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Geometry? Postulates, Corollaries & Theorems?


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This is probably my fault, lol. I thought dd would like Geometry b/c she's logical and visual, but I feel like we're just mucking along here.

 

Dd did well with Foerster Algebra 1, and is picking up the trig she needs for basic physics without breaking a sweat, but she is not getting the "true or false" or "may be true" or sometimes answers requiring the postulates, corollaries and theorems correct in Jacobs 2nd edition. And she complains about proofs, a lot, but doesn't really seem to mind them. She just thinks they are a waste of her time.

 

She can zip through anything that requires a construction. I think mostly the problem is, that in Jacobs, everything has a Jacobs-only label rather than a name (ie Postulate 8 in Jacobs is only that in Jacobs, Postulate 8 is something else in a different textbook). I tried to make her memorize them in the first few chapters, but that was a bust, "How can I tell Corollary 1 from Corollary 2?"

 

I'm looking at the Fresh Approach book, but there's no "list" anywhere- they are spread out all.over.the.book.

 

First off, I assume I should have her memorize these things, but is there a list somewhere of what they are conventionally called?

 

I looked online, but most of what I see is specific to a textbook. Jacobs has a list in the back, too. Should I just tell her to suck it up and memorize them for each chapter? This is a skill she doesn't have. Even in foreign language she mostly retains vocabulary from doing the book work.

 

We're finishing Chapter 6, and while I can tell she understands the big ideas behind the lessons, she's not scoring well (80-85%ish). I think part of it might be tad bit of slacking (why work an extra 20 minutes for another 2 correct answers?), and part of it is that she's just not excited by the material at all.

 

Should stop here and make sure she's "got it" before moving forward... or switch to another program now?

 

I think she likes Jacobs because she can do it fast. At first she liked the Set 3 problems, but now she just wants to get done. She really liked the first chapter on Logic b/c we'd talk about the answers, but doesn't want my help now because it takes longer. She gets antsy if school goes much past lunch.

 

Any thoughts, suggestions or BTDT?

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I guess I don't understand. 

 

You don't learn the numbers of the theorems (postulates, etc), you learn the theorems themselves.  I doesn't matter what they're numbered.  You can agree on how to abbreviate them when she writes them down.  You'll find that some are used way more often than others.  I never made my kids memorize them.  I just photocopied the list in the back of the book for them to use.

 

What do you mean by scoring well?  Are you grading the practice problems?  If so, I would not.  The practice problems are for practice and it's not fair to gauge her understanding by how she's doing on them.  Also, there are multiple ways to do proofs, and the answer given in the teacher's guide is just one possibility.  You need to be able to do the proofs yourself to see if she did them right.

 

I would give a test at the end of each chapter.  There is a test book that goes with Jacobs 2nd, but it's difficult to find.  

 

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DD#1 had trouble remembering all the different theorems & postulates when she was attempting to complete proofs. One poster (maybe quark?) on here explained how she had her kid write them on little notecards & keep them in a small 2-ring index card binder. She used it when she did daily lessons & I allowed her to use it for quizzes & tests. Eventually, she was able to remember the more commonly used ones - and it also helped her remember that a certain one existed that she needed to prove something, even if she didn't quite remember all the details.

 

Here's another thread that talks about this issue: Geometry Question

I found others - many of which included making index card notes. It is important that she understand what each one means and that there isn't any one correct answer for a proof.  So, if hers doesn't exactly match the solution manual, it doesn't mean it is wrong. I literally had to think through each of the proof answers on homework, quizzes, and tests to see if I could follow DD's logic to the correct end.

Edited by RootAnn
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I could have used this thread a month ago! Thank you for the ideas for the list of theorems or note cards. My 15yo really would have benefited from such, but I didn't think of it at the time. I will keep this in mind for the next kid. Thanks for posting!

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First, I would suggest that you and your daughter watch the video on proofs on the DVD that came with your copy of A Fresh Approach.  Or, if you've lost the DVD, here's a link to the same video:

http://aplusses.com/zencart/index.php?main_page=page_2

Please watch the video with her, and pause it frequently while the two of you discuss it.  And please make sure to print the document that it tells you to print.  That may help her understand how to dissect what the different definitions, postulates, and theorems tell her in the future. 

Second, I think you might find the Quick Reference Guides I sell on my website useful.  I can't say that they cover everything in the book, but they probably cover about 3/4 of it.  Also, some of statements of the definitions, postulates, and theorems will vary from book to book, but, for the most part, they can be used with any curriculum.

 

I hope this helps! 

 

ETA:  As far as your question about memorization, I made my students memorize everything when I taught Geometry fifteen years ago.  But things have changed because many books and teachers don't teach proofs any longer.  Here in Georgia, for instance, the Department of Education expects the teachers to cover almost all of Geometry in one semester, and proofs often get skipped.  I had a (public school) tutoring student that I saw last week who told me that her teacher had told the class that there would be a proof on the upcoming test, but, because he didn't have time to teach the concept, the students were supposed to memorize the proof and write the proof as they saw it on the study guide.

So, here's what I would suggest.  I would ask your daughter to do all the parts of the tests that don't require her to write a definition, postulate, or theorem without the help of note cards (or, if you choose to purchase them, my Quick Reference Guides).  This will help her do better on the SAT and/or ACT.  Then give her any note cards she's made (or, if you have them, my Quick Reference Guides) and let her do the problems that require her to quote the definition, postulate, or theorem.

Edited by Christy Walters
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This is me! I'm sitting here checking out the forums instead of checking the geometry work that is right beside me. :laugh: When I finally check the work, I have to get my daughter to explain things to me.

I hate grading (or checking) geometry.  

 

My empathy is all I can contribute.  It's one of the reasons I'll be doing a happy dance when this year is over:  my youngest will have finished geometry and is going to high school.  

 

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This is me! I'm sitting here checking out the forums instead of checking the geometry work that is right beside me. :laugh: When I finally check the work, I have to get my daughter to explain things to me.

 

Ha! I should be grading papers for my coop class, but here I am.

 

I'm just avoiding the whole Geometry thing right now. "Let's do a little algebra review this week. With AoPS." It is kind of funny because I really never thought she'd go for it. She was in a very good mood while she was working, so I think she probably just needed a change of pace.

 

I think we'll jump back in by doing the AFA video for proofs then do review sections from every chapter up until where we are, and then go forward from there.

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ETA:  As far as your question about memorization, I made my students memorize everything when I taught Geometry fifteen years ago.  But things have changed because many books and teachers don't teach proofs any longer.  Here in Georgia, for instance, the Department of Education expects the teachers to cover almost all of Geometry in one semester, and proofs often get skipped.  I had a (public school) tutoring student that I saw last week who told me that her teacher had told the class that there would be a proof on the upcoming test, but, because he didn't have time to teach the concept, the students were supposed to memorize the proof and write the proof as they saw it on the study guide.

 

 

I suspect this has to do with the changes in the SAT. There is less Geometry on it and more Algebra 2. I think schools are trying to get students as much Algebra 2 as they can ASAP.

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