X posted - need advice for advanced math student, past calculus

[blue daisy]

I'm at a loss as to what to do for my 9th grader this year.  In middle school, he was fortunate enough to take part in a program specifically for advanced math middle schoolers - Algebra 1 and 2, geometry and pre-calc in 6th and 7th grade.  He did great and was challenged for the first time.  In 8th grade, he took calculus 1.  The program continues for 2 more years with calc 2 and 3 in 9th and 10th grade and he is currently enrolled.  BUT, it got REALLY hard last year in calculus.  He got a good grade, but he really did not understand everything, especially the last half of the year.  He would spend hours working on the homework with little results. He basically had no free time last year (and part of the reason we homeschool is to give our kids more free time!)  He managed to score well on all the tests but he really did not feel confident about the material at all.  He just started a summer review assignment and is not getting it at all.  And the thing is - he's 14 - he has plenty of time for these classes, but I'm worried if he takes a break, he'll feel even more behind if he tries to re-enroll in a couple of years.  His mental health did suffer last year (I don't know if it was math or just a combination of things) but has improved with a more relaxed summer.

The program he's involved in is through our state university.  It's a great program - he's with kids his own age, there is a lot of support, and a friend of his who graduated the program already is available this year to help tutor him.  If he goes to our state university, the credits automatically transfer, so he already has the credits from calc 1.

Some ideas I have:

*stay in the current program, his friend will tutor him.  I worry that he will still struggle.

* skip this year and review calculus with other programs, take calc 2 next year through through the program we started with.  I'm worried he will lose more and struggle to catch up.

* be done with this program, take some time off from calculus and explore other math options.  He likes AOPS and there are some courses he has not done there.  Statistics is another option.  Take Calc 2 if needed with dual enrollment in 11th or 12th grade.

He does want to go into a science/engineering field.  I don't know why this feels like such a hard decision.  (For the record, my second child is mathy as well, and we're sticking to a traditional, slightly accelerated pace so we don't run into this problem!)

[lewelma]

I don't really know what to advise. I just know that you definitely need to get his calculus rock solid before moving on. If he doesn't know it, he needs to go back and redo it.  My older boy who is quite mathy (as in very very mathy!) did calculus twice.  Once with AoPS for the theoretical approach and once with Anton to grab all the engineering applications.  Also, you may want to see how rock solid his Algebra 1 - precalc sequence is.  Doing the whole thing in 2 years, and at a young age is unusual. Not unheard of, but still, I would check his understanding.

[kokotg]

I'd lean toward having him redo calc 1 with another program and then go from there. There's no reason to be doing advanced calculus in 9th or 10th grade if it's stressing him out; if he has calculus on his transcript for 9th grade he's going to be more advanced than the vast majority of students, even the ones who are strong at math and science and plan to go into those fields. 

[daijobu]

I'm scratching my head wondering what he's not understanding about calculus.  I'm guessing he must have had some challenging material prior to calculus, that is arguably more difficult to grok.  I'm worried that he isn't solid on some prerequisite, and perhaps he rushed through some material on his way to calculus, without being 100% solid.  

I think being respectful of his mental health, we don't want to butt our heads against calculus right away.  

If you aren't in a position to detect any possibly math deficiencies, I might prescribe something entirely different.  I recommend he study old AMCs.  Start with AMC 8's.  If those are too easy (he scores at least 20 out of 25), then bump him up to AMC 10 and AMC 12.  Review all problems he doesn't know how to solve.  Really review them.  If he's forgotten any theorems, go back to the old AoPS textbooks and do some sample exercises and problem sets.  That should jog his memory.  And hopefully diagnose anything that he didn't really understand the first time and help him when he decides to tackle calculus again.  

Since you can't really spend an entire year doing nothing but old exams, I also recommend he study out of one of the non-core AoPS books: intro NT, intro C&P, or intermediate C&P.  (There's also a intermediate NT class, but no textbook.)  

After a  one year break, return to calculus.  It really should not be such difficult material to learn, once you get the epsilon-delta proofs.  I thought a lot of the material in precalculus was much more difficult.  

Edited August 12, 2019 by daijobu

[blue daisy]

1 hour ago, daijobu said:

I'm scratching my head wondering what he's not understanding about calculus.  I'm guessing he must have had some challenging material prior to calculus, that is arguably more difficult to grok.  I'm worried that he isn't solid on some prerequisite, and perhaps he rushed through some material on his way to calculus, without being 100% solid.  

I think being respectful of his mental health, we don't want to butt our heads against calculus right away.  

If you aren't in a position to detect any possibly math deficiencies, I might prescribe something entirely different.  I recommend he study old AMCs.  Start with AMC 8's.  If those are too easy (he scores at least 20 out of 25), then bump him up to AMC 10 and AMC 12.  Review all problems he doesn't know how to solve.  Really review them.  If he's forgotten any theorems, go back to the old AoPS textbooks and do some sample exercises and problem sets.  That should jog his memory.  And hopefully diagnose anything that he didn't really understand the first time and help him when he decides to tackle calculus again.  

Since you can't really spend an entire year doing nothing but old exams, I also recommend he study out of one of the non-core AoPS books: intro NT, intro C&P, or intermediate C&P.  (There's also a intermediate NT class, but no textbook.)  

After a  one year break, return to calculus.  It really should not be such difficult material to learn, once you get the epsilon-delta proofs.  I thought a lot of the material in precalculus was much more difficult.  

 Thank you for sharing that article and for your suggestions.  In some ways, I feel the program we've been involved in is what they are talking about - it is a unique program, designed specifically for middle schoolers that are truly advanced and does provide a lot of support.  That said, just because it was a great fit in 6th grade doesn't mean it will be a great fit in 9th.

I'm leaning towards a year doing something like your suggestion (He would probably love that - he enjoyed MathCounts and took the AMC 10 last year and did well.  He picked up the AOPS Counting and Probability book because it looked interesting to him, but he hasn't had time to delve into it. Because calculus.)

Personally, my own math experience is limited.  I did take Calc in high school but never entered a field that used it and so I haven't looked at that material in over 20 years.  So I'm struggling to put my finger on what he is stuck on. My husband is an engineer so I'm going to have him work with my son to try to figure out where he went astray.

[blue daisy]

3 hours ago, lewelma said:

I don't really know what to advise. I just know that you definitely need to get his calculus rock solid before moving on. If he doesn't know it, he needs to go back and redo it.  My older boy who is quite mathy (as in very very mathy!) did calculus twice.  Once with AoPS for the theoretical approach and once with Anton to grab all the engineering applications.  Also, you may want to see how rock solid his Algebra 1 - precalc sequence is.  Doing the whole thing in 2 years, and at a young age is unusual. Not unheard of, but still, I would check his understanding.

 Thanks.  I agree that he needs to be rock solid, hence my questioning sticking with this program.  He breezed through the first year of the program, was challenged in a good way with algebra 2 and pre-calc, and then didn't really struggle until calculus. 

How did you account for 2 years of calculus on his transcript?  If we went that route, should I list it once or both times?

[lewelma]

2 hours ago, blue daisy said:

How did you account for 2 years of calculus on his transcript?  If we went that route, should I list it once or both times?

 

I'm really the wrong person to talk about transcripts, given that we are in New Zealand and are half unschoolers. 🙂 

He took 6 months to get through AoPS calc, and then 3 months to get through Anton calc.  So really just a year, so I didn't have problems with the transcript.  But if I were in your shoes, I would drop the program, and have him do some sideways classes like AoPS Number Theory and Counting/ Probability.  They won't take long, so during that year, I would put the rest of the time into redoing calc.  But honestly, I'm concerned that Precalc is probably shaky.  I think you need to get someone to assess him and figure out where things went wrong. 

My ds used AoPS for all courses. Both our kids got to calc at 14, butThe difference is that my ds compacted later than yours did, so I'm wondering if his foundation was stronger. Ds's timing was approximately:

9-11 Algebra 1

12 Geometry

13 Algebra 2, Number theory, Counting, advanced Geometry

14 Precalc, advanced number theory, advanced counting, Calc,

15 finish calc, calc 2, 

16 more advanced classes,

 

 

Edited August 12, 2019 by lewelma

[daijobu]

3 hours ago, blue daisy said:

 Thanks.  I agree that he needs to be rock solid, hence my questioning sticking with this program.  He breezed through the first year of the program, was challenged in a good way with algebra 2 and pre-calc, and then didn't really struggle until calculus. 

How did you account for 2 years of calculus on his transcript?  If we went that route, should I list it once or both times?

He took calculus in 8th grade, correct?  You are not obligated to report grades taken prior to 9th grade.  You may want to report (ironically) his algebra, geometry, algebra 2, and precalc classes, but don't use the grades or units to calculate GPA, because colleges may want to see specifically that's he's had this material.  My kids took algebra and geometry in middle school, so I did that, because I was afraid there would be box-checkers looking for those classes, even though they had taken more advanced classes in high school.  But you can pretend that calculus never happened, as far as I'm concerned.  You can just label them "pre-high school" or something similar.  

Edited August 12, 2019 by daijobu

[daijobu]

3 hours ago, blue daisy said:

I'm leaning towards a year doing something like your suggestion (He would probably love that - he enjoyed MathCounts and took the AMC 10 last year and did well.  He picked up the AOPS Counting and Probability book because it looked interesting to him, but he hasn't had time to delve into it. Because calculus.)

 

 

I'm glad you like this idea.  It reminds me of how a doctor might diagnose abdominal pain: poking around here and there, trying to figure out which organ is the source of the pain.  Similarly, because those AMCs test on a variety of different areas, it's liking poking around to see where his weaknesses are.  The most important thing is to keep him mentally healthy and enjoying math.  

[Guest]

I had a kid on that sort of similar breakneck pace. I think she accelerated in math mostly because she could see progress and feel like she was accomplishing something in a way she could not do so easily in science and the humanities, and AoPS fed her soul in a way a lot of other programs didn’t. And with one parent with a degree in math ed and another with degrees in math and CS, she had a lot of support in math.  She started pre-algebra at age 7, worked through AoPS from 7-11, and talked herself into the local college, starting just after turning 12. And then she slowed way down. What my DD did was to essentially do the high school math topics at a college level-so she’s taken algebra and geometry teaching techniques (which got Algebra and geometry on her high school transcript), statistics, finite and discrete math, is taking college Algebra and trig, and then plans to take Calculus 1 and 2, which puts her having completed the same level of math most students in her majors are likely to have completed, but multiple times. She has found her college math classes to be relatively easy, but useful-she says that she can kind of feel things locking together as it moves from just knowing and being able to do it, to being able to fully explain and discuss it (which may be being 12-14 vs 8-11), because she has found a few concepts in each that she just plain didn’t completely know. And, with her other academics getting harder (she is thriving in college social science and humanities classes, especially the honors ones, because she loves to have people to discuss with) having math be review has not been a bad thing. 

That’s not necessarily the path I would recommend for everyone, and not all kids benefit from going backwards. But for DD, it has been a good choice. 

[Arcadia]

20 hours ago, blue daisy said:

He does want to go into a science/engineering field.  

 

DS13 who wants to go into engineering or computer science did AP Calculus BC class over summer after he did AP Physics C course and exam in 8th grade. The physics C course help reinforce his math skills. 

16 hours ago, blue daisy said:

 How did you account for 2 years of calculus on his transcript?  If we went that route, should I list it once or both times?

 

DS14 is starting Calc 3 at community college. He has Linear Algebra listed as not for credit (8th grade), Multivariable Differential Calculus and Multivariable Integral Calculus as for credit (9th grade). The community college didn’t have issue with his transcript when I submitted that for dual enrollment. He did want to do it twice though, especially linear algebra as he feels he is weaker in that. His first choice major is Computer Science with Math and Physics coming close seconds.

[blue daisy]

Thanks everyone for your input! I really appreciate all the replies! You've given me a lot to think about, and even some new ideas I hadn't considered.  We're going to talk to his professors to see if they have any insight before making a decision.