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Re: Thinking Level of students



I wrote:
> Geometric relationships in general, and the earth/moon/sun
> geometry in particular, is commonly introduced in 2nd grade, and students
> are expected to (mostly) "get it" by 3rd grade or 4th grade.

Then at 10:32 PM 9/8/01 -0500, John Clement wrote:
The fact that the information is in the syllabus does not mean that they are
capable of understanding that material. The recent article in Sept Physics
Today gives the references to the research that shows that below 5th grade
students are not capable of understanding the elementary astronomy ideas.
.... The usual lecture method does not
promote conceptual understanding as the research shows.

Aside #1: As a scientist I am obliged to report all the data, even data
that disagrees with my preconceived notions, disagrees with conventional
wisdom, and (partially) disagrees with what I wrote last week.

Aside #2: One must distinguish
-- the data, versus
-- various interpretations that can be placed upon the data.

So: Prompted by what John C. has written, over the last few days I have
conducted some rudimentary experiments, asking people at various levels of
maturity to explain why the moon has phases. I started with the hypotheses
*) Fourth-graders should be able to explain this.
*) A precocious fifth-grader who is interested in science should be able
to explain it pretty well.
*) Those who couldn't deal with it in terms of mental images would do
better if they had props to work with.

Observations were as follows:
1a) The precocious 13-year-old stated that the topic had been covered in
school about once a year for the last 5 years -- but she couldn't remember
how it worked. She thought about it for a minute, and then converged on a
wrong answer. Additional time would not have helped.
1b) I told her to round up some props. That didn't help enough; she
wasn't going to get the right answer using only her own resources.
1c) I dropped a hint, namely that one side of the earth was daytime and
one side was nighttime. That got her started; she instantly realized that
what I had said about the earth applied also to the moon, and she figured
out almost all of the rest of the story in the next few seconds.
1d) She did not figure out the distinction between a new moon and an eclipse.

2) A grown-up who was definitely not very well educated was able to
rattle off correct explanation of the phases. When asked "what's the
difference between a new moon and an eclipse" he gave the right answer
immediately.

3) A college freshman fared worse than the 13-year-old. Didn't remember
the answer and wasn't motivated to figure it out.

======================

Conclusions and Non-conclusions:

A) This strongly supports one point John C. made: Just because it's on the
syllabus for a particular grade level doesn't mean very much.

B) I have reached no conclusions about what any of these people are CAPABLE
of learning. I only report what they HAVE LEARNED.

C) In particular, I am still entertaining the hypothesis that 5th-graders
are capable of learning geometric relationships. Evidence for this comes
from their ability at team sports and other activities as mentioned in my
previous note.
-- It is possible that they have to work hard to learn these.
-- It is possible that the usual passive participation in a lecture
about astronomy is insufficient.
-- It is possible that motivation is an issue.

The typical 5th grader spends many hours per week thinking about sports,
and spends not very many hours per year looking at the moon.

D) There are presumably Piagetan developmental stages involved; it may be
that less-mature persons deal with geometric relationships in one way while
more-mature persons deal with them in another way.

E) I still think that saying typical college freshmen are "incapable" of
learning geometric relationships would be overstating the case.