I run a microschool where I teach math (and I am a neuroscientist) and this is pretty obvious, and also something we see every day. And it's because we still suck at understanding learning.
Learning is not the acquisition of knowledge. Learning is all the things by which we learn to model the world. And we do that, our brains do that, because it matters.
Math in classrooms is pretty much designed to leach out all context. Meaningless symbols that need to be manipulated to arrive at some mysterious answers. Why bother, our minds scream out. The why is evident in street settings. Also, we are designed to pick up patterns in such meaningful settings and learn. You don't even need to teach it.
Fixing learning and education means being able to articulate answers to five questions: why, what, how, when, where we learn. And all our current answers are outdated and one-size-fits-all
There is also the matter of learning design. Math we use is highly compact because of its efficiency. But these can be hostile starting out. There are ways to explore mathematical concepts without using mathematical symbols.
Resonant learning requires the interplay of building competence (how) and comprehension (why) and this can be done well only in meaningful settings (where)
Also, the most profound revelation I've had about learning is from working on our book. Journey of the Mind. Spent twenty years at the intersection of neuroscience and AI but never really got to "understand" and "learn" how the mind works and learns until diving in and then trying to tell its story in an accessible manner. If you are interested in any of this lease do check it out
>>> Meaningless symbols that need to be manipulated to arrive at some mysterious answers.
I get what you're saying, and agree but with a caveat: Please don't take this away completely. There's always going to be a few of us freaks who came to math because of this feature: Math as an exercise in pure abstraction. We have no other refuge. As I've mentioned in this thread and others, proofs were what made math come alive for me. And I didn't struggle with applied math at all.
Agree! And that's because there are some who just get this and are able to explore this in the space of ideas the same way we all have very different tastes in music and literature. Math has both practicality and poetry and many problems are introduced when the focus is one on. What one responds to is personal.
Abstraction can be learned with purpose, eg if they want to program physical movement in a game, X and y need to be variables, not because we are just using abstraction for the fun of it. Even proofs can have meaning and purpose if you can show how they are useful. Algebra, calculus, liberal algebra at least, all make more sense (and easier to accept by new learners) when you actually use them to do something.
Comedian Bengt Washburn describes his school-learning experiences of high-school geometry: "Hours of study. Straight 'A's. And now we are a comedian who can calculate the volume of a cylinder. Height times Pi R squared. You think that comes in handy?"
Learning is not the acquisition of knowledge. Learning is all the things by which we learn to model the world. And we do that, our brains do that, because it matters.
Math in classrooms is pretty much designed to leach out all context. Meaningless symbols that need to be manipulated to arrive at some mysterious answers. Why bother, our minds scream out. The why is evident in street settings. Also, we are designed to pick up patterns in such meaningful settings and learn. You don't even need to teach it.
Fixing learning and education means being able to articulate answers to five questions: why, what, how, when, where we learn. And all our current answers are outdated and one-size-fits-all
There is also the matter of learning design. Math we use is highly compact because of its efficiency. But these can be hostile starting out. There are ways to explore mathematical concepts without using mathematical symbols.
Resonant learning requires the interplay of building competence (how) and comprehension (why) and this can be done well only in meaningful settings (where)
https://blog.comini.in/p/why-khanmigo-will-fail
https://blog.comini.in/p/what-happens-in-math-class
Also, the most profound revelation I've had about learning is from working on our book. Journey of the Mind. Spent twenty years at the intersection of neuroscience and AI but never really got to "understand" and "learn" how the mind works and learns until diving in and then trying to tell its story in an accessible manner. If you are interested in any of this lease do check it out