The last higher math I ever use is making a right angle with 3-4-5. Analytical geometry as prelude to calculus was an absolute, total waste of time. A little accounting would have been helpful through the years.
I’m not good at math at all. In my high school, much of Algebra II was a rehash of Algera I, which meant I got an A. It was the last math course I ever got an A in. Actually, it was the only math course in high school I got an A in. I got an A minus in Statistics in college only because I had the world’s most patient TA helping me.
My college roommate senior year was a math major. She’s brilliant at it, but had to take a stats course to fulfill some requirement and hated it. I helped her with her stats homework and she kept saying, “This isn’t real math” over and over. (She did pass the course.)
Boy, can I relate. Helping my daughter with stats homework (and, before her, my cousin’s wife) made me realize that when you make things easier for non-math people, it makes it seem twisted and convoluted and needlessly complicated to math people.
I graduated high school in 1967. At that time, you needed two course credits in math to graduate*. They never said what two math courses you had to take, so most people just took arithmetic courses and never needed to take algebra at all.
Of course, I was the Math Guy (senior year: Who’s Who in Math!), so I took Alg I in my freshman year, Alg II and Plane Geometry in my sophomore year, trig and solid geometry (1/2 course credit each) in my junior year, and Elementary Analysis (pre-calc+) in my senior year.
My issues were with the classes I had to take in history and civics, of which, certain values of course credits had to be met. I could have done without those, but, today I find myself very more interested in history and how governments work than I ever would have thought back then.
*Also needed were 2 credits of science, 2 in PE, 4 in English/literature, two and a half in humanities (history/gov’t, etc.). The remainder of the 20 credits needed to graduate (9.5, iirc) were electives. I don’t know how I would have collected all of those credits if I hadn’t had higher math courses to take.
This is an important aspect being ignored in the proposal.
Calculus opens the mind to perceiving motion and change in a different way. It’s inspired by the real world and allows intellectual consideration of nature that would otherwise be an unending mystery.
Frankly, a proposal from a political hack about how to teach math smacks of “why teach the peasants anything they don’t need to work the farm?”
I think I had a different “algebra II” than everybody else did; I think the only thing close to calculus was an introduction to limits and series. The higher-end stuff was more Trigonometry and Analytic Geometry.
Of the high school math courses I had, I think the one that was the least use to me now was Geometry; it was almost all proofs of things I rarely use (e.g. “if one side of a triangle is a diameter of the circumscribing circle, then it is the hypotenuse of a right triangle”).
However, making basic statistics part of the curriculum isn’t a bad idea - in fact, in 1983, the University of California changed the computer science degree requirement to require a statistics course.
There is once school of thought that says that it is precisely the proofs themselves, and not the things that are proved, that make studying geometry so useful, because it trains the mind in deductive reasoning and thinking logically and recognizing what constitutes a valid proof. In favor of this view, one could cite such authorities as Abraham Lincoln and, arguably, Plato.
I went through Calculus in high school. I have never used anything more complex than basic algebra or basic geography since then. I’ve used my Basic Stats class a thousand times more.
My high school algebra is nearly 50 years in the rearview mirror, so other than that Algebra II included trigonometry, I really can’t remember what material went in Algebra I and what went in Algebra II, so it’s hard for me to take a stand one way or the other on the value of Algebra II.
I agree that the point of college-track high school math (and certainly that includes Algebra II and everything up from there) is to keep students’ life options open until they discover what they really want to do with themselves, since math skills are expected in a fair number of majors and careers. Students who know they aren’t college-bound, though, don’t need any of that. But everybody should have an introductory statistics course.
I’m an engineer and, though never directly solving algebra and calculus problems by hand, I have to frequently read and interpret math functions and occasionally write code that implements these functions in a workable way. I’m expected to have an intuitive knowledge of the scope, bounds, pitfalls, benefits etc of what an expression can and cannot do, even if I never do the brute force chalkboard drudgery to get from point A to point B.
If a student never had algebra, and never learned the number theory concepts of linearity, rationality, etc then there is no way that they could be expected to excel in technical engineering, science, or programming careers.
I think algebra and calculus should be less proof and derivation focused (leave that for background reference only) and more “applied math” focused. Also, less time spent on laborious by hand solving tricks that are effectively obsoleted by computers. Students should be graded on the implementation and evaluation of concepts more than whether they tripped up memorizing the ‘integration by parts’ cookbook steps correctly.
I’d even go so far as to suggest that at a high school level, it doesn’t even need to be a calculation-heavy, “math-in-disguise” course (like my undergrad statistics course for my computer science degree was).
The things I’d think you’d need to know would be things like what distributions are, what standard deviations are (and how they relate to distributions and just how common something really is), confidence intervals, sample sizes, central tendencies, variance, mean, median, mode, correlations, etc…
But there’s no point at that level, to make some poor kid grind out R-squared on a dataset , or actually calculate what a standard deviation is, etc… The actual calculations themselves are either easily done by computers, if someone really needs to do them, or the results are given to you in most cases.
Understanding the results is what is most important to most people, but for some reason, there seems to be an entrenched idea that there’s a lot of utility in making someone grind out the work on some of these things.
If I seem bitter, it’s because I always understood the statistical concepts well, but was never good at the actual calculation part. I got a C in undergrad, where we had to grind all that shit out, and a runaway A in grad school, where our prof let us use Excel (or whatever statistical program we chose) to do the scut work, because he was more interested in our use of the statistical concepts.
I liked Algebra. I liked Calculus. I also was pre-Med in college, so I needed that stuff.
I can appreciate that not everyone wants or needs the material, but isn’t that why there are separate tracks? Or is that something not all schools offer? (I’m guessing the latter.)
I wish my HS math teacher had been something other than an ancient, humorless, boring, monotone who wore the same dirty, tattered coat every day.
I really liked math until Algebra II. I rocked geometry and algebra I but I was completely lost in Algebra II. The only thing that class taught me was how to be a better cheater. I squeaked by with a D.
I was able to avoid whatever math was for seniors. Calc? I had extra study hall, because I had enough credit to not take math.
My BFF, on the other hand, flourished in Algebra II and it was a total turning point in his education. Before that he was just a regular, if not under-achieving, student. In Algebra II he was suddenly considered a genius and it even did well for his social life (all of my smart friends from our Smart Kids Educational Tract finally knew who he was).
My BFF went on to be a computer science major and I went on to journalism. I was stoked because I could take Spanish instead of math in my freshman and sophomore years. That requirement has since changed in the school catalog.
We’re both software programmers now, however. But he does more math-centric stuff and I do more user-experience stuff. And I have a way better command of the English language than he does!
I like math. I’m in a math heavy field. I use multivariate calculus (which I basically self-taught. I never took vector calc). I agree that basic stats would be far better for the average person to learn. Algebra 2 is useful, but it’s not worth teaching given that there’s other better things.
Especially since I recall Algebra 2 being… weird. Most of the stuff I don’t use, and a lot of the stuff I do use was retaught in context far better. It took me forever to connect Domain/Co-Domain/Image/Range to programming, and even when I did it wasn’t super helpful. Asymptotes are probably more interesting, but I’ve never been sure why we teach them before calculus since the entire thing is secretly limit analysis.
It was this weird mishmash of topics that I’d almost sum up as “calculus without calculus” with a smattering of unevenly applied baby’s first real analysis thrown in.
Edit: Note this is all Algebra 2. Algebra 1 was mostly okay. Solving for variables, quadratics, rational numbers, basic rate equations, exponentials and compound interest, etc.
I loved Algebra II in high school, in fact, I loved all the math I took through college too, with the exception of Calc III, and I took pretty much every math class I reasonably could, Number Theory (SO much fun), Linear Algebra, Stat, etc. As a Comp Sci major, I don’t use advanced math too much in my day to day job, but I did in some of my projects in grad school and my PhD work (that I didn’t finish) or in my fun projects, and I’d like to get into a job more like that.
All of that said, I agree that Algebra II just isn’t useful to most people. IMO, Statistics is FAR more useful to the average person and it’s depressing how little the average person understands about it and can get misled, deliberately or accidentally, into making poor decisions or bad purchases as a result. They absolutely should still offer Algebra II and Calc to students in more advanced math tracks, but at least a basic understanding of statistics should be part of a high school education. Frankly, I’d put it higher than most of what I learned in Geometry to, in terms of what I find useful in everyday life.
I definitely agree that we shouldn’t teach solely based on utility. But not all of stats is going to be useful. Hell, we can still teach geometry, most of which is only dubiously useful in a direct sense.
But stats is so important that I think subbing out algebra 2 for it makes a ton of sense. Algebra 2, IMO, should just be discarded for calc since as I said above, I recall the subject matter just being calculus topics in a weird vacuum without the background knowledge to understand or derive anything you were being taught.
But hey, people taking kinematics without calculus too somehow. I don’t know how, I suuuuucked at physics in high school until I took the calc version in college. Obviously some of that was having seen some of the material before, but having the background to meaningfully talk about the mathematics was astoundingly helpful for putting things in context. Algebra 2, I feel, is the same way, most of the topics are just horrible without the background.
I semi-disagree. I think you get a lot better understanding of what standard deviations (for example) are if you’ve actually calculated at least one or two of them. You see how the calculation involves taking into account how far each individual number is from the mean, for instance.
That said, the less “grindier,” the better: working through a simple example is one thing, but I suspect it doesn’t help, and possibly hurts, the conceptual understanding gained by doing so if the example involves a large number of data values, or big ugly numbers.
As a practical matter, I wouldn’t expect a statistician to calculate a standard deviation “by hand”; but I’d question his understanding of statistics if he was unable to. Kind of like I’d expect anyone adding a bunch of big numbers together to reach for a calculator, but if they couldn’t do something like 13+22 without a calculator, I’d think they don’t really know what addition is.
Is there a standard definition of what “Algebra II” is? I get the impression that a lot of us are coming at this with widely differing ideas in our heads of what “Algebra II” involves; and it doesn’t seem worthwhile to debate whether or not it should be taught if we don’t even know what it is.
Fully agreed. I don’t understand why math has to justify its existence for practical reasons and yet we don’t do the same with the rest of the curriculum. I have never, in my entire life, had any use for the three years of Spanish I took. I have never use my knowledge of history or other social studies in my job. Although parts of English have been useful, I have never written a standard 5-paragraph essay in my adult life.
Obviously the answer is that learning these things make me a more well-rounded individual, and one that’s more capable of functioning in a complicated society. The same is true of math. Learning to think abstractly and precisely is important for everyone, not just technical people.