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Calculus isn’t the only option. Let’s broaden and update the current math curriculum | Op-ed

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> Students who take another route in high school can still learn calculus in college, rather than retaking it, as many do, after a high school calculus experience they didn’t appreciate. In fact, in college, two-thirds of all high school calculus students retake calculus or take a more foundational class, suggesting that a rush to calculus isn’t beneficial for most students.  

The problem I have with people wanting to get away from calculus as the end class for high school mathematics is that this is typically the argument. This argument, imo, boils down to "calculus is too hard." Switching from calculus to statistics or whatever other alternative sweeps the real problem under the rug, namely that students are ill prepared. Calculus requires you to synthesize a lot of the information from algebra and trigonometry that you've already learned and really think about the steps you're taking.  
  
For instance, I have a function I want to maximize over an interval. Okay, to do that, the theorem tells me I want to find critical points by finding the derivative and seeing where it's zero or undefined. Okay now that I've done that, I have this sub-problem of how to solve f'(x)=0 and find where f'(x) doesn't exist, so I need to do that. Next, I know where f'(x) is zero/undefined, so I need to use that to figure out where it's positive and negative so I can classify my critical points. All of that requires a lot of thought and mastery of the concepts it entails. Statistics at a high school level gets around having to work with the prerequisites calculus demands. Rarely do you have to find the zeros of a function, let alone use that as a step to solving a larger problem.  
  
I think before you offer a "fix" for the ending class, you should look at fixing the underlying issue.
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This doesn't really offer any good alternative to calculus.  Yes, not every profession will require daily use of calculus. The same can be said for much of trigonometry. These aren't good reasons to skip teaching these ideas.

When someone said our smartphones can solve these things, I shook my head. You still have to know what you're doing. I know people who don't understand percentages. They rely on their calculators, but they can't identify when they make a mistake and their answer is completely wrong.
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I do tend to agree that math curriculum needs to change, because past basic number sense and arithmetic, math is genuinely not necessary to produce educated citizens. Students ask "when will this be useful" and the true answer is "probably never". Instead we teach mathematics because it trains the mind to think rigorously and logically about abstract ideas, and to express this reasoning in a clear way, and to understand this sort of reasoning when explained by others, which is useful for everyone and is a skill that every citizen should have. I believe that math and science courses for non-specialists should be designed with this goal in mind.

For technical specialists, calculus is such a basic foundation of so much of mathematics, physics, and statistics that it really should be required even if it is not strictly necessary for day-to-day work tasks. In this way I disagree with the author's main point that the wide breadth of mathematics used in applications means calculus is not as important.

>The sequence of courses taken by most high school students — Algebra, Geometry, Algebra II — was set in 1892

Mathematics is one of the slowest changing fields at the core (everything Euclid wrote is recognizable as valid mathematics to a modern mathematician. Not so much Aristotle's *Physics* to a modern physicist), so it makes sense that if we're teaching mathematics the courses are going to change slowly. Therefore I think that without qualification this line of argument is not very strong.

But like I said, the point isn't really to teach mathematics, it's to teach basic number sense as well as rigorous, logical thinking. In that case the courses should change very much.

>In fact, in college, two-thirds of all high school calculus students retake calculus or take a more foundational class, suggesting that a rush to calculus isn’t beneficial for most students.

This is due mainly to perverse incentives from colleges. Having a calculus class under your belt helps you get in, but many colleges won't give you class credit for it. My calculus class in high school was *much* broader and deeper in content than the one I took in college. I would say I had a much better understanding of calculus after taking it a second time though.
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I don't really care whether students who have learned algebra go on to calculus, linear algebra, statistics, computer science, combinatorics, or whatever. The problem is with the assumption that "the students have learned algebra." Too many of them haven't -- at least, not well -- even among those who want to pursue careers in STEM fields. They aren't ready for *any* of those courses.

I don't blame the students for this. They are getting As in their high school classes, so they naturally believe they're doing the right thing. I don't blame the teachers either; it's just not possible for them to provide the necessary individual attention to all their students. Our educational system simply does not have the resources to meet today's increased demand for students with mathematical training.
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I've been tutoring high school (and college) math for over a decade.  I've worked with well over 100 students in high school math and probably another 100 who occasionally brought me some math even though we were supposed to be working on chemistry or economics or some such.  Of those 200+ students -- mostly high-achieving -- there have only been fewer than two dozen for whom I've recommended bypassing Calc 1 in college.

Of those students, the majority took IB HL Mathematics, a two-year course that undeniably prepares students for further mathematical education and covers a plethora of topics in enough detail that a student would be prepared for a college-level discussion of the same (although the latest revision sadly moves away from this approach and 2021+ HL math now resembles the old Math Methods curriculum).  Only once have I recommended a student move from AP Calculus AB to Calc 2 in college.

Bottom line: College Board's Calculus curriculum, especially AB, fails to prepare students for college math.  At best, it prepares students to repeat the topics they nominally learned in a more rigorous environment.  At worst, and as is more common, an AP Calculus AB student will have to back up and cover prerequisite topics before moving forward in college math.

Overall that's a major disconnect.  I would much rather the majority of high school students spend more time solidifying their fundamentals than rushing to a (relatively poor) calculus course as some sort of perceived capstone experience.  If those fundamentals were to include more exploration of related topics so much the better.

Instead, most current high school math curricula have been paired down to calculus prerequisites.  Conic sections, parametric equations, non-cartesian coordinates, hyperbolic trigonometry, vectors and matrices, complex numbers, probability and statistics, and discreet math play little to no role as none of them prepare students to take (and usually not even understand) AP Calculus AB.

And it's a damn shame.  The few students I've had who _have_ been forced through some of those topics (I've never had a student do _all_ of them in high school) are better prepared to think mathematically and paradoxically perform _better_ when they get to calculus.  But instead we get curriculum based on a series of linear dependencies towards a single goal.

It's past time to change that.  Best of luck to California; the state is a large enough textbook market that should they decide to fundamentally rethink their math curriculum it could spread to other states.  I don't have high hopes but this is an opportunity.
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I somewhat agree, but parts of the article seem a little silly to me. For students who are going to be doing machine learning and using all the big data we have, taking calculus in their last year of high school is much better preparation than a watered down calculus-free stats class. Taking calculus is much better preparation for students who want to do technical work. It is the basis for everything, including statistics. Serious students who are going to be working in STEM should take calculus and take probability/statistics classes after that use the calculus they’ve learned.

However, for the vast majority of students that won’t get anywhere near being machine learning engineers, a stats class that gives them a feel for how to think statistically would be way more useful. I’d love for more people to have basic statistical literacy. Just don’t try to pretend that calculus-free high school stats is better than calculus for future statisticians or data scientists. It’s not.

Also, frankly, statistics isn’t really math after high school. At most top universities, while the math department may offer a few theoretical statistics classes, they either have a statistics department for the vast majority of their practical offerings or the most useful statistics classes are found in the computer science and/or economics departments. Calculus could be seen as the culmination of a high-end high school math education for future STEM workers, while statistics could be framed as a useful class that all should take, independent of what they’re doing with their math trajectory.
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My impression is that a lot of the controversy was about the proposal not to offer Algebra I to 8th graders for equity reasons. It seems they scrapped that, and are now just suggesting that students who aren't on the advanced track have options like data science or statistics in their senior year, since these students generally won't be able to take calculus in high school. This seems pretty uncontroversial, and I wonder how many people are actually upset about this now that they got rid of the least popular proposal.
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I wish high school math focused more on proof-based math. I wish it had at least introduced the basics to me so I didn't feel so lost when i took math in college.
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>To do so, the burgeoning field of data science blends deep mathematical ideas with statistics and programming...
>So let’s step away from the entire framework for a moment and focus on one idea we should all embrace: broadening the scope of mathematics explored in California classrooms by opening up the opportunity to offer advanced electives such as statistics/data science, probability, and discrete mathematics.

So our students who are barely getting through algebra, precalc, and calc 1 are suddenly going to enjoy and understand the *deep* mathematics behind data science? I don't think so.

Hell, aside from computer science majors, discrete mathematics is even less related to "real life" applications than calculus. I can already see the discrete math class being cancelled after a year because only 5-7 students signed up per semester.

Not to mention, the issue won't be solved at the senior elective level. The issue begins much earlier in grade school and at home. We have a garbage culture here in the US--an anti-intellectual culture--that emphasizes being beautiful, having a large social media following, being a streamer or a TV star (even moreso if you're a reality TV star), owning a business, and so on as what is successful. Yes, engineers of all sorts are seen as successful, but even the culture there is only intellectual enough on average to maintain a job and professional appearance.
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yes, calculus probably is the only option if you want to ever have a chance at understanding anything even slightly nontrivial related to any field of science, math, engineering, statistics, etc.

on the other hand, there is no point in teaching calculus to 95% of people who have to take a class on it because they are too ill-prepared to be able to get even the most basic understanding of anything from it. a lot of teachers probably have no understanding of anything either.

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