Don't have much to say about the relative merits of Kahn Academy specifically, but I think there's a balance to be had here.
If you want to train people to be inventive in finding new ways to apply mathematics, and new mathematics to solve problems, then you need a process which leaves some room for questions, creativity, for open-ended challenges, and for some context around mathematics as a creative process.
The industrial production line approach may be efficient, but perhaps requires a lot of external pressure and discipline on kids to keep it on track, and can result in people who are strongly technically skilled within the relatively narrow boundaries of material they've been drilled on, but utterly lacking in imagination or passion for the subject.
In practise I suppose you need something in the middle. It takes disciplined study to develop the fluency to be creative in maths at a given level, but the discipline is a means to an end not an end in itself, and if it's so strong that people are discouraged by shame from asking the questions they need to ask to develop a deeper than rote understanding of the material, then it's got to be counter-productive.
I say this as someone who was almost put off maths for life by the latter approach, but is now doing a second masters in a mathematical field...
If you want to train people to be inventive in finding new ways to apply mathematics, and new mathematics to solve problems, then you need a process which leaves some room for questions, creativity, for open-ended challenges, and for some context around mathematics as a creative process.
The industrial production line approach may be efficient, but perhaps requires a lot of external pressure and discipline on kids to keep it on track, and can result in people who are strongly technically skilled within the relatively narrow boundaries of material they've been drilled on, but utterly lacking in imagination or passion for the subject.
In practise I suppose you need something in the middle. It takes disciplined study to develop the fluency to be creative in maths at a given level, but the discipline is a means to an end not an end in itself, and if it's so strong that people are discouraged by shame from asking the questions they need to ask to develop a deeper than rote understanding of the material, then it's got to be counter-productive.
I say this as someone who was almost put off maths for life by the latter approach, but is now doing a second masters in a mathematical field...