Illustration by Adam Hayes for the New York Times
The New York Times recently ran an opinion piece entitled Is Algebra Necessary?
It questions whether schools focus too much on trying to teach a subject that causes many students to drop out of school entirely, with some schools seeing as many as 45% failing to finish high school.
Please have a read of the full article and let us know your thoughts on this important subject.
Personally, I can't think of a single time I've used algebra in the 20 years since I left school - apart from trying to work out some of the GeekDad weekly puzzles (which I'm not even allowed to enter!), so I can see why this might make sense. I use trigonometry regularly when building stuff around the house, but algebra and calculus always seemed pretty pointless to me - and I studied Maths up to A-Level here in the UK.
The author makes a valid point about how "Making mathematics mandatory prevents us from discovering and developing young talent" - as the mathematical and artistic/creative sides of the brain often develop and work differently, but in my own case, my mathematical mind has informed my creative career. I'm a web designer with a very geometric illustration style. I like to create, neat clean code, with pixel-perfect layouts and admire minimal design, symmetry and simplicity - and I believe this all stems from learning maths at school.
I think it's important to expose children to as many school subjects as possible. That way they can decide what they like and move in that direction. I have used algebra in my personal and professional life. It might have only been solve for x, and not double replacement. I didn't need a graph, but I did need that exposure so I could solve real life problems. Considering that and the fact that the US is being left behind when it comes to math and sciences we need to show students what's out there. Should we set them up to fail by making them take four years of a subject they have no aptitude for? No. However we shouldn't just not give them the chance to succeed either.
The article's title is a little misleading. The author isn't arguing that Algebra isn't necessary, but that it's not necessary for everyone.
I have three kids: one who graduated high school last year, two who are in middle school now. Our oldest took Algebra in 8th grade, the earliest that you could when he was in middle school, unless you were off-the-charts genius. One of my middle schoolers took Algebra in 7th grade, same thing, the earliest you can take it unless... When I was in school, pretty much everyone took Algebra in 9th grade or later.
While I have no problem with pushing higher math down to younger students who can handle it, the question arises: what about other subjects? Why do we only push/reward students with mathematic aptitude? The path for the science and English curricula are basically the same as when I was in high school, 25 years ago. Ditto for art, music, athletics, history, etc.
The point the author makes is that by making Algebra so important, we overlook other gifts and aptitudes. Kids who are gifted at writing may benefit more from higher-level reading or writing classes. Instead, we force square pegs into round holes with the idea that everyone can/should do this.
In many ways this is completely missing the mark - if literacy was falling we definitely would not be talking about decreasing reading classes. Algebra is important. Plain and simple. Why? Algebra is all about functional relationships. We are surrounded by functional relationships (for instance a very simple function maps my keyboard keys to a specific alphabet). In addition, education is not about getting a job. It never has been. It is about creating a society in which the members have a solid grasp of the world that surrounds them so that they can make informed decisions concerning their lives and future.
A different question is whether we are teaching algebra in a useful way to all students? I think increasing the flexibility of teaching algebra to students is a more worthy topic - but obviously one which would not garner all this attention for the author...
Well OK, except for the fact that math isn't failing! I know it's a common theme: "the US is something_other_than_first_in_the_world in science and math scores." When someone tells you that, you should ask them to show their work. Where is the Global Math Test that was administered to all students or adults world wide to draw such a dire conclusion.
I'm a math guy. I get math. I actually fell in love with it because of algebra. But any honest dialog about this must admit that not everyone gets math the same way you and I do. You say it's about functional relationships, but to some, it's alphabet soup. Not because they are dumb, or not smart enough, but because they are gifted in other areas. And what I'm saying is that there is no parallel track for those students!
Can everyone/almost everyone "pass" algebra? No doubt. Will some struggle mightily to do so? No doubt. I argue that for those, their time might be better spent at doing something they'll love instead of something they hate and will not pursue post graduation.
This is kind of a tricky topic that causes a split of opinion even in my own mind. On one hand, I feel algebra is necessary as a stepping stone into higher math (like trig and calc). But on the other hand, I have heard that in some foreign countries, they have two separate sets of schools, one set focuses on "liberal arts" like history, language, writing, etc. and the other focuses on STEM-like subjects and kids have to decide what they are going to be when they grow up and go to the appropriate school.
On the one hand, it seems like that would be beneficial because they can focus only on the subjects that they are really interested in and will benefit their future career.
But on the other hand, pre-college education, when most kids are still trying to figure out what they want to be, should provide a wide range of "general education" to a)provide the basics of knowledge about subjects that really do affect everyday life and b)allow students to experience a wide range of subjects that might pique their interest that they never would have previously considered.
For example, when I was in High School, one of our electives we had to choose between Anthropology or Psychology. up until high school I had wanted to be either a paleontologist or archaeologist, so Anthropology would have been the safer choice, but at that time, I began to feel that being away on digs for months at a time would make it difficult to raise a family so I realized I needed to figure something else out. My brother and best friend each took the psych class and loved it so I decided to give it a try. I loved it so much I earned my bachelor's in it and, after I finish pharmacy school, hope to specialize in psychiatric pharmacy. None of that would have happened if I didn't have a school that offered it.
I have a very biased opinion (I work in software, clearly math/science/tech heavy). But algebra doesn't seem all that advanced to me. How do you use trig without algebra? How does a business person decide how much to charge for a product and still make a profit without algebra? How do you set a family budget or manage retirement plans without algebra? Even fairly manual labor including jobs in construction or foodservice would vastly benefit from knowing how to solve at least basic algebra (e.g. resource planning). Probably, those people already do algebra but they don't think of it in terms of X and Y.
Yeah, I can see how some of the more advanced parts of algebra are not that applicable to every day life, but I can't see how the basics can possibly be considered completely unnecessary for even very non-mathematical jobs.
I would fully support having our schools provide other ways to accelerate learning or exploring of topics. It is typically up to us parents to provide the advanced atheletics or music or writing (or whatever other gifts our kids have) by searching out extra curricular activities for them, though any individual school has limited resources and it isn't usually feasible to offer a subject that very few kids would be interested in taking. It would be nice of schools and communities could pool their resources more for those so-called "extras" to make them available to the kids who don't have parents with money and time to spare to go hunt it down themselves.
The problem isn't algebra. The problem is the way the education system in America works and that many parents (not all, but too many) don't have the time, inclination, skill, or some combination thereof to help their kids. (Combinations are statistics.)
If you're more than +/- 0.5 sigma off the "mean" as defined by the school system (more statistics) they can't address your needs effectively. (That's all I'm going to say about that to avoid getting into a rant about personal experiences with the local school district.)
I see some involved parents, but not many. (Again cutting off to avoid a rant about personal experiences with teachers who don't want to talk to parents.)
For what it's worth, my son blows away the state math and reading tests (like I did). He also plays clarinet (well, though he hardly ever practices outside band class), draws (not so well, but isn't willing to focus on learning to see yet), loves watching Bob Ross paint (who doesn't), and has been designing his own CCG for the past two or three years. He doesn't write well, though (organizing his thoughts, logical sequencing, details, assumes everyone gets the paragraph he's thinking from the five-word sentence he wrote.)
Also for what it's worth, I use algebra several times a week, even when I'm not checking my son's homework. (They're doing elementary algebra without calling it that.) At least, last I heard, setting up equations and solving for an unknown qualifies as elementary algebra. I do that every time I calculate a unit price while shopping or compare two prices.
I have only used calculus a few times in 20-ish years since graduating college. Linear algebra once or twice that I can recall. Differential equations never. I have used geometry from time to time, but in a basic way (solving angles of a triangle, calculating volume of a space under a shelf unit to make sure the server had room to breathe, etc.)
But I hated geometry in school because, for two of the three classes, I had the teacher from Gehenna who thought his job was to assign problems and make fun of students who got answers wrong, not teach them how to solve the problems. (The middle class, which everyone said was the hardest and was primarily proofs, I did well in, but had a different teacher. Then again, my first few jobs were "programmer" jobs, so maybe that makes sense.)
Interestingly enough, with that advanced math pedigree (and blowing away state math tests), I struggled in Algebra 1 and 2 in 8th and 9th grades and with other math-heavy subjects throughout my educational career in the class. For example, I clawed my way through the razor-wire barrier of AP Calculus in 12th grade, emerging sore and bleeding at the end--then got a 3 on the AP exam, which got me out of Calc 1 in college (good thing, it was 1-1/2 hours starting at 7:30 AM 5 days a week). That was when I started to see that classes are about pushing forward to the next thing, not looking back to see how far you've come. That I needed to make the effort to look back now and then. An important lesson that served me well in college.
So maybe early struggles in algebra--or struggles in any subject--don't translate into later struggles with algebra. (I have little problem with algebra today.) And maybe struggling with a subject isn't a bad thing. (I learned I sometimes have to do the homework to pass a class rather than just absorbing everything I needed from the lecture, that practice was necessary to learn the process I'd heard about in theory. Which also served me well in college.)
You bring up a good point. There is a lot of time spent avoiding failure instead of teaching kids to over come their issues. We just kind of shrug and say yeah you just aren't good at math, when we should be saying well you had trouble but let's try this again. The problem is that teachers just can't do that because they don't have the luxury of one on one instruction for every student. Which comes around to your other great point that parents aren't engaged. Once we drop them at school it's like we check out. Why aren't more parents engaged? Why isn't there a movement to increase parental engagement?
We spend a lot of time avoiding failure. As Adam and Jamie say, "Failure is always an option." Put another way, adversity builds character. Or, deploying educational theory, we can only learn something when we fail. If we got it right the first time, we already knew it.
I think your one on one comment is interesting. One on one is best in some ways, but small groups of peers are better (IMO) because they engage social aspects of learning and involve more exploration and less "fount of wisdom" learning. Also, I've seen teachers spend small group or one on one time with the lowest performers in the class, but the kids barely scraping by or struggling with non-academic issues are left in the lurch. I've only seen a couple of teachers who used peer tutors--getting the higher performing kids to support some of the lowest performers or some of the barely-scraping-by kids. Partly this is because of privacy/legal concerns. Partly because I think the teachers either don't think about it or are afraid/unwilling to admit a student might be as capable (or better) at teaching a peer or two than they are. (But in college, I internalized more understanding from doing homework with my peers than from lectures.)
Regarding engaging parents and teachers, speaking from what I see in my local school system, I think there is a sense of adversity between teachers, school administration, parents, and students--an anti-love quadrilateral of sorts. (Oh my! Geometry.)
Teachers tend to talk down about administrators to parents (when they talk to parents). Administrators can make a teacher's life miserable, so few teachers will oppose an administrator to their face, even in front of a parent. (Politics are the elephant when teachers, administrators, and parents are in the same room.) When they didn't know I could hear them, I've heard teachers and administrators say that parents don't know education and should just let them do their jobs because they know what's best for kids, not parents.
Parents often see administrators as process-bound obstacles to doing what needs to be done (often reinforced by teachers in private) and teachers as aloof and inaccessible or idiots (at least partly because of lack of communication and partly because teachers are more process-bound than they'd like to admit).
Students see administrators as punishers (how often do students have more than momentary interaction with administrators outside of disciplinary actions?), teachers as boring or not engaged because they're rushing through a district-provided script of materials, and parents as anything from minor gods (first grade) to more oppressive than teachers and administrators (teens)--and all of the above as trying to tell them what to do without telling them why they need to do it, which immediately makes their orders suspect and something to be rebelled against.
And sometimes, they're all correct.
As long as that antagonism exists, teachers and administrators will seek to put up barriers against parents (and each other), parents will perceive teachers as unreachable, and students will reinforce those attitudes to the extent it serves their own goals.
Divided we stand. Wait. That isn't right, is it?
"Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics."
Wonder how he worked that one out? Did he use some kind of equation? He'll be telling me next that schools are failing because almost 50% of students fail to reach the national average standard (which has been used in a newspaper headline).
In the UK a few years ago in the UK a minor celebrity appeared on a charity quiz show and was hounded in the press when she got a question about shakespeare wrong, and afterwards said shakespeare was "boring". She was called stupid despite having a maths degree from Cambridge and actually being famous for actually doing maths live(ish) on TV.
The double standard is that poor maths and science skills are things that people actually BOAST about. Imaging a Maths professor saying he couldn't read...
The article actually makes some good points about things like "machine shop maths", but that doesn't stand alone. It's part of the bigger picture which either enables or explains the practical maths. The problem isn't the subject but the teaching. When I talk to my four year old about why his robot goes faster than mine ("Daddy's robot has little wheels!") there's a foundation for all sorts of algebra that's going to be meaningful to him when he gets to it.
We use maths all the time, and the replies that say they did higher maths but don't use it probably don't realise how much of the basic/middle maths they use every day. Maths isn't always written down on paper - its a tool for unlocking the world.
You triggered a memory of a math teacher I had in high school (many years ago). He was working on an English degree to go with his math degree. He said something about English majors and math majors usually not overlapping and wanting to be able to do both.
Also, regarding people boasting about week math/science skills, I wonder if it's boasting or an attempt to make themselves feel better because they can't do it. "Well, if I can't do it, it isn't worth doing." (Perhaps a not entirely conscious attempt--a knee jerk reaction to preserve self-esteem.)