[IAEP] reconstructed maths

[Albert Cahalan]

Alan Kay writes:

> Suppose we take as a premise that the following results of surveys over the
> last 20 years were gathered well enough to form a real generalization:
>
> - only 20% of American adults can read a well written important ideas essay
>   (they used Tom Paine's "Common Sense"), and understand it well enough to
>   discuss it, write about it, criticize it, advocate it, etc. (National
>   Literacy Foundation)

That essay is a particularly useless choice, being written in
the language of 1776. I'm surprised that 20% could handle it.
Comprehension of common consumer contracts would be a far more
useful measure of reading comprehension -- not that I expect
a better success rate.

> - only 5% of American adults are "literate/fluent" enough in math & science
>   to deal with mainstream ideas, have an extended conversation with a
>   mathematician or scientist, be operational enough to put a mathematical
>   map on a set of ideas and do something with them, etc.

This is one reason to despise the fuzzy math of constructionism,
which is one cause of the lack of fluency.

Science is actively opposed by many parents. Lab work is doomed
for the same reason that the XO displays idiotic warnings when
you shut it down. (do not eat the laptop, do not eat the frog
soaked in formaldehyde, do not eat the sodium metal...)

> However, even if they had funded the study, we realized that it would be
> adding more of the largest problem of doing anything in a school with math
> or science, which is working with teachers who don't remotely understand
> their subjects

Right. The union works hard to ensure that it is impossible to
reward the good teachers or eliminate the bad ones. Because of
this, throwing money at the problem does not work.

Elementary school teachers normally can't deal with fractions
or basic English grammar.

BTW, it is probably impossible to pay a good student to help
teach others. I mean "impossible" because of teacher contracts
and other administration problems. Paying students to help out
is a very effective way to motivate them.

> another deeply important factor is that children in a single classroom
> exhibit a wide variation in motivations, knowledge, skills, maturity and
> "wiring". Different children need different approaches. A classroom is a
> tough place to learn anything (as an orchestra is a tough place to learn how
> to play an instrument). The US factory approach to education was hoping for
> economies of scales via method, but it forgot that it wasn't about just
> turning out Model-T's, but every kind and variation of vehicle using every
> kind and variation of materials and design.

Many schools avoid tracking, even up to the 8th grade. The parents
of a dumb and violent kid believe that he belongs in the advanced
class, and they may raise hell to ensure it.

There is also no ability to drop back by a fraction of a grade.
If a student misses something, there are a few bad options: they
can go on without it in the reasonable hope that it will be useless
material or taught again, they can drop back a whole grade (rare),
or they can drop down to a lower track if one is available. Both
dropping back a grade and dropping down to a lower track will
generally affect all subjects, not merely the one with a problem.

There is a severe need to reteach things. It's caused by the lack
of a national curriculum (transfer students must be dealt with),
the grade promotion of students without full mastery, distractions,
and the existence of summer vacation.

> Again, this successful scheme doesn't necessarily generalize to every
> subject. But it's strong enough to be worth considering in areas where
> "doing skills" are an important part of the subject. (One problem with
> "math" in the US is that it isn't actually "math" but only simple
> calculation skills. This isn't enough to help with actual math thinking
> (which is a special skill all its own that can indeed be taught, but isn't.)

I'm not sure what you mean by "actual math thinking". FWIW, some
places do have students doing proofs in algebra and geometry.
(what I got in Massachusetts from 1988 to 1990) I suppose that
this is not the norm.

Simple calculation skills are critical. Without them, you can not
quickly and reliably manipulate numbers in your head. Besides having
real-world value, this skill is a prerequisite for higher math.
You are unlikely to see the connections if computation isn't easy.
Stuff like 3/1.5 needs to be effortless.