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Topic: Musings about Question 1
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Ed Wall

Posts: 845
Registered: 12/3/04
Musings about Question 1
Posted: Mar 11, 2001 9:18 PM
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Professor Zhang

Let me apologize at the outset as not having time to participate
in this forum in a more through fashion. But anyway some comments as
regards your question 1 (I will try to take up other questions on
succeeding weeks).

I always wonder when the idea of 'dropping' a topic area is
broached. What exactly does this mean? For example, one might say
that plane geometry is a place where certain aspects of spatial and
relational reasoning have a beginning, someone else might point at
logical thinking, a third might emphasize deduction and exploration,
and a fourth might point to some of the mathematical elegance
embodied in theorems and their proof. All of these would be dropped?

On the other hand, I wonder how well deduction fares in a
traditional course in plane geometry. My experience is that students
become reasonably facile at parroting, but not at deducing - deducing
is a not inconsiderable accomplishment. I would enthusiastically
support a course designed explicitly to promote mathematical
deduction (and induction for that matter) - I don't think a
traditional geometry class necessarily provides that.

And logical thinking? I am not convinced that traditional plane
geometry does well there either - I am talking about enactment here.
Logical thinking - that is, a meta-awareness of one's thinking - is a
not inconsiderable undertaking. It is unfortunate that it gets so
identified with plane geometry. How many math majors take a
reasonable course in mathematical logic; perhaps they know it already
via plane geometry.

Spatial reasoning? Is dealing with two-dimensional Platonic
figures the only way? It is certainly a start, but an ending?

Beauty? Do we take time, as it has been said, to smell the flowers
or is each theorem just another page in the book? There is some
lovely mathematics and some engaging history around plane geometry.

So I would suggest that everything mathematically worthwhile -
bracketing the pedagogical (as much of what traditional plane
geometry embodies seems driven by that) - that plane geometry is said
to provide should remain in the curriculum. Should/could plane
geometry, as traditionally enacted, carry this load? I wonder if it
can. If it can't, and there is a better proposal in the offing that
addresses the pluses in a substantial way - and there may well be -
then great. Otherwise there needs to be some carefully weighing of
pluses and minuses - for example, I don't think the argument for
logical thinking is at all convincing.

Again, let me emphasize, I am talking about enactment not
potential. And this puts me at a considerable disadvantage as I have
no clear idea how a systematic course in plane geometry would be
enacted in China.

Ed Wall

>What emphasis should plane geometry have in the curriculum?

Many believe that this is critical content and the crucial place for
teaching logical thinking, but today there is no systematic study of
plane geometry in most countries.

[Background] Today, China still maintains deductive plane geometry as part
of the mathematics curriculum in 8 grade (100 hours). Many educators
suggest reducing the lesson hours and cancelling the deductive geometry
approach. There is controversy about this.

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