This article explored multiple topics
regarding geometry, its declining presence at a secondary and post-secondary
level, and the case to revive it in curriculum. Whiteley begins his article by
describing the decline in geometry first, then explaining the different types
of geometry. So it is difficult to say if the statistics he provided at the
beginning of the article refer to a certain type of geometry (suppose,
Euclidean) or if they provided an overall picture. There were multiple
applications of geometry brought up by Whiteley and were a large part of his
case for continuing geometry in the curriculum – geometry is used in
establishing the structure of chemical formulas, designing vehicular
components, etc.
I must admit, my initial reaction to this
piece was mostly indifference. I hadn’t seen much geometry in math in school
beyond basic Euclidean geometry and basic geometric proofs (which, granted, I
still don’t remember and was never really taught, just expected in some form).
I think that with geometry has made its way
out of the curriculum for two reasons. For one, geometry is no longer required
in university unless you major in mathematics. It is easy to argue that this
was taken out of the curriculum while things essential for calculus were
maintained. The second reason is the ease with which one can now teach
mathematics in the school curriculum. In my discussions with other teachers,
many did not have a great deal of mathematics experience (much less a degree)
but instead only had a calculus course. For calculus, little or no geometry is
required. So this would then begin to reinforce the lack of experience with geometry
and decrease the exposure to the subject beyond a surface depth.
If geometry is being used in specific applications
as Whiteley says, then I would sooner see geometry taken out of the curriculum completely
and replaced with some basic matrix algebra. Matrix algebra is a basic skill in
a variety of backgrounds, yet it is not taught at any level (except in the
International Baccalaureate Diploma Programme). Matrix algebra is also easy to
understand, provides a whole range of depth in topics, number of solutions,
whether or not solutions can be computed – in short, more immediately accessible
topics arise with much further-reaching applications.
The problem that I have with this reasoning is the idea of "requirement." True, you don't "need" geometry unless you major in mathematics, but what is the point of examining literature or poetry in a first-year english class? Curriculum developers seem to believe that we shouldn't push any unnecessary mathematics down the throats of students. But, it's completely ok to teach students english literature which they aren't going to use. Why is it taught? Because it is a valuable experience to be exposed to such work. Is it not a valuable experience to be exposed to geometry? Why does school mathematics need to be useful?
ReplyDeleteMoreover, it seems dishonest to not give students as full bodied of a view as possible. Couldn't we be holding a large number of students back who are very mathematically inclined, but on the geometric side? In fact, my dad was mentioning at dinner on Wednesday night how he excelled in geometry class, but somehow really struggled with algebra. This relates more to my article, but it is something to consider.
I honestly had no idea that geometry was on the decline in schools. I suppose that I haven't been teaching for very long which account for me not noticing. If it is indeed slowly being taken out of the curriculum, we need to ask why? Who is behind these decisions, and on what grounds are they making them? These have been popular questions of late, due to the complete overhaul of the curriculum, in all subjects.
ReplyDeleteWe could be seeing some effects of a positive feedback loop in which somewhere down the road less geometry was taught for whatever reason. The students of that generation, with less geometry background would go on teach the next generation, and if anything focus even less on geometry. This could potentially happen until it was no longer taught.
For what it's worth, I do wish to keep it in the curriculum. It offers a way to teach many units in math, but from a different perspective. Unfortunately, this ability to interconnect the smaller units of math doesn't seem to be recognized too often.
With technologies such as document cameras, new manipulatives, and tablet devices, geometry should be taught in class now more than ever. For this to happen, we need it in the curriculum, and we need teachers to be comfortable teaching it.
Interesting conversation here!
ReplyDelete