In general, I try not to think of Algebra in terms of, “what simple everyday life situation can this be applied to?” I’m sure you can find some, but it is true that you can definitely go through life and survive without algebra. What it teaches you, functions, their properties, and abstract generalizations between numbers, is more important in a theoretical sense than in a, “you 100% need this skill just to survive” sense. If you want to understand mathematical relations (e.g. how do interest rates affect a budget?) or to do any form of advanced math work (which is becoming increasingly important), then you’ll need algebra.
You can get by not knowing math the same way you can get by being an incompetent writer or not being able to spell. You can survive, possibly even thrive, but it certainly doesn’t do you any favors to have that gap in your knowledge.
It’s that many of us who graduated with STEM degrees and then got jobs saw that the academic pursuits stressed as important in school turned out to be not so important in the real world.
University academic programs and pursuits reflect the interests of academicians. Those interests would be graduate school and research. That’s not the goal of most students, who are going to school to be trained to enter the work force. There’s a mismatch between what academicians think is important and what students need. That especially applies to math requirements, and how math is taught.
As I never tire of saying, math as taught in school is too theoretical and not practical enough. Rather than showing students all the fascinating applications math can be used for, they’re subjected to mind-numbingly dull proofs, derivations, and pointless letter-juggling. Students don’t see the point of math, and that’s what drives them away.
I was one of those students that was terrible at math and wanted nothing to do with it. It was boring and irrelevant, so I didn’t study. I even flunked intermediate algebra in high school. What turned that around was a class at a community college in California called Applied Calculus. No proofs. No derivations. No pointless letter-juggling. Just lots of examples of practical applications of math. I was stunned to find out people actually used math. It was very motivating, and I ended up getting an A. And that one class ultimately gave me the confidence to pursue degrees in CS and IE.
It’s also why I get outright angry at the way math is generally taught and the people who defend that method of teaching. Too many kids are being turned off of math by academics who figure that because they were able to deal with proofs, derivations, and pointless letter-juggling, that’s how everyone should be taught, My theory is that 80% of students are driven away from math by our approach to teaching math. Since math teachers come from the remaining 20%, and they teach math the way they were taught, the problem keeps perpetuating itself and we keep losing 80% of the students in each generation. We need to break out of that cycle of failure.
I entrust my car to mechanics (which I sometimes wish I didn’t have to do). It would be great if I could have learned to do more than change oil, filters, and plugs. My dad and older brother tried to help me learn, but it just ended in frustration for me. It would make perfect sense when I watched it being done, but as many times as I tried I just couldn’t do it. It was similar with Algebra. When the teacher or tutor showed me what to do, it appeared to make perfect sense. When asked to do an almost identical problem, no dice.
Let’s say we make Algebra 2 a graduation requirement in all 50 states. What happens to the kids who don’t graduate because they just don’t get it? Is the kid who is a whiz at written and verbal communication but can’t pass Algebra 2 going to work at low paid jobs his/her entire life? I hope math education improves to the point that all students can achieve at a higher level. Unfortunately, just saying everyone needs to master a subject doesn’t mean everyone can. If that makes me anti-intellectual, so be it. I’d prefer helping everyone reach his/her potential despite limitations in some areas.
Except that, as far as I have read and remembered, precisely zero people in this discussion are defending the way math is currently taught in the schools. The discussion is whether basic mathematics (and unfortunately, some people are defining that as algebra 1 and others as algebra 2) should be required for high school graduations.
In my limited experience, the type of thinking in proofs has spread to other academic areas; I now think of essays and science experiments similarly, and I feel that such thinking has improved my skills.
I’ve found something quite different: while just about all of basic grade school education is important in the real world, a lot of people just don’t live a life that enables them to use that. Given that education is all about having a broad base of knowledge that you can build upon, it’s alright if you don’t end up using everything. Some people will need physics in their job, others will need history. That applies as well for subjects within your major. But prezbucky put it quite nicely and quite accurately:
Academics is about being able to go beyond just “what you need for your next job” and about getting a deeper understanding of the topic you’re trying to learn. That’s not for everyone to be sure, but at the very least it is very consistent with what a university education is supposed to teach you. Perhaps all we really need is a more effective trade/technical school system which works better for those who really have no interest in learning advanced material and just want the bare minimum to be competent at their job. As it stands, a Bachelors degree program is a weird hybrid of future academic preparation and basic job training.
I’ll give you that there are a lot of out-of-touch academics, especially those from elite schools, who are basically just ego-driven jerks who have no place being teachers (even if they are generally effective researchers, which gets them hired in the first place). High school academics also have a fair share of problems too.
But you’re painting with a broad brush and basically throwing out the baby with the bathwater. Those skills are taught because they are actually important to understanding mathematics. It’s not ivory tower elitism that put those into the math curriculum.
It’s important to be able to learn beyond what seems immediately applicable to your goals in life. There’s a good chance that your perceptions of what matters are way off-base. Almost all high schoolers have no accurate perception of what will actually be useful in the “real world.” All of those “pointless proofs and derivations” that you deride are actually very useful, and I’ve personally used them plenty in “real world” jobs. Just because you didn’t in the jobs you’ve had, doesn’t mean your generalizations are justified.
It’s fine if you don’t want to be a mathematician. We all have our own specializations and we all realize that there are things we are better at than others, and that there are generally people we can turn to for help. I don’t do my own taxes (my accountant understands all of the many contortions of dealing with the IRS much better than I do) nor do I perform difficult repairs on my own car (cars these days are really complicated and becoming more so, I’d just break things). It would be wrong if I tried to say that these things don’t matter, and that people shouldn’t be required to learn about taxes or car maintenance, just because those aren’t my areas of expertise.
Similarly, you don’t have to understand all of the complexities of compound interest, how it works, and all of the ways you can use it. I don’t either - I might need to use more than the average person for my work, but I don’t construct financial derivatives for a living either. But it would be wise to know at least conceptually how compound interest works, beyond that it’s simply a formula and that there’s a magical program that allows you not to know the math and just get an answer. At the very least, it would be smart to learn about exponential growth (a major topic of Algebra 2 in general) and about the time value of money. That kind of more abstract thinking, relying on simple but valid mathematical intuition, is definitely useful and something you can easily build upon if you need or want to learn more. That’s why you learn in the first place.
This is all, ultimately, coming down to the always-depressing “Should schooling be more about becoming aware of the world and general principles, or should schooling be more about preparation for a career path?” argument, isn’t it?
Really, a lot of it comes down to the de facto one-track education pathway in the US: you go through grade school, then you get your bachelors degree, then you go from there. Community colleges teach you a lot and they have some great programs, but they pigeonhole you and you will find a ceiling to what you can do with only an Associate Degree/Certificate. That means that the bachelors is the basic entry-level qualification for skilled work, and what comes further (Masters, MD, JD, for academics PhD) become the true “entry level” for more advanced work. So the bachelors becomes a weird hybrid of preparing less academically inclined students to start working right away, and preparing the more skilled ones to go on to further education. I personally think the system is due for an overhaul, because it could certainly use a lot of improvements (that’s almost a non-statement - everything could use improvement). But under the current system, it’s best to just accept that the degree you are after expects you to learn about both the practical and the academic side of things, and choose what path is best for you later.
It may also, as the thread has developed, point to an urgent need to teach subjects better. We all remember the droning History teacher filling the board with endless dates to memorize, the Spanish teacher who somehow taught no Spanish, the Math teacher putting kids through mountains of problems without ever teaching what we were doing. (I still do not know why we did all those proofs in Geometry.) There are still too many classrooms like that.
One of Hacker’s suggestions on improving Math teaching is the Discovery Approach. For example, students are asked "If juice cans come in cases of 24, how many cases are needed to give a can to each of the 300 children who have lunch at the school? Of course the “correct” answer is 13 (with a remainder), but students who really discuss and work with the problem may do more creative problem-solving. For example some groups may take into account the number of students absent on a given day, or those who don’t like juice and won’t drink it. My favorite answer was a just-in-time solution: “If we place an order for 25 cases that will be 600 cans or enough for two lunches. Then we won’t have to go through this long division every time.”
I like this “we won’t have to go through this long division every time”. Division sounds like a very hard and laborious process and we need to shield our children from it.
Children should learn how to effortlessly divide numbers (for this example - in their heads) before you start asking them to consider special circumstances and creative problem solving.
Creative problem solving cannot replace the ability to do simple arithmetic.
@ucbalumnus, I never said anything about not requiring math. I’ll address each area. English Literature: is it required anywhere? I had to take Western Lit in college, but English Lit wasn’t required at my HS or at my sons’ HS. Science: this is pretty general. Biology and either Chemistry or an Earth Science class. I’d require US and World History, as well as government and economics. Foreign language: 2 years. Student picks which one, of course. Art: is it required anywhere? If it’s going to be required, make it an art appreciation class. Requiring it would certainly make art majors more employable. Notice that, with the exception of foreign language, I’m not recommending 2 of anything that builds on an earlier class. I think 4 years of English can be repetitious for many students. Certainly it isn’t as bad as studying grammar from 3rd grade through the first half of 10th grade. You didn’t ask, but I don’t understand why students who get a 4 or 5 on the AP English exam as juniors have to take English again as seniors. As far as math goes, I think Algebra 1 and Geometry should be required. If a student needs more than a year to finish, that should be allowed. Learning the material should be more important than completing the class in a specific amount of time. What if I said 4 years of math, but that the pace depend on what the student is capable of?
English literature is embedded in high school English courses which also teach writing skills. Since the teachers majored in English when they went to college, they naturally use literature as the context, so writing assignments in high school English courses are mainly literary analysis.
Looking at a sample high school’s graduation requirements, I see the following (with comparison to state universities if significantly different):
4 years of English
2 years of math including algebra 1 (state universities require algebra 2 and geometry)
2 years of science
2 years total of any combination of foreign languages and arts (state universities require level 2 or higher foreign language and a year of art)
3.5 years of history and social studies (state universities require 2 years)
However, other high schools have different graduation requirements. One large district in the state has made its high school graduation requirements the same as the frosh entry requirements of the state universities, except for additional courses like health, phyiscal, and career education, and an additional history course.
If y’all don’t even know the proof of Grothendieck-Riemann-Roch or understand the cohomology of projective schemes there’s no way you’re getting a job paying > $15 an hour…yeah math is pretty important.
Defending the teaching of proofs ≠ defending the way math is taught.
You’ve committed the fallacy of composition (which is why it’s wrong, for example, to say that since water is a part of your brain, and since water does not have consciousness, your brain has no consciousness).
Notice that, with the exception of foreign language, I’m not recommending 2 of anything that builds on an earlier class. I think 4 years of English can be repetitious for many students. Certainly it isn’t as bad as studying grammar from 3rd grade through the first half of 10th grade. You didn’t ask, but I don’t understand why students who get a 4 or 5 on the AP English exam as juniors have to take English again as seniors. As far as math goes, I think Algebra 1 and Geometry should be required. If a student needs more than a year to finish, that should be allowed. Learning the material should be more important than completing the class in a specific amount of time. What if I said 4 years of math, but that the pace depend on what the student is capable of?