AoPS Geometry - need tips

[crazyforlatin]

I need tips on how to make this book doable for us. I'm not a very visual person. I think DD is more visual than me. I need to actually turn the book sideways to look at parallel lines as left to right or straight up and down. DD uses color pencils to color in same angles. We're almost done with Chapter 2, and I'm worried what the future holds in future chapters. DD seems to really like geometry and won't switch to the book that I'm tempted to use, Jurgensen.

[regentrude]

Colored pencils is exactly what I was going to suggest.

Make a drawing for every problem. Use color to mark things that are the same: sides, or angles. Use color to mark lines that are parallel.

Take your time. Don't schedule, just put in time on task - some problems will be very long and time consuming, but you'll learn a ton. Just anticipate that this will happen and don't get frustrated.

I've done the book twice. It's fabulous.

[LJPPKGFGSC]

I love teaching from Jurgenson Geometry!  

 

What about it turns off your daughter?

[wapiti]

Jurgensen is an excellent, straightforward book, though it will seem boring by comparison to AoPS Geometry.  It's great to have on hand for reference or in case a chapter in AoPS just doest go well - you can do the topic in Jurgensen and then return to AoPS :001_wub: .  And don't forget about Alcumus for more practice or for review!  Take your time and have fun!

Edited October 2, 2016 by wapiti

[crazyforlatin]

I love teaching from Jurgenson Geometry!

 

What about it turns off your daughter?

I would love to teach from Jurgensen. After going through a few AoPS books, I need a break. I could handle AoPS algebra because I'm comfortable with algebra. And I already knew AoPS geometry would be a problem for me, but DD is used to the AoPS format; she's been using it for a few years so there's the familiarity. It's hard for her to leave the AoPS ecosystem.

 

I'm also bothered by the lack of 2-column proofs. I like the look of 2 columns. It's orderly whereas now DD is writing out long sentences. It feels inefficient.

[regentrude]

I would love to teach from Jurgensen. After going through a few AoPS books, I need a break. I could handle AoPS algebra because I'm comfortable with algebra. And I already knew AoPS geometry would be a problem for me, but DD is used to the AoPS format; she's been using it for a few years so there's the familiarity. It's hard for her to leave the AoPS ecosystem.

 

I'm also bothered by the lack of 2-column proofs. I like the look of 2 columns. It's orderly whereas now DD is writing out long sentences. It feels inefficient.

 

The 2 column proof is a crutch that helps teach kids; it is not a standard people who do math actually use, and it is not a format one needs to master.

Your DD should learn to use the short hand and not write full sentences; mathematics has symbols for "therefore follows" (an arrow),

"all", "and", etc. A proof can be written concisely without the two column format. It should not need any full sentences.

 

Btw, you don't have to "teach" AoPS because the books are written TO the student to be used without an instructor.

Edited October 4, 2016 by regentrude

[kiana]

I'm also bothered by the lack of 2-column proofs. I like the look of 2 columns. It's orderly whereas now DD is writing out long sentences. It feels inefficient.

 

As regentrude said, 2-column proofs is not how mathematicians do proofs. In intro to proofs we work quite hard to get them to write coherent, paragraph-style proofs. I also think that the paragraph proofs transfer better to argumentation outside of mathematics. 

[JoJosMom]

As regentrude said, 2-column proofs is not how mathematicians do proofs. In intro to proofs we work quite hard to get them to write coherent, paragraph-style proofs. I also think that the paragraph proofs transfer better to argumentation outside of mathematics. 

 

What does this look like?  Is it at all similar to the writing problems that AoPS assigns for their online classes?  I am absolutely not a math person, so this is outside my experience.

[wapiti]

Crazy, typically the two-column proofs in school geometry texts are far more tedious than the paragraph proofs for AoPS.   The AoPS problems are usually at a higher level of thinking, for lack of a better expression (anyone know what I'm trying to say?  need coffee :) ).  When my dd started aops geometry, I was daunted by the idea of paragraph proofs but the ability to use some connecting language turned out to be a real plus. 

 

You'd only need the two-column proofs if your dd were to test out of geometry at a high school.  In that case, you'd just pick up Jurgensen and do chapter 2.

[happypamama]

Piggybacking on this to ask: Are there chapters in the geometry book that are less crucial for 9th grade? DD is enjoying the book a lot, but I'm not sure she will finish it this year. She might do some over the summer, but she might just need a full break from schoolwork too. So are there some chapters we could skip and still consider it to be a full credit of geometry? Or is there no way it's a full credit without the whole book?

[regentrude]

Piggybacking on this to ask: Are there chapters in the geometry book that are less crucial for 9th grade? DD is enjoying the book a lot, but I'm not sure she will finish it this year. She might do some over the summer, but she might just need a full break from schoolwork too. So are there some chapters we could skip and still consider it to be a full credit of geometry? Or is there no way it's a full credit without the whole book?

 

I think you can safely skip ch. 13 Power of a Point and Ch. 19 Problem Solving Strategies, as well as the starred sections.

 

[happypamama]

I think you can safely skip ch. 13 Power of a Point and Ch. 19 Problem Solving Strategies, as well as the starred sections.

Thank you! That's helpful. I think we will skip those initially, and if we have time, we will come back to them. So glad I learned about AOPS here -- both kids say it's challenging, but they both say they love it too.

[wapiti]

FWIW, I would still do the Power of a Point chapter (it's short).  My ds covered that topic in his non-honors geometry class with a Common Core text, albeit not to aops-style depth.

[StephanieZ]

AoPS is so great, I wouldn't want to skip anything at all. We do every problem in every book. :) I'd just let it take a few extra months if needed. :) 

 

If you and/or your child need/want more support than the book, don't forget to use the AoPS website's videos and their Alcumus problems, too, if needed. My general rule of thumb for my last kiddo doing AoPS is -- do all the book . . . If you get hung up on anything, watch the video before moving on . . . When she was younger and doing earlier books, I *required* her to watch the videos . . . and do the Alcumus. Now, she's so proficient at self-teaching with the books, that I don't mess with that. 

 

(She's doing Geometry this year. But, she's done all the AoPS pre-A, Intro Algebra, and Intro C&P, so she is super well prepared . . . If she were having *any* difficulty, I'd bring back the videos and Alcumus, for sure. )

[daijobu]

I would add that you redraw all diagrams, very large if you need to.  If similar triangles are being shown, redraw each triangle in isolation, side by side, with corresponding angles labeled and oriented the same way.  

 

For precision, AoPS describes segment lengths by their endpoints, like AB or XY.  And they label angles similarly: <ABC, etc.  I often had a difficult time keeping track because in my brain, AB looks entirely different from BA.  And <ABC would appear to me to be different from <CBA.   To circumvent this, when I redraw the diagrams, I label distances with a single letter, like x, and angles with a small arc and "alpha".  It just made it easier for me to keep track of congruences and do algebra on those numbers.  

 

Yes, parallel lines can be hard to see sometimes.  It helps if you label the congruent interior angles of a transversal to see the "Z."

 

 

[JoJosMom]

AoPS is so great, I wouldn't want to skip anything at all. We do every problem in every book. :) I'd just let it take a few extra months if needed. :)

 

If you and/or your child need/want more support than the book, don't forget to use the AoPS website's videos and their Alcumus problems, too, if needed. My general rule of thumb for my last kiddo doing AoPS is -- do all the book . . . If you get hung up on anything, watch the video before moving on . . . When she was younger and doing earlier books, I *required* her to watch the videos . . . and do the Alcumus. Now, she's so proficient at self-teaching with the books, that I don't mess with that. 

 

(She's doing Geometry this year. But, she's done all the AoPS pre-A, Intro Algebra, and Intro C&P, so she is super well prepared . . . If she were having *any* difficulty, I'd bring back the videos and Alcumus, for sure. )

 

Sadly, I don't think there are any videos for Geometry.

[StephanieZ]

Sadly, I don't think there are any videos for Geometry.

 

Oh, bummer!!!!!! Sorry about that!! 

 

They do have Geometry Alcumus problems, so having your child do the Alcumus alongside the book is one extra way to get help. (The Alcumus problems give solutions . . .  which is handy! Also, the review/algebra/pre-A problems will keep your kid sharp in those fundamentals that will help them solve topics in geometry, etc. . . ) Alcumus is fun, in general, and could be scheduled as a separate time/subject as the book . ..  breaking up the math hours during the day. :) 

[crazyforlatin]

I would add that you redraw all diagrams, very large if you need to. If similar triangles are being shown, redraw each triangle in isolation, side by side, with corresponding angles labeled and oriented the same way.

 

For precision, AoPS describes segment lengths by their endpoints, like AB or XY. And they label angles similarly: <ABC, etc. I often had a difficult time keeping track because in my brain, AB looks entirely different from BA. And <ABC would appear to me to be different from <CBA. To circumvent this, when I redraw the diagrams, I label distances with a single letter, like x, and angles with a small arc and "alpha". It just made it easier for me to keep track of congruences and do algebra on those numbers.

 

Yes, parallel lines can be hard to see sometimes. It helps if you label the congruent interior angles of a transversal to see the "Z."

We had a challenge problem in chapter 3 where I remembered to use x, y and z for the angles. I have the hardest time when there are many angles using 3 letters. It was so much easier just renaming name using single letter variables. Oh man, that problem took a couple of hours. And that's just chapter 3.

 

DD has said there's so much algebra in geometry.