In Oklahoma, the requirement usually is up to “algebra 2” - this is mostly domain and range, finding roots of polynomials, and logarithms.
IMHO, the world would be better if calculus was a required part of the high school curriculum. Like yeah, most people aren’t going to need the product rule in day to day life, but the fundamental ideas about rates of change seem like they’re something that everyone human deserves to be exposed to.
I think statistics is far more important for people to know than calculus.
Nah, I already know the odds. Each time I lose, the chance of winning the next time goes up! Never fails!
I mean, who needs both their kidneys?
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.
I’m certified in special education and spent two hours of my day today teaching an adult how to do subtraction. I’ve worked with kids with Down syndrome. I entirely believe that it would be possible for 95% of students, if given the appropriate support, to learn how to take a simple derivative and have some vague understanding of what they did. It just takes visuals, good use of real world examples and metaphor, and patience.
I have family working in Special Education, most of them with kids under 12, some through early adulthood. All your points are correct. But from what I know of US Education, most schools - or schools in certain states - will not receive appropriate support and the students will ultimately be hurt for it. Think of the implementation of Common Core in the mid 2010s.
Students with proper support and encouragement can accomplish amazing feats, but most students don’t have the resources to do that on their own (or with limited support and instruction.)
Believe the problem is the appropriate support part. Most teachers are struggling with keeping kids off their phones and trying not to get killed in reprisal. Classroom size, low wages and burnout are at all time highs.
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.
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 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.
In terms of utility for the average person, statistics >>>>> calculus.
I work in an engineering field, and can count on one hand the number of times I’ve had to do an integral in the last year. But I run into glorified statistics problems virtually every day both in personal and professional situations.
Having to constantly remind people of error bars, statistical significance, and the difference between correlation and causation, it would have been nice if those things were hammered home more thoroughly in school.
In my fourth semester im Uni I could choose whether to take numerical analysis or probability theory.
Most students took numerical analysis, even if the exam typically had a 80% failure rate. (Yes, one of five successed)
It was a completely different with probability theory (Wahrscheinlichkeitsrechnung). Oh, having chosen it due to these reasons now I know why: The prof loved teaching and was really good at explaining.
Ultimately this shows, people have no idea about probabilities.
Edit: fixed the nunerical typo. No it was not about catholic nuns.
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.
As a Norwegian, focusing on one kind of math per year sounds absolutely bizarre. We did a bit of everything every year in the 90s at least, and I doubt it’s changed. How do you not forget everything if you learn it one year just to not touch it again for years?
In college each group of subjects have a separate class, but doing that in high school sounds nuts.
Honestly that sounds much better
. . . 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 don’t think you can know when it will be useful, but you could need it 25 years after you leave school suddenly. Better to have the best foundation possible. So if there is a way, a method, that can teach the highest math to the youngest group then that’s the one I support, but I don’t know what that is myself I’ll admit
You could use that same argument for any other type of math. Boolean logic. Linear algebra. Hyperbolic geometry. You have to pick something for high school, and you should pick what’s most likely to be useful to anybody.
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.
Critical Thinking Skills should be an entirely separate class, required by every student to graduate.
Algebra 1, geometry 1, statistics 1
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.
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.
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.
My final year of high school (not in the US) had a finance class that had recently been split off from one part of the “current events” class into it’s own thing. We were taught how to budget and handle interest, loans, taxes, savings, ect…
Also a bunch of BS about how big corpos are great and awesome because the teacher made money on the stock market.
I do think it should be a standard class everywhere though, it’s ridiculous to not teach that stuff.
Budgeting and more probabilities/statistics are where I think it should be.
Both of those directly relate to improving your life.
And fucking Excel. Better yet teach budgeting and spreadsheet courses in one.
If people had stats, budgeting and excel it would be an incredible improvement.
Budgeting also only gets you so far in our dystopian age when you need 2 full time jobs to pay rent.
When I got to college, I had to take two math course, which I dreaded. Because I was a music major, one of the math classes had to be Acoustics. For the other, I was terrible at Algebra, and didn’t want that dragging me down, so I chose Statistics, since I was interested in politics, and would learn about polls.
I actually liked the class a lot, and to this day I track political polls closely. But I’m not a person who just accepts raw numbers. I want to know the sample size, the margin of error, etc. I know when a candidate is cherry picking his data, or leaning on a partisan poll, etc. It’s been very helpful through my life.
BTW, it was standard procedure for every music major to procrastinate on the Acoustics class until their senior year, and we got a cool math professor who was also a pretty decent amateur trumpet player. He didn’t want to be the guy to destroy our graduation prospects in our senior year by flunking us all, so he made the class interesting and challenging but not really difficult.
I learned a LOT in that class, and later I ended up working in sales for an audiophile classical record company, and my knowledge of sound and acoustics from that class allowed me to weasel myself into an additional part-time job helping out at recording sessions, some of which went on to win Grammys.
So Statistics and Acoustics were the math that worked for me, and I posted elsewhere that Business Math is something that I have also used a LOT, but picked it all up mostly on my own. NOT ONCE, have I ever said “I wished I paid more attention in Algebra.” Those two quarters of high school Algebra might have been the two most painful quarters of my educational career.
The emphasis on advanced math at the high school level is detrimental to many people. It instills a sense of failure and stupidity early on, reinforced by parents and teachers, and often develops a sense of hatred toward those who are good at it. People who struggle with advanced math would be far better served by teaching them Business Math. First week lesson: put up a pay stub, and start figuring out all the percentages of all the withholding on that paycheck. Every kid in that class will be riveted on the screen, even the thugs, who will want to know who FICA is, and why is he taking all their money?
Budgeting and filing taxes, please!
*And understanding credit card debt
“The most powerful force in the Universe is compound interest.”
No banking corporation wants people to understand this.
I tutor high school students in math and science. They’ve all taken a budgeting class. One of my students is taking calculus and I genuinely feel he has a better understanding of it than I do!
I am glad he has the option to take calculus, he’s one that gets bored at the place other students need. But I really don’t think many students need it or can fit it in their graduation tracks.
We also need to consider how difficult algebra was for some, to the point that a lot of adults think they hate math. I like the comment in the op that Applied Calculus skills (real-world story problems) are useful, and I think that would have more impact than two-three semesters of calculus.
if he can get that far into calculus, he wouldnt be having problem with math skills. its the people struggling with aritmetic, or early algebra thats problematic. i think the early books in ALG1 and 2 and geo, are just a little to convoluted for people to learn, because its mostly abstract word problems. plus the teachers in our HS dont even teach the subject properly at all, they expect you to know how to do it already in the early 2000s. same went for chemistry, and adv algebra, just poor teaching skills at least in our school. hence why alot of hs comes out with such poor math skills.
I think he doesn’t need math tutoring. He needs someone to sit with him while he does his homework, and he needs encouragement. Our education system just marches people through to graduation without giving them the chance to breathe.
But, I agree, our teachers have been struggling for decades.
precisely, no one taught me algebra, and it was vaguely mentioned in Middle school(because only above average graded kids(not gifted or exceptional) go to learn it. i partially learned it on my own, and funny enough i had to take math below algebra again, and it was just more annoying than learning algebra. just needed alot of pratice to be honest, the hs teachers expected you already know it by the time they mention the problems, outside from a portion of the students that already knew how to do the word problems most wernt taught. lets not get started with english(writing papers) that was different beast.
I just posted a similar take, but used a lot more words. Yours was much more succinct.
We had a class called Consumer Math in High School which taught all of that stuff, like how to make a budget, buying a first car, taking out a mortgage, doing taxes. It was a remedial class for the “dumb” kids. Everyone else took the standard Pre Algebra > Algebra > Trig > Calc path. So dumb.
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.
If you can’t solve differential equations by the 4th grade, are you even learning?
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.
