For the record I cannot taste all the underlying flavors of the wine. When someone tells me it’s plum or oaky – I have no clue because I cannot taste it because I have a poor sense of smell. The only time I understood was when the sommelier said a white wine tasted like wet rocks. It did – although I have no memory of every tasting wet rocks. But I am successful at choosing wines that are considered good – holistically. “I knows it when I tastes it.”
This is – my shape is drunk. We all start life thinking mathematically but school jumps much to quickly to the formal refined level when we can tell the oaky from the plum but kill the holistic by doing so. We are taught not use our holistic/intuitive processing. We need both in life and math. When a mathematician works on a new theorm they make an intuitive leap (conjecture) and then refine it to prove it. If we want students to move towards proof they must first learn to conjecture – make leaps. We need to keep math “sexy”.

Have you written about this “What’s money?” idea before? If so, I’ve missed it. If not, perhaps you could flesh that idea out further, possibly with other examples of what you mean.

Can we perhaps discuss how our classrooms might change (for the better or worse or simply for variety) if someone else – e.g., the students – determined what money is in that classroom? How do we imagine that would go?

I don’t teach. I am trying to figure out why mathematics, as taught, results in so much alienation and failure. I have experienced both, so there is a possibility I can approach the problem humanly. To keep this short, let pretend to be a wise one.

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

The concept of teachers deciding what is “money” in their classroom is a traditional approach to teaching based on the traditional structure of the curriculum that guides educators which tells educators what is “money” which in the past has largely been based on specific subject matter content.

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.