Perhaps “currency” is a slightly better word than “money”

I’ve not thought of it in these terms before. I usually think of it in improv comedy terms (note: I’ve never done improv, I just know this idea). I try and use the “Yes, and…” principle as much as possible, but especially for the “currency” I want to encourage. We gather mathematical thoughts and then explore the ones that take us where I know we need to go. I still try to validate all of them. All mathematical thinking, especially by students, has some merit. We are just limited by time.

Welcome back to the field. Sorry it’s kind of a mess right now!

Thanks.

The great thing is that even though the content may be important, it doesn’t mean there aren’t multiple ways of meaningfully engaging students and different learning routes students can take to arrive at the same understanding. These approaches to teaching are more progressive but are often was is considered “good teaching” because it is often more engaging and personalized for students.

One question that arises is, what can teachers do to empower students to determine what is considered valuable in the classroom while also maintaining roots in the curriculum?

This is an approach I have been hoping to dabble with more in my own classroom and I would love to hear others’ ideas/opinions.

What I have learned from teaching is that all good teaching is socialist. Valuing everyone’s contribution in the classroom equally is no different from paying Jeff Bezos and an Amazon warehouse worker the same salary.

So how do you convince capitalists to teach this way? When the system is clearly set up to value certain students/ideas more than others with magnet schools, college admissions, even just the existence of grades. Maybe you can convince middle schoolers, but by high school they are pretty jaded and understand the pre-existing hierarchy. A number on a report card means a lot more to them (and especially the adults at home) than a classroom discussion.

This is not to say that it’s not a great idea–clearly it is. But for some reason spreading the money around to everyone equally has not caught on in either our schools or our society.

Mathematics would not exist without the human mind. It is a matter of what a human mind can understand. On the other hand it is taught as problems for tangibly processing what senses provide: more or less the numerical and symbolic processing a computer can do better.
Do young children have a mind for a mental life. I maintain is’s a no-trainer. Can they construct a mental picture of what multiplication does in order to formulate their own problem?
Do they realize that Dan’s animation is the result of a human artifact made by someone just like them, just a little older. It is likely just a short list of instructions to a computer that is executing them over and over, In n a sense nothing is changing,.
The programmer who made it understands the abstraction of a simple language. I could not find out if this Desmos code is open sourced, if it the students can see the result

There are some parallels here but this is mostly a new metaphor I’m playing with.

Students do and should also determine what the class values. That’s a super important point and I’m glad you raised it. By virtue of their status / role / expertise (perceived or real) I think teachers will always have a role to play in assigning competence / status to students.

All great questions! I have actually lost classes more quickly when I have left comments like “drunk shape” unacknowledged rather than when acknowledge them. When I acknowledge them, I can turn them into money (as it were) and then move with the same enthusiasm to another response.