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Might / Might Not

Sun, 14 Apr 2024, 11:22 AM (-06:00) Creative Commons License

This might be a good time to grab a phone or camera.

The Texas Star and Pink Evening Primrose and Mealy Blue Sage and Salvia Greggii and the last vestiges of the Giant Spiderwort blossoms are dancing in the breeze. The Nuthatches and Wrens and Yellow-bellied Sapsuckers are singing in the trees. It has warmed up enough for the bees to come out. The noontime sun is trying to come thru the clouds. A pot of coffee sits beside the bench, and Fleetwood Mac is playing on the speaker nearby.

There is a Black Swallowtail fluttering circles in the yard, sampling each dancing, wide-open primrose, its metallic blue wing patches glinting in the slivers of sunlight.

Yeah, this could be a good time to grab a phone or camera. But I’m out here, and they’re inside. So no. This isn’t such a good time for that, after all.


Thu, 11 Apr 2024, 12:11 PM (-06:00) Creative Commons License

She wasn’t in class for the test on Thursday. When I saw her next, she had a sheepish look on her face. She knew what I was thinking. And I knew that she knew.

“You missed the test last week.”

“I had an assignment for another class.”

“Oh, I see how it is,” I said smiling. “Skip my class for an assignment in another!” 

“I know,” she said. “I’m that guy.”

I laughed.

“Can I make it up today during class?”


“Misterrrr,” she said in mock complaint.

“I know,” I said. “I’m that girl.”

She laughed.

Total Eclipse

Mon, 8 Apr 2024, 01:39 PM (-06:00) Creative Commons License

Izzy was the first to notice the growing darkness. She came out from under the bushes where she had been investigating some shenanigans. She looked up and asked to be held. 

The Wrens started singing their evening song.

And then with only moments to go, the clouds grew thick, and we could no longer see the eclipsed sun. The glimmering light turned dark. The Wrens stopped singing. KUTX streamed, of course, Pink Floyd’s Dark Side of the Moon/Eclipse with the lyrics perfectly timed for Austin.

everything under the sun is in tune, but the sun is eclipsed by the moon

Trudy was on her back in the grass, wearing eclipse glasses, hoping for the clouds to thin. I was sitting in a bouncy chair with my head back, balancing welding glass on my glasses, holding Izzy in my lap, with tears running down my face. We didn’t get to see totality, but the music that filled the backyard and the day turning to night was enough. Daylight began to return. KUTX played Deodato’s Also Spruce Zarathustra. And then, of course, Here Comes the Sun.

The Wrens started singing their morning song.  

Trudy and I danced in the growing light as Izzy sniffed at the breeze. Then Trudy turned to go back to work. Izzy followed her inside. And I added a couple more bags of oak leaves to the compost pile.

Silent Sunday

Sun, 7 Apr 2024, 06:05 PM (-06:00) Creative Commons License


Number Sense

Sun, 7 Apr 2024, 08:45 AM (-06:00) Creative Commons License

They sat in arrayed desks, a few moving when asked to make sure they were not sitting next to anyone from their school. They had pencils and pens in front of them and nothing else.

I passed out a folded sheet of paper. The proctor told them not to unfold it until the competition began. He then called out their names from the official roster, giving each their number, which they wrote in a box on the top-left of the folded sheet. 

There was a knock on the door. Four students were sheepishly looking in the window.

“Oh my heavens,” I said as I opened the door to let them in. They chuckled nervously. “Go ahead,” I said. “Pick a seat apart from each other.”  

After the full roster had been read and the students had written their numbers down, the proctor read the official instructions and then reminded them not to begin until he said “Go”. 

“On your mark… Get set…”

One of the students loudly flipped her paper open. The others looked over in horror as she realized her false start.

“Not yet,” the proctor said, and she quickly folded her paper back.


There was a great rush of rustling paper as they all unfolded the questions and began their mental calculations.

You see, in Number Sense, you solve math problems without writing anything down except your answers. No calculators. No scribbles. No scratch paper. No erasures. No corrections. Just answers to the questions.

After just a few minutes, someone on the far side of the room loudly flipped their paper over. The other students looked over in shock. There are only a few minutes for this event, and the number of questions is laughable. Many students answer fewer than ten questions. No one gets to the back.

Well on this day, almost no one. 

A Calculus Side Hustle

Tue, 2 Apr 2024, 07:26 PM (-06:00) Creative Commons License


It was the beginning of seventh period. The tardy bell was about to ring. Reginald came into the room. What was he doing here? He’s in second period.

“Hi Reginald. What’s up?”

“Well… what do you have for me today?”

He had a smirk on his face that stayed glued there. 


Reginald is a bright student. He grasps the algebra almost before I finish speaking, sometimes completing my sentences. A few weeks ago, he proudly showed off some work he had been doing with limits. He’s hungry for more than algebra, so we work together a few times a week.

After it was clear that he had a solid understanding of limits, we started discussing derivatives. He had heard of them, but not in the way I had in mind. I taught him the definition of derivatives in terms of limits. We worked an example together. He ate it up. Then he did one on his own. And another.

I gave him an assignment. “Come back and show me what you find.”


The next day he was back, going on about Taylor series and showing me his cosine and sine expansions.

“I’m not sure what this means,” he said, pointing to factorial terms like 2! and 4! in the denominators of some of the fractions. So we talked about them. And then we talked about taking the derivatives of the terms in the series one at a time. And then we were out of time.

“Take what you understand, and see if you can figure out what the derivative of sin(x) is.” I gave him a couple hints and jotted down some things on a piece of paper which I held out to him.

“Oh I don’t need that,” he said. He had already absorbed it all.


When he returned, he held out a sheet of paper where he had written the series expansion for sin(x) and taken the derivative of each of the terms and done some factoring. At the bottom of the page was his result: the derivative of sin(x) is cos(x).

The next time he came back with the derivative of sin(-x). And with very little prompting he was soon calculating the derivatives of sin(kx) and sin(-kx) and cos(x) and cos(-x) and cos(kx). And I was running out of things for us to talk about. After all, I just teach algebra. 


So there we were. And when he asked, “Well… what do you have for me today?” with a smirk on his face, waiting for me to serve up the next calculus lesson, I was prepared. 

We sketched some things on the board. I gave him the assignment of finding the derivative of sin(x) without using the Taylor series expansion that he had become so adept at manipulating. I suggested that he look it up online, figure out all the steps, and then come back and teach it to me.

“Hmmm…” he said, evidently intrigued at the notion that there might be another way.

It didn’t take long. He came back to report the results of his researches. 

And now I really am running out of things to discuss. I don’t have the time. I think I’ll introduce him to hyperbolic trig functions, sinh(x) and cosh(x). Maybe that will win me a week or so.

Silent Sunday

Sun, 31 Mar 2024, 08:56 PM (-06:00) Creative Commons License


Student Work

Fri, 29 Mar 2024, 09:20 AM (-06:00) Creative Commons License

Arly is a good artist. She comes into the room with amazing work. She usually works with a blue pen, drawing cross-hatch sketches of eyes and faces and renditions of people that any of us would frame and put on the wall. She keeps them in a notebook.

“Will you draw me one some day?” 

“Yes, Mister,” she said, smiling that wonderful smile.

That was a long time ago. And then last week she came into the room and said that she had one for me. It wasn’t a sketch. It wasn’t torn from her notebook. It was on fancy paper, painted with acrylic.

Arly's art

As she stood there, I taped it to the growing gallery of student masterpieces beside my desk.

And after the year is over, it will be in a frame on the wall at home.

Take a Break

Fri, 29 Mar 2024, 09:01 AM (-06:00) Creative Commons License

“Mister,” she asked. “Can I go to the bathroom?”

“Sure,” I said. “Sign out. I’ll write you a pass.”

The students were working on a radical expressions worksheet that day. The room was quiet (which means that this wasn’t third period — the bane of my schedule this year). 

When she knocked at the door and came back in, she sat down and continued working along with the others. And then she turned and waved me over.

“Did I do this right?”

“I don’t know,” I said. “Let’s check the answer.” 

We walked over and checked her answer against the answers that I always post on the wall. She got it right.

“Look at you,” I said. “You take a break. You come back in. And you get the problems right.”

She smiled.

“Maybe I should take a bathroom break more often!”

Doubly Old

Thu, 28 Mar 2024, 02:09 PM (-06:00) Creative Commons License

“Mister,” she asked after she finished the test. “Can I use your charger?”

When they ask this, I say to hook their phones to the cable that’s plugged into my laptop. The unspoken implication is that they have to leave their phones on my desk — far from where they sit. After they squirm for a few seconds, I show them my chargers. 

“Take one of these,” I say. “You can plug it into the socket under your desk.”

That is what she did. But then a few minutes later she came back. “Thank you, Mister,” she said, setting my charger on the desk.

“That was fast,” I said. “I thought my charger is slow.”

She smiled slightly and walked back to her desk, where one of her friends reached into their backpack and pulled out a different charger. A faster one.

“I see how it is,” I said, laughing.

Old man. Old charger.

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