AoPS geometry and staying on track

[JennyD]

DS14 (rising 9th grade) worked on the AoPS Geometry book this past year.  He loves math and adores AoPS, but hoo boy this book was a challenge.  To date he has completed through Chapter 13.  He really likes it and works very hard, but it just takes a looong time to solve some of those problems.  Before Geometry he went through AoPS PreA and Introduction to Algebra.

Our approach to math has always been that it takes as long as it takes and we just keep going through these amazing books doing all the problems.  However, now that DS14 is going into high school, I am concerned about him falling 'behind' in the math sequence.  Specifically, he will likely apply early to some TBD selective school at the fall of his senior year, and so if he is going to take the AP Calculus exam presumably that should be in May of his junior year.  But if he spends another 3 months on geometry, that will put him behind schedule for completing calculus before the end of 11th grade.  (And yes, I have read Richard Rusczyk's criticism of the 'race to calculus' and as a philosophical matter I completely agree with him.  This is yet another reason why I am unthrilled about homeschooling high school.)

DH (who has a Ph.D. in math, for whatever that's worth) wants DS to stop working on geometry and just start Intermediate Algebra.  DS wants to keep working on the Introduction to Geometry book.   

Any thoughts?

 

 

 

Edited July 18, 2019 by JennyD

[Arcadia]

42 minutes ago, JennyD said:

Our approach to math has always been that it takes as long as it takes and we just keep going through these amazing books doing all the problems.  However, now that DS14 is going into high school, I am concerned about him falling 'behind' in the math sequence.  Specifically, he will likely apply early to some TBD selective school at the fall of his senior year, and so if he is going to take the AP Calculus exam presumably that should be in May of his junior year.  But if he spends another 3 months on geometry, that will put him behind schedule for completing calculus before the end of 11th grade.  

 

1) DS13 did not do any of the challenge problems, DS14 did some. It would have taken too much time for DS13 to do all the problems in the books.

DS13 switched to the Larson AP edition book for Calculus while DS14 used the AoPS calculus book. Both my kids do not currently intend to be math majors

2) Do Math year round?

DS13 did intro to algebra with intro to geometry. DS14 did intermediate algebra with intro to geometry. Both my kids enjoy geometry more than algebra. Also the precalculus book took less time than the intermediate algebra book, YMMV of course. 

Is your husband the one overseeing your son’s math? If your husband is insistent, I would ask your son to do intermediate algebra as coursework (just to keep the peace) and let your son finish the intro to geometry book as after school/leisure/hobby work. 

[mathnerd]

I agree with doing math year around. All the mathy kids that I know of who do challenging curricula (to compete in math competitions) as well as multiple passes using multiple books for each level of math do math all year.

Rather than stopping the geometry work, could you schedule such that you rotate AOPS Geometry and Intermediate Algebra on different days of the week? For example: Mon, Wed: AOPS Inter Alg and then, Tue, Thurs, Fri: AOPS Geo. Since you homeschool, that should be easy to achieve. Also, consider longer block scheduling for AOPS.

My son does all the problems (including challenge problems) and alcumus as well. It takes a long time. But, he works year around and hence is able to push to finish in the summer when he has more time. But, we will be considering online classes for some of the books because of long time it takes to complete the courses by self-study.

[daijobu]

1 hour ago, JennyD said:

 

Our approach to math has always been that it takes as long as it takes and we just keep going through these amazing books doing all the problems.  However, now that DS14 is going into high school, I am concerned about him falling 'behind' in the math sequence.  Specifically, he will likely apply early to some TBD selective school at the fall of his senior year, and so if he is going to take the AP Calculus exam presumably that should be in May of his junior year.  But if he spends another 3 months on geometry, that will put him behind schedule for completing calculus before the end of 11th grade.  (And yes, I have read Richard Rusczyk's criticism of the 'race to calculus' and as a philosophical matter I completely agree with him.  This is yet another reason why I am unthrilled about homeschooling high school.)

Any thoughts?

 

Geometry in 9th grade isn't "behind".  That still puts you on track to take calculus in high school, if you spend a year each on intermediate algebra, precalculus and calculus.   If he's taking calculus senior year, the colleges will know this, and hopefully he will have shown enough achievement in math that it will be assumed he earns a 4-5 on calc bc.  (Is he participating in math contests like AMC?)

I also recommend schooling year round if he isn't already.  You never know when you'll need the extra time.  

I agree with skipping challenge problems, unless you son really wants to do them.  If he is determined to solve the problems, then this practice of persistence will give him a huge advantage at schools like MIT.  OTOH, you can skip the challenge problems for now, and return to them later.  Or double up on geometry and intermediate algebra.  

Intermediate Algebra and PreCalculus are significantly more difficult, especially if you plan to do all the challenge problems.  Many of them are from USAMO, IMO, and Putnam.   We ended up skipping a lot of these, although we didn't skip the challenge problems entirely.   We just took the IMO problems with a grain of salt.  

Not sure why avoiding the race to calculus is a negative for homeschooling?  

[JennyD]

Thanks so much for the replies.

DS already does math year-round and has for years. This summer, in addition to working on the geometry book, he has been taking the AMC10 prep class through AoPS.  In retrospect this might not have been a great use of time, especially since we are now going to be out of the country in Feb and he won't be able to take the exam, but that's where we are.  He's enjoyed the class and learned a lot, though.

Skipping the challenge problems is probably the way to go, although DS will surely resist this.

I don't think he can really manage both Intermediate Algebra and Geometry at the same time, especially because when we are abroad in the spring DS is likely to be enrolled in school and it will be a major challenge to stay on top of the algebra alone.   DH is indeed the one working with DS on math (and DH is very demanding when it comes to proofs, which is certainly serving DS extremely well academically but having to rewrite proofs multiple times is definitely slowing down his progress through the book) so ultimately DH will prevail on this but I have just been wondering whether I should push back.

44 minutes ago, daijobu said:

 

 If he's taking calculus senior year, the colleges will know this, and hopefully he will have shown enough achievement in math that it will be assumed he earns a 4-5 on calc bc.  (Is he participating in math contests like AMC?)

 

It's the 'hopefully' that concerns me.

44 minutes ago, daijobu said:

 

Not sure why avoiding the race to calculus is a negative for homeschooling?  

 

I did not put that very articulately.  I meant that I understand and agree with the intellectual argument for not rushing through math curricula but nonetheless feel obligated to do precisely that in order to make it possible for my homeschooled son to take the standardized achievement exams that he needs in order to apply to selective colleges.  And that kind of bums me out.   I just so enjoyed the freedom of homeschooling the younger grades.  

Edited July 19, 2019 by JennyD

[daijobu]

2 hours ago, JennyD said:

DS already does math year-round and has for years. This summer, in addition to working on the geometry book, he has been taking the AMC10 prep class through AoPS.  In retrospect this might not have been a great use of time, especially since we are now going to be out of the country in Feb and he won't be able to take the exam, but that's where we are.  He's enjoyed the class and learned a lot, though.

 

 

Don't you love it when that happens?  😉  I wouldn't sweat it so much.  In particular about the AMC, he has 3 more years of high school to take it.  Keep practicing old exams.  It'd be great if he could AIME qualify, but having a solid score is fine.  His slow pace due to devotion to the hard problems and persistence reminds me of Lewelma's ds who is currently at MIT, so he's in good company.  I actually think he's going to be fine.  Keep an eye on his pacing, but not at the expense of his happiness.  Better for him to get really good at solving problems than taking calculus in high school.  I know that's tough to swallow, especially since taking AP calculus in high school is a short hand marker for someone who knows their numbers; I would be nervous too.   

The good news is no matter how far he has gotten, he can always sign up to take AoPS online calculus his senior year.  It preps you well for the AP exam, and has lots of nice proofs.  Good luck!  

[EmilyGF]

We found Intermediate Algebra was a BIG step up compared to Intro to Geometry, at least if you use the new Alcumus problems for Intermediate Algebra. DS backed off and took Intro to Number Theory and Python in tandem instead of Intermediate Algebra and the two of them together took less time for him. 

Emily

[Arcadia]

13 hours ago, JennyD said:

I did not put that very articulately.  I meant that I understand and agree with the intellectual argument for not rushing through math curricula but nonetheless feel obligated to do precisely that in order to make it possible for my homeschooled son to take the standardized achievement exams that he needs in order to apply to selective colleges.  And that kind of bums me out.   I just so enjoyed the freedom of homeschooling the younger grades.  

 

My kids have been public school students. What has helped us was tackling any subject as what needs to be done/completed/covered for a high school credit and/or AP exam and the rest as hobby/enrichment/leisure.

For example, DS13 took and passed his AP Physics C exams before taking a formal calculus class. DS14 just helped explained calculus to DS13 whenever DS13 was stuck in his physics homework. That’s a flexibility homeschooling allows.

Another example is that DS14 took the WOOT class in 8th and 9th grade. He is not using WOOT for credit and it goes under the not for credit section in his high school transcript. 

I am assuming that your son is aiming for a STEM major since you mentioned wanting an AP Calculus exam score before 12th grade. SAT Math 2 subject test can be taken during/after intermediate algebra, just do some test prep. SAT physics subject test can be taken before AP physics, it’s all conceptual.  SAT Chemistry subject test can be taken before AP Chemistry as well. My kids’ tutor’s public school 10th grade child took two sat subject tests (one is math 2) in June because her guidance counselor advised her to do so in late April (so her child started test prep in May and didn’t have a problem). 

My kids want to commute and the only selective college within commute distance is Stanford (striking lottery might be easier 😂 ) so I can be rather “relaxed” about college admissions.

[Roadrunner]

My son says Geometry text was a good preparation for Intermediate Algebra because the text was much harder than the Intro to Algebra text. Intermediate Algebra is a torture chamber and significantly harder than the geometry book. I would keep going with Geometry and work as many hard problems as possible. 

[JennyD]

This is all helping me think this out, thanks so much!

11 hours ago, daijobu said:

 

Don't you love it when that happens?  😉  I wouldn't sweat it so much.  In particular about the AMC, he has 3 more years of high school to take it.  Keep practicing old exams.  It'd be great if he could AIME qualify, but having a solid score is fine.  His slow pace due to devotion to the hard problems and persistence reminds me of Lewelma's ds who is currently at MIT, so he's in good company.  I actually think he's going to be fine.  Keep an eye on his pacing, but not at the expense of his happiness.  Better for him to get really good at solving problems than taking calculus in high school.  I know that's tough to swallow, especially since taking AP calculus in high school is a short hand marker for someone who knows their numbers; I would be nervous too.

The good news is no matter how far he has gotten, he can always sign up to take AoPS online calculus his senior year.  It preps you well for the AP exam, and has lots of nice proofs.  Good luck!  

 

This is reassuring and I'll definitely keep in mind that he can take AoPS calculus online senior year if need be.  He so loves the AoPS methodology but he Will Not Be Rushed when it comes to math.  And there are only so many hours in a day, you know?

I keep feeling as though we basically need to do high school in three years rather than four if he's going to apply early decision somewhere, but maybe that's not (entirely) true.

11 hours ago, EmilyGF said:

We found Intermediate Algebra was a BIG step up compared to Intro to Geometry, at least if you use the new Alcumus problems for Intermediate Algebra. DS backed off and took Intro to Number Theory and Python in tandem instead of Intermediate Algebra and the two of them together took less time for him. 

Emily

 

DS14 loves number theory like a big old lovey thing but we had originally decided that he'd do that senior year, after finishing AP calculus.  It is far and away his favorite math subject, though, and in fact he frequently tries to do number-theory-type proofs on his own time.  (Or sometimes when he's supposed to be working on Geometry; see above re slow progress.)  He has taken both AoPS Python classes and thought they were terrific; I only wish they offered more.

1 hour ago, Arcadia said:

 

I am assuming that your son is aiming for a STEM major since you mentioned wanting an AP Calculus exam score before 12th grade.

 

For sure.   I doubt he'd major in math but he is very very set on being a scientist.

 

[Arcadia]

1 minute ago, JennyD said:

DS14 loves number theory like a big old lovey thing but we had originally decided that he'd do that senior year, after finishing AP calculus.  

 

DS14 learned much from the AoPS intermediate number theory class. He took the July 2017 class.

https://artofproblemsolving.com/school/course/intermediate-numbertheory

[daijobu]

1 hour ago, JennyD said:

I keep feeling as though we basically need to do high school in three years rather than four if he's going to apply early decision somewhere, but maybe that's not (entirely) true.

DS14 loves number theory like a big old lovey thing but we had originally decided that he'd do that senior year, after finishing AP calculus.  It is far and away his favorite math subject, though, and in fact he frequently tries to do number-theory-type proofs on his own time.  (Or sometimes when he's supposed to be working on Geometry; see above re slow progress.) 

 

Definitely EA and ED applicants are not necessarily accelerated.  Students who are accepted early tend to be stronger than average--depending on the school!  Sometimes admissions committees are looking for their EA/ED applicants to have greater DI.   It all depends on the school.  Even ED/EA applicants submit their senior year coursework and will eventually submit their grades, so you don't need to be finished with high school before you apply.  

In any case, a stronger student is not necessarily accelerated.  They can shine in many other ways.  Have your son take a look at AoPS Crowdmath if he is interested in math research.   (That will impress adcoms way more than any AP calculus class.) 

I'm taking the AoPS intermediate number theory class now!  I was just telling DH how much I'm learning, and it isn't very time-consuming, though I will confess I am too quick to ask for hints on the discussion board.    

[JennyD]

59 minutes ago, daijobu said:

 

In any case, a stronger student is not necessarily accelerated.  They can shine in many other ways.  Have your son take a look at AoPS Crowdmath if he is interested in math research.    

 

This is a very useful framing for me and something that I will need to think more about.  I guess that the difficulty is that it's harder to demonstrate that strength, but it shouldn't be impossible.  

I just asked DS about Crowdmath.  Apparently he knows all about it and it's "super awesome" but he isn't advanced enough to participate.  "This is why I have to do all of this geometry and algebra!"   

It has also become clear to me that I need to make an appointment with DH for the two of us to sit down and together figure out a reality-based math plan for DS.  DH loves nothing more than to spend 2 hours working through a complicated problem with DS but then for some reason he thinks that DS is going to magically work much faster on his own.