Calculus AoPS vs college class

[bibiche]

Can anyone give me pros or cons to one versus the other? DS has gone straight through with AoPS but DH thinks a different approach, with more accountability, might be better for calculus. Originally it would have been an in-person class, but now it’s online. Any BTDT? I guess I’m mainly wondering which would be more rigorous. 

[MamaSprout]

It depends on the college class.

No freshman college class will be AoPS, but there is a lot of differences between courses/ schools. We opted for a third path- Blue Tent's Calc BC. It's not AoPS and doesn't pretend to be, but the teacher, Shin Yen, teaches beyond the BC syllabus and used to teach for AoPS. Our local DE option would have been a minimal course and my dd isn't a fan of AoPS. This is a good option for this kid.

[bibiche]

Thanks for your response. When you say that no freshman class will be AoPS do you mean that it will not be as rigorous as AoPS? 
 

The option we are looking at is not a DE class, but I do wonder what the level will be if the students have not already taken calculus by the time that they arrive at university. Maybe more of a math for students who don’t love math class versus a mathy kids math class like AoPS. 
 

I will take a look at Blue Tent, thanks for the suggestion.

[Arcadia]

DS16 did the AoPS calculus class, then sat for the AP Calculus BC exam in 7th grade. He started dual enrollment for maths in 10th grade. For 8th and 9th grade, he did non credit classes for math. 
DS16’s dual enrollment math classes were more rigorous (in terms of class discussions) before COVID-19 forced all the in person math classes to be online. Zoom just make it slightly harder for discussions. Also there is the equity issue since not every student has high speed broadband so teachers do have to cater to that. 

[Roadrunner]

nm

Edited January 31, 2021 by Roadrunner

[Arcadia]

1 hour ago, bibiche said:

DS has gone straight through with AoPS but DH thinks a different approach, with more accountability, might be better for calculus. 

What kind of accountability is your husband looking for? In our case, my kids have always planned to do dual enrollment math for high school because they want the classroom environment. 

 

8 minutes ago, Roadrunner said:

It’s simply best done after a more traditional calculus class or with a parent who can recognize where the curriculum needs reinforcement and be able to do so. Now having done Bluetent course, we plan on going back and working with a more theoretical text. 

I have a collection of calculus books, though my physics books collection is bigger.

DS15 did not do AoPS calculus. He is happy with dual enrollment math classes. His aim is to be a computer science major though so he rather spend his leisure time on those interests.

[bibiche]

9 minutes ago, Arcadia said:

What kind of accountability is your husband looking for? 

The kind where you have to do your homework! LOL

[Arcadia]

21 minutes ago, bibiche said:

The kind where you have to do your homework! LOL

Dual enrollment. My teens want to maintain a nice GPA 😂 They didn’t make full effort for AoPS class homework since we didn’t use those for grades or credits. 

[lewelma]

My son was very underwhelmed by the local university classes for linear algebra and analysis. So I am very glad we did not use them for calculus. AoPS Calculus was great. He did the class first and then spent an additional 3 months working through some applied problems in Anton. 

The main problem we had with the homework sets in the local university classes, is that the were repetitive. You had to do all the problems to get a good mark, but my son only needed to do about 30% of the problems to understand the content. 

So there are definitely two separate competing goals: learning the content vs being accountable. You could use a different class than math to learn how to be accountable. 

[8filltheheart]

I know nothing about math, but my ds who loved AoPS loved AoPS calculus. It is the only cal class he took before multivariable. He went on to double in math and physics with no problems.

[daijobu]

Dd was AoPS all the way until calculus, when she switched to PAH AP calc BC.  We did that because she wanted an easy 5 with minimal work.  She did complain because the teaching is not up to AoPS quality, but she was busy that year, so it was good decision for her.    

If you do AoPS, you'll probably want to look at the College Board Question Bank and have your student familiarize himself with the somewhat idiosyncratic questions on the AP exam.  You don't want to be parsing those questions for the first time during the exam itself!  Also, I don't think AoPS will give your student much calculator training, so there's that as well.  

Doing APs gave us the highest ROI: accountability with minimal work.  

[regentrude]

AoPS calculus is much more rigorous and has a more theoretical approach than a calculus 1 course even at a STEM uni. (Our weaker students like to take the course at a different college where it is easier than at our school, so you can have a college class that does not really teach much)
A big difference in problems is that a calc 1 course at college will have a lot of drill homework that practices by repetition, while the AoPS problems are fewer, but each requires deliberate thought and is different. Does your student need a lot of busywork and jumping through hoops?

Another thing to consider is what your DS wants to do with it. If he takes a college class, credit will transfer. But he may not learn as much.

Edited January 30, 2021 by regentrude

[Roadrunner]

nm

Edited January 31, 2021 by Roadrunner

[bibiche]

The class uses Strang (which means nothing to me as I know nothing) and they have mastery testing/grading, which apparently means that you don’t have to do a lot of busy work, just show that you understand and then move on. 
He wouldn’t take the class for credit, just to learn.

He usually takes the AoPS online class, but perhaps instead he can take the college class and work through the AoPS book concurrently. 
 

Thanks very much, everyone. I really am completely ignorant so your advice is very helpful.

[EKS]

If the choice is AoPS or a run of the mill college class, and the student is on board with AoPS, I'd do AoPS.  

[Arcadia]

54 minutes ago, bibiche said:

He wouldn’t take the class for credit, just to learn.

He usually takes the AoPS online class, but perhaps instead he can take the college class and work through the AoPS book concurrently. 

In that case, why don’t you and your husband let him decide which class he wants. 
The most rigorous option might be to have a good math tutor to challenge him instead of attending either AoPS or college class.

[bibiche]

6 minutes ago, Arcadia said:

In that case, why don’t you and your husband let him decide which class he wants. 
The most rigorous option might be to have a good math tutor to challenge him instead of attending either AoPS or college class.

Well, he’d pick AoPS and not do the homework. 😝 

A tutor would be nice, but isn’t in the budget right now. 

[Lilaclady]

My dd who took AOPS classes from algebra 2 took the AOPS calculus class. I did ask KathyinRichmond for help with making sure she was prepared for the AP exam by grading some past exams but that was before AOPS was AP accredited. They did have 2 extra sessions for the kids who were taking the exam to help them with calculator use etc. I felt it was a good class and she was definitely better challenged than she would have been at the college. She got a   5. At her Tech college, most of the students ( about 90% or so) already had calc 1 or AP calc. 

[Alice]

7 hours ago, daijobu said:

Dd was AoPS all the way until calculus, when she switched to PAH AP calc BC.  We did that because she wanted an easy 5 with minimal work.  She did complain because the teaching is not up to AoPS quality, but she was busy that year, so it was good decision for her.    

If you do AoPS, you'll probably want to look at the College Board Question Bank and have your student familiarize himself with the somewhat idiosyncratic questions on the AP exam.  You don't want to be parsing those questions for the first time during the exam itself!  Also, I don't think AoPS will give your student much calculator training, so there's that as well.  

Doing APs gave us the highest ROI: accountability with minimal work.  

This just came up here. Ds has used AOPS all the way through and did the Calc book first semester. He self-studies and doesn’t do the online class. He took a practice AP calc exam and realized he had to have a calculator. We had never gotten him one, so we did. I mentioned how weird it was that he was required to have a calculator and he mentioned that on all his other standardized tests he’s done, everyone has one but him. I was mind-blown. He’s done very very well on standardized testing so it hasn’t been an issue for him but I did realize this was one of those holes in education I was blind to. I do figure that leaning to use a calculator will probably be an easier hole to fill than others would be, so it’s not too bad. But I’m glad we figured it out now in January. 

4 hours ago, Arcadia said:

In that case, why don’t you and your husband let him decide which class he wants. 
The most rigorous option might be to have a good math tutor to challenge him instead of attending either AoPS or college class.

This is what we ended up doing. Ds has used AoPS on his own all along and it’s been great. Given the choice of doing an “official” AP class or a DE class or using AOPS he chose to keep using AoPS. (The online classes don’t work for us due to timing. They are all night here and ds is a swimmer who gets up at 3:45 AM. Plus he likes the self-teaching.) So I hired a homeschool grad who was a math major and they meet once a week on Zoom. They worked through the Calc book last semester so are doing the Counting and Probability book now and also working through old AP exams. I’ts been a great solution. It’s not cheap but it would be about the same cost of a DE class or an online class and I feel like it’s working really well. If nothing else, he really enjoys having someone to talk math with who understands it. He’s used to telling the rest of us stuff and we just glaze over. 

 

[Arcadia]

@Alice SAT math calculator section and ACT math allows the use of calculator. They can be done without calculators. AP Calculus exams typically have a question requiring the use of the graphing calculator, last year’s online one hour exam did not.
DE at community college is free for us regardless of family income so it is the cheapest option for us.

[lewelma]

15 hours ago, Alice said:

 he mentioned that on all his other standardized tests he’s done, everyone has one but him. I was mind-blown. He’s done very very well on standardized testing so it hasn’t been an issue for him but I did realize this was one of those holes in education I was blind to. 

Same here.  My ds did his NZ national complex numbers exam and calculus exam without a graphics calculator. I had no idea that this was an issue until I started tutoring these exams and realized that there were a LOT of short cuts he could have used with a calculator, and that the timing of the exams was assuming you would have one.  He had to work *very* fast. 

But now at university, he is not allowed a calculator of any kind for his math and physics exams. They do all the long multiplication and long division by hand, in addition to all the other required math.  And the professors do not always give tidy or easy numbers to work with!

[TheAttachedMama]

It seems like most people are saying that a student is going to learn more with AOPS than with a DE math class.   Correct?  

Which looks better for admission purposes for homeschooled students at competitive universities?    Do colleges even know who AOPS is?   

[Lilaclady]

I think the top colleges know AOPS. I can’t say all colleges and with all things, I think it depends on the student. Most colleges( not all) have large weed out classes for  classses like calculus etc so you need to be careful. You can get excellent classes at colleges but it just depends on which one. 

[rzberrymom]

On 1/30/2021 at 11:39 AM, lewelma said:

The main problem we had with the homework sets in the local university classes, is that the were repetitive. You had to do all the problems to get a good mark, but my son only needed to do about 30% of the problems to understand the content. 

This has been my DD’s experience too. This week she’s done 100+ problems for her DE calculus class—my DH is a professor (granted, in engineering, not math) and he found that number of problems to be ridiculous. Ten hours of slogging through very very repetitive stuff.
 

I wish we had stayed with AoPS for calculus, but my DD wanted to do it this way.

Edited February 1, 2021 by rzberrymom

[SoCal_Bear]

There is another option is that WTMA is offering an AOPS Calculus class this year. 

 

[Roadrunner]

13 hours ago, rzberrymom said:

This has been my DD’s experience too. This week she’s done 100+ problems for her DE calculus class—my DH is a professor (granted, in engineering, not math) and he found that number of problems to be ridiculous. Ten hours of slogging through very very repetitive stuff.
 

I wish we had stayed with AoPS for calculus, but my DD wanted to do it this way.

Our CC calculus teacher assigns but doesn’t collect at homework. You can do it if you need to or not. The entire grade is based on 3 exams. 

[Arcadia]

17 hours ago, rzberrymom said:

This has been my DD’s experience too. This week she’s done 100+ problems for her DE calculus class—my DH is a professor (granted, in engineering, not math) and he found that number of problems to be ridiculous.

Are they all compulsory or some are just optional practice? Are they all computer graded because I am wondering how the lecturer has patience to grade.

Between my two children, none of their lecturers has assigned much homework. DS15 would have dropped the class within the drop period otherwise because he cries over busywork. They have to scan and submit handwritten homework. At least they get to practice their handwriting for maths.

[Momto6inIN]

My DS did AoPS (self study with the book, not the class) and took the CalcBC AP exam and went right to Calc 3 as a freshman. It really freed up his schedule and made it possible to take more advanced math and CS courses. He loooooved AoPS and he said he was halfway through Calc 3 before he encountered any new material. There's no way he would have got that kind of depth in a CC course.

[Not_a_Number]

On 1/30/2021 at 3:45 PM, regentrude said:

AoPS calculus is much more rigorous and has a more theoretical approach than a calculus 1 course even at a STEM uni.

Hmmm. I've taught both. I can't say I've noticed that. They seem pretty similar to me -- relatively high on the theory. You'll be expected to write more proofs in AoPS, though. 

Edited February 2, 2021 by Not_a_Number

[Arcadia]

5 minutes ago, Not_a_Number said:

Hmmm. I've taught both. I can't say I've noticed that. They seem pretty similar to me -- relatively high on the theory. You'll be expected to write more proofs in AoPS, though. 

When I was an undergrad decades ago, the freshmen calculus classes for math majors were more theoretical than those for engineering majors. My alma mater’s  lecture halls were high seating capacity so it was easy to gatecrash math lectures from different faculties/schools.

[Not_a_Number]

9 minutes ago, Arcadia said:

When I was an undergrad decades ago, the freshmen calculus classes for math majors were more theoretical than those for engineering majors. My alma mater’s  lecture halls were high seating capacity so it was easy to gatecrash math lectures from different faculties/schools.

Yes, definitely. The ones I took as a college student were way harder than AoPS, I'd say. But the ones I taught for engineering and science majors were really pretty similar to AoPS, I thought. Similar material, presented in similar order, similar level of abstractness. 

What's calculus like at most colleges? For instances, I've never taught a class that doesn't go into epsilons and deltas for limits. Is that the case elsewhere? 

Edited February 2, 2021 by Not_a_Number

[rzberrymom]

6 hours ago, Arcadia said:

Are they all compulsory or some are just optional practice? Are they all computer graded because I am wondering how the lecturer has patience to grade.

Between my two children, none of their lecturers has assigned much homework. DS15 would have dropped the class within the drop period otherwise because he cries over busywork. They have to scan and submit handwritten homework. At least they get to practice their handwriting for maths.

It’s all required. My DH was flummoxed. The only thing we could figure is that the teacher must have a grader or two.

[Arcadia]

12 minutes ago, rzberrymom said:

It’s all required. My DH was flummoxed. The only thing we could figure is that the teacher must have a grader or two.

If the TAs are doing the grading then the instructor is being a bit mean to the students and TAs. No wonder services like Chegg can do well.

[MamaSprout]

7 hours ago, Not_a_Number said:

Yes, definitely. The ones I took as a college student were way harder than AoPS, I'd say. But the ones I taught for engineering and science majors were really pretty similar to AoPS, I thought. Similar material, presented in similar order, similar level of abstractness. 

What's calculus like at most colleges? For instances, I've never taught a class that doesn't go into epsilons and deltas for limits. Is that the case elsewhere? 

Depends on the school. There is a surprising amount of variation. It's why my dd didn't use the local DE option. It's an "essentials" course and book.

[Not_a_Number]

2 hours ago, MamaSprout said:

Depends on the school. There is a surprising amount of variation. It's why my dd didn't use the local DE option. It's an "essentials" course and book.

Yeah, I’m not surprised about that being the case some places. I wish I had broader data than the two schools I taught at.

[regentrude]

10 hours ago, Not_a_Number said:

Hmmm. I've taught both. I can't say I've noticed that. They seem pretty similar to me -- relatively high on the theory. You'll be expected to write more proofs in AoPS, though. 

Our calc (for engineers, scientists and mathematicians,  as there are no longer separate versions) no longer starts with series and epsilon delta to define limits. They don't see series until calc 2. 

They use Stewart.

This is a public STEM uni. 

Edited February 2, 2021 by regentrude

[Not_a_Number]

20 minutes ago, regentrude said:

Our calc (for engineers, scientists and mathematicians,  as there are no longer separate versions) no longer starts with series and epsilon delta to define limits. They don't see series until calc 2. 

They use Stewart.

This is a public STEM uni. 

Huh. Super interesting. What makes it a STEM university? I haven’t heard that term before. 

I’ve taught at Stanford and UT Austin, both of which had epsilons and deltas and series. To be honest, I’m actually not super fond of epsilons and deltas as an introduction to limits... but they were there.

It has also been a while, so it’s possible things have changed. I should ask my husband...

Edited February 2, 2021 by Not_a_Number

[MamaSprout]

51 minutes ago, Not_a_Number said:

Yeah, I’m not surprised about that being the case some places. I wish I had broader data than the two schools I taught at.

Another data point? From a boardie who has moved on (MarkT)

From this thread: Homeschool High School Math - Page 2 - High School and Self-Education Board - The Well-Trained Mind Community

 

For rigor comparison

University of Michigan Calculus 1

http://dept.math.lsa.umich.edu/courses/115/

It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

 

http://www.math.lsa.umich.edu/~kesmith/Math115.2014.html

"Math 115 is a first course in Calculus at the college level, which is different than high school calculus, even if you took an AP course. This is an extremely hard class, and the ``curve" is tough. You need to be very disciplined to get a good grade."

[Not_a_Number]

11 minutes ago, MamaSprout said:

Another data point? From a boardie who has moved on (MarkT)

From this thread: Homeschool High School Math - Page 2 - High School and Self-Education Board - The Well-Trained Mind Community

 

For rigor comparison

University of Michigan Calculus 1

http://dept.math.lsa.umich.edu/courses/115/

It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

 

http://www.math.lsa.umich.edu/~kesmith/Math115.2014.html

"Math 115 is a first course in Calculus at the college level, which is different than high school calculus, even if you took an AP course. This is an extremely hard class, and the ``curve" is tough. You need to be very disciplined to get a good grade."

Hmmm, this does look a lot less rigorous than AoPS. 

A focus on concepts and solving problems sounds reasonable to me... I wonder if it succeeds. I never thought any but the mathiest kids I've taught got much out of something like epsilons and deltas. Just like it was the case historically, they seem like a nice thing to learn AFTER you have an intuitive understanding of limits. 

Edited February 2, 2021 by Not_a_Number

[regentrude]

45 minutes ago, Not_a_Number said:

Huh. Super interesting. What makes it a STEM university? I haven’t heard that term before.

85% of undergrads major in engineering, the rest mostly in science and math. Very few students major in the humanities.

[Not_a_Number]

Just now, regentrude said:

85% of undergrads major in engineering, the rest mostly in science and math. Very few students major in the humanities.

Got it, thanks! 

[regentrude]

49 minutes ago, Not_a_Number said:

I’ve taught at Stanford and UT Austin,

yeah, Stanford has a different caliber of students.

[Not_a_Number]

1 minute ago, regentrude said:

yeah, Stanford has a different caliber of students.

True, although the kids really varied. There was a big gap between kids at the higher and lower levels of the calculus class. 

[Not_a_Number]

4 hours ago, MamaSprout said:

Another data point? From a boardie who has moved on (MarkT)

From this thread: Homeschool High School Math - Page 2 - High School and Self-Education Board - The Well-Trained Mind Community

 

For rigor comparison

University of Michigan Calculus 1

http://dept.math.lsa.umich.edu/courses/115/

It is taken by the majority of students intending to major in mathematics, science, or engineering as well as students heading for many other fields. The emphasis is on concepts and solving problems rather than theory and proof.

 

http://www.math.lsa.umich.edu/~kesmith/Math115.2014.html

"Math 115 is a first course in Calculus at the college level, which is different than high school calculus, even if you took an AP course. This is an extremely hard class, and the ``curve" is tough. You need to be very disciplined to get a good grade."

I showed this to DH and he also thought this looked surprisingly theory-free compared to everywhere he'd ever taught calculus. 

From my perspective, this is probably the right way to do calculus for most kids, but I didn't realize that some colleges taught it like this. Fascinating.