I think statistics is far more important for people to know than calculus.

I feel like perhaps you don't know enough people from the entire range of human abilities to understand why requiring calculus might be going too far.

It should certainly be an option, and it should be a requirement for certain career paths, but making it a high school graduation requirement would just unnecessarily result in more people dropping out of school.

Let me ask you this, do you know how to budget?

We over provision for higher level arithmetic but don’t teach fundamental arithmetic for living successfully in our society.

. . . the fundamental ideas about rates of change seem like they’re something that everyone human deserves to be exposed to.

People understand the idea of instantaneous speed intuitively. The trouble is giving it a rigorous mathematical foundation, and that's what calculus does. Take away the rigor, and you can teach the basic ideas to anyone with some exposure to algebra. 6th grade, maybe earlier. It's not particularly remarkable or even that useful for most people.

When you go into a college major that requires calculus, they tend to make you take it all over again no matter if you took it in high school or not.

Probability and statistics are far more important. We run into them constantly in daily life, and most people do not have a firm grounding in them.

I would include statistics. So much everyday information is presented using statistics, often in ways that are misleading or deceptive. A bit better understanding would make people harder to trick.

I don't think rates of change or approaching a limit are things that an average person would find useful. I do think that some sort of statistics should be a requirement though, especially applied statistics.

I don't think the question is what level math to end on, but rather how math is taught. I teach psych statistics at University and the average student does the math parts mostly fine (it's just algebra) but their critical thinking and application of the math is usually what is sorely lacking regardless of their ending math course. And in the real world where we do everything with computers, the application is 99% what matters.

I've had people in middle age who dropped out in 6th grade in Mexico do better than fresh-from-US-high school calculus experienced students, and that's not even taking into account this more recent COVID-survivors generation that feels like they skipped a year of education. It's very... grim.

I would follow the guide laid out by Lockhart’s Lament. Basically, teach math as an art.

That dream aside, I wouldn’t mind aiming at statistics as a target, instead of calc… specifically to lessen the impact of people who lie using statistics, and also demonstrate that not ALL statistics are lies.

The people that tell you that you will never need it are the ones too stupid to understand it.

Math is a universal language. It is the most important thing to know. Even more than the local spoken language.

If you can’t solve differential equations by the 4th grade, are you even learning?

Some other countries build up math skills a little differently. For instance, in Portugal, they teach a little bit of Algebra, a little bit of Geometry, and a little bit of Calculus every year.

In the U.S. the students focus on Algebra, one year, then Geometry the next, then Algebra again, and finally Calculus (if they did well in the previous math courses).

So, if a student transferred for their senior year of High School from the U.S. to Portugal, they would have a different experience compared to their peers. They would find all of the Algebra and Geometry sections very easy and be able to help tutor the other students, but then they would struggle with the Calculus portions and need help from the others.

I'm not sure how common this is among other european countries. I would be curious to know how math courses are taught in other countries.

In order to change the degree so that it allows studying in many universities abroad (such as Germany), this would be needed:

• functions and graphs, mostly R->R
  • general analysis, continuity, function as a specific type of relation
  • series, sums, limits
  • derivatives
  • integration
    • numerical
    • basic approaches and when to use which
    • a few common "tricks"
• proofs: very basic direct, induction, contradiction will do
• set theory
• Vectors, limited to R³, line, plane, rotation. Very basic matrices
• introduction to imaginary numbers
• stochastics & probability

It's based on my subjective impression of weaknesses in the few Americans studying in Germany that I know.

Sorry, but I can't see the justification for it. I'm on board with everyone else who's suggesting statistics, though.

Algebra, 1 and 2nd semester at least. calculus is too much for HS these days, when thier math skill is so low as it is. geometry as well. trig maybe you can negotiate with a COMMUNITY college. they had classes in CC where people were struggling with arithmetic.

Why, in the name of all that is good and holy, should we require someone whose dream it is to be a carpenter, to take calculus to graduate high school? In what universe will that requirement be doing any good in their life? What will it serve other than a potential completely arbitrary barrier to simply graduating from high school? And a carpenter is actually far more mathematically inclined than most career paths people pursue.

Yes, learning calculus can be a revelation in mathematical beauty. But the same is true for a thousand potential fields of study. In terms of practical use to most people, they would all be equally frivolous. A case could be made that a thousand fields of study are something that people simply must be exposed to. I'm more in favor of letting people choose their own path. We shouldn't be piling on arbitrary barriers on to a diploma that is only meant to signify basic competence.

What do you propose we cut in favor of calc?

edit: core class, because calc is already an elective

I disagree with calculus being mandatory. Most students still won't need it and it will increase dropout rates.
But a pre-calculus course with calculus as an optional offering would sure be beneficial. Most highschoolers get their ass kicked by college calculus courses because the logic jump from even moderately complex algebra to differentials and integrals is fairly high. Problems become significantly more abstract with more ways to solve things rather than rigid solution paths. A good precalc class gets them strong on the trig identities and more complex algebra rules that they'll need moving on.

Dunno about algebra 2, I took that class but don't remember how synthetic division works and haven't missed it. I'd replace it with some basic probability and logic for non-nerds. They don't even have to be treated as math topics. More like: how to avoid some common mental errors. Lots of people don't think mathematically and that's ok.

I see anything higher than the algebras as STEM focused, and certainly calculus is in that category. I do like the problem solving that comes with such studies.. but I’d argue there are more important civics focused courses that should come first. Time is limited after all.

Graduating high schoolers are newly minted adult members of society and grade school should focus on ensuring they are ready for just that responsibility. I don’t think forcing calculus fits that model.

If i recall from the long long ago that was high school I think they required Algebra 2, Geometry, Calculus, and then i took Trig but it wasn't required.

Abolish school.

Algebra 1, geometry 1, statistics 1

Depends on your level and what you want to do afterwards. Then again, I'm in a country that offers different levels of highschool.