DAY 1

The secret police appear at my door and drag me from my apartment. “What about my desert island discs?” I shout, thinking this will get a laugh. A rag soaked in ether is stuffed in my mouth, and a baton hits me in the back of the head, hard.

DAY 1 (CONT.)

I am forced to get on a stationary bicycle—one in a row of thousands—and pedal to generate electricity for the Loyalist States. The power plant guard does not chuckle or show any recognition when I ask, “Is it a fixed gear, at least?” He just stares for a moment and then hits me in the temple with his baton.

DAY 1 (CONT. CONT.)

At lunch, I try to cheer everyone up with a lighthearted discussion of ways the gruel could be improved.

“Ehremgee! What if it had bacon?!” I joke.

My fellow detainees stare forward into their bowls, not even meeting my eyes.

The second time I say, “Oh my god, how can I make my budget work with all this avocado toast?” the mess hall guard clubs me with his baton.

DAY 4

I have been sent to the fields to help manage the soybean fires. We are given no personal protective equipment. I momentarily pantomime being the dog-drinking-coffee-in-a-fire-meme, popping a squat and shouting, “THIS IS FINE!” None of the others assigned to soybean-fire detail laugh. They all just keep their heads down, stoking the fires.

“Did I meet you in line for Death Cab?” I ask one of the field guards, thinking we can find common ground.

He breaks my nose with his baton.

DAY 5

Recreation day. Some of the other guys are playing basketball.

“What is the score of your sportsball game?” I ask jovially.

No one responds.

“Would anyone like to play Quidditch?” I ask.

One of the other prisoners nods toward a recreation yard guard, who approaches me from behind and hits me with a baton.

DAY 7

I have been unconscious for two days. I awake in my cell, confused. I sit bolt upright and try to catch my roommates’ eye.

“THIS WOULD SOUND BETTER ON VINYL!” I yell.

I hold up my forearms, showing the robins I have tattooed there. “PUT A BIRD ON IT!” I scream. I feel the air moving in front of the baton before the baton itself crunches into my skull.

My brain sinks deep into its fifth concussion of my first week at the labor camp. I feel myself going back, back, backward, into the long-gone world that made me. I see myself in horned-rimmed glasses, a beautiful full beard hanging low over my chest, my favorite decorative pashmina under it. My thrifted IMMACULATA PREP T-shirt is too tight and my belly hangs below the shirt tail, which is stretched and bisecting my naval. I check my Casio calculator watch, noting it’s a half an hour before I need to be at my screen-printing class. I duck into my favorite bar-cum-coffeeshop. My barista of choice, Molly, grins. “My favorite chubby hipster,” she deadpans.

I smile back and order an “Ian Curtis”—a Boddington’s and a shot of espresso.

I bring the espresso to my lips, and just as I do, I am gruffly brought back to my feet and to reality. I feel my face, bare from the compulsory shaving. My neck is cold and pashmina-less. The guard behind me barks:

“We’re sending you to support the liberation of Quebec, you insolent toad!”

“Stop trying to make fetch happen,” I mumble at him.

“What did you say?” the guard screams.

“Jesus is my homeboy,” I say, my voice still low, but filling with defiance.

“NO MORE!” the guard screams, shoving me away.

I turn to face him. Slowly, I bring my hand to my upper lip. The guard stares at me, head cocked, an unspoken dare.

I close all my fingers but the index, and then quickly flip my whole hand ninety degrees, revealing the tiny tattoo of a mustache.

“Finger ’stache,” I manage to say before his baton meets my jaw.

Fifty years ago—almost two decades before WIRED, seven years ahead of PCMag, just a few years after the first email ever passed through the internet and with the World Wide Web still 14 years away—there was BYTE. Now, you can see the tech magazine's entire run at once. Software engineer Hector Dearman recently released a visualizer to take in all of BYTE’s 287 issues as one giant zoomable map.

The physical BYTE magazine published monthly from September 1975 until July 1998, for $10 a month. Personal computer kits were a nascent market, with the first microcomputers having just launched a few years prior. BYTE was founded on the idea that the budding microcomputing community would be well-served by a publication that could help them through it. 

“You need the hardware before you can progress through the first gate of a system. A virgin computer is useless so you add some software to fill it out. And the whole point of the exercise—in many but not all cases—is to come up with some interesting and exotic applications,” editor Carl Helmers wrote in the first issue’s introduction. “The technical content of BYTE is roughly divided into the trilogy of hardware, software and applications. Each component of the trilogy is like a facet of a brilliant gem—the home brew computer applied to personal uses.” 

Dearman told me his first attempt at the site was in September of last year, but this version launched in August 2025. “Once I had a workable strategy it took a couple of weekends to put it all together,” he said. 

Dearman told me he first became interested in BYTE after his dad Chris, also a software engineer, died in early 2022. Right out of university, Chris Dearman worked at a London computer company called Whitechapel Computer Works.

“There was very little on the internet about the computers he worked on (now mostly famous for being named after a computer in The Hitchhiker's Guide to the Galaxy),” Hector Dearman said. He came across an article titled “Realizing a Dream” by Dick Pountain in the February 1985 issue of BYTE in the Internet Archive’s scans that covered the Whitechapel Computer Works MG-I, named after the fictional computer called the “Milliard Gargantubrain” in Hitchhiker’s Guide. 

“The article was amazing but I was captivated by the adverts,” Dearman said. “I kept coming back to them and the more I did the more I realized what an incredible core sample BYTE was—both of the personal computing revolution and of the changes in graphic design and printing over those decades. That compulsion eventually turned into this project.” 

Dearman said he was inspired by the Image Quilts tool that makes collages of images, and Jef Raskin’s “zoomable user interfaces.” To create the BYTE visualizer, Dearman sourced scans from the Vintage Apple archive (the Internet Archive also has a massive searchable repository of BYTE magazine issues) and converted the archive’s PDFs to image tiles. He then put the image tiles into Seadragon—around 500,000 tiles at 1024x1024 pixels each. “I wrote some custom software for this. I tried locally on my computer for a while but ran out of patience pretty quickly. Luckily it's a very parallel problem, I ended up with something that could do every tile for a given layer of the Seadragon image pyramid in parallel,” Dearman told me. “According to my Google Cloud bill I used around 500 hours of CPU time that month. For the final run I think I used 200 instances for ~20 minutes to generate the tiles—the future is pretty cool sometimes.” 

On the BYTE visualizer site’s about page, Dearman quotes pioneering computer scientist Alan Kay: "[...] pop culture holds a disdain for history. Pop culture is all about identity and feeling like you’re participating. It has nothing to do with cooperation, the past or the future—it’s living in the present. I think the same is true of most people who write code for money. They have no idea where [their culture came from]—and the Internet was done so well that most people think of it as a natural resource like the Pacific Ocean, rather than something that was man-made.” 

Looking at the massive map of BYTE issues means looking at almost 23 years of computer history, at a time when the technology was exploding from hobby to household essential. When BYTE launched in 1975, it catered to a niche group of hackers, engineers, and people trying to tinker with expensive, chunky kits. By its final issue in 1998, it was publishing a Y2K survival guide and reviews of the hot new operating system Windows 98, and running ads for the world’s first 19 inch CRT computer monitor alongside an editorial about LCD monitors asking “Does Your Future Look Flat?”

“The relationship between Computing and its history is that of a willful amnesiac,” Dearman writes on the site. “We discard the past as fast as possible, convinced it cannot possibly contain anything of value. This is a mistake. The classic homilies are accurate: Failing to remember the past we are condemned to repeat it—as often as tragedy as farce.” 

Jennifer Justus honors the unsung heroes of the school cafeteria—the women who fight to feed America’s children. Using the author’s grandmother’s 50 years of service as a backdrop, Justus explores the growing bureaucratic and funding challenges creeping into the kitchen.

She worked her way to manager at the cafeteria, retiring in the early 1980s. Over the course of her tenure, her education level sometimes couldn’t keep up with her natural-born smarts, so she’d ask for my aunt’s help on the weekends to work out the financial parts of her menus. She became known for her vegetable soups, yeast rolls, and peanut butter cookies.

Mom remembers Granny’s frustration as, over time, guidelines and budgets added complicated layers to the work and hampered the scratch cooking she preferred. The government cheese went into big batches of creamy macaroni served alongside crisp, fried fish and scoops of turnip greens. She’d sneak in bacon grease from home to flavor green beans. Sadly, her own savory cornbread eventually gave way to a quicker and sweeter mix at school. My cousin Margaret remembers a student asking her: “Mrs. Culpepper, is this cornbread — or just bad cake?”

Recently, I gave my STEP students the following discussion question.

Puzzle. A long time ago, before anyone had ever heard of ultrasound, there was a psychic who could predict the gender of a future child. No one ever filed a complaint against her. Why?

I based this puzzle on a story I once read. In the story, the psychic kept a neat little journal where she wrote down each client’s name and the predicted gender — except she secretly wrote down the opposite of what she told them. When someone came back complaining that she was wrong, she would calmly open her journal and say, “Oh, you must have misheard”.

This scam demonstrates conditional probability. The satisfied customers never came back; only the unhappy ones did — and those she could ‘prove’ wrong. Understanding probability can help my students detect and expose scams.

My students, of course, had their own theories. The most mathematical one was a pay-on-delivery scheme: if the psychic was right, she got paid; if not, she didn’t. Another innocent idea was for the psychic to keep moving. By the time the babies were born, she’d be long gone predicting future children’s genders somewhere far away.

ChatGPT offered a different explanation: the psychic never said whose future child she was predicting. If the prediction failed, she could always clarify that she meant someone else’s child. After some prodding, the idea evolved and became even sneakier: If the prediction failed, she could always clarify that she meant the couple’s next child, or, if they weren’t planning more children, a grandchild. Another brilliant, but unrealistic idea was to never charge anyone. Hard to sue someone who never took your money.

One student suggested that the psychic wasn’t wrong at all — she was predicting the baby’s true inner gender. In today’s world, rather than in the world before ultrasound, that one almost sounds plausible!

And finally, I’ll leave you to guess one more explanation — proposed, surprisingly, by several students. (Hint: they were disturbingly creative.)

To conclude: I enjoy teaching my students. Understanding probability won’t let them predict the future, but it might make them less gullible.

Here’s a question that is often hard for students.

This is pulled from a set of sample standardized test questions for 7th graders. It’s the kind of question standardized tests love to ask: it combines multiple skills in a word problem. The individual skills aren’t particularly hard, but students typically struggle to put the pieces together. I also think this is a good question. It’s useful in the world, and reflects real skills we want students to have.

In the past, I might have made this question a lesson objective. We would practice multi-step problems with a unit rate and a percent increase. The lesson would be a bit of a slog. Some students would get it right away, some would struggle. And, inevitably, most would forget.

How can I teach students to solve problems like this one in a way that is more likely to stick? Better yet, how can I teach students to apply what they know in a variety of situations, without having to model every single possible variation?

The answer is three steps: preparation, expansion, and discrimination. Here goes.

Preparation

Before helping students with this specific skill, I need to break it into pieces and make sure students are comfortable with each piece. There are three major pieces here (each of which could be broken down further, but let’s keep it simple at three). First, students need to be able to find a unit rate. Second, students need to be able to find a percentage of a number. And third, students need to know how to find a percent increase. Each of those is a skill we practice in 7th grade. My first goal is to practice those skills individually — they’re part of my curriculum anyway, so no problem there. I don’t move on to the next two steps until students have decent fluency with each of those constituent skills. One important note about fluency is that it takes time. I can’t do a quick reteach of percentages at the start of the lesson and expect students to have the fluency they need for multi-step problems. That learning needs to happen with time to practice, consolidate, and build fluency before it’s needed for more challenging work.

Expansion

My next goal is to work gradually from what students know to the problem I want students to be able to solve. This is the expansion sequence: expanding what students know how to do, from the constituent skills in the preparation stage to the more challenging problems I want students to know how to solve. Here is a sample sequence of problems:

1. Jenny earns $40 for 2 hours of work. How much does Jenny make per hour?

2. Jenny earns $40 for 2 hours of work. What are Jenny’s hourly earnings?

3. Jenny earns $240 for 8 hours of work. What are Jenny’s hourly earnings?

4. Jenny earns $240 for 10 hours of work. What are Jenny’s hourly earnings?

5. What is 15% of 20?

6. What is 18% of 20?

7. Jenny earns $24 per hour. She receives a 15% pay increase. What are Jenny’s new hourly earnings?

8. Jenny earns $24 per hour. She receives a 12% pay increase. What are Jenny’s new hourly earnings?

9. Jenny earns $20 per hour. She receives a 12% pay increase. What are Jenny’s new hourly earnings, after the increase?

10. Jenny earns $160 for 8 hours of work. She receives a 12% pay increase. What are Jenny’s new hourly earnings, after the increase?

11. Jenny earns $140 for 8 hours of work. She receives a 12% pay increase. What are Jenny’s new hourly earnings?

The goal here is to remind students of what they know, and create really clear connections from one problem to the next. This approach takes a challenging problem, shows students that it actually isn’t that challenging if we break it down into pieces, and models how to do that.

When I do this well, students retain the learning much better than just teaching this as a standalone objective. The goal is to make really clear connections between what students know and what I want students to learn. When those connections are strong, students are much more likely to remember what they’ve learned and apply it in different situations in the future.

Preparation is key. The first few questions should feel familiar to students and build some confidence. If they don’t, we need to go back and do some more work. That’s the bedrock we’re building on. If I want students to remember how to solve a problem like this, the prior knowledge we’re building on needs to be secure.

Expansion sequences don’t always work. Sometimes it’s just too many steps for students to follow. Maybe we get to problem 7 and most students start to struggle. Great, that’s fine. Let’s stop there. Tomorrow, I’ll create a new sequence, starting a bit before where students got stuck, and we’ll see if we can get further.

For me, the biggest challenge in getting students to think about complex problems is that they take one look, don’t know how to solve it right away, and give up. The best antidote to this lack of perseverance is to build confidence with a bunch of questions students know how to solve. If students are getting discouraged working through the beginning of the expansion sequence rather than becoming more confident, I’m doing something wrong. Maybe we need more preparation. Maybe the expansion sequence needs to happen in smaller, more manageable steps.

Discrimination

Expansion sequences are great, but students also won’t have that type of scaffolding every time they’re asked a question like this. Expansion focuses on making connections between problems. Discrimination is where students practice telling the difference between problems. My goal in a discrimination sequence is to give students a few problems that look similar on the surface, but ask students to use different concepts. Here’s an example:

1. Jimmy earns $140 for 8 hours of work. He saves 12% of the money. How much does he save?

2. Jimmy earns $140 for 8 hours of work on Monday. On Tuesday he works for 12 hours at the same rate. How much does he make on Tuesday?

3. Jimmy earns $140 for 8 hours of work. He receives a 12% pay increase. What are Jimmy’s hourly earnings?

4. Jimmy earns $140 for 12 hours of work. He receives an 8% pay decrease. What are Jimmy’s hourly earnings?

Discrimination sequences are hard. Not all students will be successful every time. The goal is to spend our time thinking and talking about how to solve each problem, and focusing on what makes these similar problems different from one another.

If students are struggling with a discrimination sequence, I have a few possible solutions. One is to do more preparation. Maybe students need more confidence and fluency with the constituent skills. A second is to do more expansion. Maybe students need more clear connections from what they already know to these more challenging problems. And a third is more practice with discrimination. Maybe students need more practice telling the difference between different types of problems. It’s not always easy to tell which one students need, but at least I have three solid options to work with.

Expansion Everywhere

Expansion sequences are becoming one of my favorite tools. When I think about some of the tough questions, common on state standardized tests, that I want my students to be able to solve, an expansion sequence has become my go-to. But I also use them for pretty mundane, everyday skills. In everything I teach, I’m always looking for ways to start with something students confidently know, and build in small steps to something a little tougher. It’s how math works: we are always building on what students know to learn something new. This also gives me constant data about what students know, and what is too hard.

Like many teachers I’m under some pressure to improve standardized test scores. There’s a version of test prep that I think doesn’t work very well. The teacher takes a bunch of tough questions like the one at the top of this post. Then, they tell students they need to practice test questions, give students a bunch of those questions, and then go over the questions that seem hardest. In general, this results in a lot of students saying “idk” and feeling dumb. The goal of expansion is to practice hard questions in a way that shows students how those questions are connected to what they already know, and to give students more confidence approaching tough problems.

Expansion doesn’t always magically work. I wrote in my post last week about how I was having trouble helping my students extend their knowledge of one-step multiplication equations with whole numbers to fractions. We ended up going back and doing some more practice with fraction division, and then we’ll try again. And that’s one benefit of this system. If I have a tough skill students are struggling with or aren’t retaining, I have a few good tools to try: preparation, expansion, and discrimination. In this case they needed more preparation. In other cases it’s something else.

Repetition is an important part of an expansion sequence. Let’s say there’s a ladder of skills, ABCDE. It’s tempting to have students do ABCDE all in a row. That usually doesn’t work very well. It tries to take students too far too fast. Instead, I start with ABC. If that doesn’t go well, we’ll do ABC again, or maybe mix in some extra practice with A to build some confidence and a solid foundation. Then we’ll do BCD, or maybe ABCD to really build confidence. Then CDE, or BCDE, or ABCDE.

In expansion, each skill starts as a stretch, something tenuous that’s building on the limits of what students know. Then it becomes more natural and students gain confidence. Then it’s just another thing students are confident and fluent in, and we’re building for the next thing.