On Leaving the Brick-and-Mortar Classroom

I’ve been a high school teacher for the last 25 years. I’m also leaving the classroom — but I’m not leaving teaching. Next year will be my 26th year teaching, and I’ve been told that I’ll be teaching on-line, from an office.


This is how we all taught during the fourth quarter of the last school year, except we did it from home, since brick-and-mortar schools shut down, all over the world, due to the COVID-19 pandemic. We used screensharing in Google Hangouts (shown above), Google Classroom, e-mail, and lots of other things to finish the school year . . . and we did finish it, successfully. This year, teachers won’t be at home (unless things change, due to the coronavirus), but many of our students will be staying home.

After I’d finished everything up for the 2019-2020 year, I went to school to turn in my keys. At that point, it was obvious that we were likely to have some sort of dual-track system for 2020-2021, with some students receiving instruction at school, and others at home, remotely, using their district-issued Chromebooks. I told my principal that if we did end up doing such a system, that I wanted to be on the “home team.” I don’t want to have to go to school and risk COVID-19 infection, which could then be spread to my family, some of whom are in high-risk groups for this disease. I’ve now received confirmation that I will be a remote-learning instructor next year, presumably working with students from all over the district.

I’m going to miss my old school, both the Sylvan Hills High North Campus and the Sylvan Hills High Main Campus. Sylvan Hills taught me a lot about being a better teacher. As a result, I’m leaving with an improved ability to help students, compared to six years ago, when coming to Sylvan Hills from other schools. My principals at these two campuses deserve a lot of the credit for this. I’ve worked with many administrators over the years, and these two are the ones who have helped me the most in my efforts to become a better teacher.

The coming year will present many challenges. To teach effectively, you have to get to know your students. We’ll be doing instruction and discussions with computers, webcams, microphones, and speakers, so I’m going to have to make a lot of adjustments to get to know my students as real people, while teaching remotely for a full year. The end of the last school year gave me a lot of experience I can build on.

This next year should be interesting, and I am looking forward to it.

A “Thumbs Up” for Google Classroom

This is my 22nd year of teaching, but my first year using Google Classroom. We’re finding it to be a useful tool. This, for example, is the diagram for the Atwood’s machine lab we are doing in Pre-AP Physical Science, beginning today. My students will find this waiting for them in their virtual classroom (on Chromebooks my school district provides), with discussion-prompts to get us started:


I had no idea that four years of blogging, here on WordPress, had been preparing me to use this teaching tool. However, active blogging does require one to develop some transferable skills, especially in fields (such as what I teach) which are similar to the topics of one’s blog, as is the case here.

On your nth birthday, you turn n – 1 years old.

birthday cake

As a teacher, I have had variants of this conversation many times. The specific details, however, are fictional, for this changes, somewhat, each time it happens.

  • Student: Guess what? It’s my birthday!
  • Me: Congratulations! How old are you?
  • Student: I’m seventeen!
  • Me: Well, happy 18th birthday, then!
  • Student: Huh?
  • Me: Look, on that one day, 17 years ago, when you were born, that was your birthday. That day has a better claim on being your birthday than any other day, because it’s the day you were born. That was your first birthday. But you weren’t one year old yet. You turned one year old a year later, on your next birthday . . . your second birthday. A year later, on your third birthday, you turned two years old. Do I need to continue?
  • Student: So I’m 18? I can buy cigarettes without a fake ID, and vote, and stuff?
  • Me: No, not for another year, because you’re only 17 years old — but you have had 18 birthdays. Say, here come some of your friends. Use this bit yourself, if you want to, and have fun with it.
  • Student, to other students: Hey, guys, it’s my birthday! I’m 18 today!

…At least I try. Also, sometimes, the educational outcome is better than in this fictionalized example.


[Image source: http://www.decorationnako.tk/birthday-cake/]

My Centripetal Force Joke: A True Story


In the Summer of 2014, with many other science teachers, I took a four-day-long A.P. Physics training session, which was definitely a valuable experience, for me, as a teacher. On the last day of this training, though, in the late afternoon, as the trainer and trainees were winding things up, some of us, including me, started getting a little silly. Physics teachers, of course, have their own version of silly behavior. Here’s what happened.

The trainer: “Let’s see how well you understand the different forces which can serve as centripetal forces, in different situations. When I twirl a ball, on a string, in a horizontal circle, what is the centripetal force?”

The class of trainees, in unison: “Tension!”

Trainer: “In the Bohr model of a hydrogen atom, the force keeping the electron traveling in a circle around the proton is the . . . ?”

Class: “Electromagnetic force!”

Trainer: “What force serves as the centripetal force keeping the Earth in orbit around the Sun?”

Me, loudly, before any of my classmates could answer: “God’s will!”

I was, remember, surrounded by physics teachers. It took the trainer several minutes to restore order, after that.

On Teaching Students with Asperger’s Syndrome

teaching Aspies

Teaching students with Asperger’s Syndrome is a challenge. As a teacher who also has Asperger’s, I have some suggestions for how to do this, and wish to share them.

  1. Keep the administrators at your school informed about what you are doing.
  2. Know the laws regarding these matters, and follow them carefully. Laws regarding confidentiality are particularly important.
  3. Identify the special interest(s) of the student (these special interests are universally present with Asperger’s; they also appear, sometimes, with students on other parts of the autism spectrum). Do not expect this/these special interest(s) to match that of anyone else, however — people with Asperger’s are extremely different from each other, just as all human beings are. As is the case with my own special interests in mathematics and the “mathy” sciences, it’s pretty much impossible to get students with Asperger’s to abandon their special interest — and I know this because I, quite literally, cannot do much of anything without first translating it, internally, into mathematical terms — due to my own case of Asperger’s. Identifying the special interest of a student with Asperger’s requires exactly one thing: paying attention. The students themselves will make it easy to identify their special interest; it’s the activity that they want to do . . . pretty much all the time.
  4. Find out, by carefully reading it, if the student’s official Section 504 document, or Special Education IEP, permits item #5 on this list to be used. If it doesn’t, you may need to suggest a revision to the appropriate document. (Note: these are the terms used in the USA; they will be different in other countries.)
  5. Of things done in class which will be graded, if the relevant document permits it, alter them in such a way as to allow the student to use his or her special interest to express understanding of the concepts and ideas, in your class, which need to be taught and learned. This is, of course, the most difficult step, but I cannot overemphasize its importance.
  6. Use parental contact to make certain the parent(s) know about, and agree with, the proposed accommodations/modifications. (504 students get accommodations, while special education students receive modifications. Following both 504 plans, and Special Education IEPs, is not optional for teachers — it is an absolute legal requirement, by federal law, and the penalties for failure to do so are severe. It is also, of course, the ethical thing to do.)
  7. Do not make the mistake of punishing any student for behavior related to a documented condition of any kind, including Asperger’s Syndrome.

All the Classes I Have Taught, or Am Teaching (Updated for 2016-17)

This is my 22nd year teaching. Just as a test of my memory, I’m going to try to list every class I have ever taught, or am teaching now. The italics indicate the subjects which I am most confident I can teach well, whether I am teaching them currently, or not. Classes in my 2016-2017 teaching assignment are shown in bold. As for improving the others: I’ll work more on them . . . when the current school year is over. 2016-2017 is a rare year, in a good way: the classes in bold are now a subset of the classes in italics.

  1. Algebra I
  2. Algebra II
  3. Algebra III
  4. Algebra Lab
  5. A.P. Physics
  6. Area I Mathematics at Arkansas Governor’s School — a course focusing on polyhedra
  7. Bridge to Algebra II, which I can’t help thinking of as “Algebra 1.5”
  8. Chemistry
  9. Chemistry I (no, I have no idea why that particular school called it that; I never found “Chemistry II” there)
  10. Civics
  11. Economics
  12. Environmental Science
  13. Formal Geometry
  14. Geometry
  15. Geometry Lab
  16. Informal Geometry
  17. Physical Science
  18. Physics
  19. Pre-AP Physical Science
  20. Psychology
  21. Religion, 9th grade (at a private, religious school)
  22. Religion, 12th grade (at a private, religious school)
  23. Study Skills (while student teaching)
  24. Summer School Transition Camp (for incoming high school students)
  25. University Studies (my only foray into teaching at the college level; basically, an “Intro to College” course, for entering freshmen)
  26. U.S. History Since 1890
  27. World History (while student teaching)
  28. World History Since 1450

X. In-school Suspension (ISS), also known as SAC, which stands for the horribly-misleading euphemism, “Student Assistance Center.” I used an “X” instead of a number because, as a student or a teacher, SAC is not a class, nor a subject. It is, rather, a non-class which one endures until the merciful ringing of the bell at the end of the school day.

XX. “Saturday School,” which is like ISS/SAC, but even worse, for all concerned. (I really needed the extra money at that time.)

To anyone now working on becoming a teacher: you become much more employable if you become certified in multiple certification areas, as I have. This is a two-edged sword, though, for it definitely increases the number of subjects you may be asked to teach in any given year, and that’s also the reason my list above is so long.

One other thing I definitely remember is my first year’s salary, to the cent: $16,074.00, before any deductions. You can make a living in this field, in this country . . . after you’ve been in the classroom for a few years . . . but no one should expect making it, financially, to be easy, especially for the first 5-7 years.

How I Hit My Personal Mathematical Wall: Integral Calculus

Hitting the wall

To the best of my recollection, this is the first time I have written publicly on the subject of calculus. The fundamental reason for this, explained in detail below, is something I rarely experience: embarrassment.

Unless this is the first time you’ve read my blog, you already know I like mathematics. If you’re a regular follower, you know that I take this to certain extremes. My current conjecture is that my original motivation to learn how to speak, read, and write, before beginning formal schooling, was that I had a toddler-headful of mathematical ideas, no way to express them (yet), and learned to use English in order to change that. Once I could understand what others were saying, read what others had written, write things down, and speak in sentences, I noticed quickly that interaction with other people made it possible to bounce mathematical ideas around, using language — which helped me to develop and expand those mathematical ideas more quickly. Once I started talking about math, as anyone who knows me well can verify, I never learned how to shut up on the subject for longer than ten waking hours at a time.

A huge part of the appeal of mathematics was that I didn’t have to memorize anything to do it, or learn it. To me, it was simply one obvious concept at a time, with one exposure needed to “get it,” and remember it as an understood concept, rather than a memorized fact. (Those math teachers of mine who required lots of practice, over stuff I already knew, did not find me easy to deal with, for I hated being forced to do that unnecessary-for-me chore, and wasn’t shy about voicing that dislike to anyone and everyone within hearing range, regardless of the situation or setting. The worst of this, K-12, was long division, especially the third year in a row that efforts were made to “teach” me this procedure I had already learned, on one specific day, outside school, years earlier.) It might seem like I have memorized certain things, such as, say, the quadratic formula, but I never actually tried to — this formula just “stuck” in my mind, from doing lots of physics problems, of different types, which required it. Similarly, I learned the molar masses of many commonly-encountered elements by repeatedly using them to show students how to solve problems in chemistry, but at no time did I make a deliberate attempt to memorize any of them. If I don’t try to memorize something, but it ends up in memory anyway, that doesn’t count towards my extremely-low “I hate memorizing things” threshhold.

When I first studied calculus, this changed. Through repeated, forced exposure in A.P. Calculus class my senior year of high school, with a teacher I didn’t care for, I still learned a few things that stuck: how to find the derivative of a polynomial, the fact that a derivative gives you the slope a function, and the fact that its inverse function, integration, yields the area under the curve of a function. After I entered college, I then landed in Calculus I my freshman year. Unbeknownst to me, I was approaching a mental wall.

My college Cal I class met early in the morning, covered material I had already learned in high school, and was taught by an incomprehensible, but brilliant, Russian who was still learning English. Foreign languages were uninteresting to me then (due to the large amount of memorization required to learn them), and I very quickly devised a coping strategy for this. It involved attending class as infrequently as possible, but still earning the points needed for an “A,” by asking classmates when quizzes or tests had been announced, and only waking up for class on those mornings, to go collect the points needed for the grade I wanted.

This was in 1985-86, before attendance policies became common for college classes, and so this worked: I got my “A” for Cal I. “That was easy,” I thought, when I got my final grade, “so, on to the next class!”

I did a lot of stupid things my freshman year of college, as is typical for college freshmen around the world, ever since the invention of college. One of these stupid things was attempting to use the same approach to Calculus II, from another professor. About 60% of the way through that course, I found myself in a situation I was not used to: I realized I was failing the class.

Not wanting an “F,” I started to attend class, realizing I needed to do this in order to pass Cal II, which focuses on integral calculus. A test was coming up. In class, the professor handed out a sheet of integration formulas, and told us to memorize them.

Memorize them.

I read the sheet of integration formulas, hoping to find patterns that would let me learn them my way, rather than using brute-force memorization-by-drill. Since I had been skipping class, I saw no such patterns. All of a sudden, I realized I was in a new situation, for me: mathematics suddenly was not fun anymore. My “figure it out on the fly” method, which is based on understanding, rather than memorization, had stopped working.

A few weeks and a failed test later, I began to doubt I would pass, and tried to drop the class. This is how I learned of the existence of drop dates for college classes, but I learned it too late: I was already past the drop date.

I did not want an F, especially in a math class. Out of other options, I started drilling and memorizing, hated every minute of it, but did manage to bring my grade up — to the only “D” I have on any college transcript. Disgusted by this experience, I ended up dropping out of college, dropped back in later, dropped out again, re-dropped back in at a different university, and ended up changing my major to history, before finally completing my B.A. in “only” seven years. I didn’t take another math class until after attempting to do student teaching, post-graduation . . . in social studies, with my primary way of explaining anything being to reduce it to an equation, since equations make sense. This did not go well, so, while working on an M.A. (also in history) at a third college, I took lots of science and math classes, on the side, to add additional teaching-certification areas in subjects where using equations to explain things is far more appropriate, and effective. This required taking more classes full of stuff I already knew, such as College Algebra and Trigonometry, so I took them by correspondence (to avoid having to endure lectures over things I already knew), back in the days when this required the use of lots of postage stamps — but no memorization. To this day, I would rather pay for a hundred postage stamps than deliberately memorize something.

In case you’re wondering how a teacher can function like this, I will explain. Take, for example, the issue of knowing students’ names. Is this important? Yes! For teaching high school students, learning the names of every student is absolutely essential, as was quite evident from student teaching. However, I do this important task by learning something else about each student — how they prefer to learn, for example, or something they intensely like, or dislike — at which point memorization of the student’s name becomes automatic for me. It’s only conscious, deliberate memorization-by-drill that bothers me, not “auto-memorization,” also known as actually understanding something, or, in the case of any student, learning something about someone.

I don’t know exactly why my to-this-point “wall” in mathematics appeared before me at this point, but at least I know I am in good company. Archimedes knew nothing of integral calculus, nor did his contemporaries, for it took roughly two millennia longer before Isaac Newton and Gottfried Leibniz discovered this branch of mathematics, independently, at roughly the same time.

However, now, in my 21st year as a teacher, I have now hit another wall, and it’s in physics, another subject I find fascinating. Until I learn more calculus, I now realize I can’t learn much more physics . . . and I want to learn more physics, for the simple reason that it is the only way to understand the way the universe works, at a fundamental level — and, like all people, I am trapped in the universe for my entire life, so, naturally I want to understand it, to the extent that I can. (A mystery to me: why isn’t this true for everyone else? We’re all trapped here!) Therefore, I now have a new motivation to learn calculus. However, I want to do this with as much real understanding as possible, and as little deliberate memorization as possible, and that will require a different approach than my failed pre-20th-birthday attempt to learn calculus.

I think I need exactly one thing, to help me over this decades-old wall: a book I can read to help me teach myself calculus, but not a typical textbook. The typical mathematics textbook takes a drill-and-practice approach, and what I need is a book that, instead, will show me exactly how various calculus skills apply to physics, or, failing that, to geometry, my favorite branch of mathematics, by far. If any reader of this post knows of such a book, please leave its title and author in a comment. I’ll then buy the book, and take it from there.

One thing I do not know is the extent to which all of this is related to Asperger’s Syndrome, for I was in my 40s when I discovered I am an “Aspie,” and it is a subject I am still studying, along with the rest of the autism spectrum. One thing Aspies have in common is a strong tendency to develop what we, and those who study us, call “special interests,” such as my obsession with polyhedra, evident all over this blog. What Aspies do not share is the identity of these special interests. Poll a hundred random Aspies, and only a minority will have a strong interest in mathematics — the others have special interests in completely different fields. One thing we have in common, though, is that the way we think (and learn) is extremely different from the ways non-Aspies think and learn. The world’s Aspie-population is currently growing at a phenomenal rate, for reasons which have, so far, eluded explanation. The fact that this is a recent development explains why it remains, so far, an unsolved mystery. One of things which is known, however, is the fact that our status as a rapidly-growing population is making it more important, by the day, for these differences to be studied, and better understood, as quickly as the speed of research will allow, in at least two fields: medicine, and education.

Only one thing has fundamentally changed about me, regarding calculus, in nearly 30 years: I now want to get to the other side of this wall, which I now realize I created for myself, when I was much younger. I am also optimistic I will succeed, for nothing helps anyone learn anything more than actually wanting to learn it, no matter who the learner is, or what they are learning. In this one respect, I now realize, I am no different than anyone else, Aspie or non-Aspie. We are all, after all, human beings.

The Misadventures of Jynx the Kitten, Chapter Four: Jynx “Helps” with Grading Papers, and Discovers a New Talent


This is the last day of Spring Break, and grades for the third quarter are due tomorrow, so it should surprise no one that I’m grading papers. Things were going well, too, until Jynx the Kitten decided to “help.”

I told Jynx that I did not need his “help,” since I already know how to grade papers; I even told him that I very much needed not to have his “help.” Jynx did not care. Papers were there, and he was determined to grade them.

The only problem (for Jynx) was that, before Spring Break even began, I had sorted all the papers to be graded, folded each set separately, and fastened each bundle shut with a separate rubber band, simply to organize the papers to be graded. Some of us in education call this sorting-process “pre-grading,” or something like that. Jynx didn’t like it, though, for the rubber bands kept him from getting to the papers he so desperately wanted to grade (or eat, or shred, or something).

He could, of course, get to the rubber bands, for they were on the outside of each of the bundles of papers. He has claws to pluck them, and did so. He also started trying to pull off the rubber bands with his teeth. Each time a rubber band got plucked, by tooth or claw, twang! Different rubber bands on different bundles were stretched with varying tensions, producing rubber-band-twanging sounds of varying frequency. In other words: Jynx played different musical notes.

Soon, Jynx had forgotten all about grading papers, and was simply having fun playing music for the first time. He was delighted to be playing music . . . or frustrated that he couldn’t get the bundles open . . . or possibly both.

I had also forgotten all about grading papers, and simply sat, listening in amazement, for I’ve had cats all my life, and, aside from the familiar “cat on a piano” song many people have heard, I have never before heard a cat, nor a kitten, attempt to play music.

Jynx’s improvisational rubber-band piece started to improve rapidly with practice, and soon Jynx’s music was much better than even the best-rendered version of “cat on a piano” I have ever heard before — and he’s still a kitten!

Unfortunately, I was not able to open software to record Jynx’s music in time, before he moved on to other things, as kittens do fairly often. As a result, only my wife and I know what Jynx’s music actually sounds like. I did manage to snap the picture above, of him looking up at me from his “musical instruments,” before he moved on to the next of his hijinks for the day, of which there are always many.

And, now that Jynx has decided it’s nap time, I’ll get back to grading these papers.

Zome: Strut-Length Chart and Product Review

This chart shows strut-lengths for all the Zomestruts available here (http://www.zometool.com/bulk-parts/), as well as the now-discontinued (and therefore shaded differently) B3, Y3, and R3 struts, which are still found in older Zome collections, such as my own, which has been at least 14 years in the making.


In my opinion, the best buy on the Zome website that’s under $200 is the “Hyperdo” kit, at http://www.zometool.com/the-hyperdo/, and the main page for the Zome company’s website is http://www.zometool.com/. I know of no other physical modeling system, both in mathematics and several sciences, which exceeds Zome — in either quality or usefulness. I’ve used it in the classroom, with great success, for many years.

My Complete List of Complaints About My New School

For the last three weeks, for the beginning of my twentieth year as a teacher, I’ve been teaching at a different high school. I am much happier, now, due to this change. This being a personal blog, it is my policy not to name my school, nor school district, here. However, I see no problem with posting my complete list of complaints about this new school. Here it is: