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I concur. While I appreciate that math education at the elementary and high school level is easier to author and has more data points, where I think this appro

I concur. While I appreciate that math education at the elementary and high school level is easier to author and has more data points, where I think this approach would really shine is at the college level. 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?

solipsism 8y ago
IMO most college level math isn't difficult 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?
- galaxyLogic 8y ago
  It's not either or. It's difficult to understand concepts (well) and it is also difficult to EXPLAIN concepts (well). 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.
  - galaxyLogic 8y ago
    A thought: Most people who learn to play piano do so by having a piano-teacher whom they privately meet with once a week or so. Whereas this is not the convention for learning math. Maybe it could apply equally well for math as it does for learning to play piano.
    - jacobolus 8y ago
      Note that hiring a private piano teacher for every child in the country would also be a difficult proposition, politically / economically. Especially if we expected every person to reach the level of competence at music that we expect with numeracy/mathematics. 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.
      - galaxyLogic 8y ago
        Right. It is impractical and probably wasteful for everybody to have their own private (human) tutor. But therefore I find the prospect of AI-based personal tutors intriguing. The concept of Artificial Intelligence making humans more intelligent in general. Even AI teaching itself.
- Natanael_L 8y ago
  For most people I'm certain the problem is to translate it into logic expressions they understand naturally. 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.
deanalevitt 8y ago
So true. I recently began taking college math courses online for fun and the ALEKS system was great up to Pre-calc, but once I hit calculus, and only found video lecture-based courses, things became frustrating, half-clear and confusing. Suddenly textbooks and multiple other sources became necessary to combat what you so cleverly called "math anxiety."
feanaro 8y ago
> writing proofs In this vein, there is the Incredible Proof Machine‡, an interactive visual proof assistant designed for introducing beginners to mathematical proofs. ‡ http://incredible.nomeata.de/ http://incredible.nomeata.de/

solipsism 8y ago

IMO most college level math isn't difficult 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?

galaxyLogic 8y ago
It's not either or. It's difficult to understand concepts (well) and it is also difficult to EXPLAIN concepts (well). 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.
- galaxyLogic 8y ago
  A thought: Most people who learn to play piano do so by having a piano-teacher whom they privately meet with once a week or so. Whereas this is not the convention for learning math. Maybe it could apply equally well for math as it does for learning to play piano.
  - jacobolus 8y ago
    Note that hiring a private piano teacher for every child in the country would also be a difficult proposition, politically / economically. Especially if we expected every person to reach the level of competence at music that we expect with numeracy/mathematics. 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.
    - galaxyLogic 8y ago
      Right. It is impractical and probably wasteful for everybody to have their own private (human) tutor. But therefore I find the prospect of AI-based personal tutors intriguing. The concept of Artificial Intelligence making humans more intelligent in general. Even AI teaching itself.
Natanael_L 8y ago
For most people I'm certain the problem is to translate it into logic expressions they understand naturally. 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.

deanalevitt 8y ago

So true. I recently began taking college math courses online for fun and the ALEKS system was great up to Pre-calc, but once I hit calculus, and only found video lecture-based courses, things became frustrating, half-clear and confusing. Suddenly textbooks and multiple other sources became necessary to combat what you so cleverly called "math anxiety."

feanaro 8y ago

> writing proofs In this vein, there is the Incredible Proof Machine‡, an interactive visual proof assistant designed for introducing beginners to mathematical proofs. ‡ http://incredible.nomeata.de/ http://incredible.nomeata.de/