Help from AoPS gurus...panic has set in

[daijobu]

We're close to wrapping up AoPS geometry with dd#1.  My complaint about geometry is inadequate nomenclature.  When I'm doing algebra using segment lengths, AB to me looks different from BA.  And the same angle looks different to me when it's written as <ABC and <CBA.  So it takes me f.o.r.e.v.e.r to slog through the solutions.  My advice is to call segment lengths and angles by a single letter: x or alpha or something.   I think it looks cleaner.  Like 180 - 2*a - 2*b to me seems clearer than 180 - <ABC - <CAB.  

 

But there is still the issue of translating AoPS solutions to your own style.  Sometimes there are so many points and angles and lengths that I run out of labels.  I've got some crazy diagram full of segments, triangles, circles, intersecting curves.  "I'm searching for angle QZP.  Where the heck is point P?  Oh there it is.  Now where is point Z again?"  Ugh.  

 

It's frustrating sometimes and sometimes we just give up.  I agree with PPs that videos would be enormously helpful.  While the solutions are adequate, I wish the used my 1-segment==1 letter and 1 angle == 1 letter nomenclature.  Am I the only one who prefers this?  

 

(end rambling vent)

[happyhome]

Do you have a college or university nearby? Maybe their math department could help you fnd a tutor amongst their students. Maybe a local math circle where kids are working at a higher and deeper math level.

 

Fwiw my kids did geometry as self study without the class. The solution manual was enough for what they needed. The oldest tested into PreCalc at the CC the next semester. Both kids did well on the SAT even without having used a class for AOPS.

 We do have a university.  I've reached out to their math department.  They're open to higher levels but Geometry didn't seem to light their sox on fire.  I'm trying the CC now.  

 

Regarding the AoPS classes, at the pace they're offered, I don't think they would be a fit.  But I like the idea of studying ahead of the class then taking it.  That's an option.  I'm probably overreacting anyway.  I thought all of the AoPS books would be hard and she has breezed right through.  

[happyhome]

This is an issue with every geometry text. We didn't use AoP for geometry, but dd often had proofs that differed from the book. She was able to to compare the text answer to her response and make what sounded like reasonable comments as to why the answers were both acceptable or not  :lol:

 

I would think a solid math tutor could GRADE AoP proofs (not guide her through the book, but grade the proofs). However, I honestly wouldn't worry about it if your dd feels confident in grading/reviewing them herself - kids who want to cheat their way through math aren't likely to pick AoP to begin with! 

 

I do think that a tutor, or at least an online math group, would be a big help for discussion and encouragement. My dd did part of AoP intro to algebra but didn't complete it even though she was doing well. I think a class would have helped immensely, but she is another one who could handle the book but not at breakneck speed (they're out there, AoP, are you listening??). 

 

It still did her and her brain a world of good, and was well worth the while. 

 

That's my fear...."Mom, this makes sense because of ...." - and me standing there saying "ok, if you say so."  Honestly, Geometry is the only thing that has made me wonder what on earth I was thinking when I decided to homeschool.  I know it's doable.  This conversation with these two teachers just really threw me.  It's weird because, generally speaking, I'm not easily thrown.  The good news is that, as of late last week, a couple of people here have reached out to me to offer tutoring and grading so I think we're in good shape now and my confidence is rising. :hurray:  :hurray:

[happyhome]

We're close to wrapping up AoPS geometry with dd#1.  My complaint about geometry is inadequate nomenclature.  When I'm doing algebra using segment lengths, AB to me looks different from BA.  And the same angle looks different to me when it's written as <ABC and <CBA.  So it takes me f.o.r.e.v.e.r to slog through the solutions.  My advice is to call segment lengths and angles by a single letter: x or alpha or something.   I think it looks cleaner.  Like 180 - 2*a - 2*b to me seems clearer than 180 - <ABC - <CAB.  

 

But there is still the issue of translating AoPS solutions to your own style.  Sometimes there are so many points and angles and lengths that I run out of labels.  I've got some crazy diagram full of segments, triangles, circles, intersecting curves.  "I'm searching for angle QZP.  Where the heck is point P?  Oh there it is.  Now where is point Z again?"  Ugh.  

 

It's frustrating sometimes and sometimes we just give up.  I agree with PPs that videos would be enormously helpful.  While the solutions are adequate, I wish the used my 1-segment==1 letter and 1 angle == 1 letter nomenclature.  Am I the only one who prefers this?  

 

(end rambling vent)

 

 

The fact that I have no idea what you're talking about is another sure sign that I MUST outsource this course  :lol:  :lol:

[EKS]

I really really wish AoPS would offer classes that went at a more normal speed and supported all levels with videos.

[kiana]

It'll be ok.  If you didn't really catch those topics like "incenter" and "orthocenter" the first time they came up in the book,  they'll turn up in some later class problems (insert evil laugh, but honestly, I've learned a lot!  I would have loved to learn geometry with aops).

 

You know, I made it through a math phd and never heard those terms :D

[kiana]

Ok, while we're confessing?  I cannot get the Triangle Inequality.  I've seen it in Alcumus, in Beast Academy for 3rd graders(!), in CTC's geometry, and now in EdX.  And I just. can't. seem. to get it through my thick skull.  Really, I'm a reasonably intelligent person in other areas, but I can't get my brain to keep ahold of this concept.

 

Now that one is actually pretty fundamental -- is there something in particular that you don't understand? 

[mathmarm]

Dd is finishing Intro to A book and will be moving on to Geometry soon.  Ideally, I'd love for her to take the AoPS online class but I think it will move too fast for her.  Without the benefit of the online videos, I am nervous that without help, I won't be able to discuss/grade her proofs appropriately.  

 

So, I called around to try to find a tutor to help us.  I met with two former high school Geometry teachers who have both given me some combination of "this is overkill, she'll never need this, why would you make this so hard."  Alarmingly, one told me that proofs are now done in a fill in the blank format and that two column, and definitely paragraph, formats are completely outdated and unnecessary for the EOC, SAT and college.  Is their assessment accurate or did I just get a bad lot?  

 

So, now I've started to panic.  What if I can't find a tutor that will work with this text?  What if she gets into this book and can't do it on her own?  And what if it's then too late to register for one of the non-AoPS online classes?  She loves AoPS but this last meeting with this teacher has left me feeling panicked and wanting to pull the Mommy card and just enroll her in one of the regular paced online classes and move on.  That's not what she wants but I know I can't see her through the higher levels.  Algebra II was always my limit.  Hive, please help.

You let each and every tutor know that you are not paying them for their opinions of your daughters preferred text, but for their assumed math expertise. You point out that they either have the chops for it, or not. You don't want beef-hash, but chops.

 

If they have the chops and keep their math-apathy and test mindedness to themselves you don't give a shit what they think of your daughters preferred text so long as they help your daughter appropriately.

 

The end.

 

[Chrysalis Academy]

Now that one is actually pretty fundamental -- is there something in particular that you don't understand? 

 

I really can't explain it.  I understand the concept that the length of the third side must be less than the sum of the lengths of the other two sides.  I understand drawing the triangle and collapsing it into a straight line, or extending the leg into a straight line, and thus finding the upper and lower limits of what the third side can be.  But somehow when it gets written as c<a+b and then I have to apply it to example triangles, I just can't quite make the leap.  I can't grok it, understand it intuitively and thus easily apply it, the way I can with angle measures in triangles and parallel lines, or other things.  I can't "see" it.  Does that make sense? So I can figure it out, because I know the underlying principle, but it always makes me stumble.  It's frustrating.  I don't know why I have this problem with this specific theorem.

 

Ok, end of Rose's therapy session! Unless you have any suggestions?  ;)  :D

[wapiti]

Unless you have any suggestions?

Have you tried making a system of inequalities, so that not only do you have

 

a + b > c

 

but also

 

a + c > b

b + c > a

[Chrysalis Academy]

I always have to translate inequalities into words before I can actually understand them!  But if I say "the sum of any two sides must be greater than the 3rd side" maybe that will work.  That's somehow more clear than "a side length must be less than the sum of the other two sides" for some reason.

 

Is it also always the case that c> a-b?  If a is the longer side?  I'm thinking of triangle ABC where AB=6 and BC=10.  AC has to be less than 16 and greater than 4.  Can you always subtract the shorter of the two known sides from the longer to find the lower limit of the unknown side?  You can, right?

[wapiti]

Yes.  I too have trouble visualizing and drawing these types of problems; setting up a straightforward system of inequalities seems to be the easiest way for me.

[kiana]

I always have to translate inequalities into words before I can actually understand them!  But if I say "the sum of any two sides must be greater than the 3rd side" maybe that will work.  That's somehow more clear than "a side length must be less than the sum of the other two sides" for some reason.

 

Is it also always the case that c> a-b?  If a is the longer side?  I'm thinking of triangle ABC where AB=6 and BC=10.  AC has to be less than 16 and greater than 4.  Can you always subtract the shorter of the two known sides from the longer to find the lower limit of the unknown side?  You can, right?

 

Yes. And I think putting the inequalities into words would help a lot. I phrase it as "two sides can't add to less than the third side" because for me that is clearest and if I try to draw it out it is clear to me that this can't happen. But frequently for me it is clearer to think about what can't happen than what must happen. 

[Chrysalis Academy]

Yes. And I think putting the inequalities into words would help a lot. I phrase it as "two sides can't add to less than the third side" because for me that is clearest and if I try to draw it out it is clear to me that this can't happen. But frequently for me it is clearer to think about what can't happen than what must happen. 

 

Ah, yes, that is clearer.

 

Thank you kiana and wapiti! There is hope for me yet, perhaps.  I do feel like I have no business trying to teach Geometry, though, because I have a hard time getting it intuitively.  Algebra makes more sense to me.

[kiana]

Ah, yes, that is clearer.

 

Thank you kiana and wapiti! There is hope for me yet, perhaps.  I do feel like I have no business trying to teach Geometry, though, because I have a hard time getting it intuitively.  Algebra makes more sense to me.

 

You know, it's kind of funny but one of the classes I teach every year at university is the one that I almost dropped out of graduate school over. It made NO sense to me. (now it does)

[happyhome]

You let each and every tutor know that you are not paying them for their opinions of your daughters preferred text, but for their assumed math expertise. You point out that they either have the chops for it, or not. You don't want beef-hash, but chops.

 

If they have the chops and keep their math-apathy and test mindedness to themselves you don't give a shit what they think of your daughters preferred text so long as they help your daughter appropriately.

 

The end.

 

Wow,when I read this,I could feel myself saying, "Yeah, yeah, yeah...what she said, you #^#*%^%*#!" I would normally think and say something along those lines. My kids were in public school for two years before I pulled them out. Believe me, I've faced many a clueless teacher and fought for my kids. This was my first experience with tutors of any kind and I was stunned, just simply stunned that a PAID tutor wouldn't jump at the chance to teach engaging, thought provoking math to an eager, young girl. I guess I'm just spoiled by our resident group of AoPS cheerleaders, who also happen to be physicists, mathematicians, engineers, etc.

 

Needless to say, I've learned now. I know the questions to ask and how to graciously get away from someone who doesn't support what we're doing. You'd think my in-laws, with all their false "concern for the children," would have taught me this already, but the lessons are new every day I guess.

[kiana]

This was my first experience with tutors of any kind and I was stunned, just simply stunned that a PAID tutor wouldn't jump at the chance to teach engaging, thought provoking math to an eager, young girl. I guess I'm just spoiled by our resident group of AoPS cheerleaders, who also happen to be physicists, mathematicians, engineers, etc.

 

Yeah, I can tell you that if someone came to me with an AOPS book and an eager kid I would be all over that. Heck, I'd do it half price just because it's FUN to work with kids who actually WANT to learn math and relish challenging problems.

[Chrysalis Academy]

Hah! I think I finally mastered the triangle inequality!  I was learning Heron's formula today and realized that when I got a triangle with an area of 0, it had to be a straight line - because a+b=c!  And I even knew why!  

 

Man, I sure don't remember high school geometry.  That whole year is a fog.

[regentrude]

We're close to wrapping up AoPS geometry with dd#1.  My complaint about geometry is inadequate nomenclature.  When I'm doing algebra using segment lengths, AB to me looks different from BA.  And the same angle looks different to me when it's written as <ABC and <CBA.  So it takes me f.o.r.e.v.e.r to slog through the solutions.  My advice is to call segment lengths and angles by a single letter: x or alpha or something.   I think it looks cleaner.  Like 180 - 2*a - 2*b to me seems clearer than 180 - <ABC - <CAB.  

 

But there is still the issue of translating AoPS solutions to your own style.  Sometimes there are so many points and angles and lengths that I run out of labels.  I've got some crazy diagram full of segments, triangles, circles, intersecting curves.  "I'm searching for angle QZP.  Where the heck is point P?  Oh there it is.  Now where is point Z again?"  Ugh.  

 

It's frustrating sometimes and sometimes we just give up.  I agree with PPs that videos would be enormously helpful.  While the solutions are adequate, I wish the used my 1-segment==1 letter and 1 angle == 1 letter nomenclature.  Am I the only one who prefers this?  

 

Actually, I do like their nomenclature because it is very clear which angle they are talking about, since the name contains the three points that are involved. I find it easier to correlate their names to a drawing. If they called a segment "x", you'd always have to refer to their definitions to figure out what exactly x is.

 

When I work the problem myself with my own drawing, I can label things with single characters. But in order to follow somebody else's solution, I appreciate that they make this possible to follow without a figure.

 

[Arcadia]

When I work the problem myself with my own drawing, I can label things with single characters. But in order to follow somebody else's solution, I appreciate that they make this possible to follow without a figure.

 

:iagree:

[daijobu]

Speaking of Intro Geometry, dd13 just finished the book TODAY!  And...we found what is probably an error in the solution to the very last problem, yes, the heptagon problem.  Talk about confusing: all those parallel lines and rotated points.  Ugh, that was painful.  It took some head-scratching to find the error, too.  Well, we're on to advanced algebra...tomorrow!  

[Ravi B]

Congrats to your DD!  If you're sure you've found an error, and it's not in the errata list, then you can send a message to books@artofproblemsolving.com.  The errata list can be found here:  

www.artofproblemsolving.com/booklinks

 

[daijobu]

Congrats to your DD!  If you're sure you've found an error, and it's not in the errata list, then you can send a message to [email protected]<script cf-hash='f9e31' type="text/javascript"> /* */</script>  The errata list can be found here:  

www.artofproblemsolving.com/booklinks

 

Yes, this isn't our first error.  (We found a lot in the newly published PreA.)  I always run them by Richard to see whether it is indeed an error.  (I can't always tell, lol!)  Sadly, he doesn't give out Knuth checks, or I'd be rich and famous!  

[daijobu]

It's been confirmed by Richard: the heptagon in the last problem is rotated about point A, not point D as described in the solutions.  I swear, sometimes I feel like we're the only ones who read the problems and solutions carefully enough to notice these things.  Or maybe we're the only ones who actually need to read the solutions, lol!  

[Julie of KY]

I've found a lot of errors along the way as well. Mostly little, but some big ones too.

[JoJosMom]

Yeah, I can tell you that if someone came to me with an AOPS book and an eager kid I would be all over that. Heck, I'd do it half price just because it's FUN to work with kids who actually WANT to learn math and relish challenging problems.

 

Where do you live, kiana???? (She says only half joking :001_smile:)

[happyhome]

Just wanted to update this old thread. We've decided to go with Chalkdust geometry as our main text and use AoPS for enrichment. We got through chapter 4 in AoPS but dd wasn't enjoying it. She loves AoPS but not this book. We looked at Wilson Academy for Jurgensen but dd doesn't want another online class. Then, this past weekend, we had the pleasure of meeting Dana Mosley (Chalkdust) at a conference. His style and approach just clicked. He's also available by phone and email should we get stuck. We're happy and dd feels confident again. Now I just have to line up AoPS with Chalkdust so she can pull from AoPS when she'd like a change. Thanks to all who offered to help and tutor but I think this plan best matches dd.

[Julie of KY]

Glad you have a plan.

 

On the other hand, I wouldn't bother trying to line up AoPS with Chalkdust. If looking for a change I'd pick up where you left off in AoPS. If some of AoPS seems like a review, then just skip to the harder review problems before moving on. I think most would have a difficult time jumping ahead in AoPS even if they covered the geometry elsewhere because AoPS generally goes deeper and some topics will be introduced that are not taught elsewhere.

[happyhome]

I see what you mean Julie. I just thought it would help if she wasn't jumping around too much and unfortunately, I don't have the expertise to know when/if she's jumping into something without the right level of prerequisite skill. I'll take another look at Chapter 5.