Friday, July 22, 2016

Rule #3: Respect Yourself and Others (Pi Approximation Day Post)

Today is Pi Approximation Day, so-named because July 22nd -- written internationally as 22/7 -- is approximately equal to pi.

It also marks two full years since my very first post here on the blog. Yes, I've declared Pi Day of the Century -- March 14th, 2015, to be the ceremonial start date of this blog. But the chronological start date was July 22nd, 2014. I like celebrating both Pi Day and Pi Approximation Day -- including eating pie both days -- and so I celebrate both of them as launch dates for the blog.

Let me a little introspective here. Writing on this blog has taught me many things about myself that I have not realized.

For starters, I realize that I change my mind a lot. I say that I'm going to post something about a geometry topic, then I change my mind and post something else -- and then I say that I'll post a third thing when I revisit that topic next year. From the perspective of the blog readers -- you -- it must be infuriating to read something in the archives that I say that I'll post and then move forward in the archives only to find out that I never posted it.

Last year, I used the anniversary to create a FAQ about my blog and myself. I do the same this year -- and this year's FAQ will reflect the changes that have happened to my career since last year. As usual, let me include a table of contents for this FAQ:

1. Who am I? Am I a math teacher?
2. What are the Common Core Standards?
3. Am I for or against the Common Core Standards?
4. What is the "Illinois State text"?
5. Who are Hung-Hsi Wu and Fawn Nguyen?
6. Who are "the traditionalists"?
7. What are E's, S's, and U's?
8. If I will be teaching all three Grades 6-8, why will this blog cover only my 8th grade classes?
9. What will I do about cell phones in the classroom?
10. How will I state my most important classroom rule?

1. Who am I? Am I a math teacher?

I am David Walker. I have recently earned my clear credential in Single Subject Math here in my home state of California, and I have just been hired as a full-time teacher. I will be starting my first full year of teaching at a charter middle school in Los Angeles.

This already explains some of why I change my mind so frequently. For the first two years of this blog, I was a substitute teacher, and my posts were either about whatever I taught in that day (if it was math) or otherwise I would default to Geometry. This year, I plan on using the calendar for the LAUSD district, which my charter follows (with one slight exception). Day 1, the first day of school, will be on August 16th in this district.

Notice that even though I refer to the LAUSD several times in this post, my school is officially a charter school and not an LAUSD school.

2. What are the Common Core Standards?

Common Core refers to the new ELA and math standards taught in many states, including California. In particular, I refer to the Core's new focus on translations, rotations, and reflections in geometry -- these transformations were not emphasized before the Core. Transformations appear in the standards for eighth grade and above. Because of this, even though I will teach all three middle school grades (sixth, seventh, and eighth), I will mostly blog about my eighth grade class on the blog.

The Common Core is neutral in that it supports either a traditional pathway (Algebra I, Geometry, Algebra II) or an integrated pathway. On the traditionalist pathway, of course it's mainly the Geometry class where the new geometric transformations appear. On an integrated pathway, the transformations appear in both Math I and Math II classes.

Notice that there is actually very little difference between Common Core 8 and Integrated Math I. Because of this, my blog readers who are high school teachers can apply the assignments to their Math I classes as well.

3. Am I for or against the Common Core Standards?

There are some things that I don't mind about the Common Core and some things I'd change. I know that some people oppose the Core for political reasons. I try to avoid politics here on the blog, but unfortunately the Core is inherently political. In particular, opponents of the political party that was in power when the Core was first adopted tend to dislike the Core as well.

During the first two years of this blog, I devoted many posts to the Common Core debate. But now I am a full-time teacher at a Common Core school, so I will no longer write posts debating the Core, and indeed, I will be toning down the politics once the school year begins.

4. What is the "Illinois State text"?

I use the phrase "Illinois State text" to refer to the IMaST program created by the Center of Mathematics, Science, and Technology at Illinois State University. It is the text used at several middle schools in LAUSD proper, as well as my charter school.

The following comes directly from the preface of the teacher's edition of the Illinois State text:

"The Creative Core Curriculum in Mathematics with STEM, Literacy and Arts Teacher STEM Project Edition Grade Eight book is unique. It consists of a series of learning cycles and readings specifically designed to teach all of the Common Core Content standards for 6th grade mathematics. Each learning cycle guides the students through a series of activities leading to conceptual understanding, not just memorization of facts. Concepts are taught through the activities, not just practiced or applied through supplemental projects. Although conducting activities can take longer than traditional pedagogy, it is actually a more efficient use of time since students are better able to comprehend and remember mathematical concepts."

For example, Cycle 6 of the 8th grade text is "The Capacity of Water-Carrying Structures." In this project, students actually construct four pipes using card stock -- one a triangular prism, one a rectangular prism, one a cylinder, and one a shape of their choosing. Students then compare their lateral surface areas and volumes to determine which pipe has the most efficient shape.

The Illinois State text is not the only text that I mention here on the blog, not by a long shot. But now that I am getting ready to teach full-time, I will be writing more and more about the Illinois State text and less about other texts. In particular, the Illinois State text is not the same as the U of Chicago text that I mention in most Geometry texts on the blog.

5. Who are Hung-Hsi Wu and Fawn Nguyen?

These are California math teachers who have commented on how geometry should be taught. During the first two years of this blog, I discussed these and other mathematicians many times. But again, my focus will be turning away from geometry and more towards the middle school math that I will be teaching.

Dr. Hung-Hsi Wu is a Berkeley mathematician. He has written extensively on how to teach Geometry according to the new Common Core Standards:

Wu's document describes both eighth grade and high school geometry. Naturally, my focus this year will be on the eighth grade portion of this document.

It is Dr. Wu who defines pi as the area of the unit disk -- this definition favors pi above the numbers tau and lambda. (Yes, today is Pi Approximation Day, so here's a pi reference.) Meanwhile, Wu has also created an extensive document on how to teach fractions under the Common Core:

Wu describes how to teach fractions to students in Grades 3-7, but by eighth grade, the study of fractions is complete. So I really won't discuss Wu's fraction method on the blog, as my focus will be on the eighth grade class.

Here is one more link from Wu's website. Even though he wrote this in 2005 -- before the advent of the Common Core -- Wu writes of key mathematical ideas in middle school (which in this case he defines as Grades 5-8). As it turned out, some of Wu's ideas were ultimately incorporated into the Common Core Standards. (As you can see, Wu advocated for the inclusion of transformations in Geometry years before there was ever a Common Core!)

Nowadays, I want to focus more on my fellow middle school math teachers and their blogs. The best known middle school math blogger (by far) is Fawn Nguyen. In fact, she teaches right here in Southern California. Here's a link to her blog:

Nguyen's most important post regarding 8th grade geometry and transformations is the following:

Nguyen writes:

My 8th graders are learning about rigid transformations. I want to add a bit more complexity to what our book is asking the kids to do. For example, the book is having them reflect a shape mainly across the x-axis or y-axis, or on a rare occasion, reflect it across “the horizontal line that goes through y = 3.” Well, right before this chapter, we’ve been working with writing and graphing linear equations, so I want kids to reflect a shape across any line, including one that may cut through the shape itself.

And just as Nguyen supplements her text with this transformations activity, I can use this activity in my own classroom in addition to the Illinois State text. Learning Cycles 7-8 in the 8th grade text are only indirectly related to transformations, and it does fit the project-based learning pedagogy of my classroom to add a project such as this one.

But as Nguyen is a fellow middle school teacher, I will often go to her blog for guidance regarding classroom management and other issues. Here's a link to her page describing Days 1-2 in her classroom from two years ago. (Unfortunately, she didn't post at all last August.)

Nguyen writes:

Tomorrow is the day. I’m excited to meet my new Math 6 students — all 71 of them, two classes of 36 and 35. I should know about half of the 33 Math 8 kids because I taught half of them in 6th grade.

So as we can see here, Nguyen teaches both sixth and eighth graders. I, of course, will be teaching seventh grade as well.

Nguyen writes that she begins the first day of school with a warm-up and an activity. I plan on doing the same, but my warm-up and activities will be different.

And so I will continue to look to both Wu and Nguyen for guidance through my first year of teaching.

6. Who are "the traditionalists"?

I use the phrase "traditionalists" to refer to those who oppose Common Core for mathematical -- not political -- reasons. The traditionalists tend to believe that many of the topics in the Common Core Math Standards are taught too late.

My own relationship with the traditionalists is quite complex. I tend to agree with the traditionalists regarding elementary school math and disagree with them regarding high school math.

For example, they believe that the standards in Grades 4-6 that require the use of the standard algorithm for arithmetic should move down at least one grade level. I tend to agree with the traditionalists on this point here -- most of the reasons for opposing direct instruction, rote memorization, and drill don't apply to the youngest students. I remember once learning about two nonstandard algorithms for addition -- the Left-Right Method and the Plus-Minus Method -- on an old 15-minute math show for sixth graders, "Solve It," that used to air on our local PBS station back when I was that age. For mental math, these nonstandard algorithms are great, but for a young elementary student first learning to add two-digit numbers I prefer the standard algorithm.

On the other hand, the traditionalists also prefer that high school seniors take AP Calculus in order to open the door to college STEM majors. In particular, some STEM colleges here in Southern California, such as Cal Tech and Harvey Mudd, require calculus for admission. Even colleges that don't formally require calculus are likely to send students rejection letters if they apply without having calculus on the schedule, especially if they apply to STEM majors. Therefore they want the classes leading up to senior year to prepare students to take AP Calculus -- including Algebra I in the eighth grade. They oppose Common Core because its eighth grade math standards do not comprise a full Algebra I class. I only partially agree because I don't want seniors who can't handle AP Calculus or eighth graders who can't handle Algebra I to be labeled failures. Just as AP Calculus can open the door to STEM, it can close the door to a non-STEM career if students are forced to spend too much effort trying to pass their high school math classes.

OK, so I support the traditional pedagogy with regards to elementary math and oppose it with regards to high school math. But what's my opinion regarding traditionalism in middle school math -- you know, the grades that I'll actually be teaching? In middle school, I actually prefer a blend between the traditional and progressive philosophies. And the part of traditionalism that I agree with in middle school is making sure that the students do have the basic skills in arithmetic -- since, after all, that is elementary school math, and with elementary math I prefer traditionalism.

I've referred to many specific traditionalists during my two years of posting on the blog. But the traditionalist on whom I plan to focus the most goes by the username Bill. Indeed, as I begin to teach, I'll be writing more about Bill and less about the other traditionalists.

Bill often responds to articles posted at the Joanne Jacobs website. Here is a link to that site:

Here's a link to a recent comment of Bill's regarding college readiness. As usual, I provide first the link to the article (which is just a report from the ACT test, which doesn't allow comments) and then the Jacobs website (which does allow comments, and where Bill has commented).

Bill says:
Colleges these days are about being a business model, not getting an actual education (IMO). They’ll take your money until you either flunk out and don’t come back, or run out of it…
A student with a Composite ACT score of 15.1 is un-prepared for college level work, given that the minimum for success in college is a composite of at least 21-22 (higher than that is better, of course).
Additionally, I’d like to see the grades vs the ACT scores, I suspect they don’t match, if you have a ACT composite of 15 and a GPA of 3.8, I’d say the student got some grade inflation to help them out…

Meanwhile, Bill was quite outspoken in a thread about algebra and statistics:

Bill says:

But, I wonder about college students who can’t figure out 2x + 4 = 14. It’s not rocket science..
college students who cannot figure this out have NO business being admitted to a college in the first place, this is basic algebra (or pre-algebra even) and should have been completely mastered by at least the 9th grade, if a student was planning on attending college.
Basic Stats and Probability requires a basic working knowledge of algebra, plain and simple…trying to skirt around this issue will lead to students who won’t be able to master stats or probability.
On a more sad note, in my home state of Nevada only 9% of 11th graders have the necessary skills in reading, writing, english, and math to succeed in college per exam results…

In these two comments, we see that a concern of Bill is that students can get good grades in math without actually learning anything. I actually address this in one of my classroom rules. (Rule #2: Respect Your Honesty, or Avoid trying to get an A without learning anything.)

Actually, regarding 2x + 4 = 14, I'd say that students really are learning how to solve it. It's just that students forget how to solve it over the summer, so by the time they take the ACT or a college placement exam, they've forgotten it. Yes, 2x + 4 = 14 isn't rocket science, but it isn't bike riding (that is, something that once learned is never forgotten) either. (Instead, it's more like "use it or lose it.") I'd like to address this in my classes, but this is more of a challenge -- how much control will I have over what my students still remember years after taking my class?

Speaking of rocket science, Bill mentions it in his next comment.

Bill says:

There was an illustration in Calculus for Dummies…a football QB throwing a pass to a player and missing (consequences aren’t usually tragic), but aiming a spacecraft so that it can reach the moon or another planet is way worse if you miss (and that’s what calculus can do, since it’s nothing more than very advanced algebra, and allows you to handle rate of change issues)…
Calculus – the agony and dx/dt (running really fast now)…:)

I agree with Bill here -- if we want students to learn something, we should tell them why, in order to answer the question "When is this (say, Calculus) used in real life?"

In Bill's final comment, he tells us why so many students are struggling in math:

Though this problem starts in grades K-5 (and in the home) as many parents are themselves ‘math challenged’ and when students haven’t mastered add, subtract, multiply, divide, percentages, and fractions by the time they have left elementary school, they’re going to struggle the rest of their lives in math, period, and that can have life altering consequences, when they find out how much math is involved in some careers (all of the STEM disciplines and things like data analytics, business intelligence and so on require a solid working knowledge of mathematics beyond Algebra II/Trig).
Though perhaps I’m biased, but when I watch people struggle to figure out basic math concepts or percentages, it’s a sure sign they didn’t get good math instruction in K-5 and/or at home, and many elementary school teachers don’t have the strongest math skills.

I will often use the word "dren" to describe these students struggling in basic math. A "dren" is a reverse-nerd, or someone who hasn't mastered elementary math. I usually say K-3 instead of K-5, in order to avoid calling anyone who doesn't know fractions "drens." Bill doesn't use the word "dren," but I will use it to summarize Bill's concerns in a single syllable.

Most traditionalists dislike the Illinois State math texts -- that is to say, they dislike project-based learning texts, not necessarily the Illinois State texts per se (as most traditionalists have probably never heard of IMaST). Even though a traditionalist like Bill writes about using Calculus to get to the moon, he most likely wants Calculus classes to focus only on the concepts, not projects.

One more traditionalist whose ideas I'll take into the classroom is Katharine Beals. Unlike Bill, she doesn't post at the Jacobs website, but instead has her own blog:

Beals writes a series, "Math problems of the week," where she often complains about Common Core questions -- and more recently, answers. The following is a link to a Common Core test question taken from her home state of Pennsylvania:

But there's more to it than that. This is a sixth grade statistics question, and usually she ends her weekly post with an "Extra Credit" that is usually sarcastic or rhetorical. Beals writes:

Is knowing the meaning of "quartile value" an indicator of college and career readiness [that is, the stated goals of the Common Core -- dw]?

Here is the answer to this question (the answer Beals hopes for, that is):

No, of course students don't need to know anything about quartiles -- or statistics -- for that matter, to be ready for college and career. The only things that students need to know are algebra and calculus, and so anything in the sixth grade curriculum that doesn't prepare the students for algebra, including all of stats, should be dropped from the curriculum. Indeed, more students would be ready for Algebra I in eighth grade if the sixth and seventh grade classes spent less time on stats and more time on Pre-Algebra.

Naturally, I disagree with Beals here. First of all, typing in "quartile" into Google gives the following non-Common Core, real-world links on the first page:

Furthermore, I assume that Beals has no problem with other topics, such as division of fractions, included in the sixth grade curriculum.

Here's my first Extra Credit Question:
Of fraction division and quartiles, which topic will cause more sixth graders to ask "When will we ever use this in real life?" and which topic will the students instead sit down and try to learn?

But there is one thing idea I will take from Beals and include in my own classroom. By the time we get to the eighth grade, some of the stats topics (such as trend lines) are more challenging.

Here's my second Extra Credit Question:
Of polynomials and trend lines, which topic will cause more eighth graders to ask "When will we ever use this in real life?" and which topic will the students instead sit down and try to learn?

Unlike Beals, I don't claim to know the answer to this question. And so I want to test it out in my own eighth grade class. When we reach the unit on stats, I'll simultaneously teach (some of) the students polynomials and the rest trend lines. On the test, students will be able to choose whether they wish to answer polynomial questions or trend line questions. Then based on the results, we'll find out whether eighth graders are better off learning Algebra I (as Beals and the traditionalists believe) or learning stats (which I believe is more useful in real life).

7. What are E's, S's, and U's?

So far, none of the classroom rules that I've mentioned so far address classroom behavior -- which should strike you as odd. After all, shouldn't classroom rules be all about behavior?

The letters E, S, and U are the marks given in the LAUSD for work habits and cooperation. As you may expect, E, S, and U stand for "excellent," "satisfactory," and "unsatisfactory" respectively. So just as my Rule #1 basically tells students to strive for an A in every class, today's rule tells students to strive for an E in every class.

I'd like to say that I always earned E's in all my own classes growing up, but of course this is nowhere near being true. I still remember receiving "check-marks" (somewhat like U's) in many of my elementary classes (often in "works well with others" or something similar). In fact, I remember finally receiving the "Student of the Month" reward for being the best-behaved student in my class -- during May of my sixth grade year. This was the last possible month that I could have earned the award at my K-6 elementary school, as there was no separate award for June.

In the seventh grade, I never received any U's, but I did get an N once -- here N stands for "needs improvement" and represents a mark between S and U. (N's are not used in the LAUSD.) From the seventh grade on, I always tried to behave whenever I was in front of a teacher, but the N was for something I did when I was away from a teacher -- failed to turn in enough homework. (So technically the N was for work habits, not cooperation.) After I got the N, I always made sure to meet the 75% homework threshold in order to avoid getting any more N's. (Believe it or not, I think the class in which I earned the N was Algebra I -- my academic grade was A, yet work habits was N!)

In high school I earned mostly E's -- though I did receive a few S's, but never any N's or U's. For the rest of this post, I will refer only to the LAUSD marks of E, S, and U, not N.

To me, the three LAUSD marks represent three types of students -- E-kids, S-kids, and U-kids:

-- E-kids consistently follow the rules, even when given the opportunity to break them.
-- U-kids consistently break the rules, even when given the opportunity to follow them.
-- S-kids sometimes follow and sometimes break the rules. If the teacher has a strong classroom management plan, the S-kids will act like E-kids and follow the rules. But if the teacher has a weak classroom management plane, the S-kids will act like U-kids and break the rules.
-- Most students are probably S-kids. And so this is why classroom management is important -- the ability of the teacher to manage determines the behavior for most of the students.

Notice that I've myself have been all three types of student. I was a U-kid in elementary school, mostly an S-kid in middle school, and an E-kid in high school.

Also, as a sub, I've been both types of teacher. On some days, my classroom management was strong enough to make the S-kids behave like E-kids. But unfortunately, on other days my classroom management was so weak, the S-kids behaved like U-kids. If you go back and read some of my posts from the first two years (using the "subbing" label), you'll recognize both my good days and my bad days (though I didn't use terminology like "S-kids" in those posts).

What did I do on my better days to make the S-kids act like E-kids? Well, first of all I made sure that the students always had something to do. And second, I made sure to hold the students accountable for doing that assignment.

In previous posts I've referred to a "Who Am I?" game and a group point system. As a teacher, I won't play the "Who Am I?" game everyday, but I will keep the point system. I will refer to these points as Participation Points and assign them to individuals.

At the start of each unit (that is, right after the test), each student has two Participation Points. I will award a point each time a student gives a correct answer, to a Warm-Up or any question that I ask during the main part of the lesson.

But if a student fails to participate or otherwise misbehaves, I'll deduct a point. If the student's Participation Point total drops below zero, I will begin assigning consequences, beginning with a minute of detention for each additional point below zero. I expect these detentions to be the most effective in my eighth grade classes, because based on my school's block schedule, Math 8 always meets right before nutrition or lunch, so students will want to avoid those detentions. (Math 7 also meets before nutrition on certain days of the week.) Failure to show up to detention results in a doubling of the detention time, and further consequences occur when the total detention time exceeds a certain amount.

When I was a student teacher, I ended up covering three classes -- third period Algebra I, fifth period Algebra II, and sixth period Algebra II. (Notice that third period was right before nutrition, fifth period right before lunch, and sixth period at the end of the day -- yes, you can see how I got my detention idea!) I consider two of those classes to be less successful -- fifth period, because the class has 40 students, and third period, because the students acted like, well, freshmen. In those classes, the S-kids acted like U-kids.

But I consider the sixth period Algebra II class to be the most successful class I've ever taught. The students in that class were very motivated to outdo each other and answer questions so that they can earn the Participation Points. In that class, the S-kids acted like E-kids.

It's easy for me to say that sixth period was successful because the students were more mature than the freshmen, and there weren't 40 of them in the class. But looking back, I believe that the reason for the difference was psychological. Subconsciously, I was thinking, well, I've survived my freshmen and my class of 40, and so it's all downhill from here. And that thinking showed up in the way that I taught the class -- the students knew that my expectations were high and they lived up to them. I reckon that if that sixth period class had been the only class I had to cover for student teaching, it would not have been as successful, since it was that "downhill" feeling I had after covering third and fifth periods that caused me to teach sixth period effectively.

In my less successful subbing assignments, I didn't play any game or have a point system. I usually preferred playing "Who Am I?" only in math classes, and so it was often in those other classes when I had trouble managing the class. Sometimes, there's nothing I could have done to make the students behave -- for example, I mentioned before that my final subbing assignment was a science class that was learning about the reproductive system. I couldn't get the students to work because I had to spend all my effort checking permission slips and making sure that only students who had permission were given the lesson. I couldn't start playing my game, which would have required me to ask questions from the worksheet out loud enough for students without permission to hear. So the S-kids in the class inevitably acted like U-kids. On the other hand, in other classes I had no such excuse -- I could, and should, have set up a point system so that students would be motivated to work.

My goal is for every class to be like the sixth period Algebra II class that I student-taught. I need to think about what made that class successful and manage all my classes that way. It will be tough, as my middle school students will be several years younger than my Algebra II students. But I owe it to my E-kids to manage the class effectively.

8. If I will be teaching all three Grades 6-8, why will this blog only cover my 8th grade classes?

The name of this blog is "Common Core Geometry." Therefore, it's expected that I post something related to geometry.

When I first named the blog, it was before I received my first teaching assignment, so I had no idea what class I'd be teaching, or whether it would even be middle school or high school. All I knew was that the new Common Core Geometry standards would be a major stumbling block for teachers, and I wanted to help them out by creating this blog.

As I mentioned earlier, the new geometry standards based on transformations actually begin with the 8th grade standards. Therefore, I remain true to the original title and purpose of this blog by focusing on the 8th grade classes. But I will write posts about the entire 8th grade year though, not just the geometry units (and again, Common Core 8 is nearly the same as Integrated Math I).

I wrote that I will be trying to post three days per week after school starts. I've decided to attempt to post on a regular schedule based on the school calendar using the following pattern -- I will skip posting every third day. So my first post will be on Day 1 or Tuesday, August 16th, then my next post will be on Day 2 or Wednesday the 17th, and then I skip Day 3 or Thursday the 18th, before posting again on Day 4 or Friday the 19th. Other skipped posts in August will be Day 6 (Tuesday the 23rd), Day 9 (Friday the 26th), and Day 12 (Wednesday the 31st).

As you can see, whenever the day number is a multiple of three, I avoid posting that day. This will result in posting approximately thrice a week. During some weeks I might end up posting four times, while during certain holiday weeks there might be only two posts, but most of the time there will be three posts in a week.

9. What will I do about cell phones in the classroom?

Of course, as any teacher in this era will tell you, one major behavioral issue will be the students' using cell phones in the classroom. The traditionalist Bill makes his opinion of cell phones clear:

Bill says:

Smartphones are NOTHING but a distraction in the classroom, period…they should be prohibited except during breaks and lunch…

Of course cell phones are prohibited -- but just because something is prohibited, it doesn't mean that they won't appear in the classroom.

I am on the older edge of the Millennial generation -- if one can really call me a Millennial at all. (I define Millennials as those born in the old millennium but graduated high school in the new, but I graduated high school in 1999, the old millennium.) So my school years just barely missed the advent of the smartphone. The closest I can get is when I was working at the library just before I began working on my credential. Sometimes I would look up other websites on the library computers, until my boss told me to close the browser window. I noticed that as soon as I did so, I was much more attentive to patrons and was thus a much more effective worker. And so I have no choice but to incorporate a cell phone ban into my Participation Points system.

Notice that cell phones are a highly advanced form of technology -- indeed, I once read that there's more computing power in a tiny cell phone than in the A-bombs during World War II. In theory, a generation that enjoys cell phones and video games should love math and science, the subjects that make that technology possible. In theory, no one should ever type "I hate math" on the Internet, since without math there would be no Internet. But in practice, we know this is not the case.

And so, at the end of any detention earned due to cell phone use, I will require the student to say "Without math, there wouldn't be any cell phones" before releasing them. And if by chance I must confiscate a phone, I will require the student to say the same before returning the phone.

By the way, I've written that not only do I want to write more about young people going into STEM, but young females in particular. Here is an article about a girl from right here in Southern California who not used her math and science skills to create an actual app. She convinced her high school to start offering more STEM classes:

Still, I know that some members of our generation can't go seven waking minutes without using a cell phone, and yet teachers expect them to go seven hours without using one -- that is, 60 times as long as they naturally would. Indeed, I know that for some students, the only effective incentive that will motivate them to work is a few minutes' free time on their cell phone. Again, the idea is for me, after telling the students my library story, to remind them that the people who matter (employers) will criticize -- that is, make fun of -- those who can't go a few minutes without reaching for a phone, and those who do have self-control will get more A's and E's, and ultimately jobs and promotions.

10. How will I state my most important classroom rule?

This will be how I'll state the rule in my classroom:

Rule #3: Respect yourself and others.

Students respect themselves and each other as well as me, the teacher, by following all rules and allowing others to learn the material -- in other words, by striving to earn E's in all their classes.

If this rule sounds familiar, it should -- it comes directly from Fawn Nguyen's classroom (see her first day of school link above). In Nguyen's class, though, this is Rule #1.

But today is Pi Approximation Day, and I like to eat apple pie since I associate apple pie with this time of year ("as American as apple pie," and this is the month that we celebrated Independence Day).

In honor of Pi Approximation Day, let me post some more videos about pi. The first few of these mention several ways to approximate pi.

Let's start with some scientific facts about the number pi (including ways to approximate it):

The narrator of this first video mispronounces the name Euler. I'm sorry, but I just can't help linking to a Fawn Nguyen post about the pronunciation of Euler:

The History of Pi. This video mentions that even Legendre -- the author of the geometry text we've been discussing in some of my recent posts -- contributed to the history of pi. In particular, Legendre proved that not only is pi irrational, but so is pi^2 (unlike sqrt(2), which is irrational yet has a rational square, namely 2).

This video also mentions a quote from the mathematician John von Neumann: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” We've seen Eugenia Cheng, in her How to Bake Pi, say almost exactly the same thing.

The Infinite Life of Pi:

No Pi (Approximation) Day is complete without a Numberphile video. In this video, we learn that pi is not just irrational, but is also transcendental -- that is, there doesn't even exist a polynomial f, with integer or rational coefficients, such that f (pi) = 0 (unlike sqrt(2), which is algebraic). This is even stronger than Legendre's result that pi^2 is irrational.

Here is a longer video, but it contains some more series approximations of pi:

No, I can't avoid another one of my favorite math YouTube posters, Vi Hart. Of course, in this video she argues that there's nothing special about pi at all:

Here are some formulas for the number pi. (One of them is the approximation 22/7.)

Let's wrap up with one more Pi song, a longer one this time:

I like the idea of using music to teach math, so here's a favorite, Michael Blake's "What Pi Sounds Like." I may try to find a way to incorporate songs such as this one into the classroom:

Finally, this link is not a video, but it's one of my favorite links for Pi Approximation Day. We know that 22/7 is approximately equal to pi. As it turns out, 22/7 is actually more than pi -- and we can find out why 22/7 > pi using calculus. It's possible that an AP Calculus student -- a senior on the SteveH plan -- might be able to calculate this integral:

A few other Pi Approximation Day (aka "Casual Pi Day") links:

(The last post was written by Tanya Jeffries -- another female computer scientist!)

And so I wish everyone a Happy Pi Approximation Day.

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