Geometry in the Community College Curriculum

Question

As many Americans know, the “traditional” high school sequence is:

Algebra 1

Geometry

Algebra 2

PreCalculus

Calculus

For those who take developmental education at the community college level, it consists of something like:

Developmental Algebra

Intermediate Algebra

College Algebra

PreCalculus

Calculus

While the college courses cover most of the algebra, there seems to be no Geometry in the curriculum. Why is that? If there's a good reason for it not to be covered in the Community College system, does it still have a place in high school?

Answer 1

"Geometry," the American high school course, is generally pseudo-axiomatic Euclidean geometry. I don't know whether your claim about the CC curriculum is broadly true, but assuming it is, it's probably because Euclidean geometry is simply not a prerequisite for calculus. Students need to know the Pythagorean theorem and a bit about areas and volumes, which are covered well before high school geometry; beyond that, all the geometric content in calculus is either analytic or heavily trigonometry-influenced. And trigonometry is covered mainly in precalculus.

There is a lot to wonder about whether high school geometry is a necessary course. The main argument in its favor is that it gives students a brief acquaintance with logical rigor, a very important part of intellectual culture that they otherwise won't seriously meet unless they get to a course as advanced as abstract algebra in college. But practically speaking, this isn't obviously a compelling argument; causally, Euclidean geometry is still there because Euclidean geometry was the pinnacle of early modern math education. It's not hard to argue that it would better be replaced, for instance with wider exposure to statistics and probability. But that's really just a matter of opinion.a

Answer 2

The other answers well discuss how geometry is sort of "off track" for the push to calculus and the other topics (trig, algebra) are much more integral. But I don't think they make the point enough that community college students are already behind the curve in terms of time. We are talking about kids taking remedial classes (I guess "developmental" is a euphemism...first time hearing it.) So they have even more need to prioritize than high school students (Sue does in her comment/answer). An allowable luxury for high school students is not allowable for kids that are several years behind and just need to get that calc credit so they can get their BS Nursing or Accounting or whatever. And by the way, those courses in nursing and accounting are more vital in the end than this math stuff...really, truly, for them.

Of course this is not to say no geometry is ever needed, or it is completely irrelevant to calculus. But when we work and live and make life choices, we live in a world of priorities, not of "divide by zero" rigor absolutes. There is not time to study everything. So finding isolated connections is not the same as prevalent connections. Heck, even for the basic formulas (like triangle equation in related rates problems), I remember thinking in HS geometry, how we really weren't learning much geometry (measurement of land), but seemed to be learning vast amounts of proofs.

Answer 3

Typically, a geometry class in high school teaches Euclidean geometry. Depending on how much time is spent and the exact class, Euclidean geometry as rendered today explores properties of triangle, parallelogram, and circle, while following an axiomatic system, much of which was initially laid out thousands of years ago. The purpose is less to understand these objects deeply per se but to learn how a large set of conclusions can be derived from a few simple assumptions.

In higher education past high school, modern mathematics are taught instead -- either to prepare students to research in mathematics, or to prepare students for applications of mathematics. Euclidean geometry would be rather remote from either. No current research fields draw much from the old school Euclidean geometry -- we are thousands of years past that after all. No common applications require Euclidean geometry either.

In the case of training students on logical rigor, an advanced degree have many more such opportunities. Thus no need to spend time on Euclidean geometry. For high school, some of the more intricate machineries in modern mathematics can be too abstract. Euclidean geometry thus became the quick and more viable way to expose students to an axiomatic approach.

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The competition for time should be a thing in high school too. So it's worth mentioning that, in Asian countries, Euclidean geometries are taught in junior high schools. ie. grade 7-9 (though there is little teaching in grade 9 with it being mostly exam prep) where grade 1-6 is the primary school. With that arrangement, any hypothesized benefits would be gained without taking away valuable time in high school that can be used for further education in math -- to teach foundation for calculus (including some basic analysis), probability, etc, which in turn can be especially helpful in preparing students who will enter fields that require applications of math yet won't have a lot of time to spare for math such as the various engineering fields.