What is the highest level of mathematics that should be expected to graduate high school?

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.

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 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.

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.

. . . 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 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.

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

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

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.

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.

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.

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.

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.

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, geometry 1, statistics 1

I'd require something after algebra 2, but not necessarily calculus. Calc 1 should be an option, just not the only one. Other options could include Stats / Data Analysis, or a Discrete math with CS algorithmic applications.

When I include statistics here, I don't mean the more common (and IMO useless) pre-calculus stats class where you get to calculate the standard deviation of 5 numbers and draw box plots. I'd rather a class inspired by How to Lie with Statistics. Techniques for collecting biased data, or selectively interpreting good data to reach a pre-determined conclusion. Immediate career implications for prospective journalists, politicians, marketers, etc. and also societally useful in a Defense Against the Dark Arts sort of way.

I've never used anything beyond basic algebra and basic geometry outside of a classroom. I have used statistics but I don't remember that being taught in high school, maybe that should change.

Anything beyond those should be optional but definitely made available for those who are interested.

I say there should be more emphasis on the practical applications of the more basic math.

Too many people barely understand interest rates on car and home loans and can't figure out what they can actually afford. More high level math isn't going to help them deal with every day issues involving math.

I think applied calculus should be part of physics curriculum of high school. No need to go into epsilon delta limits etc for high school.

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

I feel like calculus should probably start to be introduced in like maybe late-elementary-age? Certainly before high-school-age. I don't think everyone needs a dedicated 1-year course on it, but some of the concepts are certainly useful and understandable at that age. Regardless of whether its from compulsory education or some alternative education process.

Hmm. I think algebra 1, 2, intro stats, and geometry for core curriculum. Anything beyond like calculus(I took) as elective or college credit. It’s been years but I think I took stats over trig.

Personal finance should be taught but not at the expense of other maths.

What do you propose we cut in favor of calc?

edit: core class, because calc is already an elective

When I was in school in North Carolina, you could be on different "tracks." Almost like a college major.

"University Prep" was for the AP kids who were going to graduate with a 5.0 GPA and half a semester of college credit. They took up through Calc 1, sometimes at the local community college, they did two extra semesters of English class (11th and 12th grade English were full year courses) and such.

"College Prep" was the "Hope you get good SAT scores" tier. A bit more room for electives, you were usually in "honors" classes, and graduated with no college credit to your name but ready to start in the fall as a Freshman at a state school. You typically took up through pre-calculus Algebra in college and Trigonometry or Calc 1 would be in your first semester of college. Two semesters of a foreign language were required, which is why I can kinda sound out French.

"College Tech Prep" was "Sew your name to your shirt because you're going to trade school." They had their own math classes which I think got most of the way through Algebra 1 and 2. They took shop classes, which didn't trust the student to have ever been awake in a math class in their lives, hell I've gone to trade school at a community college, the first week they spent "teaching" us addition of whole numbers. Or, you were in JROTC.

"Career Prep" was the "You're gonna be a parent before the end of high school, knock over an Advanced Auto Parts when you're 20 and spend the rest of your life in and out of prison" tier. These were the kids that did eight semesters of PE, some of them could read.

Yeah, I feel like what you're asking for would have to be a more holistic thing, like the concept of rates of change could be covered in physics quite naturally alongside momentum/impulse.

I have a math minor so have taken through calc 3, abstract algebra, and quite a bit of matrix math. Like 90% of concepts from those classes wouldn't really help people in the world around them, not just "they won't use integrals daily" but rather they won't be taught in a way where they'll connect differentials to what they see in the world or news.

Now, Finland, they have the right idea. They're teaching classes on spotting disinformation and how to find trustable answers. That seems way more important to me and likely to have a higher impact.

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.

I feel it's in a good spot. at least where I went to school.

Arithmetic, algebra, geometry, stats, trig. Calculus is offered but not required.

I really struggled hard with Algebra. My Dad was a Math major, and my younger brother inherited his his Math gene, and is a genuine fucking genius, but I was a musician, and had trouble even memorizing the multiplication tables.

I'm old now, and over my entire life, I've never said, or even thought, "I wish I'd paid more attention to Algebra." Perhaps there were times that it might have helped me, but it made so little sense to me, that I wouldn't even recognize when it would be required. Once, a friend who was good with math asked me "Didn't anyone ever explain Algebra to you using a circle?" and I told him I had no idea what he was talking about, and I still don't (I think it was a circle, I don't know, this stuff is totally alien to me).

OTOH, I ended up being self-employed, and I use BUSINESS MATH every single day. Calculating percentages, profit margins, interest rates, budgets, accounts receivable and collectible, etc. I'm really good at that type of math, and often do the work in my head as I'm driving. If I could have had that type of math in high school, it would have been helpful, and my grades would have been better without being dragged down by D's from a charitable teacher who must have realized what a hopeless Algebra dunce I am.

High school students need to be given the choice between Algebra/ Calc/ Trig, and Business Math. If a kid is on a Science/ Engineering track, then sure, let them take the Algebra and stuff. But if a kid is going to be doing most regular jobs, Business Math is going to be more useful, and is even useful in tracking your household economy. Algebra is something most people will seldom if ever use, but Business Math is something that EVERYBODY uses, every day.

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.