"Thank you."

Crystal Miller receives a phone. This one does have signal. It's made of some kind of ultra-light plastic, and a few seconds of tapping starts activating the projector, letting her get a big screen view of everything happening the wall opposite the door into the dorm. Thomassia has sappy, slightly cliche romance movies; these are about a couple first meeting and growing ever more intensely in love, before returning to the place they first met and reminiscing on everything that happened.

By the time she's done with the quarantine, the thomassians, adults and children both, are excited and curious to learn from this mysterious human who teleported to their school. The kids were excited to have their first class with her, with her wearing a lightweight and transparent face-mask made from a transparent film that left a faint bluish sheen over her nose and mouth.

Crystal is very glad she has not gotten terribly sick and somewhat worried that might change. The first big thing she wants before teaching a class is to watch one. Ideally without distracting the kids too much.

She also turns her mind to what she should teach. The basics are probably out, math science and vocabulary are all things where it's pretty likely their teachers are pretty out of sync and pre-requisite knowledge is usually pretty important. Well, maybe not necessarily. She could split them into groups and try to have them work on a puzzle of some kind. It's just hard to gauge difficulty level there. Literature could also work she has some short stories on her original phone and maybe reading and discussing one together could be good. The last option is history... history has always been a hard subject to teach finding the balance between being honest about the many mistakes of the past without making it sound like everyone in the past was just an awful person is hard. She usually ends up erring on the side of making things sound better than they were.

She explains all of this to the local teachers and asks for their thoughts.

Clarissa nods at Crystal's suggestion to watch a class before teaching one herself. She finds a recording of a class and projects it onto the wall of Crystal's room, showing another teacher in the middle of a science class. It's a class explaining energy and how it can come in many forms: energy in a battery, moving a car forward, in an exploding a stick of dynamite, and spinning turbines in nuclear reactors.

The teacher in the recording repeatedly underlines how the phenomena are connected, and fundamentally commensurable, by explaining how each of these examples of some amount of energy, can be measured by comparing it to another example. How an EV battery has as much energy as you spend on 400 miles of driving, how many miles of driving needs as much energy as is found in one stick of dynamite, how many sticks of dynamite are needed to release as much energy as a nuclear power plant makes in a day, and how a nuclear power running for a day can fully charge all these EV batteries.

The heart of the idea is seeing connections, unity, and context: seeing how energy can come in many different forms, and be measured in many different ways, but ultimately only be one concept.

Alright, have the kids in question been taught about the scientific method and about how to test out ideas?

The kids have in fact gone beyond that. They not only learn about the scientific method, but they even learn about the design of experiments and how information theory and multi-armed bandits can be used during assignment in adaptive trials, so you don't need as much time or resources to perform the experiment and learn whatever you wanted to learn!

Oh... she hasn't ever heard of multi-armed bantits. So Petals Around the Rose would be too basic for a lesson then? Where are they with math do they know algebra and exponents?

They know both algebra and exponents (and also logarithms), extremely well! The Heaviside school is mostly an opportunity for kids who aren't too strong academically to enjoy nature; it has a kind of poor academic reputation.

Petals Around the Rose seems like a really fascinating thing to have a lesson about. It'd be cool to show off how inductive reasoning and exploring hypotheses really is universal; it can even work for something that nobody has seen before.

Oh good, she can definitely do that.

Clarissa prepares a classroom for Crystal; there are 25 kids, with a statistics/probability book on their desks. They have their phones out, ready to take notes on what Crystal's saying. Clarissa has brought her phone and placed it on a stand, filming the dice tray from above. The dice are black, with gold pips; they're the ones Clarissa uses for her tabletop games.

"Everyone, this is Crystal! She comes from a different dimension. She wants to teach us by using an inductive reasoning and inference puzzle that's popular in her home dimension. It's going to be so cool to see how induction really is universal, even letting you understand total aliens! Now, Crystal, roll some dice. And see how induction and hypotheses work to help us understand absolutely everything!"

Crystal obligingly rolls six dice there's a 1, 3, 5, 6 another 1 and a 4. 

"The name of the puzzle is 'Petals Around The Rose' whenever I roll the dice I can give you a number which matches to that dice roll. In this case the number is 6.

"Does anyone have any questions before I roll again?"

The students quietly tap their phones a few times, but don't ask any questions. They focus intently on what Crystal's doing. After a few seconds, one of them speaks up.

"I think it's quite obvious that one dice roll isn't enough? You know, underdetermination of hypothesis by data? So I think we should just do the next roll already."

"Not every question needs to be a guess of what the rule is." She still rolls again. This time the dice come out in two neatish rows: 1, 3, 4 and 5, 3, 6. "Eight this time."

The students keep their eyes on Crystal. A few of them nod; they smile, thinking that they had just gotten quite lucky.

When she rolls the dice next time one of them lands where the camera can't see. She picks this one up but doesn't put it back down the other dice are 5, 5, 3, 6, 3. "Twelve."

One of the kids looks up at Crystal, with a face indicating that he's had a revelation. "I actually have a pretty good idea, already. Can you roll another 6 dice, but not tell us the number? It really helps when sifting through hypotheses, to kind of have a question in front of us."

"Of course. If you have a guess first you can tell me the number you think it is. If you get three in a row then you can send me a message with your guess. That way everyone has a chance to figure it out themselves." This time the dice form an arc: 5, 5, 1, 5, 1, 3.

The same student who asked for one more roll then closes his eye. "Everyone, I have an answer! No peeking!" Eventually, all the students close their eyes, and the excited student holds up two hands. He lifts one finger on one of them, and 4 fingers on the other. Clarissa nods quietly. "Yup, I think you'd know if your answer was correct. I'm sending you feedback now." Then the class opens their eyes again, looking stunned at the student who said he had an answer.

Crystal is also impressed. "Okay, does anyone else want to make a guess before I roll again?"

All the other students seem too unsure to be willing to take a guess. "Please roll again. I'm hoping that getting a super-low number could make a huge difference."

The next roll is 5, 3, 3, 2, 5, 1.

"Well, uhh. Could you also say the number? Just for the newest roll, not the last one."

"This one is twelve."

Almost the entire class raises their hands at basically the same time.

She calls on someone in roughly the middle of the room.