Monday, August 31, 2020

Lesson 1-1: Dots as Points (Day 11)

OK, so now I'm hearing the purple color for Orange County might result in the schools having to remain closed after all:

https://edsource.org/2020/color-purple-will-determine-whether-california-schools-can-open-for-in-class-instruction/639303

On the OCDE website, I see the following link:

https://newsroom.ocde.us/state-releases-new-color-coded-county-monitoring-system-replacing-the-covid-19-watchlist/

According to this link, each county must stay on its colored list for at least three weeks. Thus the earliest Orange County can finally become red is September 8th. The county would then have to remain red for two weeks, taking us to September 22nd. And as we've seen, districts will likely add a two-week buffer to this -- instead of the September board meeting, the reopening date would have to be discussed at the October board meeting. A logical reopen date then would be October 6th.

LA County, home to my old district, is of course stuck on the  purple list. The county is nowhere near advancing to red.

And of course, if at any point it appears that the schools won't reopen quickly, then I reserve the right to go right back to my spring/summer Java project. I need to find a way to get out of this trap where it's considered unsafe for me to get any work.

This is what I wrote last year about today's lesson:

Our focus is now the U of Chicago text. Just like the Serra text, it's an old Second Edition (1991), and there are newer editions in which the chapters are ordered differently. Since my plan this year is to follow the order strictly, let's revisit the chapter order in my text:

Table of Contents
1. Points and Lines
2. Definitions and If-then Statements
3. Angles and Lines
4. Reflections
5. Polygons
6. Transformations and Congruence
7. Triangle Congruence
8. Measurement Formulas
9. Three-Dimensional Figures
10. Surface Areas and Volume
11. Coordinate Geometry
12. Similarity
13. Logic and Indirect Reasoning
14. Trigonometry and Vectors
15. Further Work With Circles

Let's compare this to the modern Third Edition of the U of Chicago text. The first thing we notice is that the new text has only 14 chapters, not 15. We observe that the first twelve chapters are more or less the same in each text, and so it's Chapter 13 that is omitted in the new version. Instead, the material from the old Chapter 13 has been distributed among several different chapters.

You might recall that in the past when I used to juggle the lessons around, it was Chapter 13 that I moved around the most. So you could argue that when I was breaking up Chapter 13, I was actually adhering to the order in the new Third Edition -- unwittingly, of course!

Let's look at Chapter 13 in the old text, and I'll give the lesson in the new text to which the old Chapter 13 material has been moved:

  • Lessons 13-1 through 13-4 (on indirect proof) are now the first three lessons of Chapter 11, just before coordinate proofs. (Lesson 13-2, "Negations," is no longer a separate lesson in the new text.)
  • Lesson 13-5, "Tangents to Circles and Spheres," is now Lesson 14-4, in the circles chapter.
  • Lesson 13-6 through 13-8 (on exterior angles of polygons) have been incorporated into Lessons 5-6 and 5-7 (on Triangle Sum).

Some of these changes are those I once made by myself -- for example, including tangents to circles with the other circle lessons.

Besides the breakup of Chapter 13, here are the other major changes made in the Third Edition:

  • Chapters 4 through 6 exhibit many changes. In my old version, reflections appear in Chapter 4, while the other isometries don't appear until Chapter 6. In the new version, all isometries are defined in Chapter 4. With this, the definition of congruence (and some of its basic properties) have now moved up from Chapter 6 to Chapter 5. Only Triangle Sum remains in Chapter 5 -- the properties of isosceles triangles and quadrilaterals have been pushed back to Chapter 6.
  • With this, Chapter 3 has a few new sections. Two transformations are actually introduced in this chapter, namely rotations and dilations. This may seem strange, since rotations are still defined as Chapter 4 as a composite of reflections in intersecting lines -- and reflections themselves don't appear until Chapter 4. It appears that the purpose of rotations in the new Lesson 3-2 is to introduce rotations informally, as well as tie them more strongly to the angles of Lesson 3-1. (Rotations appear before reflections in Hung-Hsi Wu, but Wu does for different reasons.) Arcs also now appear in Lesson 3-1 instead of having to wait until 8-8. Meanwhile, the new Lesson 3-7 on dilations (which are still called "size transformations") is essentially the old Lesson 12-1 and 12-2. Again this is only an intro -- dilations are still studied in earnest only in Chapter 12.
  • Chapter 7 is basically the same as the old text, especially the first five sections (except that SsA in Lesson 7-5 now has an actual proof). The new Lesson 7-6 is the old Lesson 8-2 on tessellations. I see two new lessons in this chapter, Lesson 7-9 on diagonals of quadrilaterals and Lesson 7-10 on the validity of constructions. (David Joyce would approve of this -- but he'd take it a step forward and not even introduce the constructions until this lesson.) Meanwhile, the old Lesson 7-8 on the SAS Inequality (or "Hinge Theorem") no longer appears in the new text.
  • Chapter 8 has only one new section -- Lesson 8-7, "Special Right Triangles," is the old 14-1. This is so that special right triangles are closely connected to the Pythagorean Theorem.
  • Chapter 9 was always a flimsy chapter in the old book -- it's on 3D figures, yet most of the important info on 3D figures (surface area and volume) don't appear until Chapter 10. Now surface area has moved up to Chapter 9, reserving Chapter 10 for volume (except for the surface area of a sphere, which remains in Chapter 10). The old Lesson 9-8 on the Four-Color Theorem has been dropped, but that was always a lesson that was "just for fun."
  • The last section of the old Chapter 12 (side-splitter) is now the first section of Chapter 13, which is the new trig chapter. Lesson 13-2 is a new lesson on the Angle Bisector Theorem, and Lesson 13-4 is a new lesson on the golden ratio. I've actually seen these ideas used before -- including on the Rapoport Daily Epsilon of Math -- but this is the first time I've seen them in a text as separate lessons. This is followed by lessons on the three trig ratios. Vectors, meanwhile, have moved up to Lesson 4-6, so that they can be closely connected to translations.
  • Chapter 14 should be like the old Chapter 15, but there are a few changes here as well. Ironically, I, like the text, moved tangents to circles to this chapter (Lesson 14-4) so that it would be closer to the other important circle theorem, the Inscribed Angle Theorem. But inscribed angles have been moved up in the new text to Lesson 6-3. This places that lesson closer to the Isosceles Triangle Theorem, which is used in the proof of the theorem. Meanwhile, Lesson 14-6 technically corresponds to 15-4 ("Locating the Center of a Circle") of the old text, but it has been beefed up. Instead of just the circumcenter, it discusses the other three concurrency theorems (important for Common Core) as well as the nine-point circle of a triangle.

Meanwhile, of immediate concern are Chapters 1 and 2 of the new text. Unlike the others, these chapters haven't changed much from the old text. The only difference in Chapter 2 is that Lesson 2-3, on if-then statements in BASIC, has been dropped. (After all, who uses BASIC anymore, except on the Mocha computer emulator for music?) In its place is a new lesson on making conjectures.

Two of the lessons of Chapter 1 have been dropped. One of them is actually today's Lesson 1-1, as its material has been combined with the old Lesson 1-4. Meanwhile, Lesson 1-5, on perspective, has been delayed to Chapter 9 (which makes sense as perspective is definitely related to 3D). The last lesson in Chapter 1 is on technology -- a "dynamic geometry system," or DGS. (That's right -- goodbye BASIC, hello DGS!) Officially, it still corresponds to the last lesson of the old Chapter 1, since this lesson still introduces the Triangle Inequality Postulate (but now students can test out this postulate for themselves on the DGS).

On the blog, I'll continue to follow the old Second Edition of the U of Chicago text. But if I ever get to sub in a classroom again, the classroom has priority over the U of Chicago order. In this case, if an important lesson is skipped, I could sneak the lesson in by following the Third Edition order instead.

Okay, without further ado, let's finally start the U of Chicago text!

Lesson 1-1 of the U of Chicago text is called "Dots as Points." This lesson has the first description of a point:

First description of a point:
A point is a dot.

This is the start of a new school year. Many students enter Geometry having struggled throughout their Algebra I class. Now they come to us in Geometry, and after all the frustration they experienced last year, the first question they ask is, "Why do we have to study Geometry?" Well, the answer is:

A point is a dot.

The old U of Chicago text writes about dot-matrix printers. This isn't relevant to the 21st century, and indeed they don't appear in the modern edition. But here's another question to ask students -- if you didn't have to take math, what would you do at home instead of math homework? And if the answer is "play video games," then guess what -- video game graphics consists of millions of dots. Or, more accurately, they consist of millions of points, since:

A point is a dot.

Images on video games don't come out of nowhere -- someone had to program in the millions of dots, treating them as points -- therefore using Geometry. So without Geometry, video games don't exist. If you want to answer that question -- "What would you do if there was no math?" -- then next time choose something that doesn't require math to build.

In the modern version of the text, there is a brief mention of pixels as part of both computer images and digital camera images. Again, it's not emphasized as much, since "dots as points" must share the new Lesson 1-3 with "network nodes as points."

Here is the Blaugust prompt for today:

Letter to my first-year teacher self…

I choose this prompt because it's the 31st prompt on Shelli's list, and today's date is the 31st. But it's only fitting that this falls on the final day of the month, since a letter to my first-year self is exactly what I need to tie up everything that I've written in the previous Blaugust posts.

When Shelli first included this prompt in the list, she probably intended the letters to say something like, "I know teaching is tough now, but it'll become easier after a few years." But obviously, that's not what I want to write. My first year of teaching was by any stretch of the imagination a failure, and so what I need to write myself is information that would have made myself a better teacher.

The sender of this letter is my current self. The recipient of this letter is myself on the day before my very first day of teaching -- August 15th, 2016. This letter will contain a few links, but I'll be careful to link only to pages that existed before August 15th, 2016.

2020 update: The first version of this letter was written in 2018 -- the last time that August 31st fell on a weekday. Since then, I've updated it to reflect decisions I've made about how I should have taught the class -- most notably in science, after having witnessed some science classes while subbing. In particular, this version has me teaching science two days a week rather than one, since now I know that one day a week doesn't really do the subject justice.

Other changes I've made include being more positive at the start of the year, emphasizing interactive notebooks (which were only hinted at in the 2018 version), and adding Sara VanDerWerf's 1-100 activity (as the 2018 version already mentioned her Name Tents).

On the other hand, as tempting as it is to write "Watch out for a pandemic in 2020!" I don't write anything like that.

With those changes, this letter supersedes the 2018 version of the letter.

From: David Walker, August 31st, 2020
To: David Walker, August 15th, 2016

Dear Past Self,

This letter serves a warning from four years in the future. Tomorrow is the first day of school, and I know that the hard work will begin. Unless I heed this warning, I won't complete this first year of teaching and only make it to the Long March.

Section 1: Classroom Management

I'm aware coming in to the year that classroom management is not a strength -- and the main reason that it isn't a strength is because I lack a strong teacher tone.

First of all, it's good to begin on a positive note. On the first day of school tomorrow, while the students are trying to learn procedures, try praising the ones who are following them. This positive start of the year will make the students more likely to listen to me as the year goes on.

I can be successful this year if I make up for the lack of teacher tone with a teacher look. The old poem goes:

No more pencils, no more books,
No more teachers' dirty looks!

So just as pencils and books are essential in the classroom, so is teacher look -- especially to someone like me who lacks teacher tone. I know that I don't have teacher tone, but I've never really tried out teacher look. I must remember the Fred Jones book, where the author refers to teacher look as the Queen Victoria look. Teacher look is the first step to becoming a good classroom manager this year.

Here are some common student sayings and how I should respond to them:

Student: I wasn't talking!
Teacher: (teacher look)

Student: I still wasn't talking!
Teacher: (say student's name, followed by teacher look)

Student: He/she really wasn't talking!
Teacher: (ignore, not even a teacher look)

Student: I'm not chewing gum! (hides gum under tongue, shows empty mouth)
Teacher: Stop hiding it under your tongue and spit it out. (plus teacher look)

Student: I'm not chewing gum! This is really paper in my mouth.
Teacher: Spit it out. You're not allowed to chew paper either. (plus teacher look)

Student: I'm eating in class because I'm hungry.
Teacher: Tough! No food in class. (plus teacher look)

Student: I'm not using a cell phone. This is really an empty phone case.
Teacher: Put it away. You're not allowed to have a phone case out either. (plus teacher look)

Student: You're the only teacher who enforces this rule.
Teacher: Tough! (plus teacher look)

Student: We act this bad in every class.
Teacher: (teacher look)

Student: Why?
Teacher: Because I said so!

When in doubt, just use teacher look.

I am a teacher. Sometimes I'll have to make unpopular decisions. I'll catch someone breaking a rule and not only will be rule breaker tell me that I'm wrong to enforce the rule, but all of the surrounding students will tell me that I'm wrong. But I must enforce the rule anyway. There might be some students who, deep down, know that I'm correct to enforce a rule, but won't say anything out of fear of being labeled a "snitch." Most of the time, no one will say anything. If I wanted to be applauded for my decisions, I should have become an entertainer, not a teacher.

Many times students will say that I am "unfair" or "mean" to enforce a rule. But I should go ahead and enforce the rule anyway. I'd much rather have every single student in class hate me for enforcing rules than have even one student like me because I let him/her get away with breaking rules.

I remember the week I subbed in a middle school class three months ago (May 2016) when one girl was bullied by other students. I expect bullying to be common here, and must stop it if I see it. The victim will probably say nothing, yet deep down will be grateful when I enforce the rules here.

I should not rely on deducting participation points as a punishment. This is because many smart students misbehave (sometimes like myself as a young student), so they rack up points for getting right answers, and then their points never become negative when they misbehave. If there are to be participation points at all, I should start each student at zero and only add, not deduct points.

Students should earn a short detention (nutrition, lunch, after school) if they repeatedly fail to follow my directions. The detention should double if they fail to serve it.

I never again want to be in a situation where I'm afraid to tell students to do something because I'm certain that they won't do it. I should emphatically tell the students to do it and be prepared to punish them if they don't.

Every time students stand up and leave their seat, I should ask them what they are doing. Even if they are merely sharpening a pencil, I should force them to declare it anyway.

One of my rules should be "Follow all adult directions the first time they are given." On the other hand, the so-called rule I blogged about, "respect order," is not a valid rule. Students respect order in class only when they respect the teacher and fear the teacher's punishment. Therefore "respect order" is a thinly disguised way of saying "respect the teacher."

In his book, Harry Wong stresses the importance of procedures. Some activities are obviously procedures (such as taking out and putting away laptops), but almost every activity can be considered a procedure (such as Warm-Up and Exit Pass). Students may complain that they have to follow these procedures at first, but I must enforce the procedures anyway. Chances are that once I enforce each procedure ten times, the students will stop complaining about it.

As for the laptop procedure, I'm currently considering labeling the laptop slots with numbers. I must not go home today (August 15th, 2016) until the slots have been numbered.

I remember subbing at middle schools in my old district where some teachers came up with the call and response, "Class Class? Yes Yes!" By the end of the first week, I should establish a similar call and response procedure and enforce it. This means that if I ask the class to be quiet and even one student is still talking, I stop and use teacher look. Otherwise, more than one student will start talking and the call and response procedure is never enforced. Until I come up with such a procedure, I should use teacher look when students talk out of turn.

As the school year is about to begin, I start wondering whether my student support aide is a good classroom manager or not. As it happens, she's excellent at classroom management -- and unless I heed this warning, the students will listen to her, not me. My having the rank of "teacher" isn't enough to prevent yet another situation where students listen to everyone in class except me. She is destined to become the new teacher of this class by next year unless I change my habits.

Many of the things I say in this letter reflect what my mentors have told me before -- most notably my master teacher from when I was student teaching. My mentors never explicitly tell me to do anything I mention in this letter, because classroom management comes naturally to them, and they do all of this without thinking. Since I'm not a natural classroom manager, I use deliberately choose to follow the actions suggested in this letter.

Section 2: Avoiding Yelling and Arguments

Because I lack a true teacher tone, whenever I raise my voice it turns into a yell. My goal should be to avoid yelling at all costs.

Once again, the easiest way to avoid yelling is to start out on a positive note. Instead of yelling at the students who are breaking rules, try praising the ones who are following them.

Often when I feel the urge to yell, it's because students are misbehaving and have convinced me that it's wrong to punish them. Instead of yelling at them, I should punish them.

Arguments often lead to yelling. Therefore, I should try to avoid arguments. There are certain things I often say that lead to arguments, so I shouldn't say them. Examples include:

"Because you're more likely to get an A."
Many students don't care about getting high grades in math or any other subject as much as I did as a young student. Often, students behave not because they want an A, but because they respect the teacher and fear punishment. Therefore I should be trying to get students to respect me and be aware that they will be punished. I might want to say this in response to a "Why?" question. My answer should be "Because I said so," not "Because you're more likely to get an A." But the chant "What grade do you want to earn? An A!" at the start of a quiz or test is a good idea.

"Because you should attend every single second of class."
Many students don't care about perfect attendance as much as I did as a young student. Often, students attend class not because they care about attendance, but because they respect the teacher and fear punishment. Therefore I should be trying to get students to respect me and be aware that they will be punished. I might want to say this in response to a question "Why can't I use the restroom or go to the drinking fountain during class?"

Last month (July 2016), I read a magazine article about a tomb guard who works around the clock without rest. I should not even mention this in class as a reason not to let students go to the restroom.

The idea of handing out restroom passes at the start of the trimester is sound, but many students whom I'm sure have passes have often lost them when they need to go. I know that I'm trying to avoid keeping track of two things (participation points and restroom passes), but there's no real way around it. I must keep track of the passes rather than expect students not to lose them.

I can either go the traditional "three passes at the start of the trimester" route for everyone or, if I don't mind keeping track, let the students earn passes for A's.

Music break is a great idea. But students should still need a pass if they leave during music break. I should get the class quiet so that students are either listening to me or singing along during break.

The idea that a student who doesn't know basic math is a "dren" is sound. But some special ed students might be offended by the concept, and this might lead to arguments. I should emphasize that a "dren" is someone too lazy to do basic math.

Indeed, the word "dren" is such a negative word to use so often at the start of the year, and so it helps to balance it out with a positive word. I've already thought of using the word "hero," but I should actually say that word in class, or "almost hero" for those who are working hard.

Either today or tomorrow (August 15th-16th, 2016), I'll receive an email from the administration that students in sixth grade and above must have uniforms on the first day of school -- the grace period is only for fifth and below. But this will lead to arguments if I try to enforce it. The email will come from the sister campus, where perhaps all middle school students have uniforms. But at our campus, some students just barely enrolled last week. I should only enforce the uniforms if the other middle school teachers are actively enforcing them. Instead, I must focus more on enforcing classroom rules.

I should enforce the no cell phone rule only in my own classroom, rather than outside. In particular, I shouldn't worry about cell phones used during P.E. at the end of the day or on field trips. Only experienced teachers are respected enough by students to enforce rules outside. I should only enforce no cell phones if the other middle school teachers are actively enforcing it (that is, by actually walking up and down during P.E. and confiscating phones). Instead, I must focus more on enforcing my classroom rules.

In fact, during P.E. time it's a good idea to hang out with the other middle school teachers and discuss our respective days.

To avoid arguments, it's okay to relax certain rules with special ed students when appropriate. In a month or two I'll finally see IEP's for special ed students. But there are some commonsense things that I can do to help special ed students even without an IEP.

To avoid arguments, it's okay to talk occasionally with students about something other than math. If I have stronger classroom management, I will feel more confident that I can have a short conversation without losing control of the class.

To avoid arguments, I should be more careful about markers. The STAPLES store sells small boxes of a dozen markers, so I should look for these. I can purchase a new box of these markers each time that a whiteboard lesson is scheduled. Then the larger markers can be reserved for teacher use on the front whiteboard.

If I tell students to do something and they don't, I should repeat the request. Then I should say "Third Time!" and repeat the request. Then I should say "Fourth Time!" and repeat the request. If by then they still refuse to do it, I should punish them. If the students comply, then thank them. The word "Finally!" should not be part of my vocabulary at this point.

When in doubt, if I feel the urge to yell and don't know what to do instead, just use teacher look.

Section 3: Avoiding Mention of Past Incidents

Sometimes, a student will ask "Why do I have to follow this rule?" Often, my answer will be something like, "To avoid (past incident) from occurring again." This isn't a good response. Instead, it's always better to answer "Because I said so."

Again, focus on the students who are following the rules and try praising them. I should set them up as examples for the other students to follow.

Sometimes, a student will claim "It's impossible to follow this rule." Often, my answer will be something like, "I was able to follow it as a young student." This isn't a good response, since usually the student will counter with "That's you, not me."

Students often say "That's impossible!" when they mean "That's difficult!" or "I don't want to." I should enforce the rules even if they claim that they're impossible to follow. They'll suddenly realize that the rules are possible to follow once they see that I'll punish them unless they follow the rules.

It might seem better to say, "The other class was able to follow rules," instead of "I was able to follow rules," but it's not. The student will counter with "That's them, not me." Indeed, I should never compare my current class to either myself or another class unless it's a favorable comparison.

If a student says, "Prove that I was talking," nothing I say or do will ever be accepted as a valid proof by that student. Instead, I should give teacher look. The idea is for "Prove it!" to disappear. If I show strong classroom management from the start, "Prove it!" will never appear.

Section 4: Faster Warm-Ups

The Illinois State text contains a Five-Minute Daily Assessment. Therefore Pappas-based questions where the answer is the date should become the Exit Pass, not the Warm-Up.

The Daily Assessment should take only five minutes. At first, students will complain that I'm not giving enough time unless I establish a procedure. At first, I should give warnings such as "Four minutes to go," "Three minutes to go," and so on. I should encourage students who haven't started working that time is running out. I should gradually give fewer minute warnings, perhaps giving only "One minute to go." In a few weeks, I should be able to dispense with all minute warnings, since students will have learned the Warm-Up procedure.

For the Exit Pass, at some point most of the students will catch on that the answer is the date and just write an answer with no work. I should not give these students credit unless they show work, even if it means denying credit to more than half the students. I should make sure to warn the students that they won't get credit unless they show the work.

In fact, the plan for tomorrow, the first day of school, should be the reverse of my original plan:

  • Warm-Up: "If you don't know the answer, at least know..."
  • Name Tents
  • Music Break: The Dren Song
  • Bridge Problem
  • Exit Pass: 2 * 2 * 2 * 2 = ?
Here I also replace Dan Meyer's "Personality Coordinates" with Sara VanDerWerf's Name Tents:


I was torn between whether to give "Good Luck" notes once at the end of the year, or once at the end of each trimester. I shouldn't wait until the end of the year or even the end of the trimester to connect to my students. Instead, VanDerWerf name tents allow me to connect to students from the start. While Personality Coordinates allow the students to connect to each other, Name Tents allow the teacher to connect to the students.

Section 5: Student Engagement

I never want to be in a situation hardly any student knows how to solve a problem, especially when it's a review lesson. By giving up and solving the problem myself, I'm saying that "math is just hard," which makes me no better off than the students.

Regardless of how difficult a lesson is, there should be at least a few students who can solve the problem by the time of the review. If no one can solve a problem, it means that either I didn't teach the lesson properly, or else my classroom management is so weak that students can just talk through the lesson without consequences.

If someone had told me that I would have an hour of computer time at the end of the day, and there is neither a grade for the class nor any other accountability, I would have called that person crazy, since of course the students won't do the work. Yet that's exactly what's in my current plans.

Instead, there should be an IXL accountability form. This is a form that is similar to the Warm-Up form in that it contains blank spaces for students to complete approximately ten questions. Every students gets an IXL form. Since there aren't enough laptops for the students, the students with laptops can use the IXL form as scratch paper, and I record their IXL score (0-100) on the form. The students without laptops must answer ten questions that I come up with myself (but similar to the IXL questions for the day). All ten answers must be correct, or otherwise the students must continue to redo them until they are all correct.

At the end of the day, I collect the IXL forms. The students who earn at least 70 on  IXL or answer all ten written questions earn a participation point. Those who earn a perfect 100 on IXL earn a second participation point. Those who fail to reach 70 on IXL or answer ten written questions earn no points, and continued failure to reach 70 or ten results in consequences, including talking to the student as the others go out to P.E. class.

When in doubt, I should have more accountability worksheets, not fewer. It's a good idea to create worksheets for other tasks such as Illinois State projects. Yes, I fear that the copy machine will break down and so I don't want to become dependent on the copier. As for what I should do when the copier breaks down, I should cross that bridge when I reach it. Only classroom managers stronger than I should attempt to teach a class without worksheets.

I should post IXL and other passwords on the wall so that students can look up their passwords themselves rather than ask me for them over and over.

Section 6: Illinois State Implementation

Many members of the MTBoS integrate projects throughout their lessons. While these aren't the same as the "bells and whistles" of the Illinois State text, those teachers would agree that the different components of their own respective lessons can be helpful to weaker students. Therefore I owe it to the students to implement all parts of the curriculum. I will be judged by whether I implement all parts of the curriculum, including the trickier parts such as DIDAX manipulatives and die cuts.

I know that pacing guide on the Illinois State website is difficult to decipher, but I should spend more time analyzing it. The lessons are listed there in Common Core order, which is the same order as the "traditional textbook." This means that both sixth and seventh grade lessons start with all of the RP lessons, then NS and EE, and so on.

I know that I'm fond of the order of the lessons in the eighth grade STEM text. But in fact, considering that I must teach both math and science, it's better just to forget the STEM text altogether -- the only projects I should give are from the science text (from the online Illinois State science text). My counterpart at the sister charter school is basically ignoring the STEM text, and so should I.

Here are possible lesson plans for the first few weeks of school:


  • Tuesday, August 16th: Name Tents, Bridge Activity (reverse order from original plans)
  • Wednesday, August 17th: Rule Posters
  • Thursday, August 18th: 10's Dren Quiz, Patterns (consider Sara VanDerWerf's 1-100 activity, https://www.saravanderwerf.com/100-numbers-to-get-students-talking/)
  • Friday, August 19th: Building Activity
  • Mon.-Tues., August 22nd-23rd: Math Benchmark Tests
  • Wednesday, August 24th: Science: Parts of a Microscope
  • Thursday, August 25th: Benchmarks, Day 3
  • Friday, August 26th: First Science Project
  • Monday, August 29th: Coding Monday
  • Tuesday, August 30th: Traditional Textbook (6th-7th -- RP1, 8th: NS1)
  • Wednesday, August 31st: Science Benchmark Tests (Study Island)
  • Thursday, September 1st: Fraction Fever Activity (including DIDAX manipulative)
  • Fri.-Mon., September 2nd-5th: Holiday
  • Tuesday, September 6th: Traditional Textbook (6th-7th -- RP2, 8th: NS2)
  • Wednesday, September 7th: Second Science Project
  • Thursday, September 8th: Interactive Focus Tutorial, Math Assessment (RP1, NS1)
  • Friday, September 9th: Continue Science Project


Then the pattern continues with coding on Mondays, math on Tuesdays and Thursdays, and science on Wednesdays and Fridays.

The Illinois State text doesn't provide many die cut lessons for middle school. One of the few that appears is the square root activity demonstrated to me last week. This lesson fits eighth grade NS2, and so it's perfect for September 15th Learning Centers.

When submitting lesson plans to the administrators, I should provide an extra copy of the lesson plans to my student support aide. She's a professional who deserves to know my lesson plans. If I lift the burden of classroom management from her shoulders, then she might be willing to help me out, especially with Learning Centers and finding materials for the STEM Projects. I should try to submit the plans as early as possible. It shouldn't take much work on my part, since the basic framework for every week is the same. All I have to do is change the Common Core standard.

I am required to give the online Illinois State homework. As usual, I should print it out and pass it out to the students. Those who complete it online can indicate so on the worksheet and turn it in, leaving the questions blank. Others can choose to answer the questions directly on the worksheet. I should pass out homework at the start of the week and collect it at the end of the week.

Consider using Concrete, Pictorial, Abstract for teaching math:

https://sis4teachers.org/2016/01/concrete-pictorial-abstract-what-is-that/

This is compatible with the Illinois State text. One way to make this fit the weekly plan with science lessons above is Concrete on Thursdays (including Learning Centers and DIDAX), Pictorial on Fridays (if the kids have finished the science project, this includes die cuts, which can begin on Thursday and extend into Friday), and Abstract on Tuesdays (traditional lesson). The homework given on Mondays matches the Abstract lesson on Tuesdays. And one way to remember this pattern is C->P->A, where Concrete leads to Pictorial, which leads to Abstract.

For the LA County Fair field trip on September 16th, I should plan my itinerary for the field trip in advance rather than walk around aimlessly with the students. In particular, we should board a tram and head out to the farm area as soon as possible.

Section 7: Online SBAC Review

The SBAC is an online test. I should be familiar with the SBAC website and what the test looks like for students, especially in the weeks leading up to the test.

http://www.caaspp.org/

I admit that the SBAC website is difficult to work with, which explains why my blog posts from three months ago (May 2016) were on PARCC review, not the SBAC. But I owe it to my students to be familiar with the SBAC website. I will be judged on how well my students are prepared to take the SBAC test online.

The multiple-choice portion of the SBAC math test is divided into two sections. The first section is non-calculator while the second is calculator. I should be familiar with how to access the calculator in the second section. I should not attempt to access the calculator in the first section.

I was shocked to find out last week that I had to teach science in addition to math. I am already aware of the transition to NGSS Standards. I should have performed a Google search for ngss site:lausd.net the instant I found out that I had to teach science. This will link to a description of how the LAUSD is making the transition. I should also check out the SBAC website to find out as much information as possible about the new California Science Test for eighth graders.

I misinterpreted administrators last week. They never said that I didn't have to teach science. What they really said was that our sister charter would get the Illinois State science textbooks. Instead, I should access the texts online. My teachers editions of the science texts will arrive in a few months.

The old test covered only eighth grade physical science, but the new test covers all three grades of middle school science. Therefore I should teach science to all three grades. I can use the LAUSD website to determine what science to teach each grade. Most likely, eighth graders get physical science and seventh graders life science, but sixth graders get the new integrated NGSS science.

I feared that teaching science would make me feel as if I have six preps. To make it easier, I can replace the Thursday STEM projects for math with science projects from the online text. It's very important to type my own worksheets for these since the students don't have copies of the text (and the Illinois State website won't let me print them). This is, in fact, exactly what my counterpart at the sister charter is doing. She is only giving the science projects, not the math projects.

In fact, from the very start of the year, I establish Thursday as science day. The first Thursday of the year is the building project, since it's a science-like opening activity. The second Thursday of the week is a science Benchmark Test. I won't be given a specific science benchmark, so instead I can make it up. Study Island provides a bank of questions as a pretest.

Yes, it's a good idea to use the eighth grade Study Island block on Wednesdays for science. This is something that I shouldn't print. Instead, let them read the articles and answer the questions online.

Ironically, the Illinois State website actually provides arts projects for science. So I can use these as part of Wednesday Learning Centers.

Otherwise, all science is on Thursdays. It's a good idea to have the students take notes in an Interactive Notebook for science, which they can use for math as well. If I fear that some students will go the whole year without ever buying a notebook, then I can provide the first one for them. There should currently be a sale at the Staples store where each notebook costs only a quarter. There is a limit of five notebooks, but my classes are small enough that by even purchasing five per day starting today, I can buy one notebook for every student by the third week of school and the first real science lesson.

It might be tricky to schedule the science lessons. A four-week rotation might work:


  • Week 1: Dren Quiz
  • Week 2: Math Quiz
  • Week 3: Science Assessment
  • Week 4: Math Test

The math assessments listed above can be given on Thursdays -- as soon as students finish, they can start the Concrete lesson as Learning Centers for the next standard. The science assessments can be given on Fridays.

One project every two weeks fits the requirement that we submit photos of a project to Illinois State every other week. The projects occur the same weeks as the Math Quiz and Test.

If I fear that I won't be able to keep up with having three different science projects in the three grades each week, then I can start with one particular project in all three grades the second week -- one possibility is LS1 (from the Life Sciences text online). This project is about cell structure and might require the microscope -- hence the lesson on microscopes two days before the project. The students will see the microscopes around the room and be intrigued by them, so oblige them with a microscope project early. I should ask my student support aide to help me with the microscope project if I need it. Once I get accustomed to giving science projects, then I can start assigning appropriate science projects in each grade.

The idea of dren quizzes is great, but I'm not quite sure where they fit in this scheme. Ironically, they might actually fit on Thursdays before the Concrete lesson. Only one dren quiz per four week cycle is truly needed to cover the 10's and 2's through 9's. The original three-week cycle that I'd imagined doesn't fit with Illinois State. And besides, I'll have a student support aide to help me grade tests, so there's not really a need to stagger the assessments. Consider using the name "Hero Quiz" rather than "Dren Quiz" in order to maintain a positive tone in class.

Last week on my blog, Shelli, the leader of the Blaugust challenge, suggested signing up for a Twitter account. It's actually a great idea. As the only middle school math and science teacher at my school, I need all the help I can get, and the best place to find it is on Twitter. Two teachers in particular to pay attention to are Wendy Menard and John Berray.

I know teaching is tough now, but it'll become easier after a few years. In particular, even though there will still be a single math/science next year, two years from now there will finally be separate teachers for math and science at my school. And there's a good chance that the charter will not be renewed after the third year, so I must be successful now in order to be hired as a math teacher at a new school after my third year. But the only way that I can make it to my third year to be that math teacher is to follow the instructions in this letter.

Sincerely,

David Walker, August 31st, 2018

Retuirning to 2020, I admit that the scheduling here is tricky. I like the idea of Concrete, Pictorial, Abstract and how it fits with the Illinois State math components, but it's tricky to find time for all this along with science as well. If I schedule math for Tuesday and Thursday and science for Wednesday and Friday, the students can work on the other subject if they have any extra time. Thus I only have to plan for three preps each day and avoid the six-prep problem of having to teach both subjects to all three grades everyday.

Notice that in this letter, I hint at the charter not being renewed. Of course, even if I survive all three years at the charter, I'd no longer be working there once the school is shut down, which means that I could still be in the same boat I'm in now -- with no teaching job, forced to work as a sub, waiting by the phone for subbing calls that never come, staring at the purple and red spots on maps.

The idea that I hint at to end this letter is that if I survive and complete three successful years at the charter, that's three years' worth of solid experience to mention on my resume. With a stronger resume, I'm more likely to be hired as a teacher in the summer of 2019 -- and thus I'd currently have a job during the distance learning stage. Hopefully, my new school would be a public school, so I'd not have to worry about working at another charter school only to have the charter not renewed. I might even welcome the purple status if I fear that working in person might expose me to the virus, but only if I already have a steady job teaching online.

In this post, I mention joining Twitter, which was suggested to me by Shelli. Notice that I mention Wendy Menard, who passed away earlier this month. As it turns out, John Berray is another math teacher who left this life too soon, due to a car accident. This was just before the virus closures -- I noticed several math teachers on Twitter mourning his loss, yet I didn't know who he was. He was most active on Twitter around the years 2013-2015, but some of his tweets were likely still visible on his account in 2016. He left the classroom to become a math coach, hence he posted less often to his blog and Twitter in his last years. Since I linked to Menard's blog, I might as well link to Berray's:

https://johnberray.wordpress.com/

His last post was during my third week at the old charter school, and it's on using the tops of the desks as whiteboards. (My old school had whiteboards, so Berray's idea wasn't necessary for me -- but still, it does show that I could have found more excuses to use whiteboards in my class.)

John Berray was a Southern California high school math teacher -- he worked in San Diego County. I wonder how he'd feel about his school being in a county that's slow to reopen despite being red. The activities I see on his blog (such as desks as whiteboards) work much better in person.

In remembering Berray, the other tweeters mentioned what he said about being a "math person." (He doesn't say this on his blog, so it must be something he tweeted years ago.) Of course, this all goes back to the idea that some students think that they simply aren't good at math, and so they would rather just leave their assignments blank.

Thus Berray's "math person" idea is similar to my "dren" idea -- except that I focused on the negative (being a "dren") while he focused on the positive (being a "math person").

Today's Blaugust participant is Stephen Dull:

https://tweakingfornoreason.wordpress.com/2020/08/31/ifr/

The title of his post, IFR, refers to "instrument flight rules" -- Dull makes an analogy here between flying a plane and teaching during distance learning:


I need a plan. On purpose. As Wikipedia says about Instrument Flight Rules: “Instrument pilots must meticulously evaluate weather, create a detailed flight plan based around specific instrument departure, en route, and arrival procedures, and dispatch the flight.”
I need a way to know if my kids are engaged with what we’re doing. Or if they are even in the same room.
He tries to convert one of Dan Meyer's activities into an online format -- no, not Personality Coordinates (which we've already seen attempted by another teacher), but one on linear functions. He also mentions finding a way to combine this with Desmos (which as we've seen recently is adding features made specifically for distance learning):

Of course, someone thought of that long ago. Wish I would have done the search while I was planning instead of when I was doing a post mortem. But, new school, Google Classroom rather than Canvas, building the plane as I fly it. One of a million things that slipped through the cracks on me.

And for me, my entire blog entry today is a post mortem -- in my letter, I wrote about all the things that I could have searched for while I was planning at the old charter school. The only difference is that Dull can easily try his Desmos activity with the students tomorrow -- I, on the other hand, don't have a class with which I can fix my errors and omissions.

Oh, and the undisputed champion of the Blaugust challenge is Denise Gaskins:

https://denisegaskins.com/2020/08/31/morning-coffee-31-august-2020/

She posted 29 out of the 31 days in August -- everyday from August 3rd until today. I'm not sure whether she even sees herself as a Blaugust participant -- she regularly posts on Mondays (in her "Morning Coffee" series) and starting August 3rd, she just went on a blogging roll and simply kept posting until today. But since Gaskins is mentioned on Shelli's blog, I'm calling her a Blaugust participant and champion.

Many of her posts this month are about a book she's writing, Prealgebra & Geometry. Based on this title, this book sounds as if it's for middle school students. Her book comes out next year, so there's no reason to mention it in my letter to 2016 above (though I did use one of her activities, Tax Collector, with my actual sixth graders).

Here are some of her posts from the first week, when Gaskins was quoting from her new book:

https://denisegaskins.com/2020/08/03/
https://denisegaskins.com/2020/08/07/

And here's a link to another one of her games, Moving Patterns. As its title implies, this game is for kinesthetic learners:

https://denisegaskins.com/2020/08/06/

And so another Blaugust is in the books. I definitely hope that I'll become a full-time teacher by next Blaugust so that I can be a true participant in this challenge.

Here is the Lesson 1-1 worksheet:



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