2024: The Year in Review, Part 1

Happy New Year!

Part 1 of my look back reflects on my writing career. Part 2 will cover the blog, the comic and teaching in general.

A Look Back at Writing and Publishing

Portions of the following text appeared in Burke's Lore Bites my newsletter.

Although my self-publishing career started in the final days of 2023, I didn’t receive my Author Copies of Burke’s Lore Briefs: A Heavenly Date / My Damned Best Friend until early January. I learned a few lessons about what to do and what not to do with future books. That first batch batch of books sold well.

Two more Burke’s Lore Briefs were published in 2024: “Portrait of a Lady Vampire & Other Vampiric Cravings” and “I See What You’ll Do There” (containing one reprint story, see below).

With these books launched, I created a mailing list (thank you for joining it) and a Substack account for posting updates. I’m still figuring out what works best for me.

In February, “A Sliver of Pi” from In A Flash 2020 was reprinted in Free Flash Fiction.

In March, a new story, “On My Shoulders” was published in Short Beasts Literary Magazine.

In April, my editor Danielle Ackley-McPhail surprised me with the cover for A Bucket Full of Moonlight, which is the biggest collection of “Burke’s Lore” to date, with 30+ stories, although it doesn’t bear that brand. The Kickstarter would launch in the summer, and the book appeared on Library Thing in October, garnering five reviews.

In May, the humorous RPG-Lit story “I See What You’ll Do There” appeared in the Spring 2024 edition of Sci-Fi Lampoon.

In July, AHOY Comics purchased “Death’s Last Man” which appeared as text in the comic Deadweights #5. My name was even on the cover!

And finally, October brought a two-fer with “What You Needed” appearing in the anthology A Little Fantasy Everywhere (Jersey Pines Ink) and two 42-word stories (one under the pen name Ben Carter) were included in 42 Stories Anthology Presents: Book of 42².

It was an amazing year, and I hope it continues into 2025!

For more news on my writing, and for links to books which mostly appear on Amazon, check out my Author Page at mrburkemath.net.

Happy New Year 2025!

(Click on the comic if you can't see the full image.)

(C)Copyright 2024, C. Burke. "AnthroNumerics" is a trademark of Christopher J. Burke and (x, why?).

HAPPY NEW YEAR 2025!

There was a lot to put into one comic and I couldn't compress the graphs anymore without some of the lines disappearing on me or unless I was willing to dealing with a lot of pixelation. Since I had a lot of shading to do, I did not want the pixelation.

Besides, I wanted you to see all 2,025 of those wonderful little colored boxes!

The funny part is that I had an illustration in a math journal I kept more than a dozen years ago that I wanted to use. The problem was that the page, which was more than 45 boxes tall was not 45 boxes wide. It was a little more than 36, so I had an 36 by 36 square and everything in the comic about was there, but based on the smaller number.

So I recreated it from scratch.

Now, since 2025 is a a perfect square, and the only one that I'll see in my lifetime, until I live until 2116, another 91 years from now, there are a lot of fun facts because it is a perfect square. For one thing, squares are always the sum of two consecutive triangular numbers. Think about splitting a square along the diagonal, but instead, make steps. One triangular number will be one less than the other. Moreover, if you eliminate the center square, you can split the rest of the square into four congruent rectangles, each of which can be divided into two equal triangular numbers. So you'll have 8N + 1, where N is a triangular number.

Finally, N to the second power can always be represented by the sum of the first N consecutive odd numbers.

The bonus to all this is that 45 is itself a triangular number, being the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9, so that just allows even more number play to occur. And though it seems like the oddest coincidence that (1 + 2 + 3 + ... + n)² will always equal 1³ + 2³ + 3³ + ... + n³

Enjoy the New Year! It should be wonderfully mathematical!

I also write Fiction! The NEW COLLECTION IS AVIALABLE! A Bucket Full of Moonlight, written by Christopher J. Burke, contains 30+ pieces of short stories and flash fiction. It's available from eSpec Books! Order the softcover or ebook at Amazon. Vampires, werewolves, angels, demons, used-car salesmen, fairies, superheroes, space and time travel, and little gray aliens talking to rock creatures and living plants.
My older books include my Burke's Lore Briefs series and In A Flash 2020.
If you enjoy my books, please consider leaving a rating or review on Amazon or on Good Reads. Thank you!

Come back often for more funny math and geeky comics.

2017: The Return of the Itinerant Teacher ... To Being Itinerant

2017: A Teaching Year in Review

There's an adage that annoys teachers: Those who can, do; those who can't, teach. And yet we will also ponder the fate of those who "can't teach" -- often they become "consultants" after a year and a half in the classroom, becoming self-appointed experts at telling the rest of us how to do it.

In my case, it's not a matter of "can't teach" as much as "won't let me". Now, I'm not assigning blame, for a couple of reasons: first, I don't wish to burn bridges, nor kill my own career; second, I'm not entirely blameless in the situation. Stuff happens.

Looking back, 2017 started as a year of promises, and in five and a half months, many planted seeds seemed to be taking root and flowering. Bearing fruit, if you will. And then someone razed the garden.

In December 2017, after a few months in the ATR (Absentee Teacher Reserve) Pool, subbing for a few different schools, I received an inquiry about a math position in Park Slope. My previous school year had been dreadful, resulting in a "Developing" rating and the loss of nearly 20 pounds. I had been happy to be in the pool for those months, subbing for other teachers, occasionally pushing into and assisting in math classes, and generally covering whatever needed covering. As restful as this was, however, I couldn't see this being a career path for me, so I looked into the school that had contacted me.

There was several pluses that stuck out: it was in my old neighborhood, which was easy enough to get to; it was a small school inside a big building, shared with other small schools; and I had previously worked in the building, so I knew that there wasn't a history of "trouble" in the halls and stairwells.

The principal and AP were nice people, answered my questions as well as they could. Note that my first question, considering previous experiences, was "Is this position provisional or permanent?" Was I being hired to teach math at the school or to fill a void until the end of the year?

Honestly, I couldn't tell you at the time which answer I expected or even which I would've preferred, so long as I had an answer and knew what to expect. I was told that he had been told by "downtown" that whomever he hired that's who he hired. That was it.

So in January 2017, I was making progress getting to know my new Algebra and Geometry students, just as they were making progress. I found strengths in some low-performing students. A few others were suddenly "turned on" to math, which they hadn't been in middle school. And I made important connections with a couple of students who seemed troubled in their own ways. I found ways to reach them, to be able to talk to them (somewhat). They knew they could talk to me if anything was troubling them, disrupting their class time, distracting them from learning.

I made enough progress that I was once able to say to a reluctant talker, "I'm sorry but I only have a minute, so can we jump to the point where you start speaking to me?"

It was abrupt, but she opened up right away and asked what she had to, and I was able to answer her. Next time, I let her go back to her natural process before speaking, but I noted she spoke up a little sooner.

By spring, we could practically have a conversation without prompting. By June, she told me that she saw me as a kind of "mentor" figure. That same day I was called into the office for a meeting. I thought it was a post-observation conference or the end-of-year review (a little early). When I saw the ELL teacher in the room, I wondered if there had been an issue with one of my students.

No, the ELL teacher was also the union rep. She was there because I was being excessed. Let go. From a "permanent" position. I chose my words carefully because I didn't want to end my career. And I might have. I felt betrayed. And I felt I was betraying my students who had made connections with me and whom I thought I'd see again the following school year.

In the principal's mind, the position hadn't been filled yet. He was still searching, not that he'd ever mentioned this in the prior six months. Any protest or argument from me was cut off with a simple question: would I like to still be considered for the position?

As much as I wanted to tell him to shove it -- OF COURSE, I WANTED TO BE CONSIDERED FOR THE POSITION. I thought it was MY position. I was already making plans for next year, what to change in the curriculum, how to approach Geometry with my current Algebra students, how I wanted to redo the classroom. That ended it. Except I knew I wasn't going to be considered or we wouldn't be having the conversation. I'm too expensive, and new teachers are easy on the budget.

So I started making my good-byes to some of the students. I hope they do well. A couple of them were following me on social media and still contacted me early in the fall semester, but the contact has fallen off. I hope they found new mentors, ones that aren't going anywhere.

This would be a good point for a musical interlude, in place of my summer break, so I can stop rambling and recollect my thoughts.

The end of the summer brought another plot twist: the city and the union agreed to change the rules about placement. If I didn't find a position, if a school did not hire me, then there was a good chance that the city would select an open position somewhere in Brooklyn (possibly beyond) and place me there anyway, whether or not I wished to go there and without regard to the school's desires or ability to fit me in their budget. And that placement would be permanent unless -- here's the catch -- the teacher received a developing or unsatisfactory rating!

So what did this mean for me as a teacher: I could find myself in a horrible school, in a horrible neighborhood, in a horrible situation like the one that caused me to drop to a weight beginning with the number 1 (which I hadn't seen since the year started with the number 1). I might not be able to get out of it, if I couldn't find an open position. Moreover, if the school didn't want me there, then they could make my life miserable so I'd get an unsatisfactory rating!

Granted, it was no picnic for the schools, either, and it was no surprise that I got a few inquiries after this announcement, while at the same time, open positions started disappearing. I applied to quite a few places, but, sorry, I wasn't going back to middle school, and I wasn't traveling to the Bronx. (Note: it's a minimum two-hour travel, one-way, by subway to get to the Bronx from my house.)

Making my search more desperate, an email arrived stating that my first temporary assignment was at Cobble Hill High School for American Studies. Nice neighborhood, not a lot of teenagers in it. I spent one single week at that school and I rated it as probably the worst week of my teaching career. That week was an absolute disaster, and I didn't want to repeat it. I only name the school so I can give credit where it's due. I had maybe 1 or 2 difficult assignments during my eight weeks there in September and October. While the school still has its share of problems, I didn't encounter anything like the last time. And I'll give a shout-out to Stephanie (I hope I spelled it right), for taking good care of me and the other ATRs assigned there. On my last day there, I told her that I wish I could take her with me.

Okay, so what about that forced assignment? It might still be coming for all I know. We keep hearing that math is a shortage area. And there are openings, but schools are still playing games.

In mid-September, a former colleague, now an assistant principal reached out to me through the DOE email and through Facebook (we're not "friends" on Facebook) to let me know about an opening in Queens. I wasn't thrilled with the idea of Queens, but with the future uncertain, it paid to check it out. Basically, it was a temporary position for someone who might be coming back soon, might be filing an extension, or might be retiring (after exhausting extensions). I met with the principal, saw the classrooms, spoke with some students, and, honestly, couldn't think of a reason not to be there, except the location and the travel time wasn't that bad. I was "basically" hired right there and they were going to put the paperwork through. By the middle of the following week, I got an email from Datacation, saying that an account had been set up for me with the online grading system at the school. I checked online and saw the rosters for four of my five classes. I just waited for the call to report.

And I waited.

And I waited.

And I checked the online grading system. I was still in there, but I only had one class, and it didn't have any students in it.

I can only assume that the teacher returned to work. You might think that someone might've informed me of this, especially after they pursued me and framed it as doing them a big favor. I was more disappointed about the snub then about the loss of the position.

Speaking of snubs. When the summer was drawing to a close and prospects were dwindling, I reached out to my old AP at the school I taught at for a decade (most of that before the current AP was there). The school that had excessed me -- twice. Why would I do such a thing? Because I still go back to their end-of-year parties to say good-bye to retiring colleagues. Last June, that school lost two-thirds of (non-ISS) math teachers. That is, they lost two out of three. Now considering that the AP of Operations told the Summer School principal that I am the "go to" guy for math, you might think that they would give me a call about coming back there.

You would be wrong. The call never came. I am Facebook friends with my former AP (although I have reason to believe that she's "muted" me), so I knew that she and her husband were on a European vacation this summer. When she returned, I contacted her through DOE email (not through Facebook -- that would be tacky). No response. Not even, "we have somebody." And here's the thing, she was at the end-of-year party. We'd spoken. She heard about what had happened to me, so she knew that I was available. We didn't discuss it -- again, it was a party and that would be tacky.

One last one: One school I contacted in the summer didn't return my messages, and then it no longer listed an opening. Early October they send me an email telling me that they've scheduled me for an interview AND a 20-minute demo lesson with such-and-such parameters and expectations, and it would be the day after I read the email. EXCUSE ME? I emailed back, "Sorry, but tomorrow is my annual check-up, and I need to be in the doctor's office. Can we reschedule?" They never replied.

So that's the way my year was going. I'm currently at a nice school close to my home. The UFT representative even approached me about staying there on my first day. If he asks me on my last day, I might ask him to see what he can do.

Life can be easy for someone in my situation if you can roll with it, but I can't see keeping myself afloat like this for another ten to fifteen years.

So while I'm happy for a relaxing end to 2017, I'm hoping to a more satisfying 2018.

A Young Pickpocket Learns A Valuable Lesson

Something happened a couple weeks back while I rode the Bay Parkway bus one weekday afternoon shortly after school let out. The bus was crowded as it usually is even before it got to my stop, by the train station. Naturally, it's a transfer point where many commuters are making a connection.

For those who haven't ridden a bus in New York City (and I haven't ridden elsewhere, but I imagine it's similar), you get on through the front door, the driver says move on back so more people can get on, and generally, people ignore him after moving about 10 feet. Resistance is met with surrender -- if you can't get past two people who refuse to move, you'll likely stop and add to the problem.

I do try to move back as far as I can. For one thin, plenty of people exit through the rear door, so if you can break through the logjam, there's usually breathing room in the back (and sometimes a seat with a bag on it that you can shame someone into removing).

There are a couple of semi-valid reasons for not moving toward the back of the bus. First, you are with someone who managed to get a seat, so you wish to stand near them, which requires you to sway out of the way of people pushing past. (Note: this is difficult to do if you are oblivious to the fact that you are wearing a bulky backpack sticking straight out into the "aisle", which is basically inches wide. Take it off!) Second, you have packages or a bag on wheels with a handle, either of which would be difficult to navigate through crowds.

On this day, there was an older woman with a travel bag with the handle extended immediately to her left, and she also had a sizable pocketbook hanging from left shoulder. I had my briefcase in my left hand, with its strap still on my left shoulder. I was also wearing a pair of earbuds with the wire running down to and disappearing into the right pocket of my jacket. Everything inside my pocket was secure; it always is. I was basically sidestepping through the crowd, leading with my bag to wiggle through, saying "Pardon me, excuse me, pardon me" like an old Bugs Bunny cartoon. My right hand was grasping and moving along the overhead bar because the bus pulled away from the curb rather abruptly. (Schedules!) I noted both of her bags and was being careful.

Now there is an alternate explanation about the events which happened next: it is possible that the wire could've caught on either of her bags. It is possbile that the woman shifted and her elbow caught the wire. It's possible that this was just an odd occurrence. But not likely in the slightest.

This is why: I have had the wire to my earbuds snag on things before. The result is always the same -- the earbuds are pulled from my ears. Action/reaction. I think that there was one time that the wire came loose on the other end. However, the path of least resistance, the weakest link in the chain, is the connection to my ears, not to my pocket. Never -- I repeat, NEVER! -- has any snag yanked anything out of my pocket. (Like a little boy's, a grown man's pockets run deep, and they collect many things.)

Here is what I believe really happened. Someone, likely a school-aged individual, saw an opportunity. They saw the wire disappearing into my pocket and my right arm raised over my head, giving them a clear path. They either thought that they could easily lift my phone out of my pocket by the wire, or maybe that if they pinched the wire, my motion to the back of the bus would lift it out on its own. Their objection, I suppose, would be to yank the wire free, palm the phone and swing about in their seat, essentially disappearing into the crowd, leaving me without anyone to accuse. It's not like a cop would stop the bus and search all the passengers, right?

But the little sticky-fingered bandit didn't get away with it. Like Snidely Whiplash with two binomials, his plan was foiled because he hadn't counted on something. There was something he hadn't expected and probably never would have before now.

And so my little pickpocket friend, you have now learned a valuable lesson.

You now know what a Sony Walkman looks like.

(Blog): MATHice in Scienceland

Only three days into my new substitute assignment, and I have a few observations. Now, i don't want to get political or start anything -- that's not me. I try to roll with it, whatever it is, and not stir the pot. Especially, considering that I have to revisit this pot for the next month. But, here goes ...

One of the school's Living Environment teachers has been out sick. (I don't know how many the school has.) I've covered her classes every day this week, so far, and likely will continue to do so. I don't mind, but the kids do. They're objecting to the work posted on the board with no one to teach them. They're frustrated and confused and don't like to be told to read the text book. Some of them do what they have to do and try their best. Some of them, I think they just want a teacher to tell them the answers to the questions. And some don't seem to care at all. And none are happy that there's a math teacher in their science class.

Today, I tried to talk to a few of them. It was a good day for this because many of the freshmen were gone on a trip and some of my classes had fewer than a dozen students present. Unfortunately, they just wanted to complain (which is fine, so far as that goes), but they didn't want to hear any solutions -- not the ones that are possible or likely. They need to step up and take matters into their own hands, but they don't have the maturity for it.

Have you heard me complain lately that today's freshmen are less mature than the junior high school students I needed to get away from a dozen years ago?

I don't have all the facts, just some anecdotals. At my last school, while they were losing teachers to budget cuts, I knew that the Living Environment (aka Biology) teachers were safe. (This is my impression, mind you, not a statement of facts.) They were needed more than any of the other science teachers because they were the freshmen class, and everyone has to pass that class and Regents exam. If I extrapolate this, Living Environment teachers are likely in high demand, meaning that they have options as to what school they teach in. Which means that they'll leave a poor school in a heartbeat if something better becomes available.

Without passing judgment, I tried to explain to the kids that if someone was looking for a position, would they pick a school that's been around for 50 years or one that was reopened in the past five? That's not the perfect measure for adults, but that's something the kids could understand without feeling insulted.

Not all 50-year-old schools are great, but they've "reorganized" the poorer performing ones in recent years. But if you're looking for a position (which I've done too much of in recent years) and you see a school where, say, 80% of the kids graduate in 4 years and 70% go on to college, and a second one where, say, 40% of the kids graduate in four years and who wants to contemplate the low number going to college, which do you think the teacher is going to lean toward? If one school has staff who have been there for more than a decade, and the other is only five years old and no one's been there for more than three of those five years, which do you think the teacher is going to lean toward?

If a teacher were to walk into my classroom while I was subbing and saw what little respect the students had not only for me (the sub), but for the property of their actual teacher and (let's face it) for themselves, would they want to come to this school?

End result: if the school is poorly-performing, then you aren't going to be able to attract a qualified teacher whose future depends on the performance of immature individuals who have been taught to respect themselves above all else to the exclusion of having any respect for others, without actually recognizing that they aren't respecting their own future as they find "disrespect" in everything anyone tells them that is contrary to their own preconceived (and immature) notions of reality.

Is that the school's fault? Is it the kids' fault? The parents' fault? The teacher's fault?

I don't know. I'll play it safe. I'll blame Bloomberg. He didn't create the mess. He just made it worse by trying to remake the schools in his own image. And he's not my boss anymore, so I can get away with that now.

Blog: Knew It Was Going to Happen, And Yet . . .

Taking me cue from the discussion the other day about randomness and probability, we come to my last day at my current school. I stepped in to a temporary position while another colleague was on maternity leave, and now she is returning. As luck would have it, today was also the last day of the marking period. Normally, I'd be bringing a massive amount of work home to grade, but since I won't be going back to return anything, I had to leave a pile for me to check. I left answers keys and hints that she might just want to "check" the work and score it all. At this point, most of the kids are "good" about leaving two-thirds of the papers blank if they don't know what they're doing. Anyone finishes the page in what looks to be a neat and unrushed manner probably has a handle on things.

Today's events: I brought in doughnuts and put them out in the Teacher Center a dozen at a time during my preps. Some of the folks who hang out there (many stay in their rooms or elsewhere where there are conference tables) knew that today was my last day and that I'm having a birthday next week, when I'll obviously no longer be there. It was a little busy today. Friday's are little crazy because the periods are very short and there's 90 minutes of PD (professional development) at the end of the day for the teaching staff. (This was something that was voted on my the teachers last year.) I was doing double duty making sure that I packed what I wanted and tied up loose ends while creating work for the kids who I'd kept in the dark about the switchover. There can be some troublesome elements in the class, and they didn't need encouragement to misbehave, which they'd do despite the fact that I'm handling the second marking period grades this weekend.

Now, before I forget, when I arrived at work this morning, there was a bag with a bottle in it on my desk. I believe it's essentially an Italian version of Bailey's, which was confusing because it was a gift from a lovely Russian woman. So by the time that PD came around at the end of the day, after a lot of well-wishing (and an incident I'll mention at the end), I hadn't thought more about it. I had to go to the library for yearbook photos and I was going to take the remainder of the doughnuts, and I was supposed to go out for a drink with one or two coworkers.

That's when I ran into Pamela. (I'll call her "Dr. Pamela" this once, just to give her her due on the title, but I'm leaving off the last names right now. I don't know why.) She apologizes that it's Friday and the end of the day, but it's my last day, and could I help her set up that document camera she found in her desk drawer. (True story: I put it in that desk drawer a year and a half ago because it was the only piece of the computer not tied down. No one noticed since. I wasn't in the school all last year.) Well, sure thing. We'd talked about it once, and I hadn't done it, so it was the least I cou---

SURPRISE!

Seriously? The document camera? You lured me into a surprise party with a document camera??? Points for originality. So I celebrated my last day and my landmark birthday with my Math Department colleagues. Unfortunately, my boss couldn't make it, being pulled in "six directions at once". (I'm guessing: each way on the x, y, and z axes.) And others from the Teacher Center were likely corralled with their own departments at the moment, so they missed out.

And the thing is, I knew it was coming. I thought I knew. And yet ... Still a random moment and I expected none of what was there. And just to show you that I'm not the only person who think mathematically all the time, take a look at the equations and expressions on this word wall:

I'm leaving that school in capable hands. And, who knows, I might find myself returning.

As for the unfortunate incident, the less said the better. In literally the last minute of teaching at this school, a fight broke out. I'd hope it was just a flare-up, some hurt feeling that a slap on the arm would resolve and diffuse and not go anywhere else. Sadly, it did go somewhere -- out into the hall. A crowd did form, but I have to give a shout-out to students who tried to separate, restrain(*) and calm the participants. (*: when it comes to "restraining" a student, many are looking to be held back just to save face. However, that was true only for the instigator.) The kids came to each others' aids before it got worse. But like the inevitable car wreck you witness, you know what's about to happen. I wish I could say more, but I've probably said too much already. I was bummed out for the prep period before my PD, which in itself was a bit silly to go to, so I was even happier about the little diversion. Maybe it someone wants to join me for that new job/landmark birthday drink, we can talk!

Blog: Is It Still a Random Event If You Know It's Coming?

It's only the Third of December, and already there's a digression. That's why I love blogs: the very randomness about them. Randomness, probability, math. The circle of circles.

I have been bouncing around the New York City educational system for a few years now, and that's okay. I know that I'm wanted and there will be a soft landing somewhere. I figured that if I didn't get back to where I wanted to be in a reasonable amount of time, I'd find another suitable position. In the meantime, I'd be in the Absentee Teacher Reserve (ATR) pool. The downside to being in the pool is that you never know where you're next assignment will be: good neighborhood or bad, conveniently located or not. The upside? Well, no lesson plans, no mindless nights grading mindless papers writing meaningful comments, which likely wouldn't be read anyway. And I can most likely reset my alarm for a later time. Currently, I have a tendency to get to work an hour early to prep for a first period class because I don't wish to do all that work the night before when I could be sitting in front of the television, watching the insides of my eyelids.

A quick summary of the past few years: my school was shrinking because Bloomberg was trying to close it down despite its high grades on his own report card system. It stayed open but lost staff, including half the Math Department (which was three people, not counting the Support Services teachers). That event inspired this comic: Kiss Today Good-bye. After nearly a decade, I was leaving what felt like home.

That fall, I spent a month in Williamsburg at a small school that really didn't need any substitutes, and I mostly circulated the rooms, trying to help, which was easier to do when the subject was math. That was followed by a week at a school ten minutes from my home. At that point, a teacher at my old school retired, and I was on my way back. Things had changed a little. I had mostly freshmen, unlike the previous year, and the schedule was a little ... challenging. One could theorize that the classes were particularly rough because they wanted to encourage the former teacher to retire sooner. I think he had his plans set from the first day of school. It was a bit of a rough year, but I was promised a better horizons the following year ... and then I was excessed again.

My personal Year from Hell started in August. (I actually asked an A.P., who called to request an interview, if he had time the following day as I would be busy on the day he proposed, attending a funeral.) Professionally, it wasn't a bad year at all. I was called into Bed-Stuy, which sounded worse than it was, and spent a month there, watching them build the sets for The Knick, literally, right outside my window. Note: I am NOT misusing the word "literally". I have pictures. And Clive Owen even retweeted one of them! (Actually, it later turned out it was a FAN account, but I didn't know that at the time.)

This was followed by a few week in Park Slope, at my old zone school, which had been broken up years ago. Park Slope went through Yuppie-ville into Hipster Haven, but many of the kids traveled there from other areas. It wasn't an impressive place, and said to say that the teachers I worked with weren't fully versed in the topic they were teaching. I was able to nonchalantly correct a couple of things as if something was simply misspoken, but one thing in particularly was just so wrong, I kept my mouth shut. I figured that it was a tough topic and I could help individually with the students, but I couldn't undermine the teachers for the rest of the year. They weren't idiots, and I didn't want them to be thought of that way. (And I did explain their mistake later, during a prep period.)

Sometime in October, I got a call from a school in Staten Island. It would be a bit of a hike, and the Verrazano Narrows bridge has an incredibly expensive toll. (Not kidding -- even with a discount, it was costing me more than $10/day to get to work over one bridge.) It was supposed to be temporary, which worked out for me, because I knew that there was going to be an opening for me in Brooklyn at any given (i.e., random) moment. Except that there wasn't. For whatever reason that the teacher was on leave (I wasn't told; I never asked), she didn't come back. I was there until June, and I had settled in and had started to make friends. I attended a graduation dinner for a colleague, a summer barbecue. I even met a parent who I hadn't seen since we were both 13, some mumblemumble years ago.

At the end of the year, the AP asked me what was next. She didn't ask if I wanted to stay. maybe she assumed I wanted back in my old school ... or just my old borough on the other side of the bridge.

Which brings us back to randomness and inevitability. I went back to my old school during the summer for Regents Review classes, and subbing for a little spending money. One of my former colleagues was 8 months pregnant. She would be out on the first day of school. The AP of school organization started the paperwork to get me back on a temporary basis, and I was happy to go back. The only problem was that I hadn't a clue how long I would be back for. No one seemed to know how much time she would be taking. It was going to be six weeks plus whatever sick leave she had saved up (as far as I could guess) but I hadn't a clue how much that would be. Three months? A semester? Two marking periods, it turns out.

And here I am. Ready to leave again. Probably for the last time. I don't seem them -- at this moment -- turning things around. I don't see them expanding the student population, and with it, the budget. How long do I stay in the ATR pool? Sooner or later, I will have to find a position. Sooner or later, I will be subbing in a good school and I'll seek a position. (And maybe even regret not seeking last year's position again.) But in the meantime, I can count on two things:

A high probability of randomness, and an absolute certainly of zero lesson plans.

Me and Ann B. Davis, Part II

In my exuberance to get a post up quickly and start a trend in the hopes of going viral with my woeful story of a lost picture of me and Ann B. Davis ("Alice" from The Brady Bunch, as if you didn't know), I forgot to upload the photo from my journal. It's attached at the end of this entry.

Yesterday's entry was the highest one in quite a while, especially for one not linked to a spam site (like my New Year's 2014 post, which doesn't deserve all the hits is gets). Hits came in from twitter and Facebook, but the big leader was definitely reddit. However, while there were nearly 1,000 hits yesterday, I had only one comment on reddit, and a couple of Favorites on twitter, along with a retweet or two.

Wherever Dean and Marcy are, they aren't connected to this trend. By the way, I will be really, really embarrassed if I go back to that journal and find that I flubbed one of there names. I'm doing this from memory, but I remember them. Not only that, at the time, I was writing about 5 or 6 pages in my journal per day on the ride home. Well, I wrote about this trip for at least a week afterward so I wouldn't leave out the details. I put the journal back, but I can dig it out again.

Anyway, here's the promised picture:

$1.98 Mathematics, Part 2

A couple years ago, I was walking about a 99-cent store and found a quad-ruled composition notebook and a box of colored pencils. Total: $1.98. I played around with them for a while, and then they were put in a draw and forgotten about. Until recently when I found the notebook. And then last week, I posted a sketch for those pages.

Here is another one:

This was actually the first sketch from the book, but is wasn't as colorful as the other one. And it seemed to be more boring. But is it really?

The sketch (and you can click on the image for a larger version) shows a Golden Spiral created by connecting the diagonals of adjoining squares. The length of the sides of each square are determined by using the next number in the Fibonacci sequence. Obviously, the squares increased in size so quickly that I couldn't finish the 34 x 34 square.

But there was something else I noticed. I had added extra diagonals to some of the rectangles that were created in addition to the squares. I highlighted one of them in red (on the scan -- it's in pencil on the original sketch). The red line appears to be the diagonal for many of the rectangles. Four of them, in fact.

How could that possibly be the case?
(If any of my students are reading this, STOP here and look at it. Investigate. See if you can figure it out. Come back when you have it or you've had enough. I'll wait.)

The four rectangles have the following sizes: 2 x 1, 5 x 3, 13 x 8 and 34 x 21. Zooming in shows that the red line really isn't a diagonal of the smallest rectangle, so let's discard that one for a moment. The others are close enough to be errors in sketching. Since the slope of a straight line has to be constant, if we calculate the slope at any two points, we should get the same number.

Slope can be calculated as rise over run or change in vertical over change in horizontal. (You remember that "delta y / delta x" thing I keep mentioning in class? Yeah, that.)

So we have slopes of 3/5, 8/13, and 21/34, which are definitely not equivalent fractions. (How do we know that?)

If we convert those fractions to decimals, look what we get:3/5 = 0.6
8/13 = 0.615384...
21/34 = 0.617647...
and if the paper had been bigger, we might have seen
55/89 = 0.6179775...
144/233 = 0.61802565...

So the slopes are nearly identical meaning that the diagonal of the big rectangle isn't really the diagonal of the others, but it's really, really close.

Extra points if anyone keeps going, or if they can tell me the significance of a particular number that starts 0.61803...

$1.98 Mathematics

A couple years ago, I was walking about a 99-cent store and found a quad-ruled composition notebook and a box of colored pencils. Total: $1.98. I played around with them for a while and then they were put in a draw and forgotten about. Until recently when I found the notebook.

Here's one of the pictures:

There's a few things going on here. First, there's the demonstrations that two triangular numbers make a square. Second, the overall illustration shows that the sum of consecutive cubes is equal to the square of a triangular number.

Written on paper, there seems to be no reason why:
1³ + 2³ + 3³ + 4³ + 5³ = 15²,
(with 15 being the 5th triangular number)
But the visual shows it to be true. There is one box in the corner, bordering two 2x2 boxes, bordering three 3 x 3 boxes. Granted, I cheated in that all the even numbers contain two rectangles that are 1/2n x n.

I didn't finish coloring it. Probably got bored. Likewise, in the actual notebook, the bottom of the page has four 9 x 9 boxes lightly penciled, but the other five would be off the edge of the paper.

Now that I found the book again, I may start doodling some more... assuming I find the colored pencils.

EDIT: I replaced the image with an annotated version. The original, larger image (click on the picture) is still annotation-free.