Aldous Huxley, on What We Fail to Teach Our Children, and Why

Posted on 23 May 2015 by RobertLovesPi

Source: Brave New World Revisited, chapter 11.

“You Majored in WHAT?”

Posted on 8 April 2015 by RobertLovesPi

I’m in my twentieth year of teaching mostly science and mathematics, so it is understandable that most people are surprised to learn that I majored in, of all things, history.

It’s true. I focused on Western Europe, especially modern France, for my B.A., and post-WWII Greater China for my M.A. My pre-certification education classes, including student teaching, were taken between these two degree programs.

Student teaching in social studies did not go well, for the simple reason that I explain things by reducing them to equations. For some reason, this didn’t work so well in the humanities, so I took lots of science and math classes, and worked in a university physics department, while working on my history M.A. degree, so that I could job-hunt in earnest, a year later, able to teach physics and chemistry. As it ended up, I taught both my first year, along with geometry, physical science, and both 9th and 12th grade religion. Yes, six preps: for an annual salary of US$16,074.

History to mathematics? How does one make that leap? In my mind, this explains how:

History is actually the story of society over time, so it’s really sociology.
Sociology involves the analysis on groups of human minds in interaction. Therefore, sociology is actually psychology.
Psychology is the study of the mind, but the mind is the function of the brain, one of the organs of the human body. Psychology, therefore, is really biology.
Biological organisms are complex mixtures of interacting chemicals, and, for this reason, biology is actually chemistry.
Chemistry, of course, breaks down to the interactions of electrons and nuclei, governed by only a few physical laws. Chemistry, therefore, is really physics.
As anyone who has studied it knows, physics often involves more mathematics than mathematics itself.

…And that at least starts to explain how someone with two history degrees ended up with both a career, and an obsession, way over on the mathematical side of academia.

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

Posted on 29 March 2015 by RobertLovesPi

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.

Public Education in Arkansas Is Under Attack — By Our Own State Legislature!

Posted on 24 March 2015 by RobertLovesPi

For details on the efforts of the majority of the Arkansas State Legislature to ruin public schools in Arkansas, please watch this music video:

The AEA (Arkansas Education Association) is doing everything they can to resist this flood of anti-education legislation. If you are eligible for membership in the AEA, and join, that will help with these efforts — for the strength of the AEA grows as our number of members increases. If you work in an Arkansas public school, you can join. Students can join also, and so can those who have retired from work in the field. For information on how to join, please click here.

The Most Disturbing Thing I Ever Witnessed in a College Class

Posted on 22 March 2015 by RobertLovesPi

The Year: 1993
The College: The University of Central Arkansas
The Course: Educational Psychology

In a class called “Educational Psychology,” the bell curve, a statistical concept often used to describe the distribution of intelligence in humans, should be expected to receive some attention, and, when I took the class, it did — for about five minutes. I found the image below here; in this class, the professor drew a somewhat simpler version of it on a chalkboard.

The professor (who should be glad I do not remember his name, since I would blog it) proceeded to describe, briefly, characteristics associated with different “columns” of the bell curve, as some in academia apply it to intelligence. He then said, “Actually, what I’ve always really wanted to do was to get rid of these people.” He then added an “x” to what he’d drawn on the board. I’ve made it red, simply to make the location where he drew his “x” easier to see.

I sat, in shocked silence, as the majority of the students in the class laughed. Laughed.

Once I could move again, after the initial, paralyzing shock turned into a deepening horror, I looked around the classroom. No one looked appalled, as I was; no one else even seemed to be disturbed, nor even slightly upset. Some were still visibly amused, in fact. I considered objecting, directly to the professor, but I was so affected by the whole episode that I was experiencing severe nausea. I couldn’t speak, for fear of throwing up.

The professor may not have known this — in fact, I would be surprised if he had — but what he was “joking” about has actually happened. It was called the Cambodian genocide, and was carried out by one of the most brutal regimes of the 20th Century, the Khmer Rouge. One of their tools used to stay in power was intimidation, taken to an extreme. In this photograph, from the article linked immediately above, you can see one form of this intimidation: the public display of the skulls of their victims. One need not be able to read to understand the message of such a display; below, the reason why this was important to the Khmer Rouge should become apparent.

I’ve studied this genocide. From just 1975 to 1979, the Khmer Rouge, driven by a radical Stalinist-Maoist and extremely anti-intellectual ideology, managed to reduce the population of Cambodia by an estimated 25%. They targeted, among many others, teachers. They separated children from their parents, since parents are often known to teach their children. They killed people who were seen wearing glasses — because glasses are often used to help people read books. They did their utmost to wipe out as much of the high-intelligence part of the bell curve as possible. They did their best to eliminate literacy.

Those who survived this horror were still devastated, for a whole nation had been traumatized — just imagine an entire country with PTSD (post-traumatic stress disorder). To make this situation even worse, the very people who could have helped most with the post-Khmer-Rouge recovery (doctors, therapists, teachers, clergy, etc. — all professions which require education) were almost entirely wiped out, and the people who could train new recruits for such professions had also been killed. As a direct result of this targeting of intellectuals for slaughter, the effects of the Cambodian genocide lasted far longer than the regime which perpetrated it.

I was thinking about this as the class period ended. In a daze, I walked away — far away. Even though I did return for future class sessions, since the course was a requirement for teacher certification, I never listened to another word that professor said, for he had permanently lost all credibility with me. At the end of the term, I left his class with an “A,” and a renewed determination to oppose those who, like the Khmer Rouge, try to “dumb down” society — at every opportunity. As for the people of Cambodia . . . they are still recovering, and will be, for many more years.

Wiping out a group of people — any group — simply isn’t funny.

Meet the NEA President, Lily Eskelsen Garcia

Posted on 21 March 2015 by RobertLovesPi

In my last post (click here to see it), I made a case for Arkansans who work in public schools to join the Arkansas Education Association, a state affiliate of the NEA, or National Education Association. I’d now like to introduce you to NEA President Lily Eskelsen Garcia. This video was recorded while she was still the NEA Vice-President, but it remains a great introduction to the kind of person she is.

I don’t often simply yield my blog-space to others . . . but I’m one of Lily’s fans, and have been since I first saw her perform this song, so she gets “airtime” here — without even having to ask for it.

Teachers’ unions are under attack by corporate-backed politicians — all across the country. It’s important that we fight back. The more members we have, the more effectively we can resist the current efforts to reduce the legal rights of those who work in schools (both teachers and support staff). If you are eligible for membership in the NEA (see this page to check on that, and join, please, if you can), I hope you will not only join, but recruit others to join, as well. The more members we have, the stronger we are. The stronger we are, the more likely we are to prevail — over those who trying to destroy public education in this country.

The NEA, and its affiliates, protect the working environment of America’s teachers — and that is also the learning environment of America’s children. Helping the NEA save American public education is, therefore. in the best interests of everyone.

If you teach, or work in some other capacity in an American public school, this is your fight. Please join us.

The Arkansas Education Association, or AEA: How (and Why) to Join

Posted on 21 March 2015 by RobertLovesPi

The Arkansas Education Association is the oldest, largest, most effective, and most well-established professional organization (and union) for educators in Arkansas. I’ve been a member for years, and will explain why, below. First, though, here are three ways to join:

A local affiliate of the AEA exists in every school district in Arkansas. My local is called PACT, the Pulaski Association of Classroom Teachers. In the nearby Little Rock School District, the local AEA affiliate is the LREA: the Little Rock Education Association. If you know members at your local, ask them to put you in touch with the teacher at your school who serves as the Representative, or “Rep,” for your school. You can then simply ask your Rep for a membership form, fill it out, and return it to them. The Rep will take it from there.
A second way to join is through the AEA’s website, at http://www.aeaonline.org/how-join. This involves filling out and printing a paper form, and then mailing it to the AEA’s office in Little Rock, using the address at that website.
There’s also a third way, and it doesn’t require paper forms, nor postage stamps. You can join our national organization, the NEA, through their website, at https://ims.nea.org/JoinNea/, and this will automatically make you a member of your state and local affiliate at the same time. Also, this works for educators and support staff in other American states, the District of Columbia, and Puerto Rico, as well — unlike items #1 and 2 above.

So . . . why join these affiliated local, state, and national organizations? Well, first, let me give you some idea what it costs to be a member. I pay dues of $23.08, by paycheck deduction, twice a month, and that’s the total of my NEA, AEA, and PACT dues. (This amount will vary in other school districts, since each local sets their own dues.) In return, I have a network of people dedicated to (1) protecting my rights as a teacher, everywhere from my own classroom to Capitol Hill, (2) helping me develop professionally as a teacher (through collaboration with an extensive network of colleagues, as well as formal, for-credit Professional Development opportunities), and (3) being ready to come to my legal defense, should I need such assistance.

It is important to remember that a teacher can do absolutely nothing wrong, and still end up in a situation where such assistance is needed — to defend yourself against a false accusation, for example. I’ve been falsely accused of unethical conduct, via an anonymous complaint, in the past; it isn’t a fun situation. Because I was already a PACT/AEA/NEA member, help was provided at no extra cost, and my name was fully cleared. Had I not been a member, I might have had to hire an attorney in that situation — if affording one was possible, but it wasn’t. Few teachers have tens of thousands of dollars on hand to privately hire an attorney, should such a need arise in connection with their jobs, and I was no exception — but union membership takes care of that, if (and only if) you are already a member when trouble strikes. If I consider the dues I pay, vs. what attorneys charge when hired by individuals, I realize the truth: union dues are one of the best bargains available — anywhere.

It is a sad reality that some (not all, but some) administrators have a nasty habit of bullying teachers. In fact, such bullying was exactly what drove me to join PACT/AEA/NEA in the first place. The bullying continued after I joined, so I then reported it to my local’s contacts, and the organization intervened to protect me — successfully. Later, I witnessed similar bullying, of my fellow teachers, by a different administrator, and that’s what prompted my move from being a dues-paying union member to being a much more active union member, and a building Representative as well. In that role, I had the privilege of intervening personally, to do my best to stop such adult-on-adult bullying, and enlisted the help of others, whenever such help was needed. Again, such efforts were successful, although our own confidentiality rules do not allow me to describe the specifics, for we carefully protect the privacy of our members. (Important side note: all of this bullying described above happened in schools other than the school where I currently teach. This is not a coincidence; I am at my current school on purpose, so that I can work with good administrators every day. When teachers are well-treated, as is the norm at my current school, we can do a much better job focusing on, and meeting, the educational needs of our students.)

This is what union members do: we help each other. We protect each other. We support each other. Until the miraculous day when every single person in management and administration suddenly begins behaving ethically, 100% of the time, unions will be needed, and our work will continue to be important. We protect the working environment in schools — and that same working environment is the learning environment for America’s children.

There are other, more dollars-and-cents-oriented reasons to join, as well. For example, through the NEA, I have a quarter-million-dollar life insurance policy which costs me only $32.73 per month — an excellent price. Shopping discounts exist in abundance. There even exist benefits which I haven’t even used yet, simply because there are so many.

Of all the benefits of membership, there is one, above all others, which makes the argument for membership most compelling to me, and that is related to the legal right of representation. For AEA members, the statement below is both vital, and true:

“An employee shall be entitled to and shall be offered the opportunity to have a witness or representative of the employee’s choice present during any disciplinary or grievance matter with any administrator.” This is an Arkansas state law (A.C.A. 6-17-210). Any time an administrator in my district breaks this law, by denying any PACT or PASS member’s request for representation, it is imperative that union leaders be informed of this illegal act, without delay. (One way to reach them is by calling the PACT/PASS office, at 501-374-4955, during business hours.) PACT is our teachers’ union, and PASS is our union for support staff. We work together, which is as it should be. (Those AEA members in other locals, in similar situations, should contact the corresponding leaders of their own locals.)

Union members have representation provided to them upon request, whenever the need for it exists, at no extra cost — for our dues, and the dues of our colleagues, have already paid for it. Those who are not members, by contrast, are at the mercy of the market to find representation, on their own — with no well-organized, powerful organization backing them up, as we have as AEA members. In my opinion, this seals the deal — if you work in an Arkansas school, you can’t afford not to join the AEA, for the benefit of representation, alone. As for the numerous other benefits, they simply make membership an even sweeter deal.

One last thing: should anyone who tries to join the AEA encounter any difficulties doing so, feel free to ask for my personal help, in a comment to this post — and I promise to make certain you get the help you need.

A Simple Cheating-Prevention Idea, for Teachers with Students Sitting at Tables

Posted on 21 March 2015 by RobertLovesPi

With just two pieces of cardboard and a pair of scissors, you can partition a table which seats four into four sections — one per student. This makes cheating much more difficult, and that’s a good thing for everybody. No tape is needed; each piece of cardboard holds up the other one.

Other materials can be used as well. For one-time use, posterboard is adequate. For something more permanent, wooden boards are recommended.

The Human Reaction, When Mathematics No Longer Seems to Make Sense: What Is This Sorcery?

Posted on 15 March 2015 by RobertLovesPi

Unless you understand all of mathematics — and absolutely no one does — there is a point, for each of us, where mathematics no longer makes sense, at least at that moment. Subjectively, this can make the mathematics beyond this point, which always awaits exploration, appear to be some form of sorcery.

Mathematics isn’t supernatural, of course, but this is a reaction humans often have to that which they do not understand. Human reactions do not require logical purpose, and they don’t always make sense — but there is always a reason for them, even if that reason is sometimes simply that one is utterly bewildered.

In my case, this is the history of my own reactions, as I remember them, to various mathematical concepts. The order used is as close as I can remember to the sequence in which I encountered each idea. The list is, of necessity, incomplete.

Counting numbers: no problem, but what do I call the next one after [last one I knew at that time]? And the next one? And the next? Next? Next? [Repeat, until everyone within earshot flees.]
Zero exists: well, duh. That’s how much of whatever I’m snacking on is left, after I’ve eaten it all.
Arithmetic: oh, I’m glad to have words for this stuff I’ve been doing, but couldn’t talk about before.
Negative numbers: um, of course those must exist. No, I don’t want to hear them explained; I’ve got this already. What, you want me to demonstrate that I understand it? Ok, can I borrow a dollar? Oh, sure, I’ll return it at some point, but not until after I’ve spent it.
Multiple digits, the decimal point, decimal places, place value: got it; let’s move on, please. (I’ve never been patient with efforts to get me to review things, once I understand them, on the grounds that review, under such conditions, is a useless activity.)
Pi: love at first sight.
Fractions: that bar means you divide, so it all follows from that. Got it. Say, with these wonderful things, why, exactly, do we need decimals, again? Oh, yeah, pi — ok, we keep using decimals in order to help us better-understand the number pi. That makes sense.
“Improper” fractions: these are cool! I need never use “mixed numbers” again (or so I thought). Also, “improper” sounds much more fun than its logical opposite, and I never liked the term “mixed numbers,” nor the way those ugly things look.
Algebra: ok, you turned that little box we used before into an “x” — got it. Why didn’t we just use an “x” to begin with? Oh, and you can do the same stuff to both sides of equations, and that’s our primary tool to solve these cool puzzles. Ok. Got it.
Algebra I class: why am I here when I already know all this stuff?
Inequality symbols: I’m glad they made the little end point at the smaller number, and the larger side face the larger number, since that will be pretty much impossible to forget.
Scientific notation: well, I’m glad I get to skip writing all those zeroes now. If only I knew about this before learning number-names, up to, and beyond, a centillion. Oh well, knowing those names won’t hurt me.
Exponents: um, I did this already, with scientific notation. Do not torture me with review of stuff I already know!
Don’t divide by zero: why not? [Tries, with a calculator]: say, is this thing broken? [Tries dividing by smaller and smaller decimals, only slightly larger than zero]: ok, the value of the fraction “blows up” as the denominator approaches zero, so it can’t actually get all the way there. Got it.
Nonzero numbers raised to the power of zero equal one: say what? [Sits, bewildered, until thinking of it in terms of writing the number one, using scientific notation: 1 x 10º.] Ok, got it now, but that was weird, not instantly understanding it.
Sine and cosine functions: got it, and I’m glad to know what those buttons on the calculator do, now, but how does the calculator know the answers? It can’t possibly have answers memorized for every millionth of a degree.
Tangent: what is this madness that happens at ninety degrees? Oh, right, triangles can’t have two right angles. Function “blows up.” Got it.
Infinity: this is obviously linked to what happens when dividing by ever-smaller numbers, and taking the tangent of angles approaching a right angle. I don’t have to call it “blowing up” any more. Ok, cool.
Factoring polynomials: I have no patience for this activity, and you can’t stop me from simply throwing the quadratic formula at every second-order equation I see.
Geometry (of the type studied in high school): speed this up, and stop stating the obvious all the time!
Radicals: oh, I was wondering what an anti-exponent would look like.
Imaginary numbers: well, it’s only fair that the negative numbers should also get square roots. Got it. However, Ms. _____________, I’d like to know what the square root of i is, and I’d like to know this as quickly as possible. (It took this teacher and myself two or three days to find the answer to this question, but find it we did, in the days before calculators would help with problems like this.)
The phrase “mental math” . . . um, isn’t all math mental? Even if I’m using a calculator, my mind is telling my fingers which buttons to press on that gadget, so that’s still a mental activity. (I have not yielded from this position, and therefore do not use the now-despised “mental math” phrase, and, each time I have heard it, to date, my irritation with the term has increased.)
0.99999… (if repeated forever) is exactly equal to one: I finally understood this, but it took attacks from several different directions to get there, with headaches resulting. The key to my eventual understanding it was to use fractions: ninths, specifically.
The number e, raised to the power of i‏π, equals -1: this is sorcery, as far as I can see. [Listens to, and attempts to read, explanations of this identity.] This still seems like sorcery!
What it means to take the derivative of an expression: am I just supposed to memorize this procedure? Is no one going to explain to me why this works?
Taking the derivative of a polynomial: ok, I can do this, but I don’t have the foggiest idea why I’m doing it, nor why these particular manipulations of one function give you a new function which is, at all points along the x-axis, the slope of the previous function. Memorizing a definition does not create comprehension.
Integral calculus: this gives me headaches.
Being handed a sheet of integration formulas, and told to memorize them: hey, this isn’t even slightly fun anymore. =(
Studying polyhedra: I finally found the “sweet spot” where I can handle some, but not all, of the puzzles, and I even get to try to find solutions in ways different from those used by others, without being chastised. Yay! Math is fun again! =)
Realizing, while starting to write this blog-post, that you can take the volume of a sphere, in terms of the radius, (4/3)πr³, take its derivative, and you get the surface area of the same sphere, 4πr²: what is this sorcery known as calculus, and how does it work, so it can stop looking like sorcery to me?

Until and unless I experience the demystification of calculus, this blog will continue to be utterly useless as a resource in that subfield of mathematics. (You’ve been warned.) The primary reason this is so unlikely is that I haven’t finished studying (read: playing with) polyhedra yet, using non-calculus tools I already have at my disposal. If I knew I would live to be 200 years old, or older, I’d make learning calculus right now a priority, for I’m sure my current tools’ usefulness will become inadequate in a century or so, and learning calculus now, at age 47, would likely be easier than learning it later. As things are, though, it’s on the other side of the wall between that which I understand, and that which I do not: the stuff that, at least for now, looks like magic — to me.

Please don’t misunderstand, though: I don’t “believe in” magic, but use it simply as a label of convenience. It’s a name for the “box ,” in my mind, where ideas are stored, but only if I don’t understand those ideas on first exposure. They remain there until I understand them, whether by figuring the ideas out myself, or hearing them explained, and successfully understanding the explanation, at which point the ideas are no longer thought of, on any level, as “magic.”

To empty this box, the first thing I would need would be an infinite amount of time. Once I accepted the inevitability of the heat death of the universe, I was then able to accept the fact that my “box of magic” would never be completely emptied, for I will not get an infinite amount of time.

[Image credit: I made a rainbow-colored version of the compound of five cubes for the “magic box” picture at the top of this post, using Stella 4d, a program you may try here.]

A True Story from My Childhood: Roman Numeral Dollar Signs

Posted on 21 February 2015 by RobertLovesPi

When I was a child, I learned Roman numerals before I learned about the dollar sign. When I first encountered a dollar sign, I interpreted it as an “S” with a Roman numeral one superimposed over it. It then followed (I thought at the time) that the symbols for $2 through $10 would look like those shown above.

Fortunately, it didn’t take long before I figured out this would be impractical. I certainly would not want to have to write the symbol for $3,978, after all.