cindylee Posted April 30, 2010 Share Posted April 30, 2010 I have a dumb question. I majored in engineering. I love math and I love geometry. I have taught a geometry class and tutored geometry. This is my question. Yesterday I was discussing different geometry books with a lady who tutors for alot of the private high schools in my area. We were discussing a certain curr. and I said they don't do proofs til the last chapter and she said no, it's from the very beginning and they do proofs all thru the book. I had a copy of the last chapter of the book from a student and I showed her the chapter that was titled "Formalizing Proofs"(the chapter was about 2 column proofs). Anyway she said oh no, the schools never get to that chapter, but proofs are throughout the bookfrom the very beginning(we were talking about Glencoe geometry). WEll, I dropped the subject and I don't want to appear as a dumb homeschool mom, so could someone explain what she's talking about. I thought the 2 column proof was "proofs". Is she just talking about when you have to prove SSS, etc. without writing it out. Thank you for your help. Cindy Quote Link to comment Share on other sites More sharing options...
Pam in MA Posted April 30, 2010 Share Posted April 30, 2010 Along the same lines, I've been confused by a comment about proofs all through Foerster's Algebra. . . I only saw what I thought were two or three throughout the entire book. Is there a definition of proofs that varies from mine? Quote Link to comment Share on other sites More sharing options...
mpcTutor Posted April 30, 2010 Share Posted April 30, 2010 I have a dumb question. I majored in engineering. I love math and I love geometry. I have taught a geometry class and tutored geometry. This is my question. Yesterday I was discussing different geometry books with a lady who tutors for alot of the private high schools in my area. We were discussing a certain curr. and I said they don't do proofs til the last chapter and she said no, it's from the very beginning and they do proofs all thru the book. I had a copy of the last chapter of the book from a student and I showed her the chapter that was titled "Formalizing Proofs"(the chapter was about 2 column proofs). Anyway she said oh no, the schools never get to that chapter, but proofs are throughout the bookfrom the very beginning(we were talking about Glencoe geometry). WEll, I dropped the subject and I don't want to appear as a dumb homeschool mom, so could someone explain what she's talking about. I thought the 2 column proof was "proofs". Is she just talking about when you have to prove SSS, etc. without writing it out. Thank you for your help. Cindy One cannot reach the chapter on two column proofs in geometry without studying several theorems in geometry (and knowing their _formal_ proofs.) Geometrical proofs are introduced as deductive proofs and deductive reasoning requires them to be formal all along - whether in column form or not. Outside United States, one will rarely find textbooks describing proofs in two column form. For example, consider the introductory theorem on intersecting lines. Theorem: If two lines intersect each other, then vertically opposite angles are congruent. Traditionally, this is proved in one of the the first 2-3 chapters without the two column format. Yet the proof is formal and rigorous. Most kids understand such proof but when they are asked to reproduce it they themselves will find that they made errors. Certainly, putting proofs in column form with statements in the right hand side and reasons in the left hand side has greatly helped in visualizing the logic in the arguments. So I would teach column form proof even in the beginning if the theorem required it. Sometimes proof in the column form is not even needed since traditional form is sufficient for understanding and easy for writing. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 9:57 AM 4/30/2010 Quote Link to comment Share on other sites More sharing options...
cindylee Posted April 30, 2010 Author Share Posted April 30, 2010 Thank you, MCP. I figured that had to be the case. I think I had always thought of "proofs" as when you have to actually write out what the conclusion was and then what the theorem, etc. was. So this makes sense. Now, when one tells me that a geometry text doesn't require proofs I have to wonder, just how much geometry is there really. Thanks for your help. Quote Link to comment Share on other sites More sharing options...
hoosiermom Posted April 30, 2010 Share Posted April 30, 2010 I also tutor math and am a former public high school math teacher. I currently tutor a student who is using the Glencoe geometry book, and I can assure you that there are proofs early in the book (and by that, I mean 2-column proofs). I don't have a copy of the book here, but I know proofs began at least by middle of first semester. Quote Link to comment Share on other sites More sharing options...
cindylee Posted May 1, 2010 Author Share Posted May 1, 2010 Thanks hoosiermom! I have not seen the rest of the book. I think that last chapter must have just been a whole chapter on writing 2 column proofs for practice. This has cleared up my question. Also, as a math person myself, I'm finally relaxing about my daughter using geometry and the ACT. I've been so fearful of choosing the "perfect" text. I think I have resolved there is no "perfect" math program and opinions differ so much. Thanks for your input. Quote Link to comment Share on other sites More sharing options...
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