You can’t do probability and statistics without the basic tools of math, the tools named after an ancient math book in arabic, the mysterious ways of “Algebra”.
Weird. I haven’t found much everyday use for calculus, but I feel like I’m solving equations reasonably regularly, and I have nothing to do with a math or science field. (Hell, we even used trig a few weeks ago to estimate the altitude of a landing airplane based on how far we were away from the airport and a 3 degree glide slope, but, I admit, that is a bit of a niche use.)
The issue with dealing with probability before calc is that a lot of the sausage making in probability relies on calc. Same issue with high school physics, honestly.
From experience and the experiences of my friends, we lost most of the more advanced high school math-based stuff from stats and/or physics because it’s this rapidfire of equations and special cases without much to relate it to anything or ground or explain it.
For me physics was a slap dash array of arbitrary equations and situations that were incredibly difficult to understand or motivate because I didn’t even have the tool of an integral/derivative for linear equations which makes basic kinematics way easier. Obviously there are limits here, I’m not saying we need to get everyone bootstrapped with quantum probability and teach physics from some absurd interpretation of “derivation from first principles”, but it’s hard to retain things when it’s just a mapping of situation->process.
Similar with probability and statistics. Admittedly I opted for a different course than stats in high school, so I didn’t actually have any real exposure to probability before having calculus, so I’m going to qualify that clearly I was introduced in a way heavier way than a lot of people which may be causing my incredulity here. That said, I’m not entirely sure how you motivate a great deal of things, especially some really fundamental distributions without at least having people comfortable with limits. You can cover Bayes Theorem, I guess, and possibly probabilistic graphical models like Bayesian Networks and inference algorithms, but I feel like even that’d fall apart without some prerequisite knowledge in algorithmic thinking.
Honestly, the issue with a lot of high school math isn’t it being useless, or even useless until you’re well into a STEM degree, it’s that they spend a lot of time spinning wheels teaching things in a vacuum. I remember spending entire units in multiple different courses on domain/codomain/image/preimage stuff and… I… have… no… idea… why? We never used it except to answer questions based on it. It’s not even a particularly useless concept, it’s basically what you’re thinking about when you write a single simple function in a programming language, hell, when you have a system process to change one thing to another set of things in real life. But instead we focus on like… equations to transform the reals into the reals missing one or two elements? I don’t get the motivation, it’s so bizarre.
I remember when we were learning solving systems of equations we took a jaunt into learning about matrices and RREF, and then were forced to answer some questions on the test using by reducing a matrix to RREF. It was… bizarre? It’s just completely contextless and surreal without any foundation even 2 weeks in linear algebra can give you. And no linear algebra course assumes you’ve heard of RREF before. I guess at least if you figure it out you realize your calculator can solve systems of equations really easily with RREF.
I think this is why quadratics sticks for so many people, because you actually use quadratics to reinforce other things you do, and because you have the foundation to largely understand and even prove some of the closed form equations. Like one of the first closed form equation derivations most students see is using completing the square to get the quadratic equation.
I don’t know what I’m getting at with all this, but I guess it just seems to me that the issue isn’t the math people learn, it’s that there’s a peculiar foundation of lack of reinforcement and lack of underlying knowledge that makes math feel like spinning your wheels. So many things you never use for anything, even within the rest of your high school math career, and so many contextless magic incantations you don’t have the knowledge to understand the context of. Obviously this will always be the case somewhat, again, I don’t want everyone to learn things from first principles, but the curriculum design for math has always just felt really uneven and I think that contributes to the problem more than the math not always having immediately obvious everyday applications per se.
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How many years of HS math were you required to have?
3, and pass the Regents exam in all 3 to get a NYS Regents diploma (as opposed to the “local” diploma handed out by the school)
I, however, took 5 years, starting in 8th grade. -
How many years of HS math do you think we should require?
3 - but there should be more kinds of math class available. Including applied math, and multiple years of lower-level or remedial math in order to enable kids who are not great at math or who don’t plan to go onto college to retain basic math skills at least until they graduate. -
Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?
I would prefer that HS students have the option to take classes to learn math that they will have practical need for now and later in life. Some students will also want/need trig, calculus, etc.
To follow up: I don’t use trig or calculus at all anymore, but regularly use algebra, geometry, probability and logic in my personal life. Less so at work. Stats would be a better thing for me to know at work than most of the math I learned in HS. (I didn’t take stats in college so that lack is all on me!)
Who the heck has a checkbook to balance anymore? Hell, I don’t have any checks.
Furthermore, how does basic math not teach you to balance a checkbook if you need to do that? Surely someone with a decent grasp of basic arithmetic can figure it out on their own?
You might have to use integrals to find its center of mass.