Need some encouragement - was AoPS Intro to Geometry as hard as people say?

[kohlby]

After a great deal of thought and reading, I finally went ahead and ordered AoPS Intro to Geometry for my eldest.  I'm very nervous about it though since I keep reading how much harder it is than Intro to Alg.  My son really wants to stay with AoPS, even knowing this, so I figured it was worth trying out.  However, I also ordered Jacobs Geometry 2nd Edition so I have a back-up if we need to take a break from AoPS at any time.  I'm very, very nervous about trying AoPS Geometry.  I had been partially hoping that my son wouldn't have wanted to do AoPS so we could do a different Geometry first and then move up to AoPS.  But nope, it's what he wants and I don't want to hold him back if he can handle it - though I'm not sure.  So, not asking for advice on Geometry curriculums since I've been there, done that and just come out with more options every time.  (I have a couple more ideas filed away in my head but I can't buy ALL the ones I'm interested in!)  But I'm wanting to know if it's really as hard as people say or if others have had younger advanced math students succeed with it.  We're not on any timeline - we even overlap from one school year to the next with curriculums.  So even taking 1.5 years is perfectly fine.

[regentrude]

It is a challenging text, but it is NOT unreasonably hard.

My DD worked through the book in 9th grade at age 13 and had time during that school year to begin Intermediate Algebra. We did omit two chapters of the geometry text, Power of  a Point, and the last chapter on extra geometrical problem solving, because she simply disliked geometry and wanted to get done.

DS is 14 and in 9th grade and currently a bit more than half-way through the book; I anticipate that we finish by the end of the school year.

 

I would not say the book is so much harder, but very different. In algebra, there are systematic algorithms one can follow to get a problem started; with geometry, problems solving is more of an art, as one problem may require several tries and false starts.

We ran into some issues with 3-dimensional visualization; both DD and I are not good at that. I am curious to see how DS is going to deal with that; his spatial abilities are better.

So, go ahead, take it at your student's pace, and have fun with it.

 

ETA: I did not have DD do all the challenge problems, only selected ones, since she did not like geometry particularly. Even the regular problems and exercises require critical thinking and constitute a very strong geometry course.

[kohlby]

Thank you!  In Intro to Alg, I had him do every single challenge problem in the first half.  In the second half, I found it worked better to let him pick a certain number of challenge problems so I was planning on continuing that.  That way, he gets the extra challenge but doesn't feed like he has to do every problem if he's not interested.  He's 10 and I really have no idea how he'll do in Geometry.  I'm way more nervous about doing AoPS than him.

[Luckymama]

The text is great, challenging but not overly difficult. The online course was very tough for dd, though she rose to the challenge :)

 

I don't know how she would have handled the work load---all the text problems plus the Alcumus and special course problem sets---if she had taken the class along with other hard classes during a traditional academic year (her class ran March through September).

[avilma]

I think Intro to Geometry is very hard. Much harder than Intro to Algebra. It is also beautiful and I wish everybody had a chance to learn from it. I did the book as after schooling with a student that was in second year of high school. He is quite lazy and did not have a good math foundation so he was able to do 20% or even less of the problems. Yet in the ps geometry he was taking at the same time he was acing every test. Never got under 100%. A few months after we were done he took the SAT for the second time and got 720, a jump of 200 points from the first try. I think the key was that I worked through every problem with him. Some of those problems are so hard that even I had to look up the solution but they are all very instructive. 

[Kathy G]

It may depend on the child.  Some kids just think more algebraically, and changing gears to geometry can be tough.  I have a daughter who is very visual spatial.  AOPS algebra was very tough in spots and geometry is easier for her.  My son was the opposite.  I have another daughter with dyslexia, geometry seems to come easy for her also.  She is only 3rd grade now so we will see how it holds out.  

 

If he isn't nervous- give it a try.  I have learned that I am often more nervous than my kids.  Usually they are the ones who are right, and I have given them a lot more freedom in helping choose curriculum and classes as we have gone along.

[Julie of KY]

For my oldest, AoPS geometry was the easiest book (and he has done all through precalc). He thinks visual spacially and sees the answers to geometry problems. He turns many algebra problems into geometry problems as well in ways that I'd never think to do. It all depends on the kid.

[wapiti]

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Edited September 15, 2016 by wapiti

[regentrude]

  If the teacher for independent-study geometry is willing to use a different text with dd, should I ask him to consider AoPS Geometry?  I certainly fear the on-line class being too much for her, but would the book with a good teacher be a viable option?  Better than the book with no teacher?  (My thinking is that I, personally, am not qualified to grade proofs, at least not at this point in time.)  Or, should I consider some other text, e.g., Jacobs 2nd ed?

 

 

Maybe what I should do is have dd start AoPS Geometry over the summer just to see how it goes.  Could she get far enough in two months to have a good feel for whether she can handle the remainder?  How about one month?  (I'm thinking summer math would be every other day for the duration, probably about 10 weeks once we account for vacation, so something akin to 5 full-time weeks.)

 

The book would be a good option even without a teacher, if you have the solution manual. It is written to the student and doe snot require an instructor.

If you want to suggest the text to a teacher, you need to have a very enthusiastic teacher who is willing himself to go above and beyond. It may take even the teacher an hour to figure out the occasional problem. I could see a teacher who is passionate about math to be jumping at the opportunity to work through AoPS with a gifted student - but I can also see the reality that the teacher may be unable to spend the extra time and effort any meaningful instruction that goes beyond what is written on the page would require. (If the teacher just explains the solution manual, you don't need a teacher)

 

the book starts very gently, and you can get far in a few weeks. I honestly do not think the geometry text is so hard per se; you can always tailor the difficulty by not assigning the hardest problems, while still having a rigorous course. Let her have a look at it and see what she thinks.

 

As for grading proofs: I do not grade proofs. I have my student narrate the proof and explain the steps, and I am qualified to see flaws in the logic and see whether the proof is viable and logical. But I don't grade them. If you feel unable to follow and evaluate proofs, having an outside teacher is necessary, even with an easier curriculum, because the solution manual will only give one possible proof, but your student may have chosen a different way to correctly prove the statement. So, the need for outside help in evaluating proofs would not be limited to AoPS alone.

[wapiti]

Thanks, regentrude, I really appreciate your thoughts.  The geometry class teacher thought that the independent-study teacher would probably be open to the idea of another text.  I'm hopeful :)

 

As for grading proofs: I do not grade proofs. I have my student narrate the proof and explain the steps, and I am qualified to see flaws in the logic and see whether the proof is viable and logical. But I don't grade them. If you feel unable to follow and evaluate proofs, having an outside teacher is necessary, even with an easier curriculum, because the solution manual will only give one possible proof, but your student may have chosen a different way to correctly prove the statement. So, the need for outside help in evaluating proofs would not be limited to AoPS alone.

 

This is helpful.  Logic I can do.  It's the geometry itself that I'd need to re-learn, if that makes any sense, though AoPS is so lovely for that, especially with the full solutions.  If dd needs help, I think I could take a whack it for a summer anyway and then let the teacher finish it off properly (proofs).

[regentrude]

  Logic I can do.  It's the geometry itself that I'd need to re-learn, if that makes any sense

 

What do you mean by "geometry itself"? The properties of everything, all those theorems? I don't think that is a big deal. Because, really, geometry is just logic. To an even larger degree than algebra, since you can see the objects you examine.

I did certainly not remember many theorems.. but then, you can always re-derive them when you need them. Through logic :-)

 

It was the puzzling and thinking that was hard -and 3-d; I suck at 3-d because I have limited spatial visualization skills. If I could have a play dough model of the cube of whom I cut off a tetrahedron so I could actually see the resulting object, I could do 3-d...

[wapiti]

I am not entirely sure I understand. What do you mean by "geometry itself"? The properties of everything, all those theorems? I don't think that is a big deal. Because, really, geometry is just logic. To an even larger degree than algebra, since you can see the objects you examine.

I did certainly not remember many theorems.. but then, you can always re-derive them when you need them. Through logic :-)

It was the puzzling and thinking that was hard.

 

Yes!  That is what I meant - properties, theorems, etc. - I remember nothing (a friend and I ended up teaching ourselves whatever we needed to know the weekend before the NYS Regents exam, after which it immediately left my brain).  Puzzling and thinking and re-deriving are fine.

[regentrude]

Yes!  That is what I meant - properties, theorems, etc. - I remember nothing (a friend and I ended up teaching ourselves whatever we needed to know the weekend before the NYS Regents exam, after which it immediately left my brain).  Puzzling and thinking and re-deriving are fine.

 

I only remembered trivial stuff - sum of angles in a  triangle, triangle inequality, of that level. I vaguely recalled that altitudes intersect in one point, or that there were some theorems about various things - but really, the book teaches all that.

 

I think the issue is more the way of thinking, not the recall of specific facts. I don't want to talk you into anything, of course, but I would think having forgotten geometry facts is not a hindrance to using AoPS.  Give it a try and see what YOU think.

I found that even hard challenge problems do not typically require the recall of some obscure theorem only math gurus would know, but rather on applying and combining very basic principles, just in a hard-to-see way. (The problem over which my son sat for an entire hour today ended up using nothing but the formulas for the area of a triangle and the area of a circle and a segment thereof. A proof that took me three hours last fall rested solely on identifying congruent triangles.)

[avilma]

Hi wapiti,

since you are a lawyer you might want to know that a very famous lawyer, known also as 16th President of the United States, spent a lot of time studying geometry. Here is a quote:

"At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies."

[kohlby]

wapiti - Though we have no experience with AoPS Geometry as the book just arrived today, my experience with Intro to Alg was that my student was doing it independently 99% of the time for the second half, which could be considered Alg II.  (I was by his side quite a bit at the start of Alg I, but that was getting used to the style and having to work at math for the first time in his life for him.  Plus, as a much younger student, he needed a little extra maturity time).   So, I would guess that some students would also be able to do Intro to Geometry independently.  There's still Alcumus for the level as well, and I've found that very helpful since my child would rather learn from the book and Alcumus than from me.  Despite me being a former high school math teacher, the only teaching I did in Alg II was more from a rescue approach - he would do well In the exercises but realize he didn't have full understanding on Alcumus and I'd have to teach it to him when he became too frustrated. 

 

I'm still a bit nervous about AoPS Geometry, but he just started the last chapter in Intro to Alg, so the time is coming soon.  The "prove that" questions were the ones that caused him the most trouble in Alg, so that is why I'm more nervous about Geometry.  Ideally, I'd like him to be done with Geometry by June of 2015 though, so we have the luxury of plenty of time.  Is there anyone on here who used AoPS and Jacobs together?  I wonder if there's an easy way to combine the books. 

[jennynd]

Nm.. Post wrong post