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Justifying High-School Geometry

  1. Aug 28, 2008 #1

    symbolipoint

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    The topic has occurred on the forums before; but maybe someone has fresh ideas.

    How do we justify the need for high school Geometry for high school students who are headed for college and science or engineering careers? When such students want to earn a degree in some physical science or engineering, "remedial" Geometry is not part of the curriculum; for most purposes, students may skip this Geometry course and not notice much difference. The degree does not call for it. Students can do their Trig>PreCalc>Calc1,Calc2,Calc3>Differential Equations... Omitting "Geometry" does not hurt anything. Intermediate Algebra did not really require it; Trigonometry did not really require it.

    Geometry at the high school level is a "Foundation Level Course". Nice classification, but still not really essential for Algebra 2; and any Geometry needed in Trigonometry is usually well enough taught IN Trigonometry.

    I have found one important possible reason justifying at least one feature in Geometry - that being the Triangle Inequality Theorem.

    People, help me clarify and identify other reasons which we can use to justify studying Geometry to high school students and to other "remedial" level Math students in college.
     
  2. jcsd
  3. Aug 28, 2008 #2
    is it about learning geometry or about learning what a 'field' is and how fields work?
     
  4. Aug 28, 2008 #3

    dx

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    There's a range of geometry courses at the high school level. There's what is usually called euclidean geometry which is about straight lines, angles, triangles etc. Then theres analytical geometry which is basically using coordinate systems and algebra to solve geometrical problems. You can't get far in university math if you don't know analytical geometry. What is the course that you are talking about like? What kind of topics does it cover?
     
  5. Aug 28, 2008 #4

    symbolipoint

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    Just to clear-up the confusion expressed in dx's post: I ask about justifying the Euclidean Geometry course taught in high school. This is the one which discusses points, lines, planes, and relationships of shapes and angles, and so such. The analytical geometry which occurs for Algebra 2, Trigonometry,, Calculus, is beyond the Foundation Level Courses. The Foundation Level Courses (this is official terminology) are Algebra 1 and Euclidean Geometry.
     
  6. Aug 28, 2008 #5

    tmc

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    I wouldn't hire an engineer who doesn't know what 'sine' and 'cosine' mean.
     
  7. Aug 28, 2008 #6

    symbolipoint

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    That justifies the course on Trigonometry, but cosine and sine are relatively easy concepts which do not need to be first learned through the course on Euclidean Geometry.
     
  8. Aug 28, 2008 #7
    If anything, Euclidean Geometry at the High School level teaches students to think visually. It teaches you how to draw and interpret diagrams logically, and that's an important skill for engineers and physical scientists.
     
  9. Aug 28, 2008 #8

    tmc

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    I have to say, as a non-US student, I'm kind of confused as to what is learned in this geometry course, if you already have a trig course to learn the useful stuff.
     
  10. Aug 28, 2008 #9
    you learn how to start with a handful of axioms(?) and deduce a large number of theorems.
     
  11. Aug 28, 2008 #10
    I'm going with granpa on this. High school geometry is really the first course where students are introduced to logic and the first time they learn about proof and methods of proving. This may not be important for engineers explicitly, but it is certainly important if you want students to develop the mathematical maturity to actually understand advanced topics.
     
  12. Aug 28, 2008 #11

    mathwonk

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    beg your pardon? this is like asking why someone should learn to speak and write english in the usa. obviously you have never read euclid's geometry or you would not pose this question. please let it drop. i suggest modestly that you don't know what you are talking about.

    UNLESS!: you are distinguishing between reaL GEOMETRY, i.e. euclid's geometry, and the schlock that often passes for geometry in high school. in which case i agree withn you
     
  13. Aug 28, 2008 #12

    Ben Niehoff

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    It is an IMMENSE help in advanced math/physics courses if one can do geometry in the method of the Greeks rather than relying on analytic geometry (i.e., assigning a Cartesian coordinate system to the plane and trying to find the location of every point).

    It seems that on almost every single homework problem, I see other students essentially re-deriving the law of cosines via analytical methods, because they are so used to working in Cartesian coordinate systems and cannot think in a pure geometrical sense. It is a great hindrance and creates twice as much work to do.

    I think students fall back on analytical geometry because it is always guaranteed to work. Assign each point an X and Y value, do some algebra, and you're done. But on simpler problems, this takes twice as long as the pure-geometrical approach, precisely because the student is trying to find extraneous information (i.e., the X and Y values). Often a geometrical problem doesn't require resolving all the vertices into a coordinate system; one merely needs to use circles, parallelograms and triangles.
     
  14. Aug 28, 2008 #13
    If you don't find geometry useful, don't take it. I personally found it useful, both directly and indirectly. Triangle properties and tangents to circles are used a lot in physics.
     
  15. Aug 29, 2008 #14

    Defennder

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    High school geometry is immensely useful. It helps a lot in understanding phasors (which is used in a LOT of EE courses such as transmission lines, electric circuits etc.), crystallography geometry (guaranteed to occur in any intro solid-state course), 2nd year E&M courses where symmetry can be exploited to cut down on a lot of vector algebra/calculus, geometrical optics (the name says it all) and polarisation of light in intro physics, and that's justn what I've done in my first year in college. I imagine it would be used even more intensively in later years. In short, I don't see how anyone can do without it.
     
  16. Aug 29, 2008 #15

    Andy Resnick

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    The geometry described in post #4 by the OP was taught to my 4th grade daughter- those concepts should be introduced well before high school. They are as fundamental to life as learning how to read a map or give directions- skills that everyone should possess.
     
  17. Aug 29, 2008 #16
    Geometry is not only used in physics but in every single discipline of engineering. Yes including electrical and systems engineering? Every try creating a drive that uses space vector modulation without geometry?
     
  18. Aug 29, 2008 #17
    In my experience, geometry was taken before trigonometry so subjects like vectors or the law of cosines (mentioned by a poster above me) was not covered. It's been 5 or so years since I took the course, but honestly, the only thing that still sticks out is using a two-column proof to find an angle using the Side-Angle-Side method.

    I was in the so-called "honors" course, the "standard" course didn't even use proofs at all. I think the most useful part of the class was the introduction to actually proving something.
     
  19. Aug 29, 2008 #18
    I was very bad at geometry in school. But because I was far ahead with math, I simply solved geometry problems algebraically. E.g., in case of problems involving cubes, lines, planes, etc. where you had to use geometry to find intersections, look at triangles in there etc. etc. to find what was asked, I simply wrote down equations and solved them using e.g. Gaussian elimination.

    So, I could compensate for my weakness. I scored close to 100% on most math tests in school. If the subject was geometry I would score between 80% and 90%, because I would be penalized for not solving the problem in the way we were supposed to solve the problem. :mad:
     
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