I taught math (and other classes) from the 9th grade to College for 18 years.
At the 9th grade level, in 1978, I used an Apple computer to raise the math ability of some kids who were placed in the "Educable" track, meaning they were "dumb". The program I wrote gave them 75 math problems a session, beginning with addition and subtraction through a 12X12 multiplication and division grid. Only they and I knew how well they were doing. By the time the semester was over those kids were computing amortization tables on 5 year car loans and 30 year house loans, something the Pre-calc class couldn't do.
Now, kids have the Kahn Academy. Even better is the software Kahn has developed for teachers to use to manage the education the kids can obtain from his site.
http://www.youtube.com/v/hw5k98GV7po&rel=0&hl=en_US
I really like the way the Kahn videos "flip" the teaching paradigm to one where the kid watches the videos (over and over if necessary) and then does the practice problems given on the site. The teach tutors the kid to help him overcome the hard spots. No time is wasted trying to keep the kids lock-stepped at the same level by listening to the same teach lecture and doing the same problems at the same pace.
With this kind of instructional power I see no reason why the average kid couldn't master calculus and DiffEq by the end of their 9th grade, and certainly by the end of their senior year.
At the 9th grade level, in 1978, I used an Apple computer to raise the math ability of some kids who were placed in the "Educable" track, meaning they were "dumb". The program I wrote gave them 75 math problems a session, beginning with addition and subtraction through a 12X12 multiplication and division grid. Only they and I knew how well they were doing. By the time the semester was over those kids were computing amortization tables on 5 year car loans and 30 year house loans, something the Pre-calc class couldn't do.
Now, kids have the Kahn Academy. Even better is the software Kahn has developed for teachers to use to manage the education the kids can obtain from his site.
http://www.youtube.com/v/hw5k98GV7po&rel=0&hl=en_US
I really like the way the Kahn videos "flip" the teaching paradigm to one where the kid watches the videos (over and over if necessary) and then does the practice problems given on the site. The teach tutors the kid to help him overcome the hard spots. No time is wasted trying to keep the kids lock-stepped at the same level by listening to the same teach lecture and doing the same problems at the same pace.
With this kind of instructional power I see no reason why the average kid couldn't master calculus and DiffEq by the end of their 9th grade, and certainly by the end of their senior year.
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