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 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.)
Looking at the state of the US right now, calculus wouldn’t be where I’d devote my energy.
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.
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.
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.
. . . 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.
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 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.
Especially political polling which samples a fraction of a percent of the voter population, and is consistently wrong.
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.
Yep, critical thinking enhances all other intellectual pursuits. It is so easy to fail at the critical thinking stage and go down a blind hole pursuing something absolutely nonsensical because you didn’t check your basic assumptions.
I would want kids to learn about the Monty Hall problem, do a little Bayesian analysis, etc. I think they could learn through trying to smuggle some lies into a paper and then peer reviewing each others papers and finding the flaws. Kids are way more creative than they are given credit for and they would find ways of sneaking things through we wouldn’t ever consider. Making it adversarial would prepare them for interacting with the huxters and frauds that make up a huge amount of modern life.
Here, stochastics and statistics are the key student filters in psychology.
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
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.
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.
I’m on page 3 and already sold.
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.
I think statistics is far more important for people to know than calculus.
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.
stochastics & probability
statistics.
If everyone understood statistics and probability, no one would gamble.
- functions and graphs, mostly R->R
Sorry, but I can’t see the justification for it. I’m on board with everyone else who’s suggesting statistics, though.
Statistics and stochastics are the big killers in some university courses.
Imagine someone studying psychology because it is about ‘working with humans and emotions, not numbers’. Wrong. Statistics and stochastics are the big first term student filters. A pschologist must be able to read and understand test results and similar corrolations.
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.
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.
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.
