wendybern Posted June 28, 2012 Share Posted June 28, 2012 She successfully completed TT Alg 1 & 2 and did very well. With TT geometry, though, she has hit an early wall. She just doesn't get the proofs at all -- the logic of them, how to construct them. Confession: I don't remember this stuff myself, and I don't want to relearn it all, so I'm not much help. I could learn it to teach it; or . . . ? Is there a different geometry program or resource that would help turn on the lights as far as proofs, that we could either switch to or just detour to temporarily? THANK YOU for any advice. Quote Link to comment Share on other sites More sharing options...

Jane in NC Posted June 28, 2012 Share Posted June 28, 2012 If you are not inclined to teach the material, then I think you may need to hire a tutor or enroll your daughter in a class. Do students need to know how to do formal proofs? I like to see students exposed because the analytic thinking involved translates to forming logical arguments across the disciplines. My two and a half cents, Jane Quote Link to comment Share on other sites More sharing options...

Candid Posted June 28, 2012 Share Posted June 28, 2012 I'd switch to a text that doesn't use formal proofs. There are rigorous programs that do that. I use Singapore, they never do proofs (but I can't really suggest them to you since they integrate their material you can't just jump in and do geometry with them). Quote Link to comment Share on other sites More sharing options...

4wildberrys Posted June 28, 2012 Share Posted June 28, 2012 We have all bombed understanding proofs in this house---even mathy ds! I tried very hard to understand them to teach and explain using the MUS DVD and solutions manual, but It was no use :001_huh: Quote Link to comment Share on other sites More sharing options...

wendybern Posted June 28, 2012 Author Share Posted June 28, 2012 So what is a good program that doesn't use proofs? This is a non-mathy, non-science child who is probably not college-bound. Quote Link to comment Share on other sites More sharing options...

MIch elle Posted June 28, 2012 Share Posted June 28, 2012 So what is a good program that doesn't use proofs? This is a non-mathy, non-science child who is probably not college-bound. Skip the TT lessons on proofs and continue with TT geometry. Quote Link to comment Share on other sites More sharing options...

wapiti Posted June 28, 2012 Share Posted June 28, 2012 Well, I used the logic of writing proofs when I learned how to write legal briefs (I have always been much more a "math person" than a "language person," so the fact that I eventually became a lawyer is rather ironic). Once I figured that out, writing briefs was easy ;). Maybe you can go the other direction - have you taught anything about making logical written arguments? I don't remember much about geometry, but from reading around here, it seems that some curricula teach the two-column proof and others teach a different form of written proof. Quote Link to comment Share on other sites More sharing options...

PeterPan Posted June 28, 2012 Share Posted June 28, 2012 You could try Patty Paper Geometry to give her some hands-on for it. The guided exercises walk them into the concepts and might help her extend then to her proofs. Quote Link to comment Share on other sites More sharing options...

regentrude Posted June 28, 2012 Share Posted June 28, 2012 If you are not inclined to teach the material, then I think you may need to hire a tutor or enroll your daughter in a class. Do students need to know how to do formal proofs? I like to see students exposed because the analytic thinking involved translates to forming logical arguments across the disciplines. :iagree: Either you can learn and teach it,or you need to find somebody who can. I'd switch to a text that doesn't use formal proofs. There are rigorous programs that do that. A program without proofs can not be rigorous in a mathematical sense. Higher math is all about proving relationships, not about computation according to algorithms. Geometry is the easiest field to introduce formal proofs because it is possible to visualize relationships; the proofs required for calculus or other fields of math are much more abstract. I would highly encourage the OP to find a competent teacher instead of simply skipping proofs. Quote Link to comment Share on other sites More sharing options...

wendybern Posted June 28, 2012 Author Share Posted June 28, 2012 To be honest, I almost posted something similar when I saw your post. I've done 3 chapters of Chalkdust 3 or 4 chapters of TT and 5 chapters of BJU. Same problem every single time. He cannot do proofs. I've done a little bit of Khan academy and the regular kind of problems with angles and such he has no problem with whatsoever. He just cannot understand how to prove things.. I was going to ask what I needed to do to have him earn his Geometry credit. Someone suggested MUS Geometry. I cannot find a tutor and he will not listen to me. Oh, I mean he will sit there but you can tell he isn't really listening if that makes sense. He is working hard to raise his THEA score a few points so that he can take College Algebra with his friends in the spring at the cc. The teacher we are looking at has gotten good reviews like I never understood algebra until I had her kind of thing. His youth minister has gone back to school and will be taking the same class with the same teacher as well so that would be good as well. Anyway, we will do math in the fall, but I don't have a clue what to do to finish up Geometry credit. I'm thinking of looking for a end of course exam and having him take that to see where the holes are. Thanks for the company. :) Quote Link to comment Share on other sites More sharing options...

sattlers1 Posted June 28, 2012 Share Posted June 28, 2012 Wendy, I just want you to know that we are using VideoText geometry and the proofs are really tough. I have been posting questions on this myself. One thing that helped me is that there is more than one way to formulate the proof. The steps will not all match in order or reason. We use the two column method. As far as coming up with the statements/reasons I am beginning to think this just takes practice. Try to be kind and peak at answers a smidge to help guide. Hope that helps a little : ) Quote Link to comment Share on other sites More sharing options...

wendybern Posted June 28, 2012 Author Share Posted June 28, 2012 Wendy,I just want you to know that we are using VideoText geometry and the proofs are really tough. I have been posting questions on this myself. One thing that helped me is that there is more than one way to formulate the proof. The steps will not all match in order or reason. We use the two column method. As far as coming up with the statements/reasons I am beginning to think this just takes practice. Try to be kind and peak at answers a smidge to help guide. Hope that helps a little : ) So the answers in the teacher guide might not match her answers, but her proof could be correct? :confused: That is bad news for me, since I don't want to have to do geometry right along with her all year. A different kid, I would just work it through with her and let her watch the practice problem answers. But this kid does not like to think, and so she'll just copy the methods without understanding what she's doing, so I really need to make her think it through for herself. Maybe I do need an outside class with a teacher. Quote Link to comment Share on other sites More sharing options...

sattlers1 Posted June 28, 2012 Share Posted June 28, 2012 As simple as things could be in a different order or you could approach it from a slightly different point/perspective. I am doing VT geo with my dd so we are bouncing things back and forth between each other. Occasionally we have to pull in my mathy husband too. If these were not options, I would find a class, but make sure the teacher/tutor is good because this is tough stuff, but teaches some amazing thinking skills as did algebra. BTW my dd did great at alg 1 and 2 also. This is a whole 'nother beast! Quote Link to comment Share on other sites More sharing options...

Mom22ns Posted June 28, 2012 Share Posted June 28, 2012 So what is a good program that doesn't use proofs? This is a non-mathy, non-science child who is probably not college-bound. MUS is very light on proofs. Quote Link to comment Share on other sites More sharing options...

wendybern Posted June 28, 2012 Author Share Posted June 28, 2012 MUS is very light on proofs. Hmmm... we use MUS for my younger daughter (she would check out on the long explanations in TT). Have you used it? Liked it? Quote Link to comment Share on other sites More sharing options...

Mom22ns Posted June 28, 2012 Share Posted June 28, 2012 Hmmm... we use MUS for my younger daughter (she would check out on the long explanations in TT). Have you used it? Liked it? I have it, we'll be using it in the fall. Ds is planning to do Geometry in the fall, the Algebra 2 in the spring. Quote Link to comment Share on other sites More sharing options...

Candid Posted June 28, 2012 Share Posted June 28, 2012 A program without proofs can not be rigorous in a mathematical sense. Higher math is all about proving relationships, not about computation according to algorithms. Geometry is the easiest field to introduce formal proofs because it is possible to visualize relationships; the proofs required for calculus or other fields of math are much more abstract. I would highly encourage the OP to find a competent teacher instead of simply skipping proofs. I disagree, kind of, the crucial word is formal. Singapore does some things that show students the connections in math, but never requires what I did in geometry. Further, in the Lockhart's Lament we are told: There is nothing charming about what passes for proof in geometry class. Students arepresented a rigid and dogmatic format in which their so-called â€œproofsâ€ are to be conductedâ€” a format as unnecessary and inappropriate as insisting that children who wish to plant a garden refer to their flowers by genus and species. The problem with the standard geometry curriculum is that the private, personal experience of being a struggling artist has virtually been eliminated. The art of proof has been replaced by a rigid step-by step pattern of uninspired formal deductions. The textbook presents a set of definitions, theorems, and proofs, the teacher copies them onto the blackboard, and the students copy them into their notebooks. They are then asked to mimic them in the exercises. Those that catch on to the pattern quickly are the â€œgoodâ€ students. The result is that the student becomes a passive participant in the creative act. Students are making statements to fit a preexisting proof-pattern, not because they mean them. They are being trained to ape arguments, not to intend them. So not only do they have no idea what their teacher is saying, they have no idea what they themselves are saying. Even the traditional way in which definitions are presented is a lie. In an effort to create an illusion of â€œclarityâ€ before embarking on the typical cascade of propositions and theorems, a set of definitions are provided so that statements and their proofs can be made as succinct as possible. On the surface this seems fairly innocuous; why not make some abbreviations so that things can be said more economically? The problem is that definitions matter. They come from aesthetic decisions about what distinctions you as an artist consider important. And they are problem-generated. To make a definition is to highlight and call attention to a feature or structural property. Historically this comes out of working on a problem, not as a prelude to it. So I suspect that whatever is happening in Teaching Texts isn't very important to any true mathematical understanding and can be covered some other way with success. I'm afraid I have been very tunnel visioned since Singapore has worked well in my house. I think Saxon does not use proofs, but that's about the extent of my knowledge of other math programs. Quote Link to comment Share on other sites More sharing options...

ereks mom Posted June 28, 2012 Share Posted June 28, 2012 How long has she been at it? I distinctly remember that, when I took geometry in high school, the teacher told us that it would probably take 6 or 8 weeks or more of doing proofs every day before it began to click. At first, they made my head swim, and then I gradually began to see the logic. It was the same with both of my dc when I did geometry with them. If your dd has just started the course, give it some time. If she's been struggling for longer than a couple of months, you might want to consider a tutor. Quote Link to comment Share on other sites More sharing options...

ktgrok Posted June 28, 2012 Share Posted June 28, 2012 Kinetic Books has a geometry program. They go over it step by step, but more than that, in the practice problems the kid can ask for a hint, and get the first step. Then if they still need help, get another step. Etc. Maybe having it help her with the first step or two would help? Quote Link to comment Share on other sites More sharing options...

wendybern Posted June 28, 2012 Author Share Posted June 28, 2012 Kinetic Books has a geometry program. They go over it step by step, but more than that, in the practice problems the kid can ask for a hint, and get the first step. Then if they still need help, get another step. Etc. Maybe having it help her with the first step or two would help? Never heard of that. Thanks, I will look into it. Quote Link to comment Share on other sites More sharing options...

Deniseibase Posted June 28, 2012 Share Posted June 28, 2012 I think Saxon does not use proofs, but that's about the extent of my knowledge of other math programs. Actually, Saxon uses some two-column proofs in Advanced Mathematics, but not a lot. The Saxon Geometry book, which is not part of the 'standard' Saxon sequence, does a good job introducing proofs, but it's still not what I'd consider a rigorous and thorough treatment of proofs. On a side note, I LOVE proofs. Proofs in my Symbolic Logic class as a philosophy major in college were my first inkling that I could enjoy anything remotely math-related. I loved proofs so much that I became a TA for that professor for 3 semesters just because I enjoyed grading them so much - yes, I know, that makes me certifiable!!! :lol: But perhaps if proofs are causing problems, if your child is a 'wordy' child rather than a 'number' kid, maybe you could try your luck with a little symbolic logic stuff first to get the point of proofs across in a roundabout way? It sure helped me to see it - the structure is the same, just you are using symbols instead of those dreaded numbers, it made it a lot easier for me to grasp! :001_smile: Your local library should have some books on symbolic logic. It shouldn't be too hard to find one that will suit - I taught a co-op class on symbolic logic a few years ago and used a high school text called The Snake and the Fox - it was only a 6 week class and we did not go really in depth, and I don't have the book handy so I can't recall all the details, but it's very accessible and should help. Proofs are really the doorway to higher math. It's worth spending some time on them even for a non-STEM kid. I'm in a legal field now, and believe me, the ability to build a valid chain of evidence, the ability to THINK in the manner I was taught to think in logic class, makes a huge difference in my work. I really wouldn't just give them a miss. Quote Link to comment Share on other sites More sharing options...

Rhonda in TX Posted June 28, 2012 Share Posted June 28, 2012 No advice, but wanted to say that I never "got" formal geometric proofs either, yet I went on to get my undergraduate degree in mathematics. So there's still hope. :) Same here! :) I just wasn't ready at that age. Quote Link to comment Share on other sites More sharing options...

PeterPan Posted June 28, 2012 Share Posted June 28, 2012 Your local library should have some books on symbolic logic. It shouldn't be too hard to find one that will suit - I taught a co-op class on symbolic logic a few years ago and used a high school text called The Snake and the Fox - it was only a 6 week class and we did not go really in depth, and I don't have the book handy so I can't recall all the details, but it's very accessible and should help. Thanks for sharing that! It looks great for my dd! :D Quote Link to comment Share on other sites More sharing options...

Chris in VA Posted June 28, 2012 Share Posted June 28, 2012 Ds didn't do well in TT b/c of the proofs, either. I didn't in school, but I learned how later. I think something very helpful is to know the theorums and such backwards and forwards, and understand how a certain statement implies other knowledge. Could you maybe spend a little time going over the basics again, and showing her how one thing implies more? For example, you could show her a line cut by another line and give her one angle, and then ask her what the measurement of the supplementary angle is--then ask her how she knows that. Then right it as a proof for her--just 3 little steps. Do that with lots of the basic definitions and theorums and stuff (I'm blanking out on geometric terms here...). Do ykwim? Practice going from one step to the next. Or bag it and get someone else to teach it. ;) Quote Link to comment Share on other sites More sharing options...

EKS Posted June 29, 2012 Share Posted June 29, 2012 If you are not inclined to teach the material, then I think you may need to hire a tutor or enroll your daughter in a class. :iagree: Quote Link to comment Share on other sites More sharing options...

Lang Syne Boardie Posted June 29, 2012 Share Posted June 29, 2012 I didn't know formal proofs were optional. We just hung in there with ds until he got the hang of it. I think that's what we'll do for our others, too. Quote Link to comment Share on other sites More sharing options...

letsplaymath Posted June 29, 2012 Share Posted June 29, 2012 So the answers in the teacher guide might not match her answers, but her proof could be correct? :confused: Absolutely! This is the most difficult thing about teaching geometry proofs --- there are always more ways to do something than just the answer in the book. For example, this website lists nearly 100 ways to prove the Pythagorean Theorem. Quote Link to comment Share on other sites More sharing options...

laundrycrisis Posted June 29, 2012 Share Posted June 29, 2012 I never got proofs either...and I have an engineering degree and all the hours needed for a minor in math. I won't skip it - we will struggle through it - maybe I will finally get them by learning alongside our kids ? But I don't think they are important beyond the need for them on tests, unless a person goes on to more theoretical math classes as a grad student. Quote Link to comment Share on other sites More sharing options...

regentrude Posted June 29, 2012 Share Posted June 29, 2012 Further, in the Lockhart's Lament we are told: There is nothing charming about what passes for proof in geometry class. Students are presented a rigid and dogmatic format in which their so-called â€œproofsâ€ are to be conductedâ€” a format as unnecessary and inappropriate as insisting that children who wish to plant a garden refer to their flowers by genus and species. ... The art of proof has been replaced by a rigid step-by step pattern of uninspired formal deductions. The textbook presents a set of definitions, theorems, and proofs, the teacher copies them onto the blackboard, and the students copy them into their notebooks. They are then asked to mimic them in the exercises. Those that catch on to the pattern quickly are the â€œgoodâ€ students. The result is that the student becomes a passive participant in the creative act. Students are making statements to fit a preexisting proof-pattern, not because they mean them. They are being trained to ape arguments, not to intend them. So not only do they have no idea what their teacher is saying, they have no idea what they themselves are saying. Ah, but Lockhart does not argue against proofs themselves - he argues against "what passes for proofs in class", i.e. about poorly executed teaching of proofs, following a rigid formulaic pattern. The two-column proof is a sad example for this- artificial, formulaic, easy to grade, but far from how a mathematician would actually write a proof. Proofs are at the heart of mathematics. Just because many traditional programs do a poor job does not mean one should eliminate proofs - but rather that one should go to the trouble to teach the student well what it means to prove, and to let the students use their creativity when they create elegant proofs, not forcing them into a rigid format. I read his complaint as a complaint about the mathematics curricula. I doubt his solution would be to simply not cover stuff, but rather to use better materials and better teachers. They exist. Quote Link to comment Share on other sites More sharing options...

regentrude Posted June 29, 2012 Share Posted June 29, 2012 So the answers in the teacher guide might not match her answers, but her proof could be correct?. Yes. Often there are many different ways to prove something, and the student may actually find a more elegant solution than the teacher's manual. Quote Link to comment Share on other sites More sharing options...

sattlers1 Posted June 29, 2012 Share Posted June 29, 2012 (edited) Regentrude- Can you give a brief description of what a true, thorough proof would look like? In our geo curriculum, the student writes out an analysis of what they are going to prove, then we use the two-column method to list our statements and reasons to support. How would this be different? Since I do math with my dd, I can certainly say that we are having to reason through each step to justify the next step etc. creating that chain of logic to support the whole argument. Edited June 29, 2012 by sattlers1 additional thought Quote Link to comment Share on other sites More sharing options...

Candid Posted June 29, 2012 Share Posted June 29, 2012 Ah, but Lockhart does not argue against proofs themselves - he argues against "what passes for proofs in class", i.e. about poorly executed teaching of proofs, following a rigid formulaic pattern. The two-column proof is a sad example for this- artificial, formulaic, easy to grade, but far from how a mathematician would actually write a proof. Proofs are at the heart of mathematics. Just because many traditional programs do a poor job does not mean one should eliminate proofs - but rather that one should go to the trouble to teach the student well what it means to prove, and to let the students use their creativity when they create elegant proofs, not forcing them into a rigid format. I read his complaint as a complaint about the mathematics curricula. I doubt his solution would be to simply not cover stuff, but rather to use better materials and better teachers. They exist. I agree, but as I read his book, he suggests (using his own metaphor) holding off music theory until a child enjoys music. I assume he would take true mathematical proofs to be in that category and hold them off until the college level or higher. Although they might do fun sorts of things that come close to what we might call the spirit of proofs. I actually begin to wonder if some children might do well with real proofs but are completely flummoxed by the falseness of what passes for them in high school geometry texts. Kind of like having a non-athlete explain to you how to throw the ball. Sure some kids might just figure it out on their own, partly by ignoring what the person who doesn't know how to actually throw the ball and just doing it. The sad part of the current state of things, and we've gotten hints of it in this thread, is that some folks get to college and learn by accident that they might be more mathematically inclined by than they have been led to believe by the likes of Teaching Texts proofs. That I think is Lockhart's point. Find another source to teach this material and don't worry about it: what is being taught isn't real math and isn't real proofs. She is not missing anything of importance in this situation. Might there be something of importance with the same name? YES! But not in this particular situation. Quote Link to comment Share on other sites More sharing options...

Jane in NC Posted June 29, 2012 Share Posted June 29, 2012 (edited) Regentrude-Can you give a brief description of what a true, thorough proof would look like? In our geo curriculum, the student writes out an analysis of what they are going to prove, then we use the two-column method to list our statements and reasons to support. How would this be different? Since I do math with my dd, I can certainly say that we are having to reason through each step to justify the next step etc. creating that chain of logic to support the whole argument. Not Regentrude, but... The two column proof is a handholding device. If you were to look at an upper math text, you would see proofs that minimize English and appear quite symbolic. Also, mathematicians are speaking to each other so they do not necessarily justify each step as is done in a two column proof. If the reasoning is not clear to all, a mathematician will note "by such in such theorem". If you examine this link, you can read two (wordy) proofs of the Triangle Inequality. As has been previously noted, there are often many possible proofs of a single theorem. Edited June 29, 2012 by Jane in NC Quote Link to comment Share on other sites More sharing options...

regentrude Posted June 29, 2012 Share Posted June 29, 2012 I agree, but as I read his book, he suggests (using his own metaphor) holding off music theory until a child enjoys music. I assume he would take true mathematical proofs to be in that category and hold them off until the college level or higher. Although they might do fun sorts of things that come close to what we might call the spirit of proofs. I actually begin to wonder if some children might do well with real proofs but are completely flummoxed by the falseness of what passes for them in high school geometry texts. I am not sure that this would be a correct interpretation, because proofs are one of the first thing that are REALLY mathematics - most stuff before is just computation. I would see the computation as the boring theory part, and the proofs as making real music, aka actually doing math as opposed to only arithmetic. In my home country, math is taught completely differently from the US, and geometric proofs of triangle identities are taught in 6th grade. I was not particularly interested in what passed for math up to that point, but around that time I developed a real interest, and proofs definitely helped spark this interest. Of course it also helped to have a great teacher who actually understood what he was teaching and who could show us the beauty and elegance of proofs. We never did two column formulaic proofs, we wrote them out, in words and symbols, as a continuous argument. Quote Link to comment Share on other sites More sharing options...

TravelingChris Posted June 29, 2012 Share Posted June 29, 2012 I completely agree with regentrude. I have three children who have done or are currently doing geometry. One loved it and it was his favorite class at that time. He later switched from history to a philosophy major. Second had a very specific ld problem that made geometry more difficult. (Her brain processes her vision in parts, rather than as a whole picture). Nonetheless, she could do proofs, but it was harder for her. However, she became very, very good at writing long, logical briefs. Now, there is the third- she is the one most likely to come up with an alternate proof. BUt no problems with her. FOr the latter two, I have used LOF geometry and that was a very good way to introduce proofs. He doesn't just give you examples and then hand you a different proof to solve. He leads your thinking so you come up with answers yourself. Also, the proofs start from mostly completed and end up with totally done by the student. This is not a one lesson transition. It does take time, depending on the student. My middle one took the longest. Quote Link to comment Share on other sites More sharing options...

Deniseibase Posted June 29, 2012 Share Posted June 29, 2012 The sad part of the current state of things, and we've gotten hints of it in this thread, is that some folks get to college and learn by accident that they might be more mathematically inclined by than they have been led to believe by the likes of Teaching Texts proofs. I think you might be talking about me here :-) So I feel obliged to pop in and say I never saw a proof before college - I was a double English major in high school and took only Algebra I and Geometry, and the geometry I took was pretty remedial, just angles and figuring perimeter and area. I agree that there is a lot of bad math out there on the elementary level - I've tutored kids in our local school district. And the whole notion of cookie cutter math is a big problem, including 'cookie cutter proofs', if we take that to mean proofs that are taught as a procedure to follow instead of an argument to build. But not having seen Teaching Textbooks, I can't even imagine it, proofs that HAVE to be done only by following a specific procedure - I can't picture it. So I have to wonder, and this is JUST speculation on my part, if maybe some of the problem is perception? Like there might be some perception that proofs have to be done in a very cookie cutter manner, when really, they don't? ('Cuz REALLY, they don't!! :D ) Like I said, haven't seen TT at ALL, so I'm just not picturing it. Maybe someone could post an example? ('Cuz you've got me kinda curious now!!! :D ) Quote Link to comment Share on other sites More sharing options...

Candid Posted June 29, 2012 Share Posted June 29, 2012 I'm not going to go back and hunt through posts to see who it was that made me think that, but you could be right! However, there's another dynamic that hasn't been mentioned in this thread: some people find they like either algebra or geometry (and proofs) more than the other. So it's possible that is the case, too. I always liked both and symbolic logic in college, but I don't think I'm creative enough to be a true math person (that and my personality is not suited for it). Quote Link to comment Share on other sites More sharing options...

MIch elle Posted June 29, 2012 Share Posted June 29, 2012 I didn't know formal proofs were optional. Yes, you can pass high school geometry without doing any proofs. From what I understand, lower level high school geometry classes do not teach proofs. Quote Link to comment Share on other sites More sharing options...

EKS Posted June 29, 2012 Share Posted June 29, 2012 Yes, you can pass high school geometry without doing any proofs. From what I understand, lower level high school geometry classes do not teach proofs. In our district, which likes to pride itself on being the "best" in the state, the regular geometry class is essentially algebra with shapes, while the the honors class uses Jacobs 3rd edition, where there is some work with proofs, but not enough, IMHO. Quote Link to comment Share on other sites More sharing options...

sattlers1 Posted July 1, 2012 Share Posted July 1, 2012 took only Algebra I and Geometry, and the geometry I took was pretty remedial, just angles and figuring perimeter and area. That's all I remember. I had heard of proofs, but I don't remember having to prove them. And the whole notion of cookie cutter math is a big problem, including 'cookie cutter proofs', if we take that to mean proofs that are taught as a procedure to follow instead of an argument to build. This matches more of the concept of RightStart math that we used in elementary grades - math is a puzzle to be solved and there is not one correct way. So I have to wonder, and this is JUST speculation on my part, if maybe some of the problem is perception? Like there might be some perception that proofs have to be done in a very cookie cutter manner, when really, they don't? ('Cuz REALLY, they don't!! :D ) This would really be freeing! The idea that your whole idea is just to create this chain of an argument, that doesn't necessarily match the solutions, but as long as it makes good, logical sense, it's valid. After doing Alg 1 & 2 we learned that math is a language. That is so true. Now we get to proofs and the step method seems to take away the language part of math. This thinking on proofs would put the language back into geometry. Rather than an exact solution to find, it's an argument to build and just as no two people would build a verbal argument the same, so could be true of a mathematical proof argument. I also liked the post where it was said something like - if it's obvious no reason is given, otherwise a theorem or postulate is cited. So using this method, how would you check proofs- just check over each other's and if the reasoning flows, it's good? Because in going over some proofs (VideoText) we may have had 9 steps and they had 17. Every teeny, tiny thing that we would have assumed was obvious was stated. I still want to look over the site that was posted with the proofs done in the more mathematical, un-formulaic format. Any direction on checking over proofs would be appreciated. Since this is such a new way of thinking of math - specifically geometry proofs. I feel like a little kid just finding all these secrets out! Quote Link to comment Share on other sites More sharing options...

Deniseibase Posted July 1, 2012 Share Posted July 1, 2012 if it's obvious no reason is given, otherwise a theorem or postulate is cited. So using this method, how would you check proofs- just check over each other's and if the reasoning flows, it's good? Because in going over some proofs (VideoText) we may have had 9 steps and they had 17. Every teeny, tiny thing that we would have assumed was obvious was stated. Pretty much, yeah. If the reasoning is sound, it's fine. If they point out every obvious step, great, but there are plenty of possible ways to build most proofs, no answer book could possibly cover them all. One caution - be careful that what you allow the student to omit as 'obvious' is truly something that they understand thoroughly, and that they really can explain how to get from Point A to Point B. The whole reason two-column proofs are used with beginners is because they force the student to be explicit with their reasoning. There are PLENTY of things my DD will tell me are 'obvious', and they are to her!! And she's right! But that doesn't necessarily mean she can explain it in words the way a professional could, and that's part of the skill you are building here too. There's a difference between being right & obvious & actually knowing how to build a chain of reasoning that someone else can follow. Hope that helps!!! Quote Link to comment Share on other sites More sharing options...

sattlers1 Posted July 1, 2012 Share Posted July 1, 2012 Yes it does. Thanks! Quote Link to comment Share on other sites More sharing options...

EKS Posted July 1, 2012 Share Posted July 1, 2012 So the answers in the teacher guide might not match her answers, but her proof could be correct? This is the problem that I had teaching geometry. Unless my son's proof was fairly similar to the one in the answer book, I had to figure out for myself if his proofs were correct. I found that teaching geometry was fairly straightforward except for this issue. Even so, if I find myself having to homeschool geometry again, I will farm it out (to Derek Owens) because I don't want to deal with the grading again. (BTW, I had to hold my son's hand for the first few months of his geometry course while he got the hang of proofs.) Quote Link to comment Share on other sites More sharing options...

Musicmom Posted July 2, 2012 Share Posted July 2, 2012 She successfully completed TT Alg 1 & 2 and did very well. With TT geometry, though, she has hit an early wall. She just doesn't get the proofs at all -- the logic of them, how to construct them. Confession: I don't remember this stuff myself, and I don't want to relearn it all, so I'm not much help. I could learn it to teach it; or . . . ? Is there a different geometry program or resource that would help turn on the lights as far as proofs, that we could either switch to or just detour to temporarily? THANK YOU for any advice. Entering this discussion late, but I wanted to suggest one way of potentially breaking through the wall. We used Videotext, and I once had a phone conversation with the author that was very enlightening. My ds was struggling with the sheer volume of proofs at the time, so I was calling to ask about the workload, but anyway, the author of VT explained to me that the point is not to do proofs--they will never have to do geometry proofs ever again in later math--the whole point of the proofs is to develop the analytical thinking processes that are behind them... So with that in mind, one thing you could try would be to take ALL pressure off your dd to actually do the proofs herself, and instead have her sit down with the solutions (and a list of all the theorems/postulates, etc. handy) and have her just analyze them--see what they did, how they got to the next step, what reasons they cited, etc.... and you could do this alongside her. Once she starts to "get" how they did it, continue to have her analyze and then explain them to you. .... Often there are many different ways to prove something, and the student may actually find a more elegant solution than the teacher's manual. :iagree:Once she starts understanding the solutions that are given, and is able to explain them to you, then she could start to look for other ways of doing the proof--alternate steps that would lead to the same conclusion. If she practices doing this enough, she may well get to the point of being able to proofs on her own. And even if she doesn't reach that point, she still will have had a lot of exposure to the thinking processes and will benefit from that. Just an idea. Quote Link to comment Share on other sites More sharing options...

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