I wonder the same thing: 6th grade: pre-algebra 1?, 7th grade: pre-algebra 2?, 8th grade: pre-algebra 3?
Are the kids bored?
I am of the opinion that being repetitive to some extent is fine for most learners, but contents being diluted (like when you really can hardly tell this is a book for “rain forest” or a book for math) is bad.
I gave my child a lot of puzzle problems to solve when he was about that age. It could help improve his problem solving skills in high school and beyond.
When my child was in elementary school (or even early middle school?), I read a math textbook called Saxon Math (maybe also Kumon math sheet). It is their education philosophy that the materials need to be repeated (i.e., loop back continuously) until most students could “internalize” it. Some students may not need to loop back so many times, but the author thinks the majority of students do need to come back to relearn/refresh it a certain number of times.
I once sat in a math class at a graduate school. The professor said that after you manage to do advanced math problems (beyond the MV Calculus level) like you do simple addition and multiplication taught at grade school, we can start to learn something deep. This professor was a relatively distinguished one. Another (physics) professor said if you plan to attend a graduate school in STEM (physics in his example), it is advisable (in his opinion) to take at least one math class every semester in college and you will have enough math background to pursue graduate study after college.
you are both right. I think I am just being cynical after seeing the rather mediocre quality of math instruction in her high school. While D managed to avoid the really horrendous calculus teacher (whom others praised but I think she just gave out lots of A’s), I’m not convinced D’s teacher was much better. At least he assigned homework and graded them. She didn’t sound confident after the AP exam.
“Your enthusiasm and passion for the importance of advanced math is high school is evident throughout all of your posts. I also believe that other OPs views regarding the importance of a strong foundation in English and other areas are also important for a successful college experience .”
Actually I have nothing against a strong foundation in English. In our schools, the opportunity for this is far more limited than to get a strong foundation in math and I think that’s true in most schools. There’s nothing a family can do within the school system. There is no way to grade-accelerate so you are stuck with grade-level instruction even if your child is reading 6 grades over level. Yes, of course this is of concern to me, especially since my rising 10th grader wants to become a writer. However, she still reads books, and she still writes things for class. She can still improve her writing at her own pace rather than simply repeating things she knows. So it’s not the complete waste of time it would be if she were now enrolled in algebra1.
My son’s friend was a real math avian-ado. By 9th grade, his dad would drive him 45 miles to a college for math
Classes. He continued to take math at the local U. I don’t think it unusual for kids to use the local for classes, e.g. Math, Latin, Econ, etc.
I had no expectations that our HS could provide such classes, but was willing to pay or provide transportation to the U.
My older D tells me there was a 7th grader in her AP Calc class. Next year in 8th grade he’ll take AP Stat. Byvthe time he starts HS he will have run out of HS math classes. I don’t know what his parents & the school will do - online classes or cross enrollment with a CC or uni.
@scholarme - that’s a kid who will be in Caltech or MIT or Stanford math department.
CS often requires calculus, depends on whether it is in the engineering school or not
AB/BC = A+B+C which is 3 semesters of college math for future math, physics, engineers. It is totally appropriate for this to take 2 years for a high school-er who is not going to solve Fermat’s theorem but who will be solving our technical problems as an adult.
And then there are the other folks who spend years trying to “get” math thus the endless repetition. So we accelerate the math folks away … otherwise they would be correcting their teachers by 7th grade.
In the early 80s I had two classmates who went to UPenn and JHU a year early. I don’t think this happens anymore. In our top 300 USWNR high school, the only early graduates go to community college and aren’t exceptional.
Our school district had GT classes in most academic subjects by 6th grade. Elementary school was 1 year advanced in math starting in 1st grade and then skip 4th grade math for GT. And there were GT seminars for enrichment starting in 3rd grade, building bridges, doing research projects, writing, presentations.
If a school district is willing to do this, or have magnet schools, I think more people advance to a higher level, whether flagship honors or top 50 school or STEM or SLAC. It takes money and often it is higher educated, higher SES folks that push for this (And pay taxes to fund it).
Which can explain why some low SES folks are given a chance to prove their stuff with special opportunities in high school or admit to reach college. And, I would guess most of those, probably do succeed.
Reading through many of these posts and thought I would give my two cents worth. My son took an entrance test for school when he was 6. No one told him where to stop, so he did all of the problems, including the high school math problems. He got half of the HS math right. Math was his hobby, and he consumed every book we put in front of him. He loved math more than playing. In fact, he never played. He read everything and memorized everything. In the middle of 1st grade we put the math books away, and instead let him go outside and play. (He also was reading at a college level at 6). Each year until 7th grade he would ask if it was time to do math. I would say no, go outside and play. From 2nd grade through 6th, he had no math. In 7th grade, he got the answer he wanted. Yes. Learn math to his hearts content. There would be no limits, except whatever limits he put on himself. He finished BC calc as a junior with the highest grade possible and then took Calc 3 and Linear Algebra by special arrangement this past year. It’s a natural love and talent. During those elementary years without math, he learned to play, connect with people and even played sports, winning some awards and playing varsity in high school. The challenge for him, and many who are naturally gifted, was social, never academics.
We chose for our son to go through all of the stages of childhood and not accelerate him too early. When he was ready to take off, we let him loose to learn all that he desired.
Bravo @shoshonte!
@PickOne1 not every super advanced kid ends up at Caltech, MIT or Stanford. I don’t know why people always state that as a natural trajectory. The fact that a kid is super smart doesn’t magically make dollars appear in a parent’s pocket.
Just wanted to add, in our school the decision whether a student will take AP English is made in the spring of the sophomore year. The decision whether a student will be eligible to take BC calculus is for the most part made in 5th grade. That is why I talk about math so much more in the context of parents being aware of where their kid stands in the school or of getting a child an appropriate education. If an English placement is inappropriate, it’s easy to change from one year to the next or even during the year. If a math placement is inappropriate, it may require summer school to fix, and it isn’t so easy to switch during the year. Unfortunately those decisions are being made when the kids are fairly young and may be as much about maturity as about talent.
Actually AP calculus BC (including AB) is generally equivalent of 2 semesters of college calculus, covering single variable calculus, not multivariable calculus that is the usual third semester of college calculus.
Taking two years in high school to cover this material is about half speed, which is an odd pace for students ready to take calculus in 11th grade (two years ahead of normal) who should be among the best students in math to have been accelerated that far ahead in math.
Not sure I follow you, ucb. If AB calculus is covering one college semester of math, but is taught over a year in high school, why doesn’t that make sense? Our high school students are taking 8 classes at a time, not the 4-5 a college student would take. It might typically be 6 academic subjects and 2 electives, but it’s still 8 classes and some of those electives, like art, require a lot of time. If colleges also worked on a year-based schedule like most high schools rather than a semester-based one, you would see the same thing–students taking 8-10 courses per year, and what is now one year of college calculus taking two years. The actual instructional hours in high school are greater, but consequently the high school students spend way more time at school and therefore have a lot less time to spend doing homework.
Even so, I agree that the students talented enough to take BC calculus in high school shouldn’t need a year of AB first, but that’s more on the strength of such students being able to handle more than a typical college student and also having a somewhat lighter overall schedule than a typical college student rather than the actual timeline comparison you made.
I’m not surprised many parents have no idea what the competition from all over the world might be for the schools they envision for their child. But it is a little surprising to me that parents who expect a lot and care enough about their child’s education to be imagining they will attend a highly selective college would have little idea how their child is doing in their own school’s educational program or what levels of courses are offered and where they are placed in those levels.
If her interest in Computer Science is in the fields of optimization, machine learning or big data, she’ll definitely need calculus.
@“Cardinal Fang”, stats and other math techniques are far more useful in machine learning and big data. But yes, in those fields, knowledge of calc would be useful.
I think Calculus is required for CS and engineering, one cannot say I take stats over calculus.However, in engineering one can take stats such as engineering probability and stats course at least at my daughter college. I don’t think she has to take stats for CS.
I have the impression that CS majors and jobs seem to require increasing knowledge of related fields such as Big Data/Data Science/Operations research, Systems Engineering, Economics, Network Engineering. High level math skills such as calculus, discrete, linear algebra, and statistics are needed or helpful for these. The higher level skills seemed to be valued. Lower level coding skills can are sent to India or elsewhere off shore more easily.
Any thoughts about this impression from those knowledgeable in CS would be appreciated.
I think @ucbalumnus is more specifically commenting on schools that require a 2 year commitment to cover BC. The point being, if these students are capable enough to tackle AP Physics C:Mech and E/M in a year (although there are some HS’s that take more than a year to cover this or spend a year on mechanics only), they are also presumably able to handle BC covered in a year.
College Board AP curriculum sometimes does not make sense. Why students need to spend 2 years to take AP Physics 1 and AP Physics 2 and AP Calc AB and BC? Would it make sense to divide in these APs into AP Calc 1, AP Cal 2, AP Cal3 and AP Physics 1, AP Physiscs 2, and AP Physics 3 and each class is taught in one semester? Why do college students take final exams at the end of each semester and HS students have to wait to the end of the year to study the materials from the beginning of the year to take the AP exams? Why CB cannot offer AP exams twice a year so that HS students can have less stress?
I took up to calc 4 in college, as well as calc based stats, but I don’t think I ever had to use that knowledge in any of my CS classes or on my job in IT. In fact today I hardly remember anything about Calculus. But I can believe that if you are in a data analysis or search algorithm CS field you will use this knowledge.
Good math skills are not just limited to STEM though. It’s also very helpful in accounting and finance. In fact finance is a popular field for engineering dropouts. If you are good in math but not good enough to hack engineering math (high level calc), then finance is a good alternative, esp. if you love money.