4
$\begingroup$

In my university (a pretty large state school in the U.S.) we have only one undergraduate geometry class. Even in grades 6-12, students typically only take 1 year of geometry. Is there really not much to gain in the grander scheme of things by studying geometry?

  • 1
    If you mean studying synthetic geometry in terms of axioms, for say the basic Euclidean, nonEuclidean and maybe projective cases, then yes, it should be very rewarding ("much to gain") for anyone of any discipline. At least I think it has been used (perhaps imperfectly) to teach how proofs can be written.2017-01-30
  • 1
    Maybe universities find it difficult to bridge the gap between high school geometry and post-secondary geometry. Your college course is probably essentially reteaching a lot of things but adding deeper aspects, and I can't see any way around that. You'd need a stronger base to go on to more advanced geometry. Perhaps universities don't like the aspect of retreading the same ground, and they'd prefer to teach things not taught in high school.2017-01-30

2 Answers 2

3

There are many reasons for it. I suspect the following is one of them.

Studying is undeniably related to examinations. Geometry, unfortunately, is NOT a welcomed examinable subject from the examiner’s point of view in the sense of the distribution of marks. In the process of presenting the solution, besides stating the necessary facts, one is required to provide supporting reasons before full marks can be given. I will use a simple question to illustrate my point.

enter image description here

(1) A total of 2 marks will be awarded (1 for method/accuracy + 1 for supporting reason) if one have used “angles at a point” to get $\angle ACB = 360^0 – 315^0 = 45^0 = \angle XZY$.

(2) & (3) 4 marks will be awarded for stating the other two relevant facts.

(4) & (5) 2 marks will be given for a tip-against-tip presentation of congruent triangles and the associated supporting reason.

(6) & (7) 2 marks for applying “corresponding measurements” to set up 2h = 3k – 2h.

(8) 1 mark for accurately obtaining the required relation between h and k.

An elementary level geometric question like the above takes away a total of 11 marks. In fact, questions with same level of difficulty (like simplifying via factorization) worth only 5.

The conclusion is:- Half of the marks go to the supportive reason part according to the Euclidean framework. This makes mark distribution hard to decide.

3

I guess the main reason is that math education tends to by heavily leaned towards computation, not visualization or intuition behind those concepts. So, as soon as student is believed to grasp the basics of planimetrics, it's thought that he's capable of making all the interpretations he needs whil studying algebra and other fields.