High School Math Sequence for STEM

[silver]

I have a 9th grader that is very interested in STEM--likely engineering, but I don't want to rule out sciences, computer science, etc. He isn't sure which branch of engineering he might be interested in, either. I don't think he's going to be aiming for high tier colleges like MIT, but well ranked state flagships or public engineering schools like Colorado School of Mines are certainly possibilities.

He's just starting AOPS PreCalc next week. The other AOPS books have taken him anywhere from 27 weeks (Geometry) to 47 weeks (Intermediate Algebra), I'm guessing that PreCalc will be between those two and get finished sometime in July (we school year round with random breaks). I'm trying to plot out the rest of his high school math sequence.

He's the type of kid that won't want to do AOPS Calculus at home with me only to then have to take it again in order to get college credit (especially since the CC version would be more about "boring" calculations). We have free DE available once he's in 11th grade. Our local high school doesn't allow non-enrolled students to take AP tests with them, and I haven't reached out to further away or private schools yet. 

One thing I'm leaning toward is to do approximately Calc 1 with AOPS at home and have him take the CLEP test for it. If he has more time before he can do free DE, he can do discrete math to fill that gap, and then do Calc 2 as DE at the CC. After that, I figure he'd do multivariate calc, differential equations, and either linear algebra or calc based statistics until he graduates. 

Another option would be to hope we can both get all of Calculus done before May 2023 and also find a school that would let him take the BC Calc exam. Or to put off doing Calc until Junior year and find other math subjects to do Sophomore year. 

Some of my concerns are in taking math courses at the CC. Would it be worth adding significant commute time to get him to a four year school for DE? If we can't get him in to take the BC Calc exam, would it be better to teach it at home with AOSP and take the CLEP to get out of Calc 1, or to do all of Calc as DE, not using AOPS? I feel that AOPS would give him a stronger foundation than CC Calculus, but the CLEP exam may not be accepted for credit at the college he ultimately winds up at. Would that be a problem, given that he would obviously have courses after Calc 1 completed through DE? Am I overthinking this?

[Gil]

You'll need to do a bit of research, but it's likely that he'll be repeating Calculus at the college level anyway, which isn't a bad thing. Off the top of my head, I can't think of any engineering schools that accept CLEP results, but based on a quick search, it doesn't look like the school that you mentioned accepts CLEP results either.

He needs to know that he'll be in Engineering school with many students who've had very strong preparation--many of the students that I took classes with had taken Calculus in highschool and at the CC before going to Engineering school. All the E-school drop outs that I personally know, dropped (or flunked) out because they couldn't keep up with the courses. Several said that their foundation wasn't strong enough--they could mostly, kinda, pretty much do the work, but not easily.

Students need to understand that their goal should NOT be to "go to Engineering school" but to graduate  from Engineering school and pass the licensing exams with minimal fuss.

I would encourage him to think about what he actually wants to do and where he wants to be in 10 years.
 

[8filltheheart]

How significant of a commute for the 4 yr U?  I can share what our ds who took AoPS precal in 9th did.  He took AoPS cal in 10th and self-studied for the AP exam.  He then DE at a 4 yr U and took multivariable, diffEQ, linear alg, and diffEQ 2.  (He went on to double in physics and math and then grad school in physics).  His older brother is a chemE and he also DE at a 4 yr U.    For them, they drove between 30-45 mins (different schools in different states) in order to attend the 4 yr U.  Yes, I think it was worth the time commitment for them to attend the 4 yr U in our situation bc our CCs are not geared to high performing students.  4 yr U courses are also more likely to be accepted for transfer credit at higher ranked schools.

[bensonduck]

You can also go deeply into precalc and stretch it a bit too. My kid is on the young side, but precalculus (using Foerster’s text) took us a bit longer than I originally expected. There’s so much to explore and do!  Often she’d get an idea from the book and then sort of use it in different ways.

For example, we had fun with mathematical expectation (DH had read somewhere about hole in one golf odds and prizes and she got really interested). She also really, really enjoyed rotating conic sections. We spent a lot of time exploring that. 

[Clarita]

13 hours ago, silver said:

He's the type of kid that won't want to do AOPS Calculus at home with me only to then have to take it again in order to get college credit (especially since the CC version would be more about "boring" calculations).

I would think a reputable college will make you do a bit of repeat calculus (just to make sure all the students are on the right page), and then will continue with even more calculus for an engineer. Also, when you do your first year of college for engineering it's nice to have those review classes because you are doing 4 really hard classes with professors or "teachers" who are more than happy to fail all their students if they aren't up to snuff. As opposed to try and find a way to help the students learn the material.

[Clemsondana]

I think that these are worth thinking about but I wouldn't be too committed to a plan for all of high school because there are a lot of variables to consider.  I'm assuming that your student did the Number Theory and Counting and Probability books when younger, but if not you might consider them.  But, we are in a similar situation, with our student likely to finish AoPS precal around the midpoint of their sophomore year.  We are considering several options. 

We have 2 different CC systems that are comparable distances from, and also state flagship is local, possibly closer than either CC although due to parking issues the total commute to the classroom is likely to be similar.  At one of the CCs and also State U, calculus classes meet 4 days/week, while at the other CC it meets twice a week.  We aren't sure that we want our last years of homeschooling to have school time out of the house every day, so that is one factor that we are taking into account.  Kid does some extracurriculars that will make scheduling difficult, but if they didn't then we might be more willing to consider it. 

Also, does your kid particularly like math?  If they are interested in some forms of engineering, they may need a ton of it (my husband took one extra class and picked up a minor in math due to his degree requirements), while other engineering and science programs don't so they won't gain much by taking several year of college math that will be counted as electives.  Are you trying to have your student take classes now so that they don't have to later - is graduating early or taking fewer credits each semester a goal?  If not, this may be a good time to add breadth (although breadth will vary by program - civil engineering and biochemistry don't require probability, while computer engineering did). 

How CC classes are accepted as transfers depends on where you go.  Within a state, many colleges and CCs have transfer agreements.  I know that when I taught at a CC our content was intentionally aligned with the state flagship to facilitate transfers.  The quality of CC teaching, like the quality of State U teaching, will vary.  Some college classes are taught by grad students who may or may not be great at it, and some CC instructors are committed to teaching as a calling and are gifted at it while others are just passing students along.  

In our situation, we are learning towards having kid do AoPS at home and then taking the appropriate AP exam.  After that we'll decide...continue along the calculus/diff eq path, starting wherever their AP score indicates, or do stats and maybe the second probability book from AoPS.  We are not particularly trying to graduate from college early, though, and kid has the schedule-complicating extracurriculars and both of those are considerations for us.  I also hold most plans pretty loosely, since kids, their priorities, and their goals change.  Spouse is going to design an intro to computing class for kid to try, and how that goes  that will probably be informative as to what we do over the next few years.  

[silver]

12 hours ago, Gil said:

You'll need to do a bit of research, ...

Students need to understand that their goal should NOT be to "go to Engineering school" but to graduate  from Engineering school and pass the licensing exams with minimal fuss.

I would encourage him to think about what he actually wants to do and where he wants to be in 10 years.
 

I realize that CLEP is not widely accepted. That's why I specifically asked about that issue at the end of my post. It's one thing to only have a single CLEP test in Calc and nothing past that. In my student's situation, there would be the rest of the calc sequence taken either at a local CC or 4-year. I figured he would not get the credit hours for calc 1 from CLEP, but would he get the course requirement waived, since he obviously has to know calc 1 in order to take and pass Calc 2, multivariate calc, etc? I also realize that a strong foundation is important, which is why part of my question was about providing a strong foundation (AOPS at home vs Calc at a CC vs Calc at a 4-year). 

 

11 hours ago, 8filltheheart said:

How significant of a commute for the 4 yr U?  I can share what our ds who took AoPS precal in 9th did.  He took AoPS cal in 10th and self-studied for the AP exam.  He then DE at a 4 yr U and took multivariable, diffEQ, linear alg, and diffEQ 2.  (He went on to double in physics and math and then grad school in physics).  His older brother is a chemE and he also DE at a 4 yr U.    For them, they drove between 30-45 mins (different schools in different states) in order to attend the 4 yr U.  Yes, I think it was worth the time commitment for them to attend the 4 yr U in our situation bc our CCs are not geared to high performing students.  4 yr U courses are also more likely to be accepted for transfer credit at higher ranked schools.

The local CC is about a 15 minute drive. The anchor CC for my region is about 25 minutes. The nearest state 4-year is either a one hour bus ride or a 40 minute drive (plus parking and walking time, as the lots are expensive and street parking is scarce).

 

9 hours ago, Clarita said:

I would think a reputable college will make you do a bit of repeat calculus (just to make sure all the students are on the right page), and then will continue with even more calculus for an engineer. Also, when you do your first year of college for engineering it's nice to have those review classes because you are doing 4 really hard classes with professors or "teachers" who are more than happy to fail all their students if they aren't up to snuff. As opposed to try and find a way to help the students learn the material.

If he stays in our state for college, especially if he goes to a state school, the local CC courses will be accepted for credit. It becomes less likely if he goes out of state further than one of our direct neighbors (those state schools seem to accept our CC courses, according to transferology). 

 

1 hour ago, Clemsondana said:

Also, does your kid particularly like math?  If they are interested in some forms of engineering, they may need a ton of it (my husband took one extra class and picked up a minor in math due to his degree requirements), while other engineering and science programs don't so they won't gain much by taking several year of college math that will be counted as electives.  Are you trying to have your student take classes now so that they don't have to later - is graduating early or taking fewer credits each semester a goal?  If not, this may be a good time to add breadth (although breadth will vary by program - civil engineering and biochemistry don't require probability, while computer engineering did). 

He told his grandparents he likes math, and he seems to like it (I haven't run into motivation issues with him like I have with his professing-to-hate-math siblings). He's also good at it, which probably helps him enjoy it more. The purpose of DE in his case would be to give him appropriate challenge, make sure he continues math in high school, and to (hopefully) get him some college credit both to help reduce the cost of college and to get him into engineering/science courses earlier. I know I appreciated going to college with BC Calc under my belt, because it opened up more interesting courses for me right away vs having to wait a year while I got the Calc prereqs out of the way. 

[Not_a_Number]

11 hours ago, 8filltheheart said:

How significant of a commute for the 4 yr U?  I can share what our ds who took AoPS precal in 9th did.  He took AoPS cal in 10th and self-studied for the AP exam.  He then DE at a 4 yr U and took multivariable, diffEQ, linear alg, and diffEQ 2.  (He went on to double in physics and math and then grad school in physics).  His older brother is a chemE and he also DE at a 4 yr U.    For them, they drove between 30-45 mins (different schools in different states) in order to attend the 4 yr U.  Yes, I think it was worth the time commitment for them to attend the 4 yr U in our situation bc our CCs are not geared to high performing students.  4 yr U courses are also more likely to be accepted for transfer credit at higher ranked schools.

I'd absolutely agree that this is worth it. The classes will be more rigorous, the classmates will be stronger, the credit will be worth more. 

[8filltheheart]

11 hours ago, Clarita said:

I would think a reputable college will make you do a bit of repeat calculus (just to make sure all the students are on the right page), and then will continue with even more calculus for an engineer. Also, when you do your first year of college for engineering it's nice to have those review classes because you are doing 4 really hard classes with professors or "teachers" who are more than happy to fail all their students if they aren't up to snuff. As opposed to try and find a way to help the students learn the material.

I strongly disagree with the statement that a "reputable college will make you do a bit of repeat calculus (just to make sure all the students are on the right page), and then will continue with even more calculus for an engineer."  A few private schools that dont allow or limit transfer credit, yes, but that is far rarer than not accepting transfer credit.  Even GA Tech was willing to accept all of my ds's transfer credits.

[Black-eyed Suzan]

My 9th grader is in a very similar situation: finishing AOPS Pre-Calc by the end of the school year. He is leaning towards majoring in math at this point.

Right now we plan to have him take the rest of the AOPS class sequence, including Intermediate Counting and Probability, Intermediate Number Theory, and Calculus (hopefully taking the AP exam). My son has also expressed interest in Statistics.

Of course it may be different at your CC, but a local friend cautioned me that our CC (with free DE for 11th and 12th) did not allow students to take Calculus as their first math class. I haven't checked with the CC itself to see if that policy could be changed with a sufficient placement test score, but it's something to look into if you continue to consider the CC. That, plus my belief that the quality of the instruction was unlikely to be comparable to AOPS, really discouraged me from the CC path.

I'm intrigued by the other posters mentioning DE at a nearby 4 year university! 

[8filltheheart]

1 hour ago, Black-eyed Suzan said:

I'm intrigued by the other posters mentioning DE at a nearby 4 year university! 

Our different local Us allowed DE, but they had a limited list of classes to select from. We made an appt with the registrar. Ds had test scores from 8th grade that far exceeded their freshman profile and we asked for his AoPS teacher to provide a letter describing his current level of math. They agreed  to allow him to DE in multivariable pending his AP scores (obviously needed).  They limited him to that course and cal physics. We moved and had to repeat the process there. That uni let him DE in as many hrs as he wanted after 1 semester there.

Edited October 6, 2021 by 8filltheheart

[Clarita]

6 hours ago, 8filltheheart said:

Even GA Tech was willing to accept all of my ds's transfer credits.

I guess you could take enough CC calculus to skip all of University calculus, but if it's just equivalent to AP Calculus BC then we had to take another year and quarter of Calculus. Only the first quarter was "repeated" material though. 

[8filltheheart]

43 minutes ago, Clarita said:

I guess you could take enough CC calculus to skip all of University calculus, but if it's just equivalent to AP Calculus BC then we had to take another year and quarter of Calculus. Only the first quarter was "repeated" material though. 

I really don't follow your thoughts.  The OP's ds will be ready for AP cal BC in 10th grade.   He could dual enroll in classes at a 4 yr U and take at minimum 4 semesters worth of math post cal  BC if that is what he opted to do.   He could also DE in physics or chemistry.  (My ds had completed 5 of his UG physics courses for his bachelors in physics before he graduated from high school.)

Edited October 6, 2021 by 8filltheheart

[Not_a_Number]

1 hour ago, Clarita said:

I guess you could take enough CC calculus to skip all of University calculus, but if it's just equivalent to AP Calculus BC then we had to take another year and quarter of Calculus. Only the first quarter was "repeated" material though. 

I think she's talking about classes at a 4-year university, not at CC. 

[Clemsondana]

I know several students who took 2-3 semesters of calculus at CCs and the credits were accepted when they went to college.  For one student, it was an out-of-state flagship, and the student was thrilled to be done with math before arriving on campus.  I'm a little confused at the idea of doing well on the BC exam and then still needing to take a year plus a quarter of calculus.  Other places could be different, but most places that I'm familiar with seem to have 3 semesters of calculus, then differential equations, then linear algebra (I could have swapped the order of those last 2 - as a biochem major, I was done after the 3 semesters of calc).  The CCs here don't seem to have many of the post-calculus classes, although they do have statistics.  But, CCs are generally 2-year colleges so I wouldn't expect them to have much more than 2 years of sequential math.  Statistics isn't really part of a sequence, and some kids here seem to take that as seniors instead of calc if they don't need it.  

 

Edited October 7, 2021 by Clemsondana

[kiwik]

What about distance options?  I have been looking way ahead and since I am 6 hours drive from the nearest universities and our equivalent of community colleges don't offer maths, english, classics etc the only option is distance courses at first year university level.