My son is in 8th grade. In a few weeks we will meet his student advisor to propose what courses he will take in high school. Of special interest to us is math. This is because the other courses auto select themselves. He will be taking 4 years of French, 4 year of Latin, 4 years of English, 4 years of Science in the order chosen by the school (Biology, Physics, Chemistry and then AP Physics C), and 4 years of History in the order chosen by the school (Global History I, Global History II, US History, European History). So there is nothing for us to choose. It is all pre-determined. Math in the only subject where there is flexibility and hence our choice involved. We have 4 choices.
In order through grades 9 to 12
Honors PreCalc, AP Calc BC, AP Stats, MV Calc/Linear Algebra
Honors PreCalc, AP Calc BC, MV Calc/Linear Algebra, Real Analysis (in college course)
AP Calc BC, AP CS, AP Stats, MV Calc/Linear Algebra
AP Calc BC, MV Calc/Linear Algebra, AP Stats, Real Analysis (in college course)
The first sequence is the path of least resistance that I believe he will sail through. The downside is that he will likely be bored in PreCalc. If he takes a placement test now, he will get a B/A- in PreCalc. However, I believe in a strong foundation before skipping ahead, and the one year of Honors PreCalc will definitely provide him with a complete understanding of PreCalc. My wife favors this one.
The second sequence has the same PreCalc issues as the first, and also skips Stats. But it picks up Real Analysis which I think he will enjoy far more than AP Stats which is rather … dumb (for lack of a better word). Personally I like this sequence the best.
The third sequence is no one’s favorite. However it includes the max number of AP courses, and AP CS will be a breeze for my son who programs well in Python and Java already.
The fourth sequence is the one preferred by my son. He believes he is ready for AP Calc BC (and I agree as he is pretty much done with AP Calc AB). He would rather take AP Stats over AP CS. Finally he believes he will be super bored taking Honors PreCalc.
So we have no consensus in the family about what path to pursue. I would like to hear the thoughts of CC parents. Thank you very much in advance.
Student perspective: this seems like the obvious choice to me, assuming that his foundation is as strong as you say it is, although lots of things can change in the next few years to alter this plan.
Will he sail through all of his other classes too? I’m for the strong foundation. Pick the one that will give him the strongest foundation.
And remember that his HS classes will likely be more time consuming than his MS classes. He will need time for homework…and time for pursuits outside of academics.
How good are the teachers in the higher level courses? How complete is your son’s mastery over the material he has covered already? PreCal didn’t introduce much new material, just some trig----did he have trig already? I thought of it as a consolidation course before a big plunge into new material. It is tough to find a good post calculus math teacher, especially in high school.
Stats is an easy course, and they say the AP version isn’t like the college version, so your child doesn’t need that course.
If you feel comfortable with your son’s mastery of what he has learned so far, if he has had some trig, and if the upper level teachers are good, I’d honor your son’s wishes. If he finishes high school with more than BC he will be in great shape.
Good point by ski about changes in plan. Kids do grow and change in high school. Your math fanatic could discover theater or biology or girls. Allow for some wiggle room. Also, some kids have these (not sure how to describe this) spots of cognitive immaturity when it comes to math. Like a kid who cannot grasp algebra in sixth grade can sail through it a year later. I have never heard of it with higher level math, but I suppose it could happen. It seems pretty common in algebra. Be looking for this issue.
Thumper, I believe the one that will give him the strongest math foundation is #2 which is why I am inclined towards it. But my wife feels that there is no real need for him to take Real Analysis in high school hence she prefers #1 which will be an easier sailing which also ties in with your point about high school being more difficult than middle school. He will sail through French, Latin, and English as well.
Skieurope, We always respect our son’s opinion if he wants to go slow but we worry about him going too fast.
QuantMech, He self-studied using some AP book on Calc AB and finished all the problem sets. He also signed up for an online Calc course and completed all the problem sets for that. He tells me that over summer he similarly plans to finish Calc BC as well. I would rather have him drill and kill precalc problems to form a strong foundation but it is very hard to get teens to listen to you.
Lizardly, I do not know anything about the teachers but my son has always been an autodidact. As for his mastery over precalc I believe he will get a B/A- if he is given the placement test today. I therefore feel that he should take the course for a whole year to completely master precalc and not get a single problem wrong and be able to do this without thinking, arms tied behind the back, eyes blindfolded, so to speak. He knows trig pretty well but I am not sure he can crack every single problem without thinking.
One other 5th option that he has talked about is:
AP Calc BC, MV Calc/Linear Algebra, Abstract Algebra (in college course), Real Analysis (in college course)
In middle school he has been taught a lot of abstract algebra in a special class with 3 other kids who were taken out of the regular class and put in the charge of a college math professor who introduced college mathematics to them. He loves number theory and is now ecstatic about groups, rings, fields etc. But I worry about the pressure and time commitments.
Great points so far, especially to consider the overall difficulty of his course load and to remember that he’ll have the ability to adjust these options every year. I would opt for the solid foundation of Pre-Calculus and the A grade in 9th grade, because that is the crucial choice that he is making at this meeting.
If he’s done all that studying for Calc AB then sequence five is a no brainer. Otherwise I’d go with sequence two.
I don’t think a strong math student needs to waste their time with AP Stats.
FWIW my older son took AP Comp Sci as a freshman back when there was a B version that covered twice as much material as is covered now. He’d gone in self-taught and in retrospect said he really learned nothing new. He would have been better off just taking the AP exam.
Does he have to decide everything now? I’d think he could take BC Calc next year and then if he’s feeling stressed as a junior or senior (or gets suddenly interested in the theater!) he can take one of the less stressful options like AP Comp Sci or AP Stats.
In my experience strong math students find math relaxing and get stressed about writing English papers or poems.
siliconvalleymom, No wonder both his parents are aligned with you that a solid A in precalc should come first before Calc BC. We have been thinking on how to convince him to agree with us and may give him a challenge. If he studies precalc between now and August and finishes every single problem in the text book and then gets a perfect score in the placement test then we will allow him to take Calc BC. But nothing less than a perfect score in the placement test will do and he must also do all the problems in the text book which he finds to be really boring.
mathmom, I will admit that #5 has its attractions. But first he has to cross the prefect score hurdle to take Calc BC in 9th grade. No he doesn’t have to decide the whole sequence now. He has to present a planned sequence for 4 years but I believe the school will be flexible if he deviates from it later. My son also read through the AP book for CS and told me that there is nothing new for him. I also completely agree with you on AP Stats. He does find math to be very relaxing but he is also a very strong writer and finds languages to be very relaxing as well. I think he finds anything that he can do from first principles without the need to acquire mastery over facts to be relaxing. It is when memorization of facts come in that he gets challenged and stressed. Perhaps a dual major in math (algebra) and english (creative writing) is what is in the cards for him. He may also be interested in mathematical/computational linguistics.
As a fellow parent of a very advanced math student, I say go with option 5. There’s no reason to waste a year sitting in a class where he knows the material. And I wouldn’t require he finish every problem in a book either to prove it. Try having him take a college final in the course (can usually be found online) and see how he does. The harder the challenge in math, the better my son did. And the real joy for him came when he reached the college real anaylsis levels. I also believe AP Stats is a waste for a very strong, advanced math student. I’d have him take a mathematical stats class in college instead.
Agree with others that if he is that advanced in math, AP statistics is probably a waste of time. If he wants to take statistics, he can take calculus-based probability theory and statistics in college (while in high school or after he enters college “for real”).
If you or he is concerned about precalculus knowledge, he can try these placement tests used by colleges to place students into calculus 1:
As far as making him do all of the problems in the precalculus textbook, that may be too tedious for him because most textbooks have lots of easy problems in them. Most textbooks order the problems by difficulty, so if you do want him to do problems, have him do the last few in each section, or the ones with stars next to them if the textbook uses stars to denote harder problems.
Some other questions to consider:
a. Are multivariable calculus and linear algebra college or dual enrollment courses? If they are listed as only high school courses, then he may have issues getting subject credit at some universities.
b. Is the college where he may take real analysis and abstract algebra one that has a strong math department? At least one poster has mentioned that math PhD programs seem to regard different schools’ undergraduate math courses differently, and it affects admission to math PhD programs.
Is there an option to just take a separate Differential Equations class? Or a 2 semester Multivariable Calculus class (which would cover college equivalent amount of material), and 2 semesters of Differential Equations? Some area high schools do this in conjunction with our state university, with great success. Students took actual university mid term and final, graded by the university, and received college credit hours as well.
If possible, I would consider the sequence of AP Calc BC, Multivariable Calculus, Linear Algebra, Differential Equations, and take Real Analysis as an additional class while at college.
I agree that Statistics is a better class when at college vs. what you learn in an AP class. Same with Computer Science.
Multivariable calculus is typically a one semester course in college, so a dual-enrollment high school course that runs at college pace would be a one semester course.
What about:
AP Calc BC, MV Calc/Linear Algebra, Real Analysis (in college course), …
Figure out … when you get there.
For a student with as advanced math skills as your son I would skip both AP CS and AP Stats. They are both useless and irrelevant to his academic track. Senior year, perhaps he can find more advanced coding classes, or a college stats class.
I’d go for getting the very strong foundation in pre-calc. He will still have plenty of opportunity to take higher level math in HS. The transition to HS can be difficult for some and it is not a bad thing to have one class that will be less stressful. It may also give him some time to see out some HS activities he’d like to get involved with. And I agree with that statistics is not necessary – in our HS AP statistics is consider an elective not a replacement for math.
I’ll pile on to the anti-Stats bandwagon. For a strong math student high school stats will be boring and non-rigorous. The same goes for AP CS if your S already is strong in programming.
If you need to pull back on the math, whether because it is too much pressure or because your S wants to explore some other areas of study in high school, don’t worry about acceleration. It won’t affect S’s potential future as a math major. One of my kids, who is a current phd student at a top math program, did not go beyond AP Calc BC in high school. There will be plenty of time in college for your S to take lots of math.
what’s the risk if he’s bored? Some kids will do poorly (check out etc), others will still put forth effort to obtain an easy and solid A.
what’s the rigor required for colleges he’s aiming for? Some of your options are way beyond what I’ve heard of as “necessary rigor” but perhaps necessary for Ivies? We didn’t look that high…
if you know some target schools and programs, look at what they will accept vs won’t accept (for example, ds took and enjoyed AP Stats but the school’a stats is a Soph or Jr level requ that can’t be tested out of, whereas his AP CS got him a free pass to the next level up in college). Stats wasn’t accepted but it will be familiar material when he hits it again so I won’t say it was a total waste.