My kids’ HS has non-AP calc (in addition to AB and BC). It is described as:
whereas AB is
and BC is
At Harvard Class of 2019 in High School 32 per cent took Calculus AB, 39 per cent took Calculus BC, 15 per cent MV and 3 per cent took beyond MV
Re: #900
Does not make sense. Two years and a summer to cover one year of single variable calculus, for students who are ready for calculus in 11th grade? Or does your district have a lot of students who were pushed too far ahead in math beginning in middle school?
As a math major, I think Calculus is fetishized.
“Every high school has classrooms full of juniors who don’t have a strong grasp of algebra and trig. That’s not a surprise, and there’s no shame in it. The folly is taking a classroom full of juniors who are weak in algebra and trig, and teaching them calculus recipes, instead of putting them in pre-calculus so they can get a good high school mathematics foundation.”
Alternatively they’d be better served by strong probability / statistics, because who are we kidding? They’ll never use calculus. But p/s are far more useful for non mathy people.
I agree in general that many students who are jammed into calculus lite would be better served by learning probability and statistics, which would be useful for them, instead of calculus, which would not. But these particular students were over-accelerated. They’ve been whizzed through the prerequisites in a cursory way. Now here they are, as high school juniors, with an inadequate math foundation. It’s too early to say that these over-accelerated students will never be able to study engineering, for example. Some of them could do just fine in college calculus, if they get the adequate high school preparation that their high school is so signally failing to provide them. We shouldn’t weed students out of STEM degrees as high school juniors.
They’re juniors. They’ve got two more years of high school. They can take one year for statistics, and one year for a better math foundation for their future college mathematics courses if they want a STEM degree.
Mathprof63 is impressed with the level of math discussion here! I have a middle schooler who is on the fastest math track in our district. He can take Calc bc as a junior. I really don’t think getting to calculus early is some great achievement, but there are no other options.
Advanced kids will be bored in regular paced math classes, but packing in plug and chug math at twice the speed is not a solution either. Richard Ruszyk on the art of problem solving Web site has an article detailing this. I would prefer to have advanced middle schoolers working on harder problems involving middle school math. I think mediocre teacher training in math is what holds this idea back.
Would love to have qualitative differential eqns as a capstone senior math course for those who take calculus as a junior. Ties in so many aspects of calculus and can develop advanced mathematical thinking. Discrete math is another good one.
I think all of us who posted on this subtopic should form the CC Dream Team Math School 
From your lips to the goddess’s ear.
Why does everyone neglect linear algebra, says this linear algebra fan plaintively? If a student is doing that qualitative differential equations class, and they have to take a linear autonomous system of two linear differential equations (predator and prey, for example), treat it like a matrix and find its eigenvalues, they might be glad they studied linear algebra first.
Our high school has a different approach to math education than the norm, Both of my children found that they knew 2/3 of the college linear algebra material in their college classes. After some googling I found that many don’t think you should teach linear algebra in high school. I loved linear algebra.
Also upthread some people think that a teacher that provides worksheets for hw rather than book material is making the class harder. I think the teacher is going above and beyond to cater to the students by providing relevant work. Hurrah to this type of teacher.
Linear algebra and discrete math do not actually require calculus, so, at least in theory, they can be offered as calculus alternatives for advanced math students.
But some things make it unlikely for non-elite high schools to offer those compared to calculus:
- College majors that require linear algebra or discrete math tend to require calculus, while many other majors require calculus but not linear algebra or discrete math.
- No AP tests, so less incentive for non-elite high schools to offer them, and less incentive for high school students to take them with no possibility of getting subject credit or placement for them.
- Some students consider these math courses harder than calculus, particularly if there is more emphasis on mathematical proofs in those courses.
"Would love to have qualitative differential eqns as a capstone senior math course for those who take calculus as a junior. "
Like this is remotely a reality for 90% of hs in America. Yeah, right, this will be available in inner city schools, “average” suburban school districts and rural ones. Sometimes the blinders of CC really get to me. It’s like some of you don’t even get that there are high schools where they don’t teach chemistry or physics, or that the guy who does do is the football coach who is one chapter ahead of the students. But oh, let’s dream of a world where there’s diff eq in the public schools …
This thread is not discussing the median public school district. It is not discussing remedies for a “normal” district. It is discussing a district which seems to be even more achievement-focused than CC. It’s discussing a district which has 5% (five percent) economically disadvantaged students, according to US News’ Best High Schools.
I agree that teaching linear algebra if possible is a good idea. Teaching probability and statistics correctly does require calculus!
I disagree. The calculus-based version of probability and statistics is deeper and more fun, but a conceptual version of probability and stats is still valuable. You don’t need calculus to figure out, for example, the number of possible combinations of numbers for Powerball, or to figure out the expected number of unpicked number combinations for Powerball. Most people don’t need calculus, but most people do need a basic understanding of probability.
@pizzagirl : clarification: the context of that discussion that of an affluent public school district offering accelerated math classes - not your standard high school in 99% of the United States. The district where my kid goes to school is capable of offering such a course. I teach at a directional university and am plenty familiar with what is offered in most high schools. The differences between a top district and the average ones are staggering, at least in NJ.
If high school students spent a month learning what “statistically significant at a 5% level” truly means - and what it doesn’t mean - then they’d be ahead of 95% of medical doctors and social scientists and 100% of journalists.
I did say correctly! Expected value is a concept that employs calculus as well as statistics based upon continuous distributions. Most probability and statistics taught in college does use calculus. But you are correct that the non calculus version is still valuable
Actually, of the introductory statistics courses taught in colleges (as opposed to courses for statistics majors), it is likely that most students are in non-calculus-based statistics courses (and then add in all of the high school students in non-calculus-based AP statistics).
For example, there appears to be one out of over one hundred community colleges in California that teaches a calculus-based introductory statistics course (in addition to a non-calculus based one that all of them have). Apparently, there is that little student demand (including that driven by transfer preparation) for calculus-based introductory statistics.
It may also be that non-calculus-based introductory statistics courses predominate because they are often used by colleges to provide an alternative way of satisfying quantitative reasoning requirements for students who do not want to take calculus.
It is true that if the student knows calculus, a calculus-based statistics course will allow a better understanding.
Non-calc-based stats is a transfer requirement for California four years. That’s why there’s a demand for it at California CCs.
I think that mathprof63 is really on to something in writing “Advanced kids will be bored in regular paced math classes, but packing in plug and chug math at twice the speed is not a solution either.”
In my opinion, the heavy “plug and chug” component of a lot of high school math courses is what permits multi-year acceleration of students who would not be capable of significant acceleration in the non-plug-and-chug-math that was more typical when the current group of parents were in school.
The local school district has eliminated proofs from geometry, and uses textbooks for algebra that do not contain many (if any) hard problems. Needless to say, there is no non-Euclidean geometry, such as my spouse had in his not-very-accelerated, fly-over country high school years ago. The demands for mathematical maturity are lower than they used to be.
Richard Ruszyk at the Art of Problem Solving makes a good case for avoiding “the calculus trap”–i.e., avoiding the idea that one needs to reach calculus as swiftly as possible. In principle, it would be superb if challenging non-plug-and-chug pre-calculus math could be offered in many school districts. In practice, I think there are many things in the high schools that are not dreamt of in Ruszyk’s philosophy.
For example, regular math classes here have featured assignments such as making posters on one’s favorite number (in middle school). A class that was merely boring might be preferable.