Re: What Went Wrong with New Math?

In article <X0Rme.2924$s64.76@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
W. Watson <wolf_tracks@xxxxxxxxxxx> wrote:
>Yes, what did go wrong? I believe that got rolling in the 70s but somewhere a
>long the line went out of style. Did something replace it?

It got rolling in the late 50's. It was started because
a mathematician found that his daughter, who could do
arithmetic well, had no idea what numbers were except
objects to be manipulated knowing the formal procedures.
This was found in the 40's.

Anyhow, several mathematicians set out to prepare materials
to teach the cardinal concept of arithmetic, and these were
tested on tens of thousands of children, mainly in private
schools. As the results were highly successful, they were
able to persuade those who run the schools to incorporate
it in the regular curriculum. This was in the late 50's.

There was an unexpected problem; the TEACHERS could not learn
that using the cardinality concept and set union could be a
basis for understanding the integers! Instead of pointing
this out, and arguing that this meant the teachers did not
understand the integers, the materials were weakened in the
hopes (unmet) that the teachers could handle the weaker parts.
This was even worse.

Possibly something could have been done then; the situation
now is even worse. Few teachers can understand concepts in
any subject, and the educational philosophy is that one can
only learn by memorizing examples, and then hopefully finding
generalizations. Not only are concepts not taught in mathematics,
but grammar is essentially out in language. It took public
demand, plus the possibility of teaching reading with phonics
fairly easily at home, to get that back in the schools, and there
is still resistance to that.

The teachers could not learn concepts then, and if anything are
in worse shape now. I believe this is caused by teaching how
to calculate; it is hard to teach those who have learned that
way to understand the basic concepts in mathematics and statistics.`
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.