> A textbook that is able to diagnose common misunderstandings from a set of wrong answers to a problem set and evolve its teaching methods.
That'd be extremely useful to have.
That'd be extremely useful to have.
The main problem in math is that the higher level you reach, the fewer experts who exist or are willing to sit down 1:1 and tutor students.
I think an automated teaching system for analysis, writing proofs, number theory, etc is the next step in democratizing mathematics and science and bringing what is now college-level education down to high school.
IMO most college level math isn't difficult, but not missing a step in your understanding along the way to that level and the 'math anxiety' that's introduced along the way is the real hurdle to teaching. It creates a situation where autodidacts are most rewarded, so why don't we use technology to enable more people to become autodidacts?
Don't make the mistake of assuming the entire world is like you. Plenty of people struggle with lower level math. What makes you think the concepts are not difficult for them, and to blame only the teaching?
The better the explanation the easier it is to understand for more people. Whereas a bad explanation is something that assumes students understand something most of them don't.
It's really not a blame-game but more an impedance mismatch between the teacher and the students. IF you can have your own tutor the tutor can adjust their level of explanation just to you, but that is not economically feasible for most students. Therefore if automated AI-learning text-books can make progress in this direction it is great.
It may be that the biggest impact of AI will be not by having something smarter than us, but something that can teach more people to understand difficult concepts. In other words biggest impact of AI may be in education.
If we wanted to switch from the current classroom model to a private tutorial model, with the amount we currently spend per student on teachers, we could hire 1:1 tutors for only a few hours per week for each student, which would (a) not really be enough time to cover everything students are expected to learn in school, and (b) would then also leave huge amounts of time where the school wasn’t providing childcare service, which is one of its primary purposes.
However, just as upper middle class families can currently afford weekly private piano lessons or 1:1 sport coaching, you are right that they could likewise afford private math tutorials, and get better results than classroom instruction.
It's the same as how most people fail to correctly apply basic logic when presented with arbitary problems and immediately succeed when presented with a human context of person A did X.
All these low level problems needs ways to help people to generalize their existing intuition.
Suddenly textbooks and multiple other sources became necessary to combat what you so cleverly called "math anxiety."
In this vein, there is the Incredible Proof Machine‡, an interactive visual proof assistant designed for introducing beginners to mathematical proofs.