I would venture to say that Michael Keyton is not alone in wishing that geometry was emphasized more in the mathematics curriculum. Currently the secondary mathematics curricula in the U.S. are strongly dominated by algebra. Aside from a year of geometry, there is little geometry content in a student's mathematics education. I fear that the push toward an integrated curriculum will further erode the amount of geometry students see in high school in favor of heavier algebra content. (Linda Dodge's original question tends to validate this anxiety.)
How was the current balance of algebra to geometry determined? What was the rationale behind it? Was it always so? What other balances have there been? I would like to see answers to these questions before jumping to conclusions about whether to zap either geometry or algebra from the curriculum.
These two areas of study are actually complementary: algebra focuses on developing in students convergent thinking patterns (simplifying and solving) and the ability to manipulate abstractions (variables) while geometry encourages the development of divergent thinking patterns (specific example to generalization) and the visualization of abstractions (geometric modeling). Each seems to have a different function, and both are needed.
I worry when teachers focus narrowly on a single learning or teaching style and become intolerant of other ways to learn or teach. Individuals have different styles; for learning, thinking, teaching. One way of doing things will not work for everyone, nor should we expect it to. We need to develop an understanding of our own styles and a tolerance and understanding of the styles of others. Disagreement is healthy, but needs to be tempered with understanding. Our history is littered with tragedies resulting from intolerance.
Previously on the Forum, a long discussion on two-column proof covered a lot of ground. There were strong feelings about the topic, and opposing views were aired. On top of that, consensus was reached on some aspects, and some history of the procedure was unearthed.
I would like to hear what others have to say in the algebra v. geometry debate.
In article <firstname.lastname@example.org>, email@example.com (Top Hat Salmon) wrote:
> Michael Keyton (firstname.lastname@example.org) wrote: > : On Thu, 6 Apr 1995, Linda Dodge wrote: > : > Do we really need a full year of geometry, anyway? > > : I ask somewhat facetiously the following: suppose we had three years of > : geometry and one year of algebra in the curriculum, would not the > : question "Do we really need a full year of algebra, anyway?" be appropriate. > I don't see how, even facetiously, you could trun the tables this way. > The topics covered in a typical 9th grade algebra course are used far > more than the typical geometry course topics, speaking as one with 11 > undergraduate math courses from calculus on up. Three years of geometry > had better include a hell of a lot of algebra in order to be any good. > > : Yes, we need a full year of geometry, but we need a full year of geometry > : and not some year wasted without mathematics. > Agreed. > > : We need more years of > : investigations using thought and fewer years of learning meaningless > : algorithmic processes that are more easily forgotten than learned. > Like two-column proofs ? > > : We > : need years of having students learn to think through a probem, to > : understand, and to develop rather than to mimic. Do we need a full year > : of geometry? Yes, and more. > > But these kinds of problems do not occur only in geometry. I think > problems arising in a probability couse would provide the same stimulation. > I'd like to know why geometry has a monopoly on problems that need > thinking through. > > : If I had a choice of having students study 3 years of geometry and only 1 > : of algebra as opposed to the present, I would have guessed heaven had > : arrived on the wings of a TI-92. > : Michael Keyton > : St. Mark's School of Texas > > That makes one of you. > -- > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= > One World > One Operating System ! > -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-