[ExI] google classroom, was: RE: Meta question
spike
spike66 at att.net
Sun Aug 21 05:41:53 UTC 2016
>... On Behalf Of Anders
Subject: Re: [ExI] google classroom, was: RE: Meta question
On 2016-08-20 15:00, spike wrote:
> ...School is often a hindrance for education...
> --Dr Anders Sandberg
>
>>... The best part of this curriculum is that it appears to be completely
open-ended...
>...Now that is promising!
Ja! Read on please.
>>... It will be fun to watch what this cohort will achieve.
>...Yup. Cognitive enhancement doesn't have to be biomedical.-- Dr Anders
Sandberg
Thanks for that, sir!
Anders and BillW, there is a reason why I suggested that thought experiment
where I proposed estimating the number of hours a typical or high end
student would invest in studying math by the traditional means. Here are my
estimates:
A student typically is in math instruction about half an hour to perhaps 3/4
of an hour a day on the average in traditional school. We have 180 school
days a year, so close enough to 100 to 130 hours of instruction per year,
but if a student reaches for the high end of the achievement spectrum, to
finish a year of calculus by high school, requires doubling up with two math
classes, and it requires significant amounts time invested in homework.
(Did anyone here finish calculus without doing a pile of homework? Didn't
think so.)
By that line of reasoning, the time investment would likely go well above
the estimated 1200 to 1500 hours for that level of mastery. Once I take the
doubling up and the homework into account I would be hard pressed to get any
estimate less than about 2000 hours of study devoted to math-related
disciplines to complete a year of calculus.
Does 2000 hours seem like a reasonable estimate for about an 90th percentile
student reaching for completing a year of the queen of mathematics? I will
buy it, and would be more comfortable guessing higher than 2k rather than
estimating lower. Anders?
A discrete skill as defined by Sal Khan is one which can be explained in ten
minutes or less and mastered in less than an hour of practice and
assessment. Four examples of a skill might be Cramer's rule, evaluating
determinants, partial fraction decomposition, equation of a line given a
point and a slope. In Khan Academy, to get from start to end of
differential calculus requires mastery of a number of skills. That number
is... 1040.
I measured the time required to master discrete skills with my own student
and came away with an answer of about 40 minutes. So... this is a case
where a first grader started the program and mastered the 1040 skills in
about 700 hours.
So here is the insight on why I am grinding away on this and really driving
hard with this question. Compare a curriculum is designed by one person
from start to finish to a curriculum designed by a committee of individual
egos who do not talk to each other, a committee with no cohesive overall
vision or structure, a committee whose goal is to sell copies of their own
books. The single-designer curriculum will be more efficient than the
design-by-fractured-committee curriculum by about a factor of 3. This could
enable a student to master a level of proficiency in about four years rather
than the more traditional twelve years.
I can show you an example of student who has done in four what most students
do in twelve.
Anders, your thoughts please? BillW, your thoughts please?
In the next episode... the impact of high efficiency instruction allowing
students to master the higher levels of study earlier in life.
spike
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