Euclid in Public School

[BBrentW]

Main Question or Discussion Point

I'm having trouble understanding why Euclids Elements is so scarce in introductory Geometry classes. I don't remember even knowing such a book existed back in Jr. High when I took Geometry for the first time. I just graduated High School and I'm a prospective Math major, and looking back at the books that introduced me to Geometry, I can understand why so many people see math as another four letter word. These books may have colorful pictures, but they are very ugly compared to the Elements. I've helped several kids through the computational approach to Geometry and many of them hate it. It seems like so many great mathematicians first fell in love with math by reading this book. Who knows what great minds get sick of the mindless computation and never realize their potential. Does anyone have any input as to why we give every Geometry student a cookbook to carry around all year while only mentioning the greatest book written on geometry as a side note to one of their lessons? Was it just my teachers? Do they think the Elements is too hard and the students can't handle it? Do they think the students will find it boring? I hope I didn't rant to much.

 

[symbolipoint]

BbrentW,

Why do you believe that high schools' College Preparatory Geometry courses are computational
in their approach and that they do not represent the Euclid's Elements book? High school Geometry,
if done properly, emphasise proofs and and applications about shapes. The focus is on postulate,
theorems, shape & distance relationships, proofs of all these, and at least some applications. Simple
algebra is often involved in the problem solving of applications - some but certainly not all of this uses
formulas, much of it involves either drawings, or transcriptions to be performed from worded descriptions.

The textbooks also are important. Again, they emphasise postulates, proofs, theorems, and problem-solving.
(Or they DO emphasise those, if the Geometry book is made sensibly).
Also, constructions using compass and straight-edge are part of instruction... let's not neglect that.

 

[LukeD]

High school Geometry,
if done properly, emphasise proofs and and applications about shapes. The focus is on postulate,
theorems, shape & distance relationships, proofs of all these, and at least some applications.

There's the first catch tough. Most high school geometry classes are not done properly. They instead emphasize being able to do proofs formulaically and they emphasize knowing exactly what the steps of your proof are and having your proof match the book's proof (or being done in x number of steps or whatever)

Rather than emphasizing creative thinking and problem solving, the classes essentially emphasize the same skills that you used in algebra and trig classes to rearrange some equation: mostly memorization and pattern recognition.

Not to mention that Euclid's Elements uses geometry to develop basic number theory, which wouldn't even be touched upon by a high school geometry class. And ruler and compass constructions? No one would ever dream of having that taught in highschool.

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symbolipoint: In general, Math education in highschool (at least in America) is almost always terrible. I've never met anyone who did anything other than computation in highschool. Very few people leave highschool with any idea as to what Math even is. I had no idea at all what Math was until I took my first real math course in college (i.e., not a calculus course, not a course whose primary interest was to teach tools for engineering or science or whatever, not a course taught for CS students who needed to know how to calculate things so that they write programs easier, but a course whose purpose was to introduce Math students to pure Mathematics).

Since you've read Euclid's Elements, I'd say that you have a better grasp of what math is than just about anyone else who's just left highschool. You probably even have a better grasp than most Math majors who are entering their Sophomore year.