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Ed Wall
Posts:
837
Registered:
12/3/04


Musings about Question 1
Posted:
Mar 11, 2001 9:18 PM


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 metaawareness 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 twodimensional 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.



