Classes should be totally optional. Most kids would rather do something else, and motivated kids should be encouraged to explore on their own through play/book/videos.https://www.youtube.com/watch?v=xyowJZxrtbg …
As well as being a good way to explain what you were learning, it would also be a good way to motivate it, and that tends to be even more lacking.
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Voluntary, play-based, democratic-free "Sudbury Schools" have been around for 50 yrs (started by a Columbia physics prof). In surveys, former students are highly satisfied with their education and have high rates of entrepreneurship.
@numbalum89https://www.youtube.com/watch?v=awOAmTaZ4XI …
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Took "history of math" In addition to that mentioned, knowing past methods gives character and excitement to the new methods. Permission to add a length and an area as quantities is cooler when you get why it was a paradigm shifting discovery (Descartes)
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Aren't the start-ups in the education space leaning towards stripping all context in the course material, in order to condense it, and make it suitable for securing a career as against learning for its own sake. To be sure, I'm not necessarily against this.
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So, in the long run, can start-ups truly replace mainstream universities bearing in mind that, one of them is focused on learning while the other on careers. They each have different functions and they exist for different reasons.
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David Pengelley did this exceptionally well. He taught one number theory course entirely around Sophie Germain's letters https://web.nmsu.edu/~davidp/hpm-subm-2012-number-theory-course.pdf …
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One of the reasons I'm excited about starting this book: https://www.amazon.com/Infinite-Powers-Calculus-Reveals-Universe/dp/1328879984 …
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Because at the core, mathematics meets religion. If you learn about its history, you'll learn about its mysteries. Some math people have bad taste for religion. They don't want to talk about it. So they make math a robotic exercise.
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