Wednesday, October 24, 2007

Geometic Proofs



We are doing geometric proofs in my Math B class. I never liked them, not even when I was in high school. I did not like them when I first learned them and could only BS my way through them and I did not like them when I grasped them completely and got 100 on my geometry regents tenth grade. I still don't like them even though I am teaching them.

My students don't like geometric proofs either. The concepts are too abstract to them and there are too many different ways to arrive at the same conclusion. They are always looking for the correct answer and an answer, in its common meaning is not what you get when you are doing a proof. The kids don't like all the writing and they have no use for the exactness of the words. To complicate things for them, I make them write everything out. I've seen too many kids write CPCTC and have no idea what it stands for. The word midpoint alone has no meaning unless they write out what a midpoint is. I guess what I am trying to get them to do with these proofs is to think logically and make sure everything they are doing and saying makes sense. There is a difference between a midpoint dividing a line into two congruent parts and to dividing it in half. Maybe it is petty, but if the proof is going to flow, all the words must make sense.

My students are finally starting to get the hang of proofs. We start at the beginning, then go to the end and meet in the middle. We use lots of pretty colors to make our triangles stand out. They can do a proof but they still don't get them. They still don't see the purpose of them and after over 30 years of teaching, I don't see the purpose of teaching them to do proofs either. With better students, I might change my mind, but, with these kids, a good intermediate algebra class would be much more beneficial.

10 comments:

CaliforniaTeacherGuy said...

Here's one place where I disagree with you: I LOVED geometric proofs when in high school. Geometry was the only math that made sense to me, the only math I ever got an A in. I think that doing the proofs improves one's ability to think logically. That's my opinion. I'd like to hear from others!

Exo said...

I had geometry alon with algebra (2 different classes starting in 6 grade and lasting untill tenth - soviet school!) Proofs teach logic, step by step reasoning, and use of known information (aksiomes (sp?))to prove a theorem. It's highly aplicable skill for sciences or even for literature analyses. Teaching proofs makes perfect sense to me, even if it's that abstract in the beginning.

Pissed Off said...

To the kids I am teaching, these proofs make no sense. It is just too abstract. So many of them are far behind in their basic skills and algebraic manipulations. They are writing down words but these words have no meaning for them. I just think that there are much more important skills they need before they tackle the abstract.

A Workshop Model said...

Proofs are just the reason I don't teach math as a specialty. I just didn't "get" the proofs. I had a 100 on the old Algebra regent (1960's) but around a 75 on that 10th grade geometry regent. It made absolutely no sense to me, and I still need tutoring from my duly licensed math teacher friends so I can help my own students get through the proofs.Give me algebra any day!!! It just didn't make sense to me why triangles were congruent or were right triangles due to SAS or ASA. I felt like an ASS since I couldn't make sense of it. I bet if you were my teacher, the outcome would have been a lot different.

Pissed Off said...

Thanks for your kind words Workshop--most of my kids just want to get through.

Mrs. T said...

CTG, I thought I was the only one who actually liked proofs! It was really the one thing I could do - except for word problems, which I could also do well. Geometric proofs made TOTAL sense to me- I could see it, it was logical, it was verbal, which is where my strengths lie. Give me a parabola to graph and I'm lost. I remember carefully plotting points on a graph and working through the problems, only to get most of it wrong. I couldn't get it- I had a curvy line thing on the graph, how could it be wrong?
I need to remember this when I'm teaching my students the subjunctive.

Anonymous said...

Maybe your students don't like them because you don't like them... you'd be surprised how much the teacher's attitude can affect the students... something to think about.

Anonymous said...

Proofs are "elegant" are under utilized in HS Geometry. Just because they make many of our students uncomfortable that's even more of a reason to teach they. We stretch the mind by moving out of our comfort zone. Please don't quit teaching proofs....the beauty of these beasts is in the process.

Anonymous said...

I am a student and also thinnk they are domb, especially when my teacher was so board and went fast, i almost faied.

victor acharjee said...

I was a great fan of geometry proofs in my high school days .For me it was the most interesting part of maths syllabus for the freedom of thinking it offers . You can use virtually anything to prove anything without violating the chronology of the proofs .It is like an intellectual game with good benefits.I still love them. It seems that many don't like it . Either they might not have been taught properly or they don't have that kind of mind . In any case geometry does not become meaningless , it is they who not being able to sense the meaning ,and they should understand that at least .