There’s an easy way for someone to learn algebra and analytic geometry: the spreadsheet. If you can learn to set up a table, formulate cell equations and then graph the results, you’ll be more proficient than Descartes ever was.
And you can’t be an accountant if you don’t understand GAAP. You can’t be a trainer if you aren’t proficient at public speaking.
Yes, lots of professions need math. And math needs to be offered in high school. But not everyone needs higher math to do their jobs.
Algebra, geometry, and trig aren’t even higher math though.
(a+b)(c+d) = ac+ad+bc+bd isn’t much different conceptually than (19)(25)=(10+9)(20+5)= 1020+105+920+9*5. The latter concepts are taught in elementary school.
Finding the focus of a parabola may be irrelevant in most lives but the modeling and problem solving skills have utility.
The modeling and problem solving skills could be taught diagramming sentences. No one is arguing for a full semester of grammar.
So bring it down to everyday living (or Doping.) During a discussion, you can tell if a person has had little or no training in math by the following:
- thinks personal observation is diagnostic of an entire population,
- can’t distinguish between relative and absolute (ex: the ant being the “strongest” animal),
- takes any “authoritative” finding to be a hard basis,
- cannot grasp the dynamism of a given system
- over-uses single statistics such as annual GDP growth.
And many more.
GAAP is a very narrow skillset. Public speaking isn’t, and schools require some degree of proficiency in it. At any rate, I wasn’t trying to defend algebra in general–my post was a response to the posters that say “I’m a software developer and I’ve never needed heavy math”. It might be true but they’re cutting themselves off from lots of stuff.
As before, my general point is that for some reason, math has to defend itself for being practical on the job, but we don’t make the same demands of other subjects.
I was absolutely terrible at language classes. I have no innate talent for language (Note: learning a language in childhood is innate to everyone. As a teenager or adult, it requires additional skills). HS language classes were miserable for me. And ultimately, entirely worthless–I can remember how to count to 10 in Spanish and not a whole lot more. And not once in my life would these skills have come in handy.
But guess what–that’s the price of a liberal education. Language classes weren’t designed to torture me; they were designed to make me more well-rounded. The fact that they didn’t succeed at this isn’t really a counterargument, because they might well have benefited someone in a slightly different situation. Also, the fact that I don’t have language skills means I’ve avoided situations where I might need them, making me a biased sample. Likewise, “I’ve never needed math” is indistinguishable from “I’m not good at math, so I don’t do things where I might need math”.
I have some sympathy for the argument that someone destined for a trade school instead of college doesn’t necessarily need a liberal education. But that argument has nothing to do with math specifically.
Question for you math gurus:
Could you still score a game of bowling by hand? Keep track of say 5-6 players?
Sure, that’s just simple addition.
The last time I went bowling I had to explain to everyone how their scores were calculated.
I’m really intrigued as to what this Algebra II is. I grew up in the UK, where school maths is just maths, I never had an algebra, calculus or trig class. Hell, I still find it weird when kids talk about that on American TV shows. These days I have a degree in pure mathematics and therefore several university courses of algebra behind me, starting with basic set theory and linear algebra up to Galois theory, so I now have an idea of what I think an algebra course is.
So what is Algebra II?
I hate maths so I’m completely on board with any plan to get rid of stuff like trigonometry and calculus and algebra outside of university degrees that absolutely require it.
Despite what all the mathematicians I’ve encountered say, algebra etc is difficult, frustrating, not at all fun and, in my personal opinion, completely useless in every day life.
Statistics would be much more useful for the average student than theoretical maths they’ll probably hate and never use.
On the foreign language front - it isn’t though. It isn’t - at least in my state - a requirement for a high school diploma. Alg II with Trig IS. So kids who don’t pass it, don’t graduate (at least without exemptions). That restricts them to very low level jobs - they can’t get into trade school.
Other components of a liberal arts education can be dumbed down for high school kids not headed to college. You pick easier books in English and a grading rubric for papers that passes you if you completed the assignment to the minimum number of pages in complete sentences that make some sense . You give multiple guess questions in History - and enough obvious ones that anyone who cares to read the questions can squeak through with a C-. Algebra II has a really specific curriculum that is difficult to dumb down - polynomials are polynomials - you can give easier and harder problems, but if you are stuck on the whole idea of polynomials, you won’t pass - even if you do multiple guess, the answers to a kid who doesn’t get it all seem the same.
One of the fundamental problems we college professors have is the incredibly hard-coded loathing of Math that US grade school teachers instill in their students.
If taught right, it’s fun to learn with a lot of obvious implications for later life.
Anway, while I’m up here on my box another thing I want to point out.
Consider that class you took where you had to read Evangeline, Stopping by Woods on a Snowy Evening, etc. Do you ever need to cite those poems, quote them ever again? Probably not. The key thing was to learn about poetry in general. You hear poetry and prose all the time in songs, TV/Movies, etc. Why does some better to you than others? Ever bashed a pop song because the author used a hackneyed rhyme or something? Where did you learn about that?
Stop thinking about never using the formula for area of trapezoid and think about how you have a general concept of differences in area.
A random thought.
I’ve often toyed with the idea that any student should be able to blow off ONE core graduation requirement. Maybe it’s math. Maybe its a language. Maybe upper level English. PE. History.
Plenty of people that are otherwise fairly smart often have one thing they just aren’t cut out to do.
Don’t get me wrong. There should still be some absolute minimum regarding their “blow off” of choice. It’s just their minimum is a lower minimum than somebody who isn’t blowing that subject off.
My kids have barely gotten poetry. And there have been almost no grades associated with the poetry they have gotten. If you don’t “get” Robert Frost, you aren’t in danger of failing English.
Very broadly, the U.S. typically has 8 years of primary education, starting age 5 or so, and four years of secondary education ("high school ", grades 9-12), after which one can go to college/university.
IIRC, high school math traditionally splits algebra across two years, algebra I and II, often with a year of geometry inbetween. Some topics get pushed into a year of precalculus after.
Algebra II often include complex numbers, polynomials, radical equations, exponentials and logs, conic sections. But it varies.
I either never use higher math, or constantly use higher math, depending on if relational algebra is considered higher math. Informal because I never actually write it down in relational algebra form, but much of my job is just putting all the table together in my head using the theory.
As I recall (from a third of a century ago or so), I’d call complex numbers, exponentials and the like “Algebra I” - Algebra II (again, as I recall) was simultaneous equations, matrix math, etc.
P.S.
Since we’re talking - “Calculus I” is derivatives and simple integration, Calculus II is more complicated integration, Calculus III is multidimensional integration and derivatives, and “Calculus 4” is differential equations (or it was, when I was in college).
I should add that plenty of students complete one or both years of algebra prior to high school. And schools often offer a pre-algebra class prior to algebra I.
I was the same way. Algebra brought me to tears on a regular basis. I muddled through geometry, trigonometry, and statistics mostly due to a very excellent and patient teacher. I really really really didn’t want to take calculus my senior year, but that was the track I was on. This same teacher talked me into taking calculus, assuring me repeatedly that I would do fine and that if it didn’t work out she would allow me to drop it and take something else no questions asked. She was right, I aced it. I asked her one day how she knew I would be OK in calculus and she said it was in how I approached things. My way of learning didn’t work for algebra but was just right for calculus.
Fast forward 20+ years when I went back to college. I put my math requirements off as long as I could. I broke out in a cold sweat when I got that algebra book in the mail. But somehow over the last 20+ years I must have made some different connection in my brain. Algebra was so much easier for me this time. I still didn’t enjoy it but at least it didn’t make me cry!
I don’t have a syllabus from any of my old classes, but I found these topic lists for an online class:
https://www.khanacademy.org/math/algebra
https://www.khanacademy.org/math/algebra2
This homeschooling site has links to the table of contents for the Saxon textbooks that I used long ago:
http://www.christianbook.com/saxon-algebra-home-study-third-edition/9781565771239/pd/791230
http://www.christianbook.com/saxon-home-study-algebra-2-third-ed/9781600320163/pd/320163
That matches my recollections. I also recall calc2 including sequences/series and those “surface of rotation” problems that were so much easier with multivariable integration. We didn’t use the word “calculus” when describing differential equations, “diffeecues”, but it did come next in the sequence. Linear algebra was off on its own.