Lesson 0-4: Op Art (Day 4)

This is what Theoni Pappas writes on page 233 of her Magic of Mathematics:

"Food manufacturers are seeking to use genetic techniques to manipulate genes in various produce to enhance shelf life, size, taste, and resistance to pests. The altering of genetic codes can now be done in a minute fraction of the time it has taken the process of natural selection to take place."

This is the final page of the genetic engineering section in Pappas. Here she is clearly writing about genetically modified organisms (GMO's) as food. GMO's are controversial to this day, and there are any number of websites discussing the pros and cons of GMO's as food. She concludes:

"[Genetic engineers] are experimenting with life as it has evolved over millions of years!"

As we read these science pages in Pappas, I've been writing about how I should have taught these lessons to my students last year. I doubt I would have taught the about the GMO controversy in any class last year. But there's one thing in science that's on my mind today -- and I'm sure it's on many of your minds as well.

Of course, I'm talking about the solar eclipse. (California isn't in the path of totality, but only in the penumbra, so we have only a partial eclipse.)

Last year, I did teach a little astronomy to students in all three grades. The whole idea was to use the Rosh Hashanah holiday to explain how the earth, moon, and sun work, as well as why there would be no school on that day.

I believe there was one question in that lesson on eclipses -- draw the earth, sun, and moon in order to represent a solar eclipse. The right answer is that the moon should be between the earth and sun. And indeed, today, August 21st, 2017, the moon is between the earth and sun -- so that's why there's a solar eclipse today.

It's awkward to think about how I would have taught my students about eclipses last year. A much more interesting question is, had I not left my old school, how would I have used today's eclipse to teach them about astronomy?

Well, I must point out that since I left, my school has made a few changes. First of all, both my school and our sister charter have moved to new locations. The charters are no longer co-located with district schools, but instead they own their own buildings.

This means that the school calendar is no longer dependent on the LAUSD calendar. In particular, the school year started later at the charters in order to give more time to move everyone's belongings to the new sites. The first day at LAUSD was last Tuesday, but the first day at the charters is today.

It would be one thing for the day of the eclipse to fall during the second week of school, or even later during the first week of school. But instead, the eclipse occurs on the absolute first day of school. So this makes a huge difference regarding how I'd set up an eclipse activity, since it would suddenly have to double as an opening activity for the first day of school.

For example, I might want to purchase eclipse glasses so that my students could see the eclipse. I'd try to buy enough of them for all the students in whichever class meets at 10:21 (Pacific Time, the darkest moment of the conjunction).

The problem is that I can't be sure of the class size, so I wouldn't know how many glasses to buy. As teachers, we know that even if we receive rosters before the first day of school, there's no telling how many students will actually show up the first day. Some students who lived right across the street from the old school might not attend the new site -- over a mile away -- while the new location may attract students who live closer to it. And I wouldn't have met the new class of sixth graders starting middle school until just minutes before the eclipse begins.

If I don't buy enough glasses, then the students without glasses would try to look directly at the eclipse anyway. And then some of them might go blind -- a risk clearly not worth taking. There's just no way to know how many kids there'll be in the 10:21 class.

And that leads to the other confounding factor -- the schedule. Recall that I had to teach science because our school lacked a science teacher. There's a strong possibility that this year, a science teacher would have been hired. If there's a science teacher, then there would have been no need for me to teach science and thus no need to have an eclipse lesson. But I still like the idea of having an eclipse activity at 10:21 -- after all, the students in my class at 10:21 wouldn't be in the science class at that time. So it might be nice for all teachers to talk about the eclipse with whichever class they have at that time.

For today's speculative post about how I'd have taught about the eclipse, let's assume that my schedule would have been the same as last year's. On Mondays, I began with seventh grade, then eighth grade (with 10:21 about halfway through the class), and then sixth grade. Oh -- the new school starts 45 minutes earlier than the old school (so there's a possibility that the first class would leave before the eclipse begins), but we'll ignore this for today's speculative post. (For this post, I assume that there is no coding Monday today. Last year the coding teacher didn't arrive until the third week of school.)

So let's say that my day begins with seventh grade, and that this class lasts at least until after the eclipse begins. I'd have this class construct "pinhole projectors" -- the classic method of viewing an eclipse before they came up with eclipse glasses. The only problem would be whether I can round up enough shoe boxes to make the projectors. (Actually, I've heard of cereal boxes being used for this purpose as well.) I hope that there is some time left for the students to view the beginning of the eclipse before this class ends. It's also possible to have some students create an "eclipse banner" made up of black moons covering up yellow suns. They could even use the die cut machine, if there's a circle shape. (Recall that one problem I had at my old school was my failure to employ the die cut machine for Illinois State projects.)

Now eighth grade arrives during the darkest part of the eclipse. This is the class that I'd want to purchase glasses for -- but would this class be too large? Last year, eighth grade was my smallest class, but notice that this year's eighth graders would be last year's seventh graders -- and seventh grade was a larger class. I was told that the reason eighth grade was small last year was that the previous year, the seventh grade troublemakers were counselled out of enrolling for eighth grade. So if we assume the same happens this year, the resulting eighth grade class would be small enough for me to purchase glasses for all of them. I've seen some eclipse glasses on sale at 7-Eleven, and so maybe I'd only have to buy seven to eleven (or slightly more) pairs for this class. Then they can view the eclipse at its maximum coverage (almost 70% here in Southern California).

Sixth grade comes to my class as the eclipse is almost over. I let them view the last part of the celestial event through the pinhole projectors. Once it is over, I begin a project from the Illinois State science text -- a flashlight represents the sun, and balls represent the earth and moon. The intent of the project is to demonstrate the phases of the moon. But the new moon phase can be modified slightly to represent the solar eclipse position.

But alas, none of this happened today because I wasn't in a classroom. Maybe I'll be teaching in a classroom on the day of the next total solar eclipse visible from North America -- April 8th, 2024. I point out that meanwhile, the last great American eclipse was in 1979, just before I was born -- but I do remember a partial annular eclipse occurring in May 2012.

Hold on a minute, you might ask. How do I know when the next eclipse will be? That's easy -- the following website lists all of the eclipses up until the year 3000:

http://moonblink.info/Eclipse/lists/solcat

Okay, then -- now you ask, how does the owners of this website know when and where exactly all the eclipses will be? Did someone build a time machine and travel all the way to the year 3000 to find out when the eclipses are? (Or maybe Bender from Futurama sent back all the eclipse info all the way from 3000?) Actually, the simple answer is -- mathematics.

Most likely, spherical trigonometry can be used to find the location of an eclipse. Much to my surprise, there is no mention of solar eclipses in Glen Van Brummelen's Heavenly Mathematics. (That book mentions only lunar eclipses, twice in Chapter 1.)

But we can use some ideas from spherical trig to predict eclipses. According to Van Brummelen, the sun always travels along the ecliptic. (Get it -- eclipse, ecliptic?) So an eclipse can only occur when the moon crosses the ecliptic. This crossing happens approximately twice a year -- creating two "eclipse seasons," with each containing one solar and one lunar eclipse. The above link also explains when the eclipse seasons are:

http://moonblink.info/Eclipse/stats

Solar eclipses only occur during new moons, but the lunations don't line up with eclipse seasons. It turns out that a cycle containing approximately both a whole number of lunations and a whole number of eclipse seasons is called a "Saros cycle," about 18 years long. (This isn't the same as a "Metonic cycle," which is 19 years long and used to determine Easter. A Metonic cycle contains a whole number of lunations and solar years, not eclipse seasons.)

So 18 years and one month from today is September 2035. According to the link, there will indeed be a total solar eclipse that month (labeled as "Saros 145"), but it will be visible only in Asia.

But this is how I can tie eclipse to a possible math (as opposed to science class -- the fact that math can be used to predict eclipses. I've already written about what my ideal first day of school would have been like -- but what about the music break? The plan for my second year of teaching would be that I'd repeat the songs from my first year on their corresponding days. And so I'd repeat my first day of school song -- the Dren Song. But I'd make a change to one line from last year:

The Dren Song -- by Mr. Walker

I don't know why I take math.
I'm all caught up in its wrath.
I'd rather just be a dren.
I would be so happy then.
Tell me what would happen when,
I'm no longer just a dren.
What if I were great at math?
What would be my future path?
Customers won't think it's strange,
When I figure out their change.
Algebra and calculus,
Get me in a cool college.
Once I finish my degree,
Future employers will see,
Of my strong background in STEM.
I know that will impress them.
Reach the moon, be a hero! (replace with "Predict the eclipse, be a hero!")
I won't just be a zero!
I'll be great, or it may seem,
That this all is just a dream,
'Cause my math skills are so bad.
I can't subtract! I can't add!
I can't multiply by ten.
I will always be a dren.
Now I know why I take math.
Help me find a better path!
I would be so happy then.
But I'm just a dren.

Thus I make the connection between math and the eclipse -- math is used to predict eclipses.

Another song that might fit today is "Earth, Moon, and Sun." I said that I want to sing last year's songs on the corresponding days this year -- and last year I sang that song the day after the Rosh Hashanah school closure. But the charter school, no longer co-located with LAUSD, is hence no longer bound to observe district school closures. If the school is open on Rosh Hashanah (which falls in one month at the next new moon, September 21st), then it might make more sense to sing the song today -- with extra lines to describe eclipses, of course:

EARTH, MOON, AND SUN - by Mr. Walker

I know of how the earth goes,
It revolves around the sun every year.
I know of how the earth goes,
It revolves around the sun every year.
The earth's tilt is the reason,
That we have four seasons.
Winter, spring, summer, and fall,
That is all.
In the north, remember,
Winter's in December.
Tilts toward the sun in June,
It'll be summer soon.
I know of how the earth goes,
I know of how the earth goes,
I know of how the earth goes,
It revolves around the sun every year.

I know of how the moon goes,
It revolves around the earth every month.
I know of how the earth goes,
It revolves around the sun every year.
That's why every 30 days,
We can see every phase.
New moon, waxing crescent,
Half moon, waxing gibbous.
That's why every 30 days,
We can see every phase,
Full moon, waning gibbous,
Half moon, waning crescent.
Moon between the earth and sun,
That's a solar eclipse.
Earth between the moon and sun,
That's a lunar eclipse.I know of how the moon goes,
I know of how the moon goes,
I know of how the moon goes,
It revolves around the earth every month.

Professional songs referring to eclipses are Bonnie Tyler's "Total Eclipse of the Heart" and Carly Simon's "You're So Vain" -- but my own songs should be sufficient for the lesson. Oh, and even though I usually give out candy as a reward for A's (see my November 17th post for more info), today would be an exception as I could give out Milky Way bars, Starburst candies -- and of course, Eclipse gum.

Even though Van Brummelen doesn't write anything about solar eclipses, another book I bought at the same time -- last spring's Barnes and Noble teacher day -- was Ian Stewart's Calculating the Cosmos, and Stewart does mention solar eclipses. (Actually, all month Barnes and Noble is having more teacher discount days, and yesterday I bought a Dover text on the cheap, C. Stanley Ogilvy's Excursions in Number Theory. I may or may not write about this book on the blog, but for today let's stick to Stewart and eclipses.)

Solar eclipses appear in the prologue and first chapter of Stewart's book. Let's look at the prologue:

"Conversely, astronomical phenomena have influenced the development of mathematics for over three millennia, inspiring everything from Babylonian predictions of eclipses to calculus, chaos, and the curvature of spacetime."

So now we see who the first eclipse predictors were -- ancient Babylonian mathematicians. Let's look at Stewart's next mention of eclipses:

"Einstein saw his theories verified by two of his own predictions: known, but puzzling, changes to the orbit of Mercury, and the bending of light by the Sun, observed during a solar eclipse in 1919."

I remember watching this in an episode of Genius, the series whose first season was on Einstein. He actually tried to send a colleague to observe an eclipse five years earlier, in 1914. The path of totality passed through Russia, but World War I derailed Einstein's plans. The colleague was arrested by the Russians as a possible spy!

Stewart continues writing about eclipse predictions in Chapter 1, "Attraction at a Distance":

"People calculated aspects of the cosmos, such as eclipses, for millennia before anyone realized that gravity existed. But once gravity's role was revealed, our ability to calculate the cosmos became far more powerful."

As the first chapter title implies, this chapter is all about gravity and the scientist who first came up with the theory of gravitation, Isaac Newton.

Here is Stewart's final mention of eclipse prediction:

"So exquisitely accurate are those rules that astronomers can predict eclipses of the Sun and Moon to the second, and predict within a few kilometers whereabouts on the planet they will occur, hundreds of years into the future. These 'predictions' can also be run backwards in time to pin down exactly when and where historically recorded eclipses occurred."

Hence the website I linked to above is made possible. Not only does it predict eclipses up to the year 3000, but it also goes all the way back to 2000 BC. Here Stewart is writing about mathematical modeling -- a key Common Core Standard -- and the error terms associated with such modeling.

Okay, I can go on and on all day about the Great American Solar Eclipse. But we need to get on with the Geometry lesson.

Lesson 0.4 of Michael Serra's Discovering Geometry is called "Op Art." Serra explains what this is:

"Op art (optical art) is a form of abstract art that uses straight lines or geometric patterns to create a special visual effect."

Optical art is closely related to the concept of optical illusions. I don't even want to attempt to draw some of the more complex optical illusions by hand, so I just use a Google search instead. On the other hand, the impossible objects page comes directly from this site:

http://brainden.com/impossible-objects.htm

Unfortunately, only the Penrose triangle printed properly. It is named for Sir Roger Penrose, whom Serra describes as a British mathematician and avid puzzle enthusiast. (He is in fact still alive -- he just turned 86 this month.) So I actually had to draw in one of the impossible drawings -- "Three prongs from two?" (called "the devil's fork" by Brainden). Well, I suppose if I can draw it, then so can our students.

Well, that's it for today. I'll see you on April 8th, 2024 -- the day of the next American eclipse. It's a Monday, so it should be a school day. (Don't worry about Easter that year -- solar eclipses occur at new moons while Easter falls at the full moon. But at schools that take the week after Easter off, eclipse day will be the very first day back to school -- just like at my school this year.)

Lesson 0-3: Daisy Designs (Day 3)

This is what Theoni Pappas writes on page 230 of her Magic of Mathematics:

"In addition, they form macromolecules (enormous molecules made up of thousands of atoms strung together) such as lipids, starches, cellulose and the even more complex nucleic acids and proteins. The DNA molecule with its genes provides the blueprint for the life of a cell."

I think back to my own days as a student. A classic project is for the students to construct a model of a DNA molecule, and I did so as a sophomore taking Integrated Science II.

I don't know whether the Illinois State text includes a DNA molecule project or not. The Illinois State science text was divided into three volumes -- earth, life, and physical science -- and the life science text was the last to arrive at my school. Therefore I was less familiar with the projects in this text than in the other two science texts.

In fact, part of the reason for my failure to teach science was the lack of science texts. You see, Illinois State didn't supply us with enough science texts (as opposed to math texts) -- in fact, the students never received science texts. There were teachers editions of the earth and physical science texts -- and they were both delivered to our sister charter school.

The thing about our sister charter is that they didn't have any eighth graders. This made a huge difference when looking at their bell schedule. (See my November 9th post for more information.) At both schools, the day was divided into four main blocks followed by P.E. time. Over there, sixth and seventh graders had two blocks with my counterpart teacher -- one for math, the other for science. At my school, meanwhile, I had each grade for one STEM block and the last block was for IXL with one of the grades.

I think this was what confused me about teaching science. The administrators intended me to start teaching science, possibly by going to the Illinois State website for science materials. But I didn't, because I thought that the STEM projects in the Illinois State math text counted as science! Notice that some of the math projects in each text could double as science projects (e.g., research projects in Grades 6-7, solar system project in the eighth grade text). But in reality, I should have taught science using the Illinois State materials -- online only until my teachers editions arrived.

So there was a perfect storm of confusion regarding why I didn't teach science properly:

-- lack of science texts at start of year
-- nonappearance of science on daily schedule (replaced by mystic "STEM" block)
-- projects in math "STEM" text resembling science projects
-- lack of other middle school science teachers on campus to ask for info
-- counterpart on other campus unhelpful as she didn't teach eighth grade (the critical testing year)
-- counterpart on other campus unhelpful as her specialty wasn't science (it was really kindergarten!)
-- transition from California Science Standards to NGSS

My earth and physical science texts finally arrived at some point -- I don't recall exactly when (though it might have been close to that aforementioned November 9th date). Neither my counterpart nor I had a life science text. In fact, she ended up using the earth science text for sixth grade (which she knew matched the old standards) and thus, by default, physical science for seventh grade. (Some physical science topics, such as atoms and molecules, do appear in the seventh grade NGSS.)

Of course, I knew that at the very least, my eighth graders needed science for the state test. One day, some eighth graders complained, "Why aren't you teaching us science? In fact, do we even have any science textbooks?"

There were some old texts near the back of the classroom -- but unfortunately, they were only for sixth (earth) and seventh (life) grades. Then I tried to teach an eighth grade NGSS lesson from the seventh grade text -- but of course they rejected the lesson. And of course, no one accepted my explanation of what NGSS was, or why Illinois State didn't provide any student texts. Interestingly enough, science and math suddenly appeared on PowerSchool just in time for me to assign separate grades at the end of the second trimester (as opposed to the first trimester, when the students received only a "STEM" block grade).

Notice that it was right around the end of the first trimester when the Illinois State teacher texts arrived -- perhaps that should have been the hint that skipping science first trimester was understandable without the texts, but as soon as I had them, that was the time to begin teaching science -- to all three grades.

Well, I did start teaching science to the eighth graders at that point -- the DNA lesson. And this takes us back to Pappas. She writes about the importance of the shape of the sugars in the molecule:

"It is the pentagonal shape of deoxyribose which makes the shape of the spiral and requires 10 rungs to complete a turn."

Later on, she explains:

"When gene copying (or DNA replication) takes place the DNA double helix is unwound at breakneck speeds of over 8000 rpm, and splits along the bases separating into two strands."

Again, I could have tried to keep the mathematical models of DNA structure and replication in mind as I taught this lesson to the proper grade level -- the seventh graders.

Lesson 0.3 of Michael Serra's Discovering Geometry is called "Daisy Designs." Yesterday the students used rulers or straightedges to make designs, and today they'll use a compass.

Serra begins:

"The compass is a geometric tool used to construct circles. You can make some very nice designs with only a compass."

The students are then directed to create a "daisy" using a single compass setting. Serra points out that this construction is related to that of a regular hexagon -- which is required under the Common Core.

On today's worksheet, I take one question from the exercises  -- and the other, as usual, is taken from the project. I found a website that teaches students how to form the daisy designs:

http://geometry2014.weebly.com/daisy-design.html

(The creator of this website is Monica Zimmers, a New York high school teacher.)

The second question directs the students to use a graphing calculator to graph r = a sin (n theta) in polar coordinates, for various values of a and n. The graph of these are, well, "daisies." Of course, I don't expect all students to have graphing calculators (though I do expect them to have compasses).

Lesson 0-2: Line Designs (Day 2)

This is what Theoni Pappas writes on page 229 of her Magic of Mathematics:

"Jurassic Park has made the general public very aware of the wonders and possible horrors of genetic engineering. The drama of life unfolds within a single cell."

This is the first page of a new section, "Mathematics & Genetic Engineering." This section spans several pages, so expect me to devote several blog posts to this topic.

Cell biology, of course, counts as life science. Therefore, if I had taught science the way I was supposed to, this topic would have been covered in my seventh grade class. Instead, I attempted to teach it to my eighth graders under the NGSS standards.

I've admitted before that life science isn't my strong suit. And so I tried to use my Bruin Corps student, a molecular biology major from UCLA, to explain the details of this topic. In reality, I should have come up with a stronger science program from the start of the year -- well before the arrival of my Bruin Corps student -- and then had him supplement that curriculum, rather than try to have him be the curriculum.

Of course, I couldn't make the students enthusiastic about science if I am not enthusiastic about it. To increase my interest in life science, let's try to tie it to my best subject, math -- and this is exactly what Pappas does in this section. She writes:

"Here enter the mathematical concepts of patterns, sequences, relations, one-to-one correspondence, all playing a role in unraveling the codes and mysteries of the living cell."

We also see how Pappas ties cell biology to a branch of science I'm stronger at -- chemistry (as I wrote in yesterday's post):

"It is amazing to consider that every living cell is composed of the same six elements -- carbon, hydrogen, oxygen, phosphorus, nitrogen, and sulfur."

Again, this purpose of this is to engage myself with the lesson by tying it to my stronger subjects. But the next step is to engage the students with the material. Pappas herself suggested a way when she mentions the movie Jurassic Park.

At the time Pappas wrote her book in 1994, the first Jurassic Park film had just been released. Since then, it has expanded into a full franchise, with Jurassic World having been released two years ago and the fifth movie, Fallen Kingdom, to be released around the last day of this school year. So surely it wouldn't have been that difficult to tie the movies to the science lesson. "Have any of you watched the newest Jurassic Park movie? Do you know how the scientists in the movie brought the dinosaurs back to life? It's called genetic engineering...." This might have sparked an interest in learning the science and convince the students to let me teach them even though I wasn't a true science teacher.

I owed it to my students to teach them life science -- after all, I'd never know how many future doctors I had in my classes. One seventh grade girl once told me that she wanted to become a veterinarian when she grew up. Obviously, vets need to be familiar with life science -- and this includes genetic engineering (what is dog breeding after all).

Lesson 0.2 of Michael Serra's Discovering Geometry is called "Line Designs." In this lesson, students learn to draw amazing designs with nothing but straight lines. Serra writes:

"The symmetry and the proportions in geometric designs make them very appealing. Geometric designs are easy to make when you have the tools of geometry."

Serra explains to the students that there are many tools used in geometry -- including the compass, straightedge, ruler, and protractor. As a second day of school assignment, this is a great time to tell students to purchase these tools for use in this class.

Today's assignment officially requires only a ruler. Technically, the compass or protractor could be used to ensure that the angles are right angles, but I expect the students to have access only to rulers for this assignment.

The first question directs students to re-create two designs using only lines. Notice that the first one can also be completed using graph paper. The last two can be drawn on isometric graph paper if it is turned sideways. (Yes, I still recall the problems my class had with isometric graph paper.) One of these is Sierpinski's Triangle, a famous fractal.

Serra also writes about several famous architects -- Ustad Ahmad Lahori, the designer of the Taj Mahal (and a mathematician!), as well as Frank Lloyd Wright. I include the project based on architecture on today's worksheet.

Meanwhile, I skipped Serra's question on the symmetries of the benzene molecule. Of course, this question would be related to yesterday's and today's Pappas pages.

Lesson 0-1: Geometry in Nature and in Art (Day 1)

This is what Theoni Pappas writes on page 228 of her Magic of Mathematics:

"Mathematical objects are present in many natural occurring chemical substances. Studying the molecular shape of objects, one finds pentagons in the shape of deoxyribose, tetrahedrons in silicates molecules, double helices in DNA, polyhedron shapes in crystals and other molecular formations."

This is the only page of a new section, "Mathematical Models & Chemistry." Last week, I wrote that during these Pappas pages in the science chapter, I'll reflect on how I taught science last year -- or should I say, how I didn't teach science last year.

Chemistry, the subject of this section, falls under the umbrella of physical science. As such, it was part of eighth grade science under the old California standards. In the NGSS, however, some of the chemistry-related topics are now considered seventh grade standards. I've written before that I should have stuck to the old California Science Standards in Grades 7-8 and introduced the NGSS only to the sixth graders. This meant that the eighth graders should have received the chemistry lessons.

Of course, there was that Edible Molecule Project -- the first project in the Illinois State science project text. As you may recall, a huge argument between me and the "special cousin" -- the new girl transferring in from another school -- surrounded that project. First, she stated that the previous year, her science teacher had assigned an Edible Cell Project, which she'd enjoyed. She also told me that I was wrong to teach anything other than physical science -- since the previous year had been life science -- and ignored me when I tried to explain the NGSS. Finally, when I did finally assign the Edible Molecule Project, she continued to complain and didn't want to complete the project.

Although the new girl was just being oppositional, she did make some valid points. Chances are that if I'd taught physical science strongly from the start of the year -- as well as treated her cousin (the "special scholar") with more respect -- she'd have been willing to learn science from me. Notice that if I really had taught science from the start of the year, I probably would have been past the chemistry projects in the Illinois State text and been ready to work on those that leaned towards physics.

During the Edible Molecule Project, I didn't really say much about the shapes of the molecules -- the focus of the Pappas page. I just told the students that for a molecule like H2O, each hydrogen atom is bonded to the oxygen atom, not to the other hydrogen. I didn't say, for example, that the bond angle in H2O is 105 degrees.

It's a shame that I wasn't able to teach chemistry to my eighth graders better. After all, I wrote before that I prefer physical science to life science -- and in fact, I have a special affinity for chemistry. Back in February 2016, I explained why:

One last thing I want to mention in this post -- when I was young, I remember being fascinated by an old college chemistry text. Some of the problems in this text required algebra, and one of them was a slope question which used the notation slope = delta-y / delta-x -- where the symbol "delta" stands for something like "difference" or "the change in." So when my Algebra I teacher assigned some slope problems, I started writing "delta" in all of my answers. I still remember her response: "Delta is one of my favorite Greek letters." Believe it or not, I've since noticed that nowadays, some Algebra I teachers actually use "delta" when teaching slope!

And then eleven months later, I wrote about how well I did in my chemistry classes:

I think back to my own days as a science student -- which contain many highs and lows. As a high school freshman, my general science teacher saw some promise in me and wanted to promote me to an Applied Bio/Chem class, but I moved to another school before the end of the first quarter. Two years later, my Integrated Science III teacher at that new school similarly thought I was gifted and not only recommended me for Chemistry, but convinced the magnet at our school to accept me!

But unfortunately, I didn't extend my chemistry fascination to my eighth graders. I could have had fun telling them about tris, a molecule Pappas describes as having the shape of a Mobius strip:

"Tris is composed of chains of carbon and oxygen atoms and ends in alcohol groups, which lend themselves to being clipped easily together after the chain is given a half-twist."

Today is the first day of school according to the blog calendar. The blog calendar is based on one of the districts from which I hope to receive subbing calls. This district is not LAUSD, but in fact is the district whose calendar I used three years ago -- the first year of this blog.

I could have used another calendar -- a charter school who might also hire me as a sub. This calendar is closer to the one used at LAUSD. In particular, the charter's first day of school was yesterday. The reason I favor the district calendar is that it's more convenient for my purposes.

The two calendars more or less agree (staying within one day of each other) until winter break. But the charter follows the LAUSD three-week winter break and completes the first semester on December 15th with 80 days. The other district calendar agrees that December 15th is Day 80, but its winter break is only two and a half weeks long. After December 15th there are more days of school before winter break -- and these are the days for finals.

Recall that I'm following the digit pattern for days in the U of Chicago text. Chapter 7 is the last chapter of the first semester, and it contains eight sections. Following the district calendar puts Lesson 7-8 ("The SAS Inequality" or Hinge Theorem) on Day 78. Then Days 79-80 can be review days for the final, to be given on Days 81-83.

On the other hand, following the charter calendar forces Days 78-80 to be finals days. One could argue that the SAS Inequality isn't that important (and I often skipped it myself in the past), but Lesson 7-7, "Sufficient Conditions for Parallelograms," really is important. The charter calendar would force this lesson to share Day 77 with review for the final -- and Lesson 7-6, "Properties of Special Figures," would also be affected by finals review. Therefore the district calendar, with 83 days in the first semester, is more convenient for my purposes.

Of course, notice that the district calendar starts the second semester with Day 84, which would be the day for Lesson 8-4. But Lessons 8-1 through 8-3 can be waved away. After all, Lesson 8-1, "Perimeter Formulas," can be summed up in a single sentence ("Just add up all the sides!") Then Lesson 8-2, "Tiling the Plane," can be skipped entirely. Lesson 8-3, "Fundamental Properties of Area," does give the formula for the area of a rectangle, but then this can easily be sneaked into Lesson 8-4 ("Areas of Irregular Regions"). So I still prefer the district calendar because I find Lessons 7-6 and 7-7 to be more valuable than Lessons 8-1 and 8-2.

In the end, this is the only true difference between the calendars. The two day counts remain within three days of each other the entire year, and both stay within three days of LAUSD. You can refer to my posts from my first blog year (2014-15) to see this district calendar in action. But for future reference, here is a pacing guide for the entire year:

Chapter 0: August 16th-29th
Chapter 1: August 30th-September 13th
Chapter 2: September 14th-27th
Chapter 3: September 28th-October 11th
Chapter 4: October 12th-26th
Chapter 5: October 27th-November 9th
Chapter 6: November 13th-December 1st
Chapter 7: December 4th-15th
Semester 1 Finals: December 18th-20th
Chapter 8: January 8th-17th
Chapter 9: January 18th-31st
Chapter 10: February 1st-15th
Chapter 11: February 16th-March 2nd
Chapter 12: March 5th-16th
Chapter 13: March 19th-April 9th
Chapter 14: April 10th-23rd
Chapter 15: April 24th-May 9th
State Testing Window: May 10th-June 1st
Semester 2 Finals: June 4th-6th

Notice that Day 14 is the day after Labor Day. This means that teachers at schools that have a Labor Day Start, but wish to follow my pacing guide, can simply pick it up at Lesson 1-4, "Points in Networks" -- which was my traditional first day of school lesson for the first three years of this blog.

But at the district whose calendar I'm following on the blog, today is the first day of school. Actually, there was a "Freshman First Day" yesterday, so ninth graders attend 181 days of school. We could thus count yesterday as "Day 0" -- but if I were a regular Geometry teacher in this district, I wouldn't bother to teach any math on Day 0 anyway. Some of the Geometry students might be freshmen, but many would be sophomores, and so the first real lesson would be today, Day 1.

Even though there is no Day 0 on the blog, there is a Chapter 0, covering Days 1-10. Since the U of Chicago text doesn't have a Chapter 0, we use Michael Serra's Discovering Geometry instead. Don't forget that my copy of Discovering Geometry is an old text, dated 1997 (Second Edition). My old version goes up to Chapter 16. The modern (3rd-5th) editions only go up to Chapter 13. But Chapter 0 is essentially the same in all editions -- the only difference is that Lessons 0.5 and 0.8 no longer exist in any edition later than my Second Edition.

Lesson 0.1 of the Discovering Geometry text is called "Geometry in Nature and Art." In this lesson, students learn that Geometry is all around them. Serra begins:

"Nature displays an infinite array of geometric shapes, from the small atom to the greatest of the spiral galaxies. Crystalline solids..."

Atoms -- hey, this sounds exactly like what Pappas is writing about! It's fitting, then, that this Pappas page landed on the same day as this lesson. Then again, Serra focuses more on macroscopic shapes rather than microscopic shapes. His other examples, including honeycombs, snowflakes, and pine cones, appear earlier in Pappas.

The main theme of this lesson is symmetry. Serra writes about two types of symmetry -- reflectional symmetry and rotational symmetry. And so we are introduced to two of the main Common Core transformations, reflections and rotations, in the very first lesson.

I created the first worksheet of the year from questions from Serra's text. Some of these are labeled as Exercises, while others come from his first "Project." And some of these questions ask students to bring objects in to class. This seems awkward for the first day of school -- but then again, this is the very first lesson in Serra (so it's intended for early in the year). It might be good for teachers to find photos on the internet and show them to the class. Or better yet, the students might be able to come up with pictures of their own to draw -- especially the questions about art from various cultures (which include the students' own cultures).

Yet there are two questions that students might enjoy as an opening day activity. One of them asks students to find the line of symmetry in a work by British artist Andy Goldsworthy, who indeed is still alive (hint: H2O). The other asks students to name playing cards with point symmetry. They might want to draw these -- the three of diamonds has point symmetry, but not the three of clubs. Yes, they might want to try drawing the three of clubs with point symmetry to see why it is impossible.

All Fawn Nguyen Has on Classroom Management

Table of Contents

1. Pappas Page of the Day
2. Fawn Nguyen on Classroom Management
3. Observe your colleague.
4. Know what you absolutely value above all things.
5. Separate the behavior from the child.

Pappas Page of the Day

This is what Theoni Pappas writes on page 223 of her Magic of Mathematics -- a table of contents for Chapter 9 of her book:

Mathematics & the Mysteries of Life
-- Mathematizing the Human Body
-- Mathematical Models & Chemistry
-- Mathematics & Genetic Engineering
-- Body Music
-- Secrets of the Renaissance Man
-- Knots in the Mysteries of Life

Fawn Nguyen on Classroom Management

OK, I wrote that yesterday would be my last summer post. But I couldn't resist blogging today because of a post I saw on Fawn Nguyen's blog:

http://fawnnguyen.com/all-i-got-on-classroom-management/

As you can tell by the title, this post is all about classroom management. My post from yesterday was also all about management -- but given my situation, I can't have too many management posts. So let's see what Nguyen has to say on this important topic:

Not enough people write about classroom management in a practical and realistic way. But this does! Helpful tips. https://t.co/oXXwOU6xDK

— Michael Pershan (@mpershan) August 9, 2017

Classroom management is hard, and what’s “practical and realistic” for one person could be entirely impractical and unrealistic for someone else to follow. Take a math lesson taught successfully at a parochial school in a class of 12 students wearing uniforms and bring it into an inner-city public school in a class of 37 students wearing skins in shades of brown, black, and yellow, and you might find that you need to tweak the lesson a bit.

You and I are two different people. You and I are two different teachers. What irks me may not even faze you. You and I can tolerate different ranges of decibels emitting from classroom activities. You like foldables, and I like baguettes.

Your students are different than mine.

Yes, of course classroom management is hard -- otherwise I would have been a great manager last year and had no problems in the class. I find it interesting that Nguyen compares a class of 12 students at a private school to a class of 37 students at an inner-city public school. I was working at an inner-city charter school, and my eighth grade class had only 12 (well, actually 13) students. On the other hand, the Grade 6-7 classes were about halfway between her lower and upper limits. (As for the racial demographics of the class, see my January 6th post.)

Meanwhile, I can tolerate a few "decibels emitting from classroom activities." The problem with letting one student talk is that every concludes that it's OK to talk -- and then suddenly it's more than just a few decibels.

Nguyen continues:

Therefore, any advice on classroom management is making huge assumptions about who you are, what your students are like, and what your admins had for breakfast. I don’t blame you if after reading a how-to book on classroom management, and you feel stuck at step 4 below.

At this point Nguyen provides a picture of "How to Draw a Horse." The fourth step that she mentions above is, "Draw the hair" -- that is, add small details. (If you want to see the picture, follow the link above directly to her blog.)

No book is gonna help you master this thing. I’m sorry. You don’t become a chef by reading cookbooks. You just gotta go into the kitchen, roll up your sleeves, make a big mess, and voila boeuf bourguignon! Or not.

But before you accuse me of writing a post that is completely useless and unhelpful, please allow me to offer just these three tidbits.

OK then, let's look at these three tidbits. Just as we did with Lee Canter yesterday, I'll comment on how I could have applied Nguyen's "tidbits" to my old classroom.

Observe your colleague.

Intentionally schedule a time when you may come in to observe a colleague whom you hold in high regard and whom you may ask a thousand follow-up questions. It’s equally important that this colleague reciprocates the observation and gives you constructive feedback. Most likely you know this colleague better than you know any author of some book, and of course, you two share pretty much the same clientele. For optimal efficiency, and if possible, choose a time when your colleague has the same students who seem to be giving you trouble. Kids act differently for different teachers.

Unfortunately, I couldn't have observed any of my colleagues last year. Because our school lacked a separate science teacher, none of us middle school teachers had a conference period. (See any "Day of the Life" post from this past year to see what our schedule looked like.) There were three teachers to cover three grades, so each one of us had to cover a grade at all times.

If I'd been able to choose any teacher to observe, I probably would have selected the history teacher, as he was the strongest manager. Instead, he often gave both the English teacher and me specific tips, such as seating the four seventh grade troublemakers in four different corners.

As for "kids act differently for different teachers," I observed this firsthand when students behaved better for my support staff member than for me. Then again, I couldn't ask her "a thousand follow-up questions" because her job was to supervise the yard during breaks and lunch. But there's one thing I definitely noticed when she was in the classroom -- she had a strong teacher tone.

Know what you absolutely value above all things.

For me, it’s respect. Not just respect for me the teacher, but respect for all of us in the room.

I remember this from an earlier Nguyen post. Her first rule was "Respect each other," and at first I thought that I valued respect as much as she did.

Nguyen continues:

But because I know this about myself, and being proactive always yields better results than being reactive, I tell my kids of my zero-tolerance for disrespect from the get-go. I say, “I need you to be respectful. That’s the only way we are going to get along in here. Before we can do any mathematics or have any fun in here, we are going to be respectful to each other.” And may God give me the grace to apologize when I am being disrespectful to my students. I find that doughnuts help them forgive me quicker.

What I ended up valuing wasn't respect, but just outright following directions. As I wrote before, the most annoying student acts were chewing gum wrappers and playing with phone cases, in an effort to neuter the no gum and no phone rules. Of course, neutering my rules is also disrespectful. But that didn't help me when the students chewed wrappers and told me that I couldn't punish them, or when they played on the cases and told me that it wasn't against any rule.

But I do agree with Nguyen when she tells us to know what we value. In other words, teachers should have a vision about how they want the class to be run. Her own vision is a classroom in which students and the teachers respect each other. And my vision is a classroom in which I tell a student to do something and the student does it, no questions asked.

If I have a vision for the class and the students go against that vision, they are wrong, not I. And so if I tell them not to chew gum and they chew wrappers instead, they are wrong -- no matter how much they claim that they deserve no punishment. It's only when I go against my vision when I'm wrong -- such as when I give in and fail to punish students who play with phone cases.

Nguyen writes that she needs to be proactive. Lee Canter makes the distinction between proactive and reactive management as well. But it was difficult for me to be proactive in this situation, since I certainly didn't expect students to chew wrappers or play with cases. Instead, I should have had a rule "Follow all adult directions." Then I could correctly tell them that I was directing them to spit out the wrappers and put the cases away.

Another situation where having a vision was necessary was IXL time. My vision for computer time was that the students keep the laptops organized and in numerical order in the charge cart. The class would take the extra time during IXL time to pass out and pass in the laptops so that they're in order.

But first, I was wrong when I violated my own vision. If I really valued keeping the laptops in order, then I should have labeled the slots in the charge cart. After that, if the students complained about taking too long to pass the laptops out or in, then they are wrong.

Oh, and there's one more thing. I like Nguyen's idea of giving the students doughnuts when she disrespects them. But I know that if I'd done the same, the students would claim that I disrespected them everyday just to get the doughnuts.

Separate the behavior from the child.

We know this already.

Maybe I did know this already. But it's not something that I thought about often during the times that I was in the classroom.

Nguyen continues:

What happened? I don’t know exactly, but I do know that we tend to let misbehaviors slide for fear of hurting the kid’s feeling or that it’s not the best time to deal with it. Well, I always try to immediately find the time and will immediately tell a kid that her actions/words are not okay because while the humans are young, their behaviors are especially removed from their true selves. I’m reprimanding the behavior, but I’m keeping the kid. Being a parent for 22 years and a teacher for 26, I conclude that children are highly manipulative. Not because they think it’s a desirable trait, but because they can’t drive and have no income, being manipulative is their survival mode of choice.

Clearly, chewing gum wrappers and playing with phone cases for the sole purpose of neutering my rules count as manipulation. But I've never thought about why students are manipulative -- that it's a form of survival.

If I enter a classroom for the first time -- whether as a full-time teacher or a sub -- I should expect at least one student to talk during the first five times that I tell them to be quiet. And if I call that student out on it, I should expect that student to tell me I'm wrong. It's not because these students are bad, but because they are manipulative, as Nguyen tells us. Instead, I should be finding ways to counter that manipulation -- and that begins with either teacher tone or teacher look.

Students are being manipulative when they are talking when I'm alone in the classroom, but fall silent the instant my support staff member arrives. So I should have countered this manipulation. In this case, once my aide arrives and the class is quiet, I inform the class that this is how quiet I want them to be whether or not the aide is present. Then I send the aide out of the room and tell her to make some copies (even for a contrived reason, such as "I need more copies of the Warm-Up sheet"). Since I know the students to be manipulative, I expect them to start talking the moment she leaves, and so as soon as she opens the door, I'm watching them like a hawk -- and then I call out the first person who speaks. (Oh, but before she leaves, I make sure that they all have pencil and paper -- as they are manipulative, the talker would otherwise claim, "I was only asking to borrow a pencil or paper.")

Nguyen wraps up her post with something interesting:

A few years ago I was sitting in the lodge at CMC-North in Asilomar when someone recognized me from my Ignite talk and came over to chit chat. He was lamenting the frequency in which his students were asking to use the restroom pass. I asked some related questions to learn more before I realized that he wasn’t lacking classroom management skills as much as just lacking a good lesson.

So, there’s that, step 0 as I call it — find that great math task.

I've written before about students who seem to need restroom passes every few minutes can go hours and hours without the bathroom when they are doing something enjoyable. The conclusion, then, is that math lessons should be made more entertaining or fun. Not only would Nguyen agree, but she apparently blames the teacher for lacking a good lesson if there are too many restroom passes.

But then again, some math lessons just are boring. These include listening to the teacher lecture, working on problem sets -- basically anything that the traditionalists favor. So I wonder whether a strong traditionalist like Barry Garelick has problems with restroom passes. If so, what does he do about it? If not, how does he avoid it -- why don't the students ask for passes on days they don't feel like traditional math work?

In theory, the projects from the Illinois State text are enjoyable enough to avoid students wanting to use restroom passes. Still, I don't know -- there's just something about some of those projects that makes them seem less fun. I still believe that the most enjoyable day I had in math was back on Valentine's Day. (The seventh graders didn't have a project due to their different schedule.) That day, I mixed up parts of different Illinois State projects for the eighth graders, while I gave the sixth graders a project I found from an MTBoS blogger. (I meant "I teach math" -- actually, I mean MTBoS. Fawn Nguyen is the Queen of the MTBoS and this is a post all about Nguyen.)

I think back to one sixth grade girl who asked for restroom passes almost everyday. Naturally, she struggled in math. Yet at the start of the year, she told me that she really wanted to succeed in my math class.

In some ways, unlike the teacher Nguyen met in Asilomar, I really had a management problem. I always had to worry about the other sixth graders talking too much, and so I couldn't pull this girl aside and give her the help she needed.

Then again, I could have assigned her a "detention" for excessive restroom pass use -- but then during the detention, I'd give actually give her extra math tutoring. After all, I noticed that she and her older brother regularly stayed for the after school program anyway. Perhaps once I helped her a few times, she'd have been more open to my assisting her during class time. Then she might not have felt a need to go to the restroom to escape my class, and the detentions would stop. (Part of my reluctance to give this sort of detention was the fact that I had no conference period, and so after school was one of the few times I had any sort of break.)

There are some great comments on Nguyen's blog as well. One commenter is Michael Pershan, a New York math teacher (whose tweet is what launched Nguyen's post in the first place):

I think you’re totally right that classroom management is so dependent on our individual contexts. But sometimes I wonder if it’s only the most obvious case of this. I wonder if a lot of the other things we talk about on the internet is dependent on context in less obvious ways. When we share a worksheet or talk about a great mathematical moment, what are the ways that context matters there?

The other is Julie Wright, an Oregon middle school math teacher:

I love your advice to “know what you absolutely value above all things” and to let the kids know about it too right up front. Oddly enough, what I value above all things in the classroom isn’t as easy to identify for me as I would have thought, which tells me I need to think it out thoroughly NOW if I’m going to communicate it clearly to kids in 2 weeks. I believe having that bedrock would help me react to classroom management problems more quickly and clearly in the moment.

And I see exactly what Wright means here. I didn't know what I valued until after school started -- by which point it was too late.

OK, this should really be my final post of the summer -- unless, again, someone else on the MTBoS decides to write a post on classroom management and I feel the need to quote it.

By the way, I never did find Lee Canter's 1993 video that my book was intended to accompany, but I do see a few videos on YouTube that mention the Canter name. The following video is the first result:

Here are a few more loose ends that I want to tie up, since I'm writing this post today anyway. When I left my old school, I inadvertently removed five calculators from the classroom. I was intending to replace the batteries, but I never did it until last night. One calculator is a simple calculator that lacks even a square root key. Two of the scientific calculators are CASIO brand -- the brand that I couldn't figure out how to get out of fraction mode (and led to my catching two eighth grade cheaters). I finally located the MODE button -- actually, I had to press SHIFT and then MODE, which is what had confused me so many months ago.

One of the calculators is a TI-34 scientific calculator. I actually owned this type of calculator back when I was very young. This calculator is one of the few I see with binary, octal, and hexadecimal modes for working in bases 2, 8, and 16. (See my July 31st post on number bases.) The last of the calculators is a very old TI-81 graphing calculator. It is primitive by our current standards, but even it could run a version of the random name program I mentioned in yesterday's post. Thus if I ever teach in a high school classroom, I could use the TI-81 to choose random names, and then save my TI-83 for actual graphing.

And here is the sequence of theorems to prove in natural geometry (from Tuesday's post):

-- A line perpendicular to a mirror is invariant.
-- If a line is parallel to a mirror, then so is its image.
-- Suppose l is a line and l' is its image. If l | | l', then there is one possible mirror. If l intersects l', then there are two possible mirrors. If l = l', then there are infinitely many mirrors.
-- Suppose l is invariant wrt a composite of two reflections. Then each mirror is perpendicular to either the other mirror or to l.
-- Suppose l contains both a point and its translation image. Then l is invariant.
-- A line and its translation image are parallel.

All of these are true in both Euclidean and spherical geometry (though some are only vacuously true on the sphere). The goal is to prove them all in natural geometry.

But I won't be doing so soon. In my next post -- which should be on Tuesday or Wednesday -- I will begin the school year posts with Chapter 0 of Michael Serra's Discovering Geometry, before moving on in the U of Chicago text two weeks later.

Lee Canter's Succeeding with Difficult Students

Table of Contents

1. Pappas Page of the Day
2. Lee Canter's Succeeding with Difficult Students
3. Worksheet #4 Scene #1: Cynthia
4. Worksheet #4 Scene #2: Rodney
5. Worksheet #4 Scene #3: Jessie
6. Airtight Hierarchies for Other Infractions
7. Traditionalists and Politics
8. Plans for the New School Year

Pappas Page of the Day

This is what Theoni Pappas writes on page 222 of her Magic of Mathematics:

(nothing)

That's because this is the first page of a new chapter. It's only fitting that in this, my final post of the summer, we start a new chapter in Pappas. Chapter 9 of the Pappas book is, "Mathematics & the Mysteries of Life." As usual, this is the chapter intro page, with the table of contents on page 223.

There is, of course, a picture on this page, along with a caption. Since you can't see the picture, I might as well type in the captions right here:

"The DNA molecule with its genes provide the blueprint for the life of a cell. [Here is] an example of one rung from the DNA ladder. The two strands of the double helix wind in opposite directions. This is why the sugars and the phosphates are in opposite locations on the two strands."

The four bases are abbreviated as follows:

A=adenine, C=cytosine, G=guanine, T=thymine

The atoms in the sugars and phosphates are abbreviated as follows:

H=hydrogen, C=carbon, N=nitrogen, O=oxygen, P=phosphorus

As I read this chapter, I can't help but think about the science I (should have) taught last year. One of the lessons I covered with my eighth grade class was on DNA. I had my Bruin Corps member, a molecular biology major from UCLA, help me out with the lesson.

There were several problems with the lesson that day. First of all, the eighth graders complained that they already learned this lesson the previous year. It all stems from the transition from old California Science Standards to new Next Generation Science Standards. DNA was a seventh grade life science topic with the old standards, but an eighth grade topic with the new standards. My eighth graders had learned science under the old standards the previous year, but I knew that they'd have to take the California Science Test based on the new NGSS a few months later.

I've explained a few months ago what I should have done on the blog -- I should have taught the old standards to Grades 7-8 and only used NGSS with the sixth graders. In other words, this DNA lesson was intended for my seventh, not eighth, graders. This would have avoided the "We already learned this!" complaint from the eighth graders -- as well as the "Why aren't you teaching us science?" complaint from the seventh graders.

I've always preferred physical science to life science since I'm a math major, and the former has a deeper connection to math. Yet Pappas writes that math and life science are related after all. Maybe I would have enjoyed teaching life science better if I had read this Pappas chapter first. Then again, I didn't obtain the Pappas book until after I'd left the school -- and if I had taught DNA to seventh grade at the proper pace, it's also likely to have been before I bought Pappas as well.

Lee Canter's Succeeding with Difficult Students

I've mentioned on the blog that my problems with science affected my classroom management. The students didn't respect me, in part, because of my problems with science. If I didn't follow the rule that I should teach science, they asked, why should they follow the rule that they shouldn't talk during class time?

Just before I left my old school, an instructional aide was assigned to help me out. She strongly recommended that I read Lee Canter's books on classroom management. I took her advice and bought his Succeeding with Difficult Students, at the same book sale where I purchased Pappas.

I've written about Pappas in every post this year. Many of those posts include topics like quaternions and topology -- neither of which did I ever teach, nor will I ever teach in a classroom. I've devoted three entire posts to Glen Van Brummelen's spherical trigonometry, which includes completing some of the exercises in his book. Again, spherical trig has nothing to do with any classroom of mine ever.

On the other hand, classroom management is pertinent to every single class. I'm no longer at my old school due to management, and if I ever expect to be in a school again, management skills will be of prime importance. And so if I felt the need to answer questions out of Van Brummelen's book, how much more of a need is there to answer questions out of Canter's book? And ironically, the Canter book, which cost me only a quarter, is so much more valuable than the fifty-cent Pappas book.

And so that's exactly what I'll do in today's final summer post. As usual, you natural classroom managers may be bored by all of these tips that I'm figuring out, but you've known all along, so again it's OK if you want to skip the remainder of this post.

Lee Canter's Succeeding with Difficult Students is billed as an "Inservice Video Package." The intent, therefore, was for teachers to watch videos on those PD days when students had no school, and answer questions in the book based on the content of the video. Of course I have no access to whatever video the book is supposed to accompany. The book is dated 1993 -- the year before the Pappas book was published. Indeed, it's possible that my own middle school teachers once watched these videos on their PD days. (I had no idea what they were doing -- all that mattered to my young self was that I had no school that day.)

Of course, at my old school we had our own inservice days. As I've written on the blog throughout the year, our school's PD training was "Responsive Classroom." Our instructional aide criticized the "Responsive Classroom" training as unhelpful -- our students wouldn't respond to the tricks it suggests that teachers do (case in point -- me). She believed that the school should have used Canter's Inservice Video Package. Well, I'm doing so now, just without the "video" part.

Canter begins:

"As an educator, you are the most valuable resource our society has if future generations are going to grow into strong, capable, knowledgeable and responsible adults. You are far too important to be frustrated, overstressed and burned out -- unable to do your job the way you'd like to do it."

The first three "worksheets" in Canter's book are highly dependent on the videos. In fact, so is Worksheet #4 -- the difference being that Canter describes the three scenes fully in his book, so I don't need the video at all.

Here are the instructions for this worksheet:

"Read each scene below. Determine the inappropriate behavior the student was engaged in, how you think the teacher felt, what the teacher did in response to the student, how the student responded in turn. Review your answers, then decide what the student's special needs are."

Well, without further ado, let's begin!

Worksheet #4 Scene #1: Cynthia

Canter describes the first scene as follows:

The teacher tells the class to clear their desks and line up for the computer lab. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to get in line. Her response is, "I'm not ready." The teacher becomes angry and says, "How dare you not listen to me? Now get up and get in line!" Cynthia argues back, "Leave me alone!"

First of all, I actually want to modify this scene a little so that it actually describes the class I taught at my old school. Computer labs are so 1993 -- instead we had laptops in our room. So let's change "line up for the computer lab" to "prepare to get laptops," which was common during the first semester when we had IXL time in the schedule.

Also, let's specify that this is my eighth grade class. After all, this Cynthia sounds just like some of my eighth grade girls. Think back to what I wrote last week about the "special scholar" -- although I actually don't think the special scholar herself would act like Cynthia. But some of the members of her clique (especially the leader) were definitely like Cynthia.

So now our scene becomes:

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher becomes angry and says, "How dare you not listen to me? Now get up and get in line!" Cynthia argues back, "Leave me alone!"

Now this sounds a lot like my own class! (Notice that there was no girl named Cynthia in any of my actual classes. The name "Cynthia" comes from Canter. I don't want to name any of my actual students, so I retain Canter's names while changing all the other details to match my classes.)

I will now answer the five questions:

1. What inappropriate behavior was the student engaged in?

Well, Cynthia was combing her hair instead of clearing her desk for a laptop.

2. How do you think you would have felt if you were the teacher?

I admit that I probably would have felt just like the teacher in the video. And I'd most likely have done the same thing -- argue and yell. But as the video shows us, arguing isn't effective at all.

3. What did the teacher do?

The teacher asked Cynthia again to prepare to get a laptop. When she refuses, he yells at her. (I don't know the gender of the teacher in the video, but here I'm using male pronouns because I'm imagining myself as the teacher.)

4. How did the student respond to the teacher's actions?

Cynthia says, "Leave me alone!" That is, she asserts that her right to comb her hair takes priority over the teacher's instruction to work on the laptop.

5. Based on your answers to the above questions, what does the student need from the teacher: more attention, firmer limits, or additional motivation?

My answer is that she needs additional motivation. She's clearly not motivated to work on IXL, and so I need to provide her with that extra motivation.

In my actual class, I actually did try to motivate "Cynthia" to learn. To this end, I reminded her that students who work on IXL are more likely to earn A's, and that she should try to earn as many A's as she possibly can. Her response was that she was tired of hearing about A's. (I mentioned this back in a June post, and this hearkens back to a July 2016 post where I stressed the importance of A's.)

At this point, we clearly see my error. Cynthia says she's tired of hearing about A's, thus she doesn't care about earning lots and lots of A's. She would be unfazed if someone were to walk up to her and say, "You're no good at math." Therefore my attempt to motivate her by telling her she can earn an A in my class was doomed to failure.

So what does motivate Cynthia, if not grades? Well, let's notice what she did instead of work -- she was combing her hair. In other words, it's not grades that motivate her, but looks. She doesn't care if someone says to her, "You're no good at math," but there's no way she'd let anyone walk up to her and say, "You're ugly!"

In fact, in my class there was a mirror on the wall. And so I could have changed "She remains in her seat combing her hair," to "She walks up to the mirror combing her hair." There were several girls in that eighth grade class who would do this.

Because IXL time is right after lunch, I would sometimes ask, "Cynthia, why didn't you comb your hair at lunch in order to avoid missing any class time?" Her response was something like, "Because it wasn't messed up until lunch was over." Of course, "Because there's no mirror outside" would also have been a logical response -- and indeed, if her hair was messed up during the course of lunch, she might not have discovered this until approaching the mirror after lunch.

Now that we've eliminated ineffective motivating statements, we search for effective motivators. The ideal classroom manager knows that in this case, the only real way to motivate such a student is to threaten her with consequences. She might not care about getting an A, but she certainly doesn't want to get in trouble.

So we need a discipline hierarchy -- an airtight hierarchy, that is. I've seen so many of my discipline hierarchies get neutered because students figure out where the loopholes are. In fact, the most obvious punishment in a computer class would be to take the student's laptop away. But Cynthia doesn't want to use the computer, so denying her the computer would be a reward, not a punishment!

The first step in creating an airtight hierarchy is to make sure that it ends with something that the students can't neuter or escape. More often than not, that step is a parent phone call. No matter how much Cynthia complains that my rules are unfair and that I should let her do whatever she wants, she can't prevent me from getting out my phone 30 minutes after school is out and dialing her home phone number (as by then she'd be no longer sitting in my room).

But as we already know, the ideal classroom manager doesn't become too reliant on phone calls. This would send the wrong message to the parents -- their child is out of control, or else the teacher doesn't know how to control students. And so the ideal manager inserts more steps in the hierarchy below the phone call.

If parent phone calls are the capstone of the hierarchy, what is the cornerstone? Well, the cornerstones of any effective discipline plan are teacher tone and teacher look. These are how students realize that the teacher means business. As I've written before, I lack a strong teacher tone. Therefore the teacher look must become my primary go-to for discipline.

So let's look at the story so far, where the teacher handles Cynthia more effectively:

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher gives her the teacher look.

Now just the teacher look could be enough to make Cynthia choose to put her comb away. If it isn't, then we must reach the next step in the hierarchy.

In previous posts, I've written that the main problem with IXL time was that it was ungraded, so students were never held accountable for it. Instead, I should have had some sort of IXL accountability worksheet. Students who don't work on the laptop are required to answer eleven questions on paper instead. (My eighth grade class was small, so there were enough laptops for every student, but IXL accountability worksheets become more important in sixth grade, where there were always students without laptops.)

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher gives her the teacher look. She still doesn't clear her desk. The teacher hands her the accountability worksheet.

Now it could be that threat of a worksheet -- which is less enjoyable than the laptop -- is enough to make Cynthia choose to put her comb away. But maybe it isn't. She might simply ignore the worksheet, or even throw it to the floor and refuse to work it. What's next?

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher gives her the teacher look. She still doesn't clear her desk. The teacher hands her the accountability worksheet. She throws it on the floor and says, "I'm not doing this!" The teacher gives her the teacher look again.

This step is very tricky, because the temptation is for me to yell at her again. In fact, sometimes I'd just scream, "That's a parent phone call!" This is premature, because when I yell she yells, but if I remain calm, she no longer feels that she must get the best of me. So it's theoretically possible that she might complete the worksheet, or even get the laptop and work on IXL. The teacher look here is actually to watch to make sure that she doesn't cheat. Remember that Cynthia's the leader of her clique, so there are always other girls who are more than willing to do the worksheet for her.

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher gives her the teacher look. She still doesn't clear her desk. The teacher hands her the accountability worksheet. She throws it on the floor and says, "I'm not doing this!" The teacher gives her the teacher look again. She picks up the paper and starts to hand it to one of her friends. The teacher says, "Don't do that," and continues to give her the teacher look. Finally, the class ends, and Cynthia doesn't even bother to hand in the worksheet since it's not complete. The teacher says, "I'm calling your parents."

Oh, there's one more part that I forgot here. The worksheets are numbered 1-11, but all the questions are blank, because the students must copy and answer these off the board. (Typically I would choose the day's IXL lesson, then log into IXL myself and write down the first eleven questions.) This leaves the door open for Cynthia to say, "You're wasting your time writing those on the board." The best response is just to ignore this and write the questions anyway.

The teacher tells the eighth grade class to clear their desks and prepare to get laptops. Cynthia doesn't clear her desk. She remains in her seat combing her hair. The teacher reminds Cynthia to prepare to get a laptop. Her response is, "I'm not ready." The teacher gives her the teacher look. She still doesn't clear her desk. The teacher hands her the accountability worksheet. She throws it on the floor and says, "I'm not doing this!" The teacher starts to write questions on the board for her to copy, but one of her friends says, "You're wasting your time writing those." The teacher ignores this and finishes writing down the questions, then gives Cynthia the teacher look again. She picks up the paper and starts to hand it to one of her friends. The teacher says, "Don't do that," and continues to give her the teacher look. Finally, the class ends, and Cynthia doesn't even bother to hand in the worksheet since it's not complete. The teacher says, "I'm calling your parents."

And at long last, we have a complete airtight hierarchy. I, as the teacher, avoid yelling and replace it with the teacher look. At each step, Cynthia, not I, is the one making choices. She must choose to give up and start behaving, or continue to argue and climb the hierarchy towards the phone call. By completing this hierarchy, I'm actually completing Canter's Worksheet #5, where I identify the behavior that she needs to be taught (i.e., how to work during IXL time) and how I'd teach it.

There are a few more things I want to say about this before we move on to Scene #2. Recall that for IXL, each student had a numbered laptop, and I had the students pick up the laptops in order. So if Cynthia had laptop number 611 and she refused to get it, then she would be blocking the next student from getting laptop 612.

In practice, I'd skip 611 and go straight to 612. The real problem was when it was time to put the laptops away. I wanted the students to place the laptops in the slots where they could charge -- and I wanted them to do so in order. Now suppose Cynthia took laptop 611 after all, but then starting combing her hair at the end of class instead of putting it back. If I skipped up to 612, then that student wouldn't leave a space between 610 and 612, so the laptops wouldn't be in order. So I would insist that Cynthia put 611 away and avoiding calling 612 until she complied. But this often led to student 612 complaining "You're taking too long, Mr. Walker," leaving her laptop on her desk, and then going out to P.E. (which was after IXL). The other student therefore left without being dismissed (or putting up her chair, since P.E. is the final class of the day) and with the laptops still not in the correct slot (since it's on a desk). And all the while Cynthia is still combing her hair with her own laptop not in the correct slot (since it's on a desk). Eventually I'd give up, just tell everyone to leave, and then I'm spending half of P.E. putting chairs on desks and laptops in the correct spot.

The laptops being in order was important to me, since that was the only way I could tell that a laptop was missing, along with which laptop was missing. And so I should have simply numbered each of the slots where the laptops belong (with slips of paper and lots of Scotch tape). This would have allowed me to skip to 612 if Cynthia refused to put 611 away, since the correct slot for 612 would already have a label. And any student who put a laptop in the wrong slot, leave a laptop on the desk, or refused to put the chair up on the desk at P.E. time would be denied a laptop the next IXL day. And now being denied a laptop really was a punishment, since that student would have eleven questions to copy and answer on the IXL accountability form.

"Cynthia" is a name from Canter's book, but I based my "Cynthia" on a real eighth grader in my class (whose real name is not Cynthia). The history teacher told me that "Cynthia" was much worse behaved as a seventh grader than as a eighth grader -- apparently when she was in seventh grade, she'd had family issues (that of course I don't disclose on a blog). So despite the problems I had with her, I was getting the better-behaved "Cynthia."

On my final day in the class, "Cynthia" had dyed her hair green -- most likely because St. Patrick's Day was approaching. She asked me whether I liked her new hair, and I replied, "Yes, it's nice." That was the first time I had ever said anything positive to "Cynthia," and I know she appreciated it, since I had complimented her on that which matters most to her -- her looks.

Worksheet #4 Scene #2: Rodney

Canter writes:

Rodney doesn't want to do the reading assignment...

And we already need to make a change here to make this fit my class. So instead of a "reading assignment," of course it's a math assignment. I suppose I could say "science assignment" here, but I'm imagining Rodney to be one of my seventh graders -- and as I wrote earlier in this post, I didn't really teach the seventh graders science.

There's one more change to make -- the teacher in Canter's video here is female, but of course I'm changing it to male, since I am the teacher in my version of the story.

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher becomes frustrated and decides to ignore Rodney and continue working with the other students. Eventually, Rodney's refusal to work becomes disruptive. He starts bothering the student next to him.

1. What inappropriate behavior was the student engaged in?

Rodney refused to work on the assignment and gave excuses instead.

2. How do you think you would have felt if you were the teacher?

Once again, I probably would have acted just like the teacher in the video. Many of the seventh graders really were hard-working, and I'd really want to help those students out, rather than pay attention to Rodney.

3. What did the teacher do?

He ignored Rodney.

4. How did the student respond to the teacher's actions?

Rodney bothered the student next to him. Notice that at this point I'm not quite sure whether he's merely talking to the other student or outright bullying him.

5. Based on your answers to the above questions, what does the student need from the teacher: more attention, firmer limits, or additional motivation?

I'd say that he needs firmer limits. He's disrupting the class, and so firm limits would prevent him from disrupting.

Let's come up with an airtight hierarchy to fix this problem. The first mistake the teacher makes is to ignore Rodney, so we begin by changing this to the teacher look:

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher gives him the teacher look.

To save some time, I put in the rest of the discipline hierarchy suggested by our instructional aide:

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher gives him the teacher look. He refuses to work. The teacher gives him a warning. But still, he refuses to work. The teacher gives him the teacher look. But still, he refuses to work. The teacher assigns him a 150-word essay. He refuses to write the essay. The teacher gives him the teacher look. But still, he refuses to write it. Finally, the class ends, and Rodney doesn't even bother to hand in the essay since it's not complete. The teacher says, "I'm calling your parents."

Notice that I assign Rodney an essay, but not Cynthia. This is because Cynthia's infraction occurs during IXL, so it's more logical to assign the IXL accountability worksheet instead. I assume that Rodney's infraction occurs during the regular math class (as I didn't even have the seventh graders for IXL), so he gets standards.

Again, this is based on my instructional aide's standards. But I modify these by inserting "teacher look" several times throughout the hierarchy. The aide is a natural classroom manager, and so she automatically uses teacher tone and teacher look when the situation warrants it. I'm not a natural manager, so I must explicitly insert teacher look into my hierarchy.

So far, my hierarchy omits the fact that Rodney starts bothering another student. So let's try to insert it in the hierarchy:

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher gives him the teacher look. He refuses to work. The teacher gives him a warning. But still, he refuses to work. The teacher gives him the teacher look. But still, he refuses to work. The teacher assigns him a 150-word essay. He refuses to write the essay, and instead starts bullying the student next to him....

If the student is really being bullied, then the time for teacher look and hoping that he'll start writing the essay is over. In order to protect the victim, I must send Rodney out of the room immediately.

Of course, ideal classroom managers also try to avoid excessive office referrals. The administrators in the office won't want to see Rodney in the office every other day.

The history teacher told me that there were four seventh grade boys who had always caused him problems the previous year as sixth graders. So at the start of seventh grade, he separated them by seating one in each corner. So far, I haven't identified the "Rodney" in my actual class (whereas I'd identified "Cynthia" right away), but it's safe to say that one of these four boys is "Rodney."

But in my class, I didn't separate the quartet. This is because I still hadn't learned the students' names yet, and I feared that if I tried to change their seats, they would disobey me and keep switching back before I could learn their names. Notice that this is the opposite of an airtight hierarchy -- I'm afraid to implement a consequence (seat change) because I'm sure that they'll neuter or escape it.

Instead, I should have made the seating change and determined what I'd do if they tried to escape. (So even if I hadn't learned the kids' names yet, I should at least have learned those four names.) In this case, my response would depend on what they did when out of their seats. If they bully then I'd send them out of the room, but if they merely talked then I would revert to the original hierarchy -- meaning that I should give them a teacher look as soon as they left their seats.

Even without the seating change, two of the boys left their seats anyway. That's because those two boys actually had girlfriends in the class:

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher gives him the teacher look. He refuses to work. The teacher gives him a warning. But still, he refuses to work. The teacher gives him the teacher look. But still, he refuses to work. The teacher assigns him a 150-word essay. He refuses to write the essay, and leaves his seat to be with his girlfriend. He starts bothering her.

So at this point I've narrowed the "Rodney" in my class down to two, since only two of them had girlfriends in the class. At this point, I assume that Rodney isn't bullying his girlfriend (only talking to her), so I can safely restore the rest of the hierarchy:

Rodney doesn't want to do the seventh grade math assignment. He says that he "can't do it." The teacher encourages him and offers his help, but Rodney won't even pick up his pencil. The teacher gives him the teacher look. He refuses to work. The teacher gives him a warning. But still, he refuses to work. The teacher gives him the teacher look. But still, he refuses to work. The teacher assigns him a 150-word essay. He refuses to write the essay, and leaves his seat to be with his girlfriend. He starts bothering her. The teacher gives him the teacher look. But still, he refuses to return to his seat and write the essay. Finally, the class ends, and Rodney doesn't even bother to hand in the essay since it's not complete. The teacher says, "I'm calling your parents."

Of the two "Rodney" candidates, one of them moved away right after winter break. So let's assume that "Rodney" is the remaining seventh grader with a girlfriend.

One thing about this "Rodney" is that the final step, the parent phone call, isn't a threat to him. His parents' phone number led only to a voice message box that they never answer. In fact, he never wrote his essays, since the only punishment for not doing so was a parent phone call (ergo nothing).

The history teacher told me that he never phoned "Rodney," since he already knew that the seventh grader's parents were not responsive. Does this mean that this hierarchy should have a capstone other than a parent phone call?

Suppose I were to stop calling Rodney's parents. Then Rodney has no incentive to write the essay -- and knowing myself, I'd be tempted to stop assigning it to him.

Now the other students see Rodney acting out of control without an essay or phone call. So the other students choose to start acting up as well. This is the E-S-U effect -- when the U-kid (Rodney) acts up without punishment, the S-kids start acting like U-kids.

But then I know that one S-kid's parents, unlike Rodney's, is responsive to phone calls. And so I start assigning the essay and phone call to the S-kid. At this point, the S-kid can say, "That's unfair, because you let Rodney do whatever he wants but not me." And if this S-kid is a girl, she can even claim that I'm sexist.

And so I break with the history teacher, and continue to call Rodney's parents. Notice that the ideal manager avoids excessive phone calls that annoy parents. But since Rodney's parents don't respond to the calls, I can call them everyday without retribution. The ideal manager only needs to avoid calling parents who actually pick up the phone.

The purpose of the calls is not to motivate Rodney, but to motivate the rest of the class. They see that Rodney is acting up everyday, but they also see that he's being assigned essays -- and phone calls, once he refuses to write the essays. Those S-kids with responsive parents know not to mess around in class, since they know that they'll be punished. They can no longer claim I'm being unfair or sexist because I'm punishing them and not Rodney.

I can also take advantage of Rodney having a girlfriend -- if he leaves his seat and the couple starts talking instead of working, then I punish both students equally. Rodney might not care about the essay or call, but his girlfriend might -- and she could tell her boyfriend to return to his seat so that she won't get in trouble.

Eventually, the girlfriend of my "Rodney" moves away as well. Even without her, my hierarchy shows me how to control a student who is completely uninterested in learning. Canter writes that he "becomes disruptive," and the hierarchy shows how to minimize his disruption via firm limits.

The last thing I remember about "Rodney" is one day, the English teacher had assigned a ten-minute after school detention for all seventh graders, which I had to enforce because it was when I had seventh grade as the last class of the day. "Rodney" and two of the other three "corner students" ran out of the classroom during the detention. I didn't want to let the English teacher down, so I chased after them. They were hiding right outside the door -- the whole thing was just a prank to watch me make a laughingstock of myself by running after them.

The correct response was just to let them go outside the door, inform the English teacher, and then double the detention. If they failed to attend the doubled detention, then call home (as the other two boys had responsive parents).

Worksheet #4 Scene #3: Jessie

Canter writes:

The teacher asks the class a question. Jessie frantically waves her hand and shouts out, "I know the answer. Call on me!" The teacher reminds her not to speak until she is called upon. Jessie pouts and the other students grin. A few minutes later she is calling out again. The teacher is losing patience and begins to feel annoyed because Jessie refuses to follow directions. He says, "Jessie, what's wrong with you? Can't you follow directions like the rest of the class?"

This Jessie sounds a lot like some of the girls in my sixth grade class. In my class, I actually select names at random using a short TI-83 program. (I actually mentioned this program only once on the blog, back in a January 2016 post, but I used this program all the time.) So if this were my class, I'd be using the calculator to choose names, and apparently "JESSIE" isn't coming up. If there were a "Jessie" in my class, she'd claim that my calculator is "broken" because her name won't appear when she wants it to.

It's tough for me to consider Jessie to be a "difficult" student. After all, I could only wish that obvious troublemakers like Cynthia and Rodney were as eager to answer questions as Jessie. But Canter, by including her in a book about difficult students, is implying that Jessie is just as "difficult."

1. What inappropriate behavior was the student engaged in?

Jessie shouts out answers and speaks without permission.

2. How do you think you would have felt if you were the teacher?

This is a tough one. Sometimes I tried to be resolute and insist on calling the name that appears on the calculator display (but that's not the same as punishing Jessie). At other times, even the instructional aide who admires Canter says that it's okay just to call Jessie when she's so eager to answer.

3. What did the teacher do?

Even though he calls Jessie out, he doesn't punish her.

4. How did the student respond to the teacher's actions?

She simply calls out the answer again.

5. Based on your answers to the above questions, what does the student need from the teacher: more attention, firmer limits, or additional motivation?

Well, the answer obviously isn't "additional motivation." On the contrary, this Jessie is too motivated to work that she can't follow the rules. Strangely, the answer might be "more attention." As I wrote earlier, she's a "difficult student" who doesn't appear to be difficult, and I'm likely to ignore her and let her continue to break the rules.

Let's construct our airtight hierarchy. As usual, we begin by inserting a teacher look:

The teacher asks the sixth grade class a question. Jessie frantically waves her hand and shouts out, "I know the answer. Call on me!" The teacher reminds her not to speak until her name appears on the calculator and she is called upon. Jessie pouts and the other students grin. The teacher gives her the teacher look. A few minutes later she is calling out again.

At this point, we can follow the rest of the hierarchy. There's one more thing here -- recall that even though I don't deduct participation points anymore, I still award them for correct answers. So Jessie might be motivated by participation points, which is why she wants to give the answer. Thus it's a good idea to deny (not deduct) her participation points for answering out of turn:

The teacher asks the sixth grade class a question. Jessie frantically waves her hand and shouts out, "I know the answer. Call on me!" The teacher reminds her not to speak until her name appears on the calculator and she is called upon. Jessie pouts and the other students grin. The teacher gives her the teacher look. A few minutes later she is calling out again. The teacher tells her that she won't be able to earn a participation point the rest of the day. A few minutes later she is calling out again. The teacher gives her the teacher look. A few minutes later she is calling out again. The teacher gives her a warning. A few minutes later she is calling out again. The teacher gives her the teacher look. A few minutes later she is calling out again. The teacher assigns her an essay. A few minutes later she is calling out again. The teacher gives her the teacher look. A few minutes later she is calling out again, instead of writing the essay. The teacher says, "I'm calling your parents."

There's one more thing to say here. I can easily see Jessie here writing the essay -- then go right back to shouting out the answers. The next step on the hierarchy would be the parent phone call -- which she'll claim that she doesn't deserve, because she wrote the essay and the phone call is for those who don't write the essay! In other words, what happens when a student finishes the essay, then continues to misbehave? I think the best answer is extend the essay. Instead of 150 words, now it's 200. Then phone calls can be reserved for those who refuse to write the essay.

There were several candidates for "Jessie" in my sixth grade class. I might as well choose the girl who had the highest grade in the sixth grade class. I believe I had to call her parents only once -- that was enough to get her to improve her behavior.

The above hierarchy is repetitive -- "teacher look" appears over and over again. But that's what I needed to do much more often in the classroom.

I think back to my days as a student teacher. There were two situations when I should have used a teacher look more -- restroom trips and cell phone use. I kept threatening to give students detention for going to the restroom or using a phone. The students kept complaining, "No other teacher gives us detention for restroom or phones" -- almost implying that their other teachers allow them unlimited restroom trips and unlimited phone use during their classes.

In reality, those other teachers used teacher look -- and maybe teacher tone as well -- whenever students asked for those things. The teacher look or tone was enough to get the students to stop asking to go the restroom and put the phone away. The students were compliant without the teacher having to give a detention or other consequence. I, on the other hand, lacked teacher tone and didn't use teacher look, so I had to give detentions to obtain the same level of compliance. I gave detentions when other teachers didn't, so I, ironically, appeared to be crueler than the teachers who had a strong teacher tone.

So the hierarchy contains several "teacher look" steps in order to reduce the frequency of consequences in my class. The ideal classroom manager seldom gives consequences, because teacher tone and teacher look are usually sufficient to obtain compliance.

Airtight Hierarchies for Other Infractions

Phone calls aren't the only possible capstone for an airtight hierarchy. Recall that a capstone must be a consequence that the students can't fool me into neutering.

Another possible capstone consequence is a low grade -- especially a zero for cheating or talking during test time. No matter how much the students claim that they weren't cheating, they can't prevent me from entering a zero on PowerSchool after school or over the weekend, since they'd be far away from the computer where I'm entering the grades.

The most common infraction in any class, of course, is talking. And so it's definitely worth it to see what an airtight hierarchy for talking looks like. We'll begin it with the call-and-response that I mentioned back in June:

The teacher begins the call-and-response, "When I say 'Listen,' you say 'Up!'" But one student continues to talk, saying, "This is juvenile!" The teacher gives the teacher look. The student continues to talk. The teacher gives the student a warning. The student says, "I wasn't talking!" The teacher gives the teacher look. The student continues to talk. The teacher assigns the student an essay. The student continues to talk and not write the essay. The teacher gives the teacher look. The student continues to talk and not write the essay. Finally, the class ends, and the student doesn't even bother to hand in the essay since it's not complete. The teacher says, "I'm calling your parents."

Remember that if all of this is occurring during a test, the capstone consequence is a zero score. In fact, I'd probably give the zero at the step where I assign an essay, since it's awkward to have the students write an essay during a test. Of course, if the student continues to talk after I assign the zero, I might have to assign the essay or call home anyway.

I'm thinking back, of course, to my eighth grade class, when the special cousin was talking during the test and giving the special scholar the answers. I didn't really want to punish the special cousin since it was her first week at a new school -- and I knew that she was smart, and so I didn't want to ruin her grade at her new school by giving her a zero. Somehow, I convinced myself that another student was talking instead of the special cousin -- indeed, I blamed the girl I called "Cynthia" above. But "Cynthia," who in this case was innocent, didn't even complain -- she probably didn't know any of the answers and realized that she was going to fail it anyway, so why argue about the zero? (Not having to take the test gave her more time to comb her hair, just like Canter's original Cynthia.)

As I feared, the zeros I did assign that day ruined my grading scale. I've already written how the low grades caused me to make a later extra credit assignment be worth too many points -- then this inflated the grades of the students who didn't earn zeros that day.

The airtight hierarchy might have prevented this -- but most likely I would have ended up giving the special cousin a zero. I didn't want to be cruel to the special cousin her first week, but by not being cruel, the cousin felt that she was in control of my classroom the rest of her time at our school.

There was another time when I wanted to show compassion to one of the students. It was during my final days at my school. One of my sixth grade girls had injured her leg, so she missed about two weeks of school. When she returned, she was on crutches. Yet not only was she very talkative, she actually tried to run around the classroom (without crutches). By this point, the instructional aide and I had established the hierarchy, and the girl had reached the parent phone call step. But I didn't really want to call her mother, since I knew the mom wouldn't want a call about how disruptive her daughter was on her very first day back. So of course the sixth grader continued to disrupt.

But there is room for compassion in the discipline hierarchy. The whole idea is that I don't make the choice whether it's too cruel to pursue the hierarchy -- instead, it's the student who must make the choice whether to change her behavior.

So to the special cousin, I should have said, "You don't want to earn a zero on your very first test at your new school, do you? Then be quiet during the test." Chances are that she would have been quiet at that point. If she continues to talk, I then tell the special scholar that she must move to a different seat for the duration of the test only, or else both she and her cousin will receive zeros. If I reassure her that the move is only temporary and that the cousins will be reunited as soon as the test is over, the special scholar probably would have complied. And then I wouldn't have had to give zeros to anyone in that class at all.

Notice that if I had established the airtight hierarchy earlier, during the main lesson, then students would have already known not to talk, and I might have had better control of the class when it was time for the test. Moreover, I might have been able to teach the lesson more effectively if the class was quiet. "Cynthia" could have learned enough that she wouldn't have just taken the zero, and perhaps even the special scholar might have understood enough to avoid needing her cousin's help.

This also leads to another important idea -- the students need to follow the rules even when they believe that they don't matter, so that they'll follow them when they do matter. Of course, the students might ask, "Why are you making us do this when it doesn't matter?" The only proper response, of course, consists of those four magic words, "Because I said so."

For example, I wrote about enforcing the seating chart with my seventh graders. The eighth grade class was small enough that I could seat them two to every cluster of four seats. But many of the kids sat one seat away from where I'd placed them on my seating chart, since naturally there were so many empty seats.

I didn't say anything about this, since I knew it would lead only to fruitless argument. But last year (in a Blaugust post!) I'd written that I would assign five minutes of detention to anyone who switched seats, even if they were just one seat off.

I should have enforced the detentions and made the students sit in, say, the right seat (as opposed to the left seat) in each cluster. At the start, I make it clear that they are not to sit in the left seat, and if they ask why, the answer is "Because I said so." This fits into an airtight hierarchy -- if they skip the detention, it doubles to ten minutes, and if they skip it again, it becomes a phone call. "You don't want me to call your parents just because you were one seat off of the chart, do you?"

Traditionalists and Politics

This is my final summer post. It's my last chance to mention politics since I try to keep the school year posts politics-free. It's also my last chance to link to the traditionalists for a while. Once the school year begins and we return to the U of Chicago text, I'll restore my pattern of posting about the traditionalists on test days.

Here's a link to a recent article I found about the Common Core:

https://www.commondreams.org/views/2017/07/24/middle-school-suicides-double-common-core-testing-intensifies

This is a political site -- "Common Dreams" bills itself as "Breaking News for the Progressive [i.e., left of center] Community." Even though opposition to Common Core is associated with President Trump and the right, the author, Steven Singer, appears to oppose the Core from the left:

Here’s a high stakes testing statistic you won’t hear bandied about on the news.

The suicide rate among 10- to 14-year-olds doubled between 2007 and 2014 – the same period in which states have increasingly adopted Common Core standards and new, more rigorous high stakes tests.

Singer's issue with Common Core appears to be mostly with the high-stakes testing, but he wrote an article last year where he has the same concern with Common Core arithmetic as the traditionalists:

https://www.commondreams.org/views/2016/08/28/common-cores-new-new-math-has-same-problem-old-new-math

One commenter, a self-described "Leftist," disagrees with Singer. Like the traditionalists, Leftist believes that Common Core math, particularly in secondary school, isn't rigorous enough:

Sorry, there may be arguments against “standardized testing” (even though there have always been such tests) but Mr. Singer’s argument that: “Middle school children’s brains are still growing. They are only physically able to learn certain concepts and skills, but we’re forcing them to deal with increasingly advanced and complex concepts at younger ages…” …is complete bullshit. US school students are typically two years behind their counterparts in Europe. When a US family moves to the UK, their kids get put back two grades. And want to talk about “high stakes testing” has Mr. Singer ever heard of the UK’s O levels and A-Levels and similar tests in continental Europe?

(Recall that O-levels and A-levels are the inspiration for J.K. Rowling's O.W.L.s and N.E.W.T.s from her Harry Potter books.)

And the final commenter, lamonte7, definitely sounds like a traditionalist:

Well somebody has to do something. The US is at the bottom of the list in the OECD and kids finishing highschool have no idea what they are doing. My wife went to get her second Maters degree and was all stressed out about college algebra 101. Turns out it they were studying the quadratic equation for. Where we went to school, we did that grade 8. Next she learned how to determine min and max of certain functions. Somehow they taught her that with no concept of derivatives. We had done that grade 11. No need to say she just sailed thru those courses.Another one was basic organic chemistry, I think that was grade 9 or 10. The US ed system needs huge overhaul and kids need to grow a pair.

A majority of highschool grads i work with are incapable of adding or subtracting two 5-digit decimal numbers without the use of a calculator. I have yet to see one that can calculate a 15% tax on an amount under $100 in their head.

Again, I saw this in my own class. Here the problem is that too many students believe that adding five-digit numbers without a calculator is something that only smart "nerds" can do. People who can do arithmetic are ostracized, while people who can't are normal. They didn't believe me when I told them that 50 years ago, it was the other way around. People who could do arithmetic were normal, while people who couldn't were ostracized. I tried to bring that idea back via the "dren" label.

Let's get back to our main traditionalist, Barry Garelick. Here is his most recent post:

https://traditionalmath.wordpress.com/2017/08/08/count-the-tropes-dept/

Yet another in an unending series of articles about math education and what parents should (and should not) be doing to help.  This particular one is from Chicago Parent and contains the usual tropes/mischaracterization about how math used to be taught and why the new ways are so much better.

Garelick mentions a prolific education critic, Alfie Kohn:

In arguing why traditional math is ineffective, Kohn states “students may memorize the fact that 0.4 = 4/10, or successfully follow a recipe to solve for x, but the traditional approach leaves them clueless about the significance of what they’re doing.  Without any feel for the bigger picture, they tend to plug in numbers mechanically as they follow the technique they’ve learned.”

Now Kohn is strongly progressive (in pedagogy -- I don't know his politics). Not only does he criticize traditionalism in math and other subjects, he doesn't even like the idea of assigning students letter grades! (I've purchased some of his books at the library book sales for $1 or less.) This sounds extreme, but I noticed that even Fawn Nguyen questions the idea of grading students:

http://fawnnguyen.com/lillian/

(OK, I was wrong to emphasize grades with "Cynthia" in my class, but the idea of not grading students at all, as expressed by Kohn, Nguyen, and especially "Gloria" who commented in the Nguyen thread, seems a bit extreme to me.)

Let's get back to Garelick. Both he and many of his commenters start writing about traditionalist texts that they use to supplement the schools' progressive texts. Indeed, Garelick even sneaks some of these texts into his middle school classroom and uses them instead of the district-suggested texts.

For example, concerning his sixth grade class, Garelick writes:

Saxon Math is good but I prefer the older editions by Hake to the newer ones. I started using Saxon 7/6 for 6th grade. The thing about Saxon is that it’s a total commitment because of its spiraling technique. They do spiraling in a good way, not like Everyday Math’s [U of Chicago elementary texts -- dw] spiraling.

Here's what he uses in his seventh grade class:

I agree with [commenter] Tara [Houle] about JUMP Math and am going to be using it for my 7th grade math class this year.

And here's his eighth grade text -- which of course is an Algebra I text:

Algebra books: You can get books by Dolciani; I prefer the ones written in the 60’s and 70’s. If you got beyond the 80’s her name is on the book, but she had died by that time. They are rewritten and not as good. I currently use the 1962 “Modern Algebra” by Dolciani, Berman and Freilich, which is available on Amazon fom $25 up though prices vary with supply and demand. I used it in my 8th grade algebra class. You do have to supply some explanation because her written explanations are somewhat formal at times. (The books were written in the 60’s New Math era so contain a bit more set theory than is really necessary. But not too bad, and one can easily skip over some of the overly formal sections.) The word problems are excellent and are distributed throughout the book; they use whatever skill/procedure the chapter they appear in is using. Thus, word problems in the chapter on fractions use fractional equations, etc. Excellently laid out and presented. Some of the used books contain only odd numbered answers, so keep your eye peeled for teacher’s editions.

Recall that I actually own a copy of a Saxon text (except that it was Saxon 65, not 76), and I even tried to use it in my sixth grade class. Back when the history and teacher came up with the idea of homework "packets," and so I copied some pages from Saxon 65. But this quickly fell apart -- not because the students neutered the idea, but because of the heavy-handed Illinois State text. Garelick clearly had more freedom to introduce traditionalism than I had, since Illinois State even controlled the homework -- I was required to assign online Illinois State HW. In the end, I could have created HW packets, with the first page from Illinois State, and then Saxon to round out the packet. This might have suited some of my students who lacked HW access, and extended the idea that there should be more written worksheets, like the IXL accountability form, with the online assignments.

I've mentioned that I used the Dolciani texts as a young Algebra I student. But I was born in 1980, so most likely it was the newer version that Garelick prefers less.

Plans for the New School Year

I will be following the U of Chicago text, covering every section in order. Despite what I've done in previous years, and despite what I wrote about "natural geometry" in my last post, I'll be going in order rather than jump around to fit the way I want Geometry to be taught. I found out first hand in the class I taught last year about the dangers of jumping around the text without a real reason.

I'll be following the digit pattern again, so Lesson 8-5 (areas of triangles) will be on Day 85, Lesson 11-1 (coordinate proofs) on Day 111, and so on. But this means that we will not start in Lesson 1-1 until Day 11. The U of Chicago text doesn't have a Chapter 0 -- but Michael Serra's Discovering Geometry does. I'll cover introductory activities from Serra's text during the first ten days of school.

The only deviation from the digit pattern will be if and when I sub in a Geometry class (or any math class covering a geometric topic). Just as in the past when I subbed, math in an actual classroom takes priority over math in a text.

I still haven't finalized my subbing plans for next year, though. I'm still trying to get in touch with both a charter school and a district (one where I've subbed in the past). The first day at one of them will be on Tuesday the 15th, while at the other it will be Wednesday the 16th. So as of now, I don't know whether my next post will be on Tuesday or Wednesday.

I'm hoping to have a successful year as a sub so I can return to full-time teaching soon. Of course, I'll be practicing good management skills whenever I can -- but this time, I'll actually write about management here on the blog, especially when I cover a class other than math.

Each day when I sub, I want to be able to leave with the students thinking, "I like this sub. He knows his math, and he helped me to understand math much better." But a student's first inclination, especially with a sub, is to try to avoid learning anything at all. Classroom management, therefore, is the key to getting through to my students.