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Q&A #918

Teachers' Lounge Discussion: Geometry Textbook "Discovering Geometry" by Michael Serra

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From: A parent <cvt7@yahoo.com>
To: Teacher2Teacher Public Discussion
Date: 2001121519:37:40
Subject: A dissenting voice

As a parent of a student who uses DG in the 9th grade, I am
disappointed by the approach.

There are two issues here, I believe. First, the traditional
approach of using proofs was intended as an end in itself, as that
portion of one's education that demonstrates the structure and
meaning of mathematical reasoning.

Assuming one dispenses with the relevance or usefulness of
teaching the deductive nature of all mathematics, all that's
left is the teaching of geometry as a practical skill -- the
sort of thing a carpenter would need, for example, or a physicist.
(That's not why mathematics has been considered a basic component
of a liberal education, by the way).

Secondly: How good is DG at what it attempts to accomplish?
If the objective is to teach the facts, formulas, and methods
of geometrical measurement and construction, one could teach
it like the sciences -- physics or chemistry, for example.
In that case, the group investigations of DG would be like
labs, demonstrating the principles. But would anyone write
a physics or chemistry book which expected the student to
arrive at all physical laws and formulas on his/her own, from
the labs? I don't think so. DG would be a wonderful book for
a "math lab" or "fun with math" course, but, as a main course
text, it leaves too much to the student. (There are no facts
in DG. Only questions, and instructions on how to find the answers).

Not only is the inductive approach to mathematics fundamentally
invalid (math is deductive! science is inductive!), it can
also be very misleading in practice. For example: Some
triangle-related investigations in the book begin with "draw a
scalene triangle, and ...". Well, drawing a scalene triangle is
not as easy as it sounds. Most people, when asked to do so, will
draw an isosceles triangle lying on one of its equal sides.
Try to do an investigation on this triangle, and you will
think that many of the properties of an isosceles triangle
are those of the scalene. The devil is in the details. (And don't
expect the text to correct you. All important statements
in the book have blanks to be filled in by the student).

Also, group investigations are always tricky, disregarding
the fact that different students learn at different speeds,
and *in different ways*. The brightest student always dominates
the group, and the others are made to follow, without understanding.

I can say a lot more. The author obviously loves geometry
and his passion is welcome and it shows in the book. Again,
there is a place for this approach on the side of a main course.
But as a main approach to teaching geometry, I believe that
this concept falls wide of the mark both in its objective
and in its methodology.

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