Calculus BC 8th Grade/Honors Science Middle School

She doesn’t need credit for BC Calc, she just needs to be placed in the correct math level when she gets to college. Colleges will have placement tests. SATs in 8th grade disappear unless you petition to have them stay, but APs are another thing entirely. She’ll get credit whenever she takes the exam. My son was not nearly as advanced as your child, and was on track to have no math to take his senior year in high school, but by the time senior year rolled around there were enough other kids who’d gotten on the same track that they offered a Linear Algebra class for them. You can’t count on it of course, but there are online options.

@vox_nihili

The question I would ask the school administration, is whether the counselor’s understanding is accurate. It doesn’t make any sense to me that a student who has run through the entire math program offered by the school a couple of years earlier than most students enrolled there would be unable to qualify for the STEM track.

I do know a student who was highly gifted in math and physics who ran through his school’s classes and the courses offered at the local university on a schedule similar to the one proposed here. That student left high school early and started college full time at age 15. You may want to contemplate something like that for your daughter.

Most of high schools, private or public, don’t start math higher than BC at 9th grade, regardless how advanced the students are. Your kid can always take the BC exam and lock the score if it is good. I know several kids who were in similar situations. They took the SAT and scored perfect in math at 6-7 grade and took the BC and AP stats at 8th grade.

One way to show her math talent is to go through AMC 10/12/AIME competition. For girls, there is the math-prize-for-girls contest. This is a difficult path to travel.

@vox_nihili,

As it seems you are committed to this school, I would definitely work very closely with them, and encourage them to help you lay out a long term math plan that is satisfactory to both you and your daughter, knowing of course that you’ll still take it a year at a time.

Our educational paths are quite different, as I homeschooled my mathy son, but I thought I would share a bit in case you see some parallels.

My son followed a fairly meandering, unschoolish path in math until high school, doing Algebra in 2nd and 3rd grade, Geometry in 4th, back to Algebra using another textbook in 5th (because I hadn’t a clue what I was doing 15 years ago), 1/2 year of Trig/Alg II in 6th, pre-calculus at the local community college in 7th and Calculus 1 at the local community college in 8th. We opted not to do BC in 8th, though he could have since Calculus 1 is only one semester.

Though he did take AP Physics B in middle school along with taking the SAT I in 7th and 8th, and two SAT IIs in 8th, my son ultimately did not attend college full time early.

Summer after 8th, he took a statistics course at the CC. In 9th, he took Calculus II and Calculus III along with the BC exam. In 10th, he took Linear Algebra and Differential Equations, which was as far as the community college went.

They were just starting AoPS classes back then, so my son didn’t do any of the academic online courses except for an AIME prep class in 10th grade, but he did find challenge by joining the local math circle from 10th-12th grade, and participated in AIME three times along with the local math olympiad.

The tricky part was what to do with his last two years of high school. He opted to go back to his unschooling roots, and he studied with an online mentor once a week or twice a month for the last 2 1/2 years of high school, going through a separate Differential Equations text book, learning Dynamical Systems and finishing with Real Analysis.

Since he wasn’t in a public or private school, we didn’t worry about “official” A-G courses, and my son never applied to the UCs as he wasn’t interested in them (too big).

In the end, he graduated from MIT. He was able to get transfer credit for all his CC math classes at MIT, which was really nice (but not for any of the math he did his last two years of high school).

Your daughter could take the BC exam in 8th grade or wait until 9th grade if it’s all the same to her, depending on what math she’ll take in 9th. I would hope the school might allow her to take either CC or university math courses if she wanted in order to be able to take math all four years. She could do one course a year: 9th Calculus III, 10th, Linear Algebra, 11th Discrete Math, and 12th Differential Equations. Or, she could opt to study Real Analysis at a UC or CSU in 12th if the school was agreeable.

My son also took a bunch of college physics courses during middle and high school, which complemented the math courses well.

Colleges will be flexible with your daughter whether or not she has these courses on her transcripts. She’ll eventually have letters of recommendations, transcripts and essays that tell the story of this passionate learner, so I wouldn’t worry too much about “official” credit. I have worked with students who have backgrounds like hers, and her passion for learning really speaks for itself. She sounds like a great young lady!

“There is truly no reason for your daughter to rush things.”

I strongly agree with this.

@vox_nihili, there is some very good advice in this thread; but I’m a little concerned that your daughter is rushing through things, and will have major gaps in her background, no matter how mathematically talented she is.

AoPS does not recommend going directly from Algebra A to Algebra B. The recommend taking at least one of Introduction to Probability and Counting or Introduction to Number Theory between them, and they caution about rushing too fast to get to calculus, and about the need to include discrete math, which is sadly lacking in the standard school math curriculum - and these are the guys who train many of the top math kids in the country. I would suggest reading the following articles from the AoPS website:

https://artofproblemsolving.com/articles/calculus-trap
https://artofproblemsolving.com/articles/discrete-math

I personally don’t see much benefit into rushing into BC calculus in 8th grade. Your daughter is already 3 standard deviations ahead of the curve, and there is much more risk in rushing and having huge gaps in her background - gaps which can be fatal when it comes to being able to do math at the next level - than in the danger of missing out. Students who rush and have gaps - no matter how gifted - often struggle at higher levels, because the skills that they excelled at in high school math are only a small piece of what it takes to succeed.

I like the idea of taking time to do AoPS Number Theory, and Probability and Counting (perhaps at both the introductory and intermediate levels) before rushing into BC calculus. You might also look at online programs which provide an different approach, like iMACS’ Elements of Mathematical Foundations, which is used as the course for the most advaned math students in Brouward County Public Schools; iMACS also offers online college level courses in logic and set theory, which are important foundational skills for higher math.

Once your daughter gets through calculus BC, whether in 8th or 9th grade, she will have to figure out what to do next. School offerings, dual enrollment classes, and online courses are the main options. There are tons of MOOCs, or varying quality, on places like Coursera and MIT EdX. Stanford Online High - and Stanford Pre-Collegegiate Online Math and Physics, which offers the same courses in a less structured online format - have extensive course offerings in post-calculus math, which could keep your daughter occupied well beyond calculus. But I think there is no need to rush, and a lot of reasons to slow down just a bit and make sure that your daughter fills in some gaps and builds a really strong foundation for exelling at higher mathematics.

Good luck!

My son commented that some of the math he learned in Game Theory and Probability at a CTY camp was math he didn’t meet again until college, it’s really too bad that high schools give such short shrift to whole swathes of mathematics. It turned up in some physics classes as well.

^ If you look at competitive math programs such as AwesomeMath, they essentially give equal weight to 4 foundational areas of mathematics: algebra, geometry, combinatorics (probability and counting) and number theory. Only the first 2 are generally govered in the school curriculum, and geometry is usually covered poorly.

https://www.awesomemath.org/summer-program/during-camp/curriculum/#tab-id-3

I would strongly suggest progressing as usual and having your daughter continue to take classes with her friends. I think your daughter’s case is a bit unique because slowing down means losing her old peer group, and having to adjust to a new peer group that is much older than her. Usually, it’s the other way around, which is why I think a lot of people are advising to slow down. The concerns over GPA are not necessary I think - if you are really concerned you can make sure the issue is noted in her application when she applies. But it’s much more likely that your daughter will have other accomplishments that will make up for this.

@renaissancedad The OP’s daughter already took Number Theory and Intro to Probability and Counting from AoPS. Or are you saying that she should take those courses again?

^ No, I missed that she took those AoPS intro classes (post 15; they weren’t mentioned in the OP). My mistake, and thanks for the correction. But I think taking the intermediate classes would be good, including Intermediate Algebra. In the AoPS curriculum, Algebra A & B, Intro to Number Theory, Intro to Probability and Counting, and Intro to Geometry are all part of the introductory series. There’s a whole series of courses between those and calculus - Intermediate Number Theory, Intermediate Probability and Counting, Intermediate Algebra, and Precalculus.

OP, my daughter followed a similar math track, with AP Calc AB in eighth grade and BC in 9th. She is about to start a a math Ph.D. at Stanford, so we didn’t mess her up too badly. Here are some random observations:

  1. For college credit, not one college that we approached had any problem granting credit for APs taken in middle school (she had 5 as a homeschooled middle schooler). Sure, there may be an exception, but I’ve never found one, and we asked probably 6 or 8 schools.
  2. For the GPA bump or high school rank, I would not waste one second worrying about that unless you are somewhere like Texas that gives automatic entry to UT for the top 10% (or whatever). I refer to parents who make a big deal of GPA at the expense of rigor as quality point whores (“quality points” is how our local schools refer to the GPA bump–I don’t know if that is universal). You will run across plenty of them. My daughter spent her last two years of high school taking graduate-level math courses on campus at a major research U. I fought to get them awarded the same GPA bump that was awarded to the easy APs–psych, enviromental science, etc. I finally got it straightened out, but it was a waste of my time. When you have a truly exceptional high school transcript, as your daughter probably will, no one cares whether there was a GPA bump. I don’t even know where my daughter ended up in her class rank. She was collaborating with professors and post-docs on original math research instead of taking AP Psych or stats as a senior; trust me–no one cared about her high school class rank.
  3. Tune out anyone who tries to slow her down. Seriously. You know your daughter, and if she loves math, encourage her to go all-in. The math world will be amazingly welcoming to a girl who loves math, but the path will be infinitely easier if she looks like a prodigy because she’s run out of math in ninth grade. And by this, I don’t mean to ignore other branches of math in a rush to calculus, but I would let her take all of the math she wants to take. AoPS is often recommended for gifted math kids, but it is not the only way to learn other levels of math and, really, if Calc BC is the easiest thing to take in ninth grade, by all means, take it. There is no reason to wait on calculus (and break her up from her friends), rather than taking calc now and combinatorics or number theory later when she will be older and can possibly take them through DE if that is a better option than AoPS.
  4. Definitely investigate local colleges for advanced math offerings she can take through dual enrollment. Your GC is probably not even the best resource for this. I did the research and legwork to make it happen for my daughter, and we found out that multiple “facts” relayed to us by her GC were not. MULTIPLE facts. Not that I’m bitter. . . Anyway, a college math department will probably also be a good resource for mentorship opportunities and advice. Just ask. There are plenty of math professionals who will be more than willing to invest some time into your daughter. My daughter has had one negative experience with a mathematician that might, possibly, theoretically been rooted in sexism or, equally plausibly, could just have been due to the fact that this guy is a jerk, and she’s met, collaborated and studied under hundreds who have bent over backwards to invest in her.
  5. Math contests are one way to show math passion and talent, but they are not the only way. A lot of kids don’t enjoy math competitions; there’s nothing wrong with that.
    Best of luck to you both. I’m always happy to hear of other math girls!

Game theory is a junior class for math major in college. It doesn’t mean to be taught at high school. The only real attempt to offer probability in high school is in AP stats class.

The bigger problem is the missing link between algebra/precalc to physics/chem/stats. I guess precalc says clearly what it is for.

The discrete math is sometimes a weed out class for CS, like the CMU’s concept in math, which includes set, logic and prob.

Math can become really difficult for everyone, no matter how good you are at middle/high schools, when the he faces real analysis and partial differential eqn. It is more important for the person to have a raw talent and dedication in math than how much he knows at middle/high school.

My dauhter isn’t as advanced as yours, but we’ve been looking at similar issues,

The value of s peer group can’t be underestimated, For kids like this it’s huge. There are no guarantees that they’ll still be there for their full high school years, or that your kid will be there for all four high school years, but it’s there now and it’s a factor.

With kids like this, we’ve always taken the approach that we figure out what’s best for right now, and figure out what happens later when we get to that point. If she’s ready for Calc BC, I’d do it. You won’t get that class on her transcripts, but you’ll be able to self report her AP test score on college apps.

I’d then go through the other classes available at the high school and figure out senior year when you get there, the UC a-g requirements are for three years of math, which you’ll have. If at that point you end up with a college class, AOPS, JHU-CTY or something else it shouldn’t hurt UC application status.

As for the miss of the “boost”, that applies to weighted GPA, class ranking and valedictorian status, and will depend on how the school policies. Do you or your daughter care if she’s in the running for valedictorian? Most of the kids (and parents of kids) with this kind of advanced schooling realize that class rank really doesn’t matter. Other than that, the schools will see a kid who has taken classes “above and beyond” and that will count for a lot.

I have never been a fan of AOPS. It is a for profit company that is owned by an ex Wall Street bond trader. For profit educational institutions always seem to have their own agenda. When you cut through all the covering surrounding AOPS it makes its money by pushing contest math and contest physics to extreme limits. Contest math is often extremely detrimental to women in the math field such as OPs daughter . Math as a field suffers from gender discrimination enough . It is not necessary to add more fuel to the problem.

My D was very advanced in math. She took BC in 7th grade and went on from there with EPGY which is closely associated with Stanford online high school and college classes. She did graduate with an honors degree in math from a top university but there were challenges with the gender issues in college. Math is not a race. OP take your time and have your daughter learn fundamentals well. Learning is the most important thing and colleges will recognize a true learner.

She should take whatever math classes she feels ready for. If she finds precalc easy, I don’t see a reason to hold her back. Hopefully she will be able to take some college math classes while in high school, or online classes. My guess is that so much acceleration in math will mean a lot more for colleges than a small bump in GPA.

OP, I say don’t hold your daughter back. I’ve got a kid who just did math on their own from 3rd through 6th grade (no classes at school), then took precalc in 7th and calc AB in 8th (schedule at the LPS made BC impossible). BC in 9th. None of it has been particularly challenging.

I would encourage your daughter to try contest math. Math is a competitive field, and it is important to get a sense of how you deal with failure. It is not much challenge for a motivated +3 SD sort of kid to get through the standard high school curriculum (including calculus) by 7th or 8th grade. But what school classes won’t tell you is how you deal with failure and coming up against your own limits. Even recognizing that competitions can be demoralizing for some, I think that facing these questions - limits and failure - are inherently good aspects of the standard competitions. It’s worth trying. The AMC8 is easy, no real time pressure, and at this stage should be a lot of fun (assuming she hasn’t already been doing them). AMC10/12 and ARML are also fun. I have never been a fan of MATHCOUNTS - too much emphasis on speed over substantive thinking - but the format might just click. You never know till you try.

As well, competition preparation will help your daughter “find her tribe” and also allow her to delve more deeply into some of the high school topics, as mentioned above by someone in relation to AwesomeMath, which BTW my kid found to be a great experience.

I would also look into summer math programs. From personal experience of our kid, MathPath is excellent for middle schoolers (ages 11-14), and Canada-USA Mathcamp is supposed to be fantastic for older kids (14-18). As with competition, these camps can sometimes be humbling experiences. At MathPath, ours encountered another kid who had already finished up linear algebra in addition to having solid contest results (not quite USAMO, but just off a tiny bit on the selection index). The kid who had completed LA was eleven years old.

As for other classes in high school, at some point I would highly recommend that your daughter get some exposure to real analysis, either through a course or through working on something like Abott’s “Understanding Analysis” text, and also some exposure to abstract algebra. She will no doubt want to repeat these subjects in college, but her reaction to higher level mathematical thought at this early stage will help inform her choices later on. Math is a great subject to study in college, and useful for a variety of fields from hard sciences right through to philosophy. High school exposure to “real” math would help her figure out whether pure math is something she really wants to pursue, and some competition exposure at this stage would, imo, help her develop the toughness that you need in the field (yes, it is very male-dominated and very competitive, and no that is not going to change in the next few decades).

Anyway, congratulations on having a daughter who is so interested in math. As another poster wrote above somewhere, there are tremendous opportunities for girls and I wish you the very best!

Thank you all very much for your responses! There have been some really useful comments. Also many of you seem to have very exceptional kids. I was very impressed reading about their accomplishments and the paths some of these mathy and/or physics-inclined students took. Congratulations to you for raising these wonderful children.

I’m inclined toward the advice given by posters who recommend my daughter continue on her path with the same math cohort, with continued assessment of course.

I’ve previously read the breadth vs depth argument which I definitely agree with. I also think there is more to math than what is taught in school and It would be wonderful if a course such as Game Theory and Probability were offered through the school. These CTY courses sound really interesting. I don’t imagine schools would offer course credit for them since they are summer courses but I’ve heard other parents rave about these summer courses.

My daughter has taken Intro to P&C and NT along with Intermediate Algebra and plans to take Precalculus through AoPS as well as the precalculus course offered by her school so I don’t think she is rushing through the curriculum toward Calculus,. She really wishes to stay with this math cohort and as long as there is no ill effect, I don’t see why she shouldn’t enjoy that social experience. It seems most posters would agree that there would be little if any effect for her to take the course while the advantage of like-minded peers is high.

For her middle school years, we are committed to this school as they have these options available to her while I expect the local public schools would not, especially since most are junior highs so would not offer high school courses. For high school, we’re willing to consider other options such as the local public school system. Does anyone have experience with how willing public schools would be in accepting college credits? What would be the advantages/disadvantages of a public school system in this situation?

There is a lot of really good advice about college courses she could take along with very useful information about summer camps, programs and math contests. I am really clueless about a lot of these topics and haven’t done any research about local college courses but did look into Stanford Online as that’s another route we’ll consider. I am also completely ignorant about suggestions such as dual enrollment.

Are there websites where I could find this information? I think I will need to talk to the school counselor/administrators to see what options she might have along with planning a curriculum for her that would see her through the high school years. I have no knowledge about class ranks or bumps on gpa and up until reading this thread I have never once given a thought as to whether I’d want her to be a valedictorian and I seriously don’t imagine she had either. I also came by here recently to ask my question but noticed a lot of other useful threads on this forum and I feel as if I am quite ignorant of a lot of the matters being discussed. I am really glad I found this resource. The posters here are really helpful. Thank you for sharing your personal experiences navigating the school years with your remarkable children! It was much appreciated.

My kid’s Mathcounts team was half girls. They had a good time. One year they qualified for states, and oh my the top ten finishers were soooo fast! (They were tested individually in front of an audience.) My son had never bothered to actually study and memorize things like they obviously had - they were answering questions before I had time to read them off the slides! He was happy to do the contests, but was not really into them. He qualified for AIME every year he was in high school, but I think his highest score was 3 (out of 15). The AMC tests are just that a test once a year. He got more interested in computer programming the older he got. If your daughter hasn’t tried CS, I would suggest that she add that to her plate.

My son did end up getting credit for a fast-paced chemistry course through CTY, which he took because of scheduling issues. But the courses like Game Theory, aren’t just math, so it wouldn’t really be appropriate for credit. And that’s fine. One of the things I liked about that course was that they learned about Apple’s marketing strategies and watched movies about the Cuban Missile Crisis and discussed the Prisoner’s Dilemma.

Our public middle school allow kids to take math at the high school. (They are next door to each other) So progression is completely normal for accelerated kids.

Skimmed posts. Some comments. Gifted kids are different- hopefully you are doing your homework on this. Lot of good info online.

Peer groups do matter as stated. Remember that your child is multifaceted. She may be globally gifted or mainly in math. Social skills and playtime count. Music, art, sports are all valuable. Plus they can be stress relievers now and in her future life in college and beyond.

It is easy to continue in math and she needs to keep going. The concept of waiting until HS for the added weighting of her gpa only matters where the school and colleges use that. Waiting so a HS math class can be taken every year-hmm. Check out area/online college options before limiting her. Easy to take AP calc and stats at the same time, btw.

Remember the whole child. Let her progress in math but concentrate on shoring up her weaker areas. Language arts may not be as easy for her. More time with that and rounding out her education is important at this stage in life. Who knows- her primary focus ten years from now may be entirely different. Work on the whole skill set to bring it up to par with her math skills. It is easy for her to want to do what she is good at, help her skills in other areas.

Do not plan her education for getting the furthest ahead in college. Plan it to let her go at her pace in math but to also work at other facets of who she is. She may discover fun with other fields once she feels as competent in them. They, too, are building blocks for a future career.

I agree with those who are suggesting that your daughter should stay with her young peer group, and plan to take AP Calc BC in 8th grade.

In terms of class rank, yes, this may affect her class rank. However, many schools no longer rank. Our local high school dropped class rank just before my daughter entered. From everything that I have read on CC, rank seems to be meaningless at present–it runs the gamut from cases where there are 100+ valedictorians, through cases where students take AP classes online without letting other students know, and cases where students drop band or orchestra because there is no GPA boost, to cases where students take physical education in the summer or somehow not at all, to avoid the GPA ding of an A in an unweighted class. This just gets ridiculous. Unless you are in circumstances where rank truly matters for a probable college of choice, I would ignore this . . . .

except to say that I am reading warning signs about the guidance counselor, based on your post.

The school seems to have its rules set up to exclude the GPA boost from AP courses taken before high school, in order to discourage extreme acceleration. Some high schools seem to want to keep their students under their control throughout the high school years. The “running out” of math to take is a commonly given excuse. If there is a university nearby, and/or if you are happy with the Stanford courses on line, your daughter will not “run out” of math to take. Transportation to the university can be a legitimate issue. The school is probably not required to provide that–the parents will have to do it. My schedule permitted that, but some parents will not be in a position to do it.

AP Statistics, while valuable, is a very “lite” “math” course for a student who is as accelerated as your daughter. There may be a better alternative. Locally, it was possible for a student to start statistics with the university course on probability and statistics that had multi-variable calculus as a prerequisite. There are a few topics around the edges–whisker diagrams, etc.–that your daughter would have to teach herself, probably, but they are no issue. She could then take the AP exam without the AP course.

The only element of the plan that raises any questions for me is actually the plan for honors high school physics in 8th grade. It depends a lot on how this course is taught. I think of mathematics as a subject that is self-contained in a way, in the sense that one can understand the topics with abstract, analytical thinking. Physics, on the other hand, tends to have elements that require experience and physical intuition, as well as practical thinking. Analytical thinking is useful for physics, of course, but mathematical maturity and maturity for physics are somewhat different. As mentioned, this depends to a great extent on how the physics course is taught. Some could be great for your daughter–for example, PSSC physics, taught the way it is supposed to be taught, by someone who understands physics pretty well. The text is no guarantee of the quality or nature of the course, though. Does your daughter enjoy construction projects? Honors physics may have them as a component. How comfortable is she with lab work? What are the physics labs like (assuming that the course has them)?