet loud students would rack up points for answering my questions, and when I took them away for talking, they'd never lose enough points for me to start giving consequences. So again, the students would talk and talk without any punishment (until I started yelling, of course) -- all because of the doublethink of conflating academics with behavior.

Eventually, I did change my participation points system. Students can now gain points whenever they participate, but now consequences are given separately from the point system. The problem is that it's far too late to introduce a change -- the students have already seen the loudest kids get away with being loud for too long, and so they're never quiet.

I remember how some regular middle school teachers quieted their classes. This was at the two middle schools where I subbed last year (the same schools, though not necessarily during the critical resolution period of January 14th - February 1st). The teachers used a "call and response" -- when the teacher says "Class, class," the students must answer "Yes, yes," and be quiet.

When I started teaching at my current school, one of the support staff members came up with a similar call and response: "When I say 'Listen,' you say 'up.'" I immediately thought it was a good idea, and so I tried it in my own class. It worked -- at least at first, until the smart, loud students took over the class.

Fulfilling the 2016 New Year's Resolution

All of this suggests what I should have done to fulfill my 2016 New Year's Resolution. The goal was to avoid doublethink and figure out which management techniques work and which ones don't.

First of all, I tell the class that I'm doing a call and response of "Class, class"/"Yes, yes." I've seen enough teachers use this in 2015 that I could implement it in every middle school class I cover in 2016, regardless of whether the particular teacher I'm covering does so.

Then, I say "Class, class" the first time the class gets loud -- which, as I've said before, is usually ten names into the attendance. In fact, before class begins, I can take the roster and mark off the tenth, twentieth, thirtieth, etc., names so that I remember the call and response. Due to doublethink, I used to believe that overdoing the call and response cheapens it. In reality, it shows the class that I'm serious about the class being quiet.

Now here is where my new point behavior-based point system comes in. Each group that is silent after responding "Yes, yes" earns a point. What will typically happen is that the first time I do this, the class really is silent, so every group gets a point. Then the second or third time I do it, one student keeps talking. Then every group except the talker's group gets a point.

Due to doublethink, I didn't want to give too many points for behavior. On November 8th, I was using the "Listen"/"up" call and response, but I still believed that points should be for academics. The first time I said "Listen," the whole class was quiet, but I only gave Group 1 a point since I didn't want too many behavior points. The next time I said "Listen," I only gave Group 2 a point. The third time, a girl in Group 3 started talking, so I awarded the point to Group 4. From the students' perspective though, there was no difference between what I did when no one talked (give a group a point) and what I did when someone talked (give a group a point). So the whole class eventually started talking, my point system failed, and I started yelling. Instead, I should have given every group a point for silence and every group but the girl's when she talked. If these means that by the end of class, every group has around 30 points, with 20 of them for behavior, then so be it. I can never give out too many behavior points. But once groups start having many points, it will be easier to deduct a point from the misbehaving group than to give everyone else a point.

The other big issue is what to do when I need to enforce an unpopular rule. Here I'm referring to something like "divide into three assigned groups" or "no drinking water in class" (or maybe "no cell phones in class," especially in eighth grade and above). The students tell me that I'm wrong and that the regular teacher never enforces the rule -- even if the regular teacher explicitly mentions the rule in the notes for the sub.

In this class, it's time to bring out the behavior point system again. I tell the students that they are to divide into the three assigned groups -- and the first group to form properly earns two points, the second group earns one point, and the last group earns no points. If the students insist on forming only two groups, then no one earns the point. Suppose I did so on January 14th, and the students formed only two groups and so earned no points. When the girl comes in to tell me that there were supposed to be three groups, I immediately give that girl two points! Then I tell the class that anyone who's in her (correct) group can join her so that they can be two points ahead as well. In this case, we see that the students are rewarded and punished right away, instead of giving a reward ticket the following day or leaving a list for the teacher to see the following week.

What could have I done on November 8th, when students wanted to drink water? I know now that informing them of the teacher's rules doesn't work, as they'll say I'm wrong, even though they're probably aware of the teacher's rules. They're just hoping that they can drink water on a sub day, a brief respite from the normal days when they can't drink water.

I don't like lying to students or making false statements in class. But many middle school students are so oppositional that often it's better for me to say something intentionally wrong -- so that they'll want to oppose me by saying something correct instead, which is what I want.

But this is yet another case of doublethink -- and here's why. Sometimes, if I am teaching math, I may make a mistake, and a student corrects me. I'm glad that the student is thinking enough about math to correct my mistake, so I award that student or group a point. In fact, I tell the student that I'm so upset at making a mistake that I pound my desk hard with my fist -- which often causes a laugh, thereby adding to the student's reward!

I'm having trouble doing this in my own classes now -- because of my yelling. The real anger I show when yelling outweighs the false "anger" I show when a student corrects me. So this is yet another reason why I shouldn't yell in class:

7. Yelling in class weakens the reward I give when a student corrects my mathematical error.

Now here's the thing -- if it's been a while since I've made a mistake, I might even make an error on purpose in order for astute students to catch it and earn the point. In other words, I take advantage of the students' desire to prove me wrong. So this is doublethink because I'm willing to say wrong things intentionally to improve academics, but not to improve behavior.

So here's what I should have said when one girl wanted to drink water: "Yes, your teacher lets you drink water, but I'm stricter than your teacher. In fact, here's an original idea of mine -- let's place your water bottle up here by the sink, and you can get it at the end of class."

At this point another student will correct me: "Hey, that's not original -- that's where the regular teacher wants us to put our water during class!" And by correcting me, the student unwittingly admits that it's the regular teacher's rule not to drink water in class, which is what I want!

If instead, another student in another group tries to help the original girl out and say "She's right -- the teacher lets us drink water in class," then I ignore the student. Notice that as long as the girl is arguing, she actually isn't drinking, which is what I want. But as soon as any water actually passes her lips, I immediately award all the other groups a point! That will probably shut the other students who might take her side up, since they're being rewarded for following the unpopular drinking rule!

To many experienced teachers, all of these ideas are "Duh!" But I had to overcome doublethink in order to implement any of these basic ideas. Also, experienced teachers may be able to implement these ideas without having an explicit point system, But since I have a point system anyway, I might as well use it.

My 2017 New Year's Resolution

What should I give for my 2017 New Year's Resolution? Well, since I broke my 2016 resolution, I might as well renew it and try to fulfill it this year:

And so I declare this to be my actual New Year's Resolution for 2017. I want to find something wrong about the way I'm teaching and managing my classroom and resolve it, so that I can become a better teacher.

Many of the ideas I've mentioned so far are peculiar to subbing. But with my participation point system, I can give more points for behavior if I so desire.

In previous posts, I mentioned that our school awards Scholar Dollars to deserving students. At first, I didn't want to deal with both participation points and Scholar Dollars, so I dropped my points system and replaced it with Scholar Dollars. Every time I wanted to give a student a point, I would give him or her a Scholar Dollar instead. In the end, I ended up giving out too many Scholar Dollars -- and then someone ended up stealing them anyway. So I returned to participation points -- and I believe my point system is now weaker than if I had used it all along.

I might bring back Scholar Dollars, perhaps with a twist. The easiest way might be, whenever a student has, say, ten participation points, I'll give that kid a Scholar Dollar. I may also surprise a few students by awarding a Scholar Dollar directly for unexpected good behavior.

When I return to school on Monday, we'll have the second Responsive Classroom training. We're scheduled to finish Interactive Modeling and move into Teacher Language. From what I see so far, Teacher Language, or saying the right things at the right time, will be key to fulfilling my New Year's Resolution in 2017. I need to reinforce positive behavior more often and students need to hear me say positive things about them right away, not later on. So many times, a student or group is quiet, but by the time I acknowledge it, the talking has resumed. Helping the students remember expectations and giving clear instructions are also important.

This concludes the post. I have one winter break post left, and I'll post it in 3-5 days.

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