I've thought about this for my work, and formed a definition, as follows. Modeling doesn't have to be about connecting math to the physical world, but it has to connect math to a WORLD. I like the old term "microworld" to define what I mean here. "Cinematic universe" or "franchise" are also decent metaphors.
To be useful for teaching, these modeling worlds need contemporary, active, lively fan communities that students can quickly join. Can we build our own little worlds for one math circle or classroom at a time? Maybe, but that's much harder.
In your panel video from 2019, the collection of human creations about mathematical sequences is a big world with a rich history, many living fans, a thriving wiki, lots of publications, and so on. "How did Han Solo make the Kessel run in 12 parsecs?" is a modeling question, even if "Star Wars" is not a real world in the same way that our Sun is real. Likewise, we can model in the world of sequences, IF we know that human-made world enough.
Not everything we learn about is a world in that sense. By my definition, not all learning is modeling. The video's example with the sequences is modeling, because for that particular audience, sequences are a big and rich world. Maybe even a universe!
Perfectly put. I appreciate the perspective of the Freudenthalians here also—that worlds aren't real or "fake" as a static property but can BECOME real through the work we do within them.
The real world vs fake world commentary got me thinking about this thinking as it relates to the post from Sara Vanderwerf yesterday regarding the definition of math....still pondering.....
Honestly I still don’t get why you have such a problem with AI in education, I am sure you have a good point but you aren’t getting it across to someone who isn’t an educator.
@Osama - I think AI has interesting applications in education, to the point that I have written and applied for a grant in the area of AI-assisted teacher-generated feedback. I don't have a problem with AI in education. But I think education poses an enormous problem to AI, and especially the technologists who don't understand it. I'd love to figure out how to better communicate with non-educators why the promises of systemic transformation will fail. Many of them have massive incentives—mostly financial—not to understand.
I wonder if it is less of an issue with AI in education and more of a case being made for the necessity for high quality human interaction in education (to put it incredibly short and sweet). So often the way we learned and continue to teach is more of a “delivery of information and content”, Sage on the stage, filling their brains. But what education should be (most the time) is thinking and communicating one’s thinking, mistake making and exploration. I’ve always appreciated Meyer’s posts and articles about technology in education and I reccomend.
I've thought about this for my work, and formed a definition, as follows. Modeling doesn't have to be about connecting math to the physical world, but it has to connect math to a WORLD. I like the old term "microworld" to define what I mean here. "Cinematic universe" or "franchise" are also decent metaphors.
To be useful for teaching, these modeling worlds need contemporary, active, lively fan communities that students can quickly join. Can we build our own little worlds for one math circle or classroom at a time? Maybe, but that's much harder.
In your panel video from 2019, the collection of human creations about mathematical sequences is a big world with a rich history, many living fans, a thriving wiki, lots of publications, and so on. "How did Han Solo make the Kessel run in 12 parsecs?" is a modeling question, even if "Star Wars" is not a real world in the same way that our Sun is real. Likewise, we can model in the world of sequences, IF we know that human-made world enough.
Not everything we learn about is a world in that sense. By my definition, not all learning is modeling. The video's example with the sequences is modeling, because for that particular audience, sequences are a big and rich world. Maybe even a universe!
Perfectly put. I appreciate the perspective of the Freudenthalians here also—that worlds aren't real or "fake" as a static property but can BECOME real through the work we do within them.
The real world vs fake world commentary got me thinking about this thinking as it relates to the post from Sara Vanderwerf yesterday regarding the definition of math....still pondering.....
If you want to hear someone who truly speaks from the heart about teaching follow
matteicheldinger on Instagram. He is an English teacher who shares his classroom experiences. It is also why AI will never replace teachers
Honestly I still don’t get why you have such a problem with AI in education, I am sure you have a good point but you aren’t getting it across to someone who isn’t an educator.
@Osama - I think AI has interesting applications in education, to the point that I have written and applied for a grant in the area of AI-assisted teacher-generated feedback. I don't have a problem with AI in education. But I think education poses an enormous problem to AI, and especially the technologists who don't understand it. I'd love to figure out how to better communicate with non-educators why the promises of systemic transformation will fail. Many of them have massive incentives—mostly financial—not to understand.
@Danielle - Thanks!
I wonder if it is less of an issue with AI in education and more of a case being made for the necessity for high quality human interaction in education (to put it incredibly short and sweet). So often the way we learned and continue to teach is more of a “delivery of information and content”, Sage on the stage, filling their brains. But what education should be (most the time) is thinking and communicating one’s thinking, mistake making and exploration. I’ve always appreciated Meyer’s posts and articles about technology in education and I reccomend.