Math Proofs

[mathman]

The purpose of teaching mathematics is to teach abstract thought. Proofs are a requisite part of abstract thought. A geometry class without solid proof doesn't belong in high school. Many students are exposed to concepts of squares and rectangles and that sort of thing when they're in elementary school or middle school. High School Geometry is NOT about finding the area of a square or circle, it's about proving things from definitions and conjectures. Geometry is used as the framework for this system of formal logic because everyone can see what's going on. You can draw an accurate picture and see the obvious truth of the things you prove. You could use other systems for establishing formal logic, but they are not as clear as euclidean geometry.

Your input?

[annettemcd]

Sometimes I think that Euclidean Geometry should have a different name. I think that I learned much more about Logic from doing proofs than I did about Geometry. Learning to do a step-by-step proof teaches one to organize facts and present them in a prescribed, precise manner.

I hated Geometry class, but I learned something which has stuck with me, though I do not think that now, 38 years later, that I could do a proof to save my soul.

[vanorc]

High school geometry was my first run in with proofs, some of the key points that need to be covered in the class are definitely the different methods of proving theorems. Induction, Logic Charting, learning how to prewrite (I still do the 2 column method with a lot of the proofs that I go through now) are completely necessary for this course. A name change definitely seems appropriate to me.

[CURower]

So I fully agree with you that high school is the place not to just teach rote formulas but also to teach students to think abstractly about problems. Proofs are certainly one avenue to achieve this and definitely should be included in EVERY geometry class (and higher). However, I think there can be a better way to go about teaching proofs...mimic the way the great mathematicians go about discovering new theorems.

Often times in Geometry classrooms, teachers will pull out their bag of theorems and write a proof up. However, when a new theorem is created, the path is not clear nor are all necessary theorems available. But when mathematicians write new proofs, they often play around with examples first then form some hypotheses and play those out. Why dont we mimic that in the classroom?

Recently I saw a great idea at a company called VisualizingMathematics.com . They have students use Geometer's Sketchpad to iterate through examples and then form their hypotheses and flush them out with traditional proofs.

Check out their Math Lesson Plans (http://visualizingmathematics.com/MathLabs.html)