This week I read "The Decline and Rise of
Geometry in 20th Century North America" by Walter Whitely, a very
interesting read from someone on 'the inside' of research in mathematics and in
math education. He begins by discussing the death of geometry in the mid
20th century. This is most notably chronicled by the decline of its
consideration as an important field. This had a cascade effect: less
research was done on the topic, so less graduate curriculum was taught on the
topic, so fewer future math educators were able to teach the topic, which eventually relegated
geometry to be a supplemental high school mathematics course. Whitely
recounts geometry's fall from grace in wonderful detail, culminating the
decline with a discussion of the nature of mathematics, that the public would
believe that "mathematics is essentially about logical intelligence,"
and that "popular culture sees mathematics as detached from spatial
intelligence" (p. 3). As
for the rise of geometry in recent years, Whitely credits much to do with the
resurgence with computers. As a resource for learning, computers provide
dynamic geometry programs which can be used for teaching, learning, and
research. They also provide an unparalleled
visual aspect that is so important for developing understanding.
Personally, geometry is one of my
favorite topics within math. Finding
unseen relationships that can be linked to a visual representation is so
satisfying. Geometry gives a way to very easily provide
the context for a problem that students can immediately understand, at least in
a visual sense. This understanding can lead
to powerful problem posing, and intuitive problem solving.
I agree with you Conrad! As a student I loved geometry and visually representing information, and I do to this day. I have found, through my teaching, that often students who may not excel in other aspects of math catch their stride in geometry, which in turn boosts their sense of self as a mathematician. I find it is interesting that you would separate logical intelligence from spatial intelligence because I would argue that one can lead into the other and vice versa. I wonder if mathematicians perhaps got lazy with the precise, sometimes complex, drawing of geometry and hence when computers began to do the bulk of the work there was the resurgence.
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