Showing posts sorted by date for query elementary functions. Sort by relevance Show all posts
Showing posts sorted by date for query elementary functions. Sort by relevance Show all posts

Wednesday, May 06, 2026

Bits

 Recently I found myself in a post-modern moment when I asked my wife if everyone else in the world takes time and energy out of each day to work on "bits."

If you happen to be on the deficit end of the concept of "bits," I will excuse your lack of insider knowledge and presume that this is not because you and those close to you don't operate in this sphere, but rather you and those close to you do not refer to these things as "bits." 

"Bits" are funny things that get passed around from person to person, not unlike unwanted viruses or opinions, but hopefully these are things that help make the day just a little more surreal. A great portion of what you read here on a regular basis is me taking what life has brought me to turn into lemonade. It is generally helpful to start this process with lemons, but most citrus will do in a pinch. As will dairy, but we try not to mix them. Nor do I advise attempting this just after you have brushed your teeth. 

For as long as I can remember, my brain has been wired to make fun of all the low-hanging fruit that comes my way, and to extend this metaphor still further, I will say that some of these end up being rotten. You know when this happens because you will not be greeted with gales of laughter but rather with a stern look of disapproval. 

Actually, now that I think about it, those disapproving looks might not have anything to do with the relative freshness of your jape. It may instead be the outward response for a "bit" that has hit its mark squarely. Certainly it can also be the problem of a "bit" being too fresh, which might cause those who encounter your jest to flinch. 

Honestly, any sort of reaction is preferable to the staid and boring discourse that presents itself to us each and every day. This attitude of mine is precisely the kind of thing that got me kicked out of Elementary Functions back in high school, as illustrated by the dozen or so blog entries in which I have previously referred to this ignominious exit.  

What did I learn from that experience? Oh, I suppose I leaned that it's probably best to know your audience, to "read the room" as they say. Of course, if you're always playing it safe, you might miss out on that one great "bit." 

You'll never know unless you try. 

Tuesday, December 03, 2024

Funny Man

 The thought of telling jokes for a living stalls out with the memory of standing in front of a couch full of stoned Arby's employees. I was the new guy, but I was definitely the funniest one at the party. 

Or so I was lead to believe. By the voices inside my head. I was always making people laugh at work. Certainly my reputation as a class clown was cemented during my senior year in high school. Why wouldn't that continue on into my twenties? 

The lesson I learned that night was about being on stage. When you are presenting to a crowd, even a half dozen wrecked fast food workers, the expectations are different. I was not clear on that when I took my position in front of the coffee table to deliver what I assumed would be a killer set about being wasted on the job. It could have been that the material wasn't that good. I had not spent an adequate amount of time working up my routine beforehand. Like no time at all. I was making it up on the spot. I was, as the pros say, "riffing." To a couch full of blank stares. 

What I had not taken into account, but I realize now some forty years later, was the intrinsic difference between standing next to someone in a classroom or at the counter of a roast beef sandwich emporium gives you an anti-authority edge. The funny bits are coming from an unexpected angle. Who talks back to their Elementary Functions teacher? Who takes sarcastic glee in someone ordering two Beef 'n' Cheddars, potato cakes, a cherry turnover and a large Diet Pepsi? Who cracks wise when the situation is not specifically designed for such japery? 

Me. Me and a whole slew of funny people throughout history who were never able to make it past open mic night, or get their own sit-com. Or make a bunch of stoned Arby's employees crack a smile. 

Every few years my wife will wonder aloud why I never became a professional comedian. The simplest answer comes from just how sour those grapes turned out to be. The longer version has something to do with that story I just related along with my lack of understand of the gulf between being a wiseacre and a comedian. 

Or a guy who writes a daily blog. 

Wednesday, March 13, 2024

Figures

 Over the last week I went down a bit of a rabbit hole. This wasn't a political vortex or a path down nostalgia lane. This was all about numbers. 

I have written here before about my love for teaching math. This came as a bit of a surprise since most of my enthusiasm for mathematics was knocked out of me by an ill-tempered high school instructor of elementary functions. He was not a fan of my approach to my senior year, which included a predilection toward the class clown end of the spectrum. But that didn't mean I didn't care about the math. This did not register on his end and he gave me the option of dropping his class before he failed me for my attitude. 

I dropped the class. 

And it was almost twenty years before I found my way back to math. 

Helping kids find patterns and connections in numbers and shapes and strands is fun for me. Watching them piece together the world around them through mathematics is a joy. This also gives me a chance to extend my own appreciation for figures and calculation. This past week had me sharing with fourth graders the fact that the product of any two even numbers is an even number, and the product of any two odd numbers is an odd number, but the product of an odd and an even number is always an even number. Which was intriguing enough for them, but after I was done with the class, I found myself wondering why there weren't more even numbers than odd if that was the case. I brought this dilemma home to my wife, and made my conjecture that this might have something to do with prime numbers. Together we imagined a sea of numbers and pictured the products of even numbers lighting up, then odd numbers in another color, then prime numbers in yet another. 

Later I turned to Reddit, where I found a thread of folks who had similar cogitations. I felt validated for having this somewhat vague quandary. And pleased that there was still some mystery left for me in arithmetic. Forty plus years after being kicked out of Elementary Functions, I was still thinking math thoughts. 

It felt good. 

Thursday, December 14, 2023

Last Century

 A very long time ago, in the late 1900s, I took over the computer lab at Horace Mann Elementary. It was a room full of Mac LCIIs connected by a series of spaghetti connections called Apple Talk. Printing was done on tractor feed machines that sounded like small arms fire when they got going. The software was a fistful of three inch floppy disks that had to be inserted in each machine to get them up and running. And the most intriguing prospect was that I inherited all of this with the large and overly complex lack of a password to unlock all of the various functions for all this Steve Jobs joy. 

The happy news came on two fronts: I learned that, as prep teacher, I was not required to have my program up and running for the first two weeks of school while we got the kiddos settled into their homeroom ruts. Additionally, I was asked to shepherd a half dozen third graders who were part of an enrollment overflow. These were my very first students, and they were kept busy with all manner of worksheets and promises of joining their own real class just as soon as one could be found or created for them. 

Eventually, I was able to create a room full of working machines: A Computer Lab. I created a mascot, Click The Mouse, to entertain the children while I scrambled about loading KidPix and Oregon Trail on the taxed memory of the barely there computers. And I thought about all this when I showed up this past Monday morning to find that all the fancy refurbished PCs had all been remotely reconfigured so my morning was full of logging in and checking two dozen plus settings for Windows and making sure they would all fire up when kids appeared shortly thereafter to begin their day in Horace Mann's Computer Lab. 

No more floppy discs. No more CD-ROMs. It's all done by network. If I had a mind to, I could sit at my desk and monitor the progress of all my little users from an app on my screen designed to keep them on the educational path and out of the ditches that Al Gore's Internet so playfully provides. No more Oregon Trail. No more KidPix. I don't have any printers left in my room. We don't print very much anymore. We send things to the cloud. Way back in the 1900s, if a kid left my room without a colorful dot matrix print of whatever their fertile imaginations could generate in sixteen bits, there were tears. 

Now the tears are mine. Longing for those days when I could simply find the right plug or blow the dust out of a disc drive to get things back in order. The good old 1900s. 

Friday, July 31, 2020

Live Through This

So sorry. In all this confusion, I must have lost track. Somewhere in the past month or so I slid on past the fortieth anniversary of my graduation from high school. Part of my surprise may stem from the fact that I just spent a few quality hours with some of the folks with whom I shared the experience of high school.
Not all of them, mind you. This is the cardinal reason I have avoided organized reunions of my graduating class is because I was not a big fan of all the people with whom I endured those years. I know this leaves me wide open for the suggestion that I am telling tales out of school. This is precisely what I am doing. The choice of the word "endured" was not one I landed on lightly. I was in band, after all. I played sousaphone in band. Which is just a sly way of avoiding saying that I played tuba. I had one date in my junior year. None in my sophomore year. The friends I made were almost exclusively those I made while practicing and marching and going out for pizza after practicing marching. The friends I had coming up from junior high drifted away, finding their own social strata and cliques.
And yet, somehow, I managed to have some fun. Part of that fun came in the form of direct confrontation with the powers that were in charge of that paramilitary group to which I belonged. In my older brother's day, these characters were known as "Band Baddies," as distinguished by their obsequious and conformative "Band Goodies." By following the path laid out by my big brother, I managed to further distance myself from anything that might have made me visible. It wasn't until my senior year that I began to feel my oats, aided in part by an increased effort to generate a social life. Not that this social life crept anywhere near the boundaries prescribed by my bandie affiliation, but a sense that perhaps the "permanent record" of which I had been so concerned all my life might not be such a big deal.
I skipped some classes. I lied to the vice principal. I was kicked out of band rehearsal. Three times. These were various smart aleck remarks and disregard for authority. It should be noted, however, that none of this delinquent behavior kept me from doing my absolute best when it came time to preform. I was still a team player, in spite of my questionable attitude. I was also kicked out of my Elementary Functions class. I was asked not to return. I dropped the class and replaced it with Selected Topics in Math. Got the credit. Graduated. Done.
On graduation day, I heard about all the parties that other people were attending. I landed on my parents' back patio. With my family, and two of those people I mentioned at the outset. There was no drunken brawl of a celebration. That would have to wait until my "gap year" when I worked at Arby's instead of heading off to college.
No word yet on when that reunion will be taking place either.

Wednesday, April 19, 2017

Elementary

For most of my life, I didn't really have a problem imagining that there were people who were smarter than me. I gave my parents the  benefit of this assumption, and my older brother. My teachers were all superior intellects and I needed only to wait for their wisdom to trickle down to me. If I sat in my seat and  paid attention. I've always been pretty good at respecting authority, and if someone was recognized as an expert, I gave them the benefit of the doubt.
It was long about the time I was in high school that I had my first real confrontation with how that reality might not be exactly the one in which I would grow old. My math teacher took me out into the hallway and threatened to fail me if I didn't cool my roll in his class. I was surprised to see that I was somehow perceived as a threat to his authority. Me? Was I more clever than this high school instructor of Elementary Functions?
Troubled by this development, I dropped his  class and enrolled in Selected Topics In Math, a course that would fill my credits and get me somewhere safe and dull.
It was this morning when I woke up to the notion that I am smarter than our "President." My problem is that I don't have another country in which I can simply drop into as I wait out the insufferable stupidity that continues to wreak havoc on our nation and planet. A year ago, I was comforted by the idea that the man in charge of the United States was much smarter than I am. He was surrounded  by a group of individuals who could easily teach me a thing or two about governance. Even back in the days of George W., there was the evil genius known as Dick "Dick" Cheney to hang all that cleverness on. Not the guy we have in there now.
On Easter morning, he greeted us tweetly with "I did what was an almost an impossible thing to do for a Republican-easily won the Electoral College! Now Tax Returns are brought up again?" and "Someone should look into who paid for the small organized rallies yesterday. The election is over!" The election is over, now begins the backlash. The guy whose mind works one hundred forty characters at a time is confounded by the resistance to his tiny-brained responses to the world around him. The rallies across the country were made up of Americans who cannot reconcile what is happening to them and those around them. They aren't being paid. They are, ironically enough, being  stirred up by the very social media he tends to favor himself. 
Could it be that the "small group" of protesters are better at organizing than the "President?" Almost certainly. Is our "President" good at estimating the size of a crowd? Almost certainly not. I wonder how he'd fare on an Elementary Functions exam. 

Wednesday, November 06, 2013

New Math, Same As The Old Math

My son and I have a favorite T-shirt that we haven't managed to buy for one another. It says, "2+2=5 - for exceptionally large values of 2." It's the kind of thinking that makes sense for a family of non-math majors. To a certain degree, we are all happy to have the latitude to use our very extensive vocabularies to extrapolate and expand upon all the potential answers to life's problems. The facts of math and science make us all a little uncomfortable. That doesn't mean, however, that I have no appreciation for the concrete nature of these subjects. I was well on my way to being an exceptional math student when my personal life got in the way. The discipline that was required to study Elementary Functions was not available to my mind as a senior in high school. After years of tracking in the upper realms of whatever math courses were available, I opted to finish off my public education with a class called "Selected Topics In Math." It was a place holder, a review, for those who needed that math credit to get them into the college of their choice. Whereupon they could choose to take exactly no further math courses.
This was true to the absurd degree that I took a class that was listed in my university's catalog as "Astrophysics for non-math majors." It would be another ten years before I would need to remember the quadratic formula. That was when I decided to become a teacher. As it turns out, the powers that be would like teachers to know more about the subjects they teach than what he answer keys in the back of the Teacher's Edition of the textbook has to offer. Suddenly, I found myself in love once again with the precision of it all. The way those equations balanced and the steps that made complete sense when followed in the proper sequence. It turned out that being able to explain to kids why there was such a thing as a perfect square gave me peace. During my years as a fourth grade teacher, I reveled in the connections that math allowed me to bring to my ten-year-olds' minds. Getting them to fold pieces of construction paper to find their own equivalent fractions was more satisfying than I can describe.
And then our school district decided that they wanted to emphasize math facts. All that touchy-feely investigation was over, replaced by the rote memorization of rules and correct answers. Never mind the "why," just get to the bottom line already. This was one of the reasons why I didn't feel particularly sad about returning to the computer lab, leaving the regurgitation of times tables to those whose temperament was more suited to such things.  Every so often, I would take a fourth grader aside and try to blow his or her mind with the amazing correlations between the diameter and circumference of a circle, but mostly I returned to my life as a man of words.
Until last year, when the pendulum of education swung back. All of a sudden, they want kids to talk about how they figured out that whole two plus two thing. The "why" is back. And I don't really mind if it's always going to be four, as long as I get to talk about it.

Friday, August 17, 2012

Pinocchio

It's that time of year again, where teachers dust off their briefcases and book bags and start heading back to the classrooms where they await, anxiously, the appearance of this year's crop of fresh faces. This is the time that we teachers gather together to discuss all the ways that we hope that we can find to squeeze that one little bit more of learning out of the marathon ahead. We call this "professional development."
Starting my sixteenth year as a teacher, I am always impressed to find the tip or technique that will help me grow as an educator. Learning, as we tell our little darlings, is a lifelong process, after all, and I expect to take something from every class, seminar and meeting I attend. But first, I have to cross the bridge we call "The Icebreaker."
Inevitably in these classes, we are asked to mix about and introduce ourselves to a colleague from the sea of faces that fill the multi-purpose room. I stand up, and shuffle about, looking for the moment of eye contact that says, "I surrender. You might as well talk to me." I introduce myself, and describe what it is that I do: I am the computer teacher at an elementary school. This is just before I get the response that chills me.
"So, you're not a real teacher?"
Not me. I'm a virtual teacher. Human cyborg, technology. I perform many of the same functions of a real teacher, but I won't immediately be confused with them. I don't have my own class. I have all of them. I don't fill out one set of report cards. I make sure they all get filled in and printed. I don't deal with the same two knuckleheads who sit in the back of the room all day long. I deal with them on Tuesday at nine. Then at ten, I get another couple of reluctant learners. At eleven I get the girls who haven't stopped talking to each other since first grade. I get them all.
I don't say this. I merely nod and smile, adding that once upon a time I did a tour of duty in fourth grade and so I can relate to the challenges of real teachers. The ones with twenty or thirty kids. They have my everlasting respect. And me? I've got three hundred and twenty-five of them, and I'm still waiting for that respect.

Sunday, October 23, 2011

Isolated Variable

When I dropped out of Elementary Functions in my senior year of high school, I didn't flinch when I dropped into Selected Topics in Math. "Sel Top," as we used to call it, fulfilled my math requirements for graduation, and it gave me plenty of time to catch up on the notes I needed to be writing to my girl friend. Sure, there was a part of me that wished that I could be cruising along at that elevated level of math genius with my very clever friends, but math had suddenly ceased to be a priority for me. On the contrary. I felt released.
From the time I had entered junior high, I was uncomfortably ensconced in the upper echelon of mathematics class. I tested high, so that's where I was placed. The trouble I encountered was that I was much better at taking tests than I was at doing class work. I struggled mightily with the repetition of problem after problem, knowing that there was an answer: one correct answer. That answer routinely sat just outside of my understanding as the hours passed and my homework became a struggle that confounded me on many occasions.
But I continued to pound away, and in spite of my parents' suggestions that I go in early or stay late for help, I was determined to do it myself. This nose to the grindstone ethic kept me going for nearly six years, and when I was confronted by my Elementary Functions teacher, not about my frustrations with the math but rather my flippant attitude in class, I was relieved to be shown the way out. In my mind, there was this thought, the one that echoes in the heads of countless teenagers: "When am I going to use this stuff anyway?"
Now I have the answer: the answer is now. Now I have a son who is doing much of the same math that perplexed me when I was his age. Now he's coming to me for help. Now I am working toward a supplemental math credential. Now I understand rational numbers and domain and range and matrices. Now I understand irony. It comes right after functions.

Tuesday, February 15, 2011

Long Story Short

My son had to write a sentence for his English class using the word "epic." He wrote this: "Dude, that was epic." He was pleased enough with his repsonse that he felt the need to share it. I asked him if his sentence illustrated his understanding of the word. He changed it to "Dude, that kick flip was epic."
I sighed. Thirteen years old. Eighth grade. I collected myself. "What is the definition of 'epic?'"
"It's a long poem that tells the story of a hero's journey."
"Really?" I was surprised by his confidence. "Can you give me an example?"
"The Odyssey."
My journey was at an end, even though I had just started. He had the right answer. He had an epic answer, but it wasn't his first impulse to write it down. It wouldn't have been very cool to simply give back the answer that his teacher had given him. He was trying to find his own voice. Oddly enough, the one he chose sounded more like a skate punk than a kid who hasn't been on his own skateboard for more than a year. But he has seen a kick flip on line, and he assures me that it was epic.
Kids these days. That's what was going through my head. Followed almost immediately by the sound of my mother laughing. I was in upper level math classes until my senior year in high school, where I began the year taking Elementary Functions. I was having such a good time with my friends that math became secondary. I was the class clown. At some point, my teacher took me aside and told me that while he couldn't force me to drop the class, he could make it very difficult to pass it. I left the room and went straight to my counselor who found me a spot in "Selected Topics In Math." I had gone from the heights of calculus to the slums of algorithmic review. It was more important for me at that moment to be social than to be "smart."
That was more than thirty years ago. A lifetime ago: my son's. Now I'm trying to make sense of this from the other side. I'm trying to keep him on the fine line between being clever and being a smart aleck. It's a wicked tough dance. It helps if you're very smart to begin with.

Thursday, August 07, 2008

A Thin Line

"Thank you very much, I'll be here all week. Please, tip your waitresses." These were the words I left my colleagues with this afternoon as I left Ballroom Number One at the Airport Hilton. I've spent the past few days in the cozy confines of the Reading First Seminar hosted by the Governor's Reading Initiative. There are twenty-some of us teachers sitting patiently at round tables beneath questionable lighting and plenty of air-conditioning. And I'm doing my very best at behaving.
I wouldn't have thought that distinction necessary, but interestingly enough, it was pointed out first by a friend of mine the day before the training began. After listening to me complain briefly about being held hostage for five days, he suggested that I was secretly looking forward to it. It would be a chance to interact with my fellow teachers and maybe even entertain a bit. "Yeah, sure," I shrugged.
Then, on the first morning, I ran into one of my instructors from a previous year who asked me point blank: "Are you going to behave this week?" Apparently my reputation precedes me. I was the kid who was asked to leave my Elementary Functions class in high school because, in the words of my teacher back then, "You're an instigator."
I've never considered myself to be "class clown." I am happy to leave that distinction to other more manic personalities. It is true that I enjoy sharing my sense of humor with most any willing or captive audience, and I find that classrooms afford me just that.
I have gone to some great pains to make sure that I don't ignore or offend my instructor. On the contrary. I have been a very enthusiastic and involved participant. I sit at the front table and I am on task and ready to go. The challenge comes when things don't go. That's where I fill in with my witty bon mot. I have been careful not to overdo it, and I am grateful to have a set of fresh faces to apply my charm. I use the following statement as my measure: "I wish there was somebody like you on our staff."
Am I just there to amuse? No. I have learned a few things, and I have, as predicted, enjoyed the company of my fellow teachers. I have one more day to make an impression. I just hope they don't remember me as "an instigator."

Wednesday, June 15, 2005

I'll Show You Fair

"If this guy could see the clowns that are operating on him, I think he'd faint." - Trapper John from MASH.
I was filling out report cards this evening - trying out various permutations of the phrase "hard worker but easily distracted." It occurred to me that I could probably find this same comment on one or more of my elementary school report cards, but the notion of "permanent record" didn't really exist then, did it?
Nonetheless, here I am, creating someone's permanent record. When I was a senior in high school, my Elementary Functions teacher Mr. Seery took me out in the hallway and said this to me: "I can't fail you for your behavior, but I can make it very hard for you to pass this class. You're an instigator." It's true. I was an instigator - at times a real cutup. So I dropped the class and ended up in Selected Topics in Math - math you can skip.
That was twenty-five years ago, and now I'm busy deciding the fates of ten and eleven year olds - or at least who gets a raise in their allowance and who gets to eat standing up for a day or two. It's a trivial bit of power, but one that I feel momentarily ambivalent about. Does anybody really read the comments on their report cards? Or are they just looking for that bottom line - Placement for Next Year?
No one in my class if flunking - pardon me - no one in my class is being retained this year. Are there students who would benefit from one more solid pass at fourth grade? Yes, there are. By the same token, there are at least a few who were ready to move on sometime in February - but that's not how we're running things this year. For now, you have to wait until Mr. Caven says it's time to move ahead one space. Mr. Caven - the Instigator.