Is Algebra Necessary?
 

Material to discuss is here. (A NYT Opinion Page)

Re: Is Algebra Necessary?
 

Yes, Algebra is necessary.

No, higher mathematics should not be required for all courses of study.

I honestly don't know what I'd do if I didn't know algebra, although I am in engineering and embedded controls, which probably biases me heavily in my use of mathematics.

That said, algebra also has applications in finance, which is (or should be) important to everyone.

Re: Is Algebra Necessary?
 

I find it difficult to say this... but I actually understand the point he's trying to make.

To help illustrate his point, a personal story. Just a couple of weeks ago, I went back home for a long weekend (one of my cousins was getting married), and while there I went to a "trivia night" with my sister and some of her friends. They're all working on PhD's in psychology, so needless to say, they're pretty smart people. However, none of them could answer a fairly simple math/physics problem that night: "What is the name of the curve that an arrow, shot into the air takes, discounting friction?" When I told them the answer, they took my word for it and wrote it down... but they asked me if I was sure about a half dozen times before we turned in the paper.

The work incredibly smart people like that do every day doesn't require any more math then they would need to balance a check book. It can be hard for engineers and other STEM related fields to remember that. After all, we use equations and force diagrams all the time in robotics.

Re: Is Algebra Necessary?
 

I tutored math for 2 years between Algebra 1 and Geometry.

One problem I've found is that most kids just see xyxyzy112+x^2(q), or a jumble of meaningless characters. Algebra is something that many students conceptualize as having no definite form, process, or structure.

A lot of students I have tutored also fail to take a broader look at equations. It seems like some students treat it as "step one, step two, step hundred threety three, answer here, repeat 50 times." I feel, though, as if most equations are generalized to begin with and the process of solving such equations means converting that generalization into a more specific form which can be used to solve the problem.

The article talks about how algebra is not necessary for most people because most people simply do not have jobs which require algebra, such as STEM jobs. This is FIRST, of course, so we know what to say about that.

I can't think of anything more to say.

Re: Is Algebra Necessary?
 

Is Algebra Necessary? If it's taught poorly, as it is by most teachers, and beaten down into a series of repetitive drills that rely solely on short term memory, then no it's not necessary. However, if it's taught properly, and used as a vehicle towards higher level problem solving and analysis, then yes, it's absolutely necessary. The skills learned when algebra is taught properly come into play every day. One of my best math teachers always used to say "I'm not teaching you math, I'm teaching you how to think. Hopefully that'll be useful to you someday..."

Re: Is Algebra Necessary?
 

It's also necessary for people to earn the standard of living they think they deserve in the future.

Re: Is Algebra Necessary?
 

You stole my thunder. Well said.

Re: Is Algebra Necessary?
 

The problem is not Algebra. Failure to pass Algebra, poorly taught or otherwise, is the symptom of a far greater cultural problem.

Re: Is Algebra Necessary?
 

What about the other side of the coin? If somebody never plans to go into a career of writing books, why should lengthy essays be required? If someone doesn't plan to become a historian, why should European History classes be taught?

It doesn't make sense. It's all part of becoming a well-rounded individual academically.

Re: Is Algebra Necessary?
 

Because both of those skills apply to your ability to function as a member of society and citizen. Algebra, when viewed as a discrete skill, does not seem to be something that a typical citizen must master.

Re: Is Algebra Necessary?
 

I could go the rest of my life and have European History not be relevant at all, but I still took it. If someone is really contemplating taking Algebra out of the curriculum, the bar is being set far too low.

Re: Is Algebra Necessary?
 

"kids seem to not be doing so well in school....lets get rid of school"

That is essentially what I get from this article.

Re: Is Algebra Necessary?
 

Then I suspect you're not paying enough attention to both national and international politics.

That's unfortunate, because that's not at all what the article was saying.

Re: Is Algebra Necessary?
 

Every high school student has whined (me included), "When will we ever need to use this?" and the answer is usually somewhere, but occluded by the piles of worksheets and textbooks which give no clue to their contents' necessity. If every student got to see math and physics being used at a UL lab or a NASA research center, and get introductory training in those fields, we could have a different story. Of course, that is impractical to do on a national scale, so teachers need to spend less time on problem number X, and more time on lab investigations and projects. Even better would be if they dropped the age-old experiments by minds long gone, and focused on something students can relate to, something making news today. I am fortunate enough to be in a school with a fantastic STEM program that also ties in to our robotics team (our lead mentor is the STEM Technology teacher), but other schools are less lucky.

I've always found math to be rewarding and pushed myself ahead in courses, but I could always see why others with less interest in the subject didn't do the same.

Think about this analogy: Do people buy cars because they love the engineering that went into them and the mechanics that make them work? Maybe you guys do, but most people don't. People learn how to use a car as a tool, and then buy cars because of what they can do for you. Mathematics (and really any school course) needs to be pitched the same way--This is how you can use math, and it will give you a fulfilling career in return. If they like it, they'll figure out the mechanics behind it too.

Re: Is Algebra Necessary?
 

I work for the U.S. Government in an area that deals quite a bit with foreign politics. I'd say I'd pay more than enough attention to both national and international politics.

The article is a cry for help because teachers fail to find a way to show how mathematics has practical real-life use, which is tragic because it closes the door to many opportunities for students who have unrealized passion for a technological area. A student may not grasp Algebra completely, but they may later find love for geometry or calculus. I had a similar issue with linear algebra in college. I excelled in differential equations, but some of the concepts in linear algebra can be abstract. But it was just the opposite situation for other students. Some found linear algebra to be a breeze, but struggled with calculus.

This is a direct quote from the article:
He wants to take it out to make high school easier. That's the direction he wants to go. It's all about making graduation rates higher. But graduation rates mean absolutely nothing if you learned absolutely nothing.

Re: Is Algebra Necessary?
 

Yes, it is necessary. It is my opinion that everyone should have some basic understanding of the math and physics that defines the world around them. It is my hope that natural curiosity would drive people to seek out this understanding. Algebra is of course (imho) a big part of this understanding.

Building along the same line that Karthik started: I recommend everyone read "A Mathematician's Lament" by Paul Lockhart (sometimes just referred to as Lockhart's Lament).

http://www.maa.org/devlin/LockhartsLament.pdf

-John

Re: Is Algebra Necessary?
 

There is a huge difference between mindless memorization of dates, names and learning about the public opinions, socio-economic conditions, and other factors that lead to things like World War II happening.

History (like other subjects) should be about teaching people how to analyze events and conditions to identify patterns and draw conclusions. A lot of people were taught that communism is bad, but few can identify the factors that lead to communism starting in the first place.

If more people were taught these critical thinking skills, then they would be better equipped to make decisions in every day life.

Re: Is Algebra Necessary?
 

I don't mean to be antagonistic, but how discrete is discrete? Analyzing the three caskets in The Merchant of Venice? Writing a 5-paragraph character sketch? Do I really need to know the Treaty of Utrecht to understand the importance of its modern ramifications? ...By the way, I don't think I was taught the latter any more than the applications of a character sketch. Is "teaching" algebra, the long, confusing, repetitive jumble of letters that has no impact on my future really that different from teaching, say, Wuthering Heights (the long, confusing, repetitive jumble of letters that has no impact on my future*)? [EDIT: What Arthur said.]

This article seems to set up a false dilemma. Algebra's not the problem, the algebra curriculum is. Basic algebraic concepts are critical to quantitative literacy in society, as the article itself explains. Karthik nailed it, but I wanted to point out an additional line that struck me as...bizarre.

I fully concur that high-tech knowledge is needed to sustain an advanced industrial economy. But we’re deluding ourselves if we believe the solution is largely academic.

What does "academic" mean? Webster's first** definition is relating to a school/higher education. Under that definition--why not? Especially when the preceding example is about a community college. Shouldn't academics be giving us the knowledge we need to sustain our society?


*I actually didn't mind this book.
**Webster's seventh is "having no practical or useful significance". Seems like a good example of the root problem.

Re: Is Algebra Necessary?
 

I really loved history in high school as well as biology, math (geometry, algebra, calc), and especially physics all because it was taught by pretty great teachers. It taught me to break down a problem, analyze root causes, and evaluate what to do next or interpret data (even in our AP history classes). AP bio was awesome when the teacher taught us how to diagnose simple diseases or predict outcomes when, let's say, a few proteins are missing. AP history classes I had really really made me learn how to analyze a situation and find a root cause/event. Heck, even AP English classes I had made me analyze (maybe over analyze) why a wall in a character's room was yellow. I loved it all though.

Maybe more kids in high school need to take AP classes or non-AP classes need to emulate the type of thinking and skills AP classes/instructors teach? These classes were more fun than my regular/honors classes.

Art's got it right, so does Karthik. You need to be taught well and without just creating a memorized pattern for a student to follow in order to solve a problem. (obviously this isn't always true in math/physics/chem/bio)

/end babbling +$0.02

Re: Is Algebra Necessary?
 

We provide "crutches" for the lack of algebra, when knowing it would save paper and money. Tax booklets have 40+ pages of tables with each income level in $50 increments printed with the corresponding tax. If the average American could do the simple piecewise function calculation:

T(x) = 0.15x for x<= 40,000 (or whatever the cutoff income is for the 15% rate)
or = 6000 + 0.28(x - 40000) for x > 40,000 (assuming 28% tax on excess earnings

it would take only an inch of paper on one page, not 40+ pages.

Lack of knowledge of compound interest is a great contributor to the mortgage crisis. A friend from China (an English major) told me "Most of us have our apartments (the equivalent of houses) fully paid off because we know the effects of the formula A = Pe^rt." We can blame our legislators and bankers, but each person is responsible for managing his/her own finances and making informed/prudent choices is something that people in many other countries seem do better than we do. In the county where I live, over 1/3 of homes owned in 2006 have foreclosed, and over 50% of the remaining currently owned homes are "underwater" (with less equity than debt). I can't help thinking that while a knowledge of algebra might not be "necessary", it could potentially save a lot of grief.

As a jr. college math instructor, I have to admit that I'm not crazy about the appeal to math as an art, with self-discovery as a necessity.

In robotics, not many students can invent the (mecanum) wheel, but many more are capable of copying and using the designs of others. Strict copying (similar to memorization and application of formulas) allows students to practice until understanding kicks in, and allows them to reach much higher levels (and generate more enthusiasm) than self-discovery would in the same timeframe. Shortly after the Vex platform was released, I watched students spend months building robots less functional than the Squarebot. That's where self-discovery without copying gets you (especially if you have solid but not stellar talents), and I would never want to return to that.

Exceptionally talented people seem to pick up the concepts and use them for their own purpose, no matter how badly a subject is taught. They're also the ones who see patterns and beauty in discovery. However, I have a child who struggles with math, and for her, "drill and kill" math has been very effective. Like washing dishes, she may find it boring, but with hard work, she can do it,and there's pleasure in doing something well, even if you didn't discover it yourself.

Motivating students to do the boring work helps, and connecting math to previously discovered concrete examples (rather than to what they can imagine/discover) seems to work well with my lower level students. For example, whenever students ask "Why do we have to know about singularities?", the Tacoma-Narrows Bridge, coupled with a discussion of resonance caused by undefined frequencies gets their attention. I don't expect them to discover the formulas on their own. And I don't see being on a time-table to teach a broad-based curriculum as necessarily bad.

Re: Is Algebra Necessary?
 

Both quoted for truth. Sad but absolutely true.

Re: Is Algebra Necessary?
 

I will preface this by acknowledging that I am heavily biased on this topic, but I see this bias as justified.

I think the writier here falls into the trap of being a sheep (if you saw Karthik's presentation from St. Louis then you know what I'm talking about). His best evidence in the entire essay are rates of failure and dropout and educators quoted as saying algebra is the problem. Where the mistake comes in is immediately assuming that taking algebra out of the equation solves the problem.

This would be akin to if you asked someone from a robotics team why they were losing 90% of their matches and they said to you "because of our ball collector". Is it then the right move to take away your ball collector entirely? Will that make you win? Certainly not, and likewise removing algebra will not better educate our society! As a student, I would be insulted that people consider lowering standards because people are supposedly not capable. Maybe I'm failing to see something because math has always interested me and come easy to me, but I strongly feel close to 100% of people are inherently capable of passing basic algebra.

The writer needs to take a closer look at what the root cause of the issue is. Is it, as he suggests, a structural problem where we are trying to educate people in a subject that they are incapable of learning and it is a waste of their time and effort? Is it ineffective teaching in mathematics (and furthermore, is this a developmental problem early on or a problem isolated to MS, HS, and early college?)? Is poor parenting the culprit? There are too many parents I have seen who are willing to blame anything but themselves or their child for failure; the problem MUST be that someone else messed something up. Is the problem with the students? Are they actually incapable or are they just unmotivated and don't want to work for their success? In my opinion, every case is different and all of these problems contribute to each failure in some way, except for the first problem which this writer suggests.

Well said. I loved the way my AP classes always challenged us to understand the "why"s and "how"s behind history, science, and mathematics. I really appreciated the teachers who went the extra mile to get us to THINK and ASK QUESTIONS. It's really given me the skills I've needed now in college, skills which many of my classmates are still struggling to learn because the expectations were never that high for them.

I still keep in touch with my favorite teachers and get together from time to time. This past week I met with my AP biology teacher and when I asked about how the next school year looked, she expressed frustration that the college board was removing the most challenging parts of the AP bio and AP US history curriculums. Specifically they are removing cellular respiration and the cell cycle from the cirriculum. The goal is to get more people to take AP courses, which I agree is a good objective, but to do so by dumbing down the expectations is ruining what made AP classes worthwhile and challenging for many of us in the first place!

"Far better it is to dare mighty things, to win glorious triumphs even though checkered by failure, than to rank with those poor spirits who neither enjoy nor suffer much because they live in the gray twilight that knows neither victory nor defeat."
-Theodore Roosevelt

Re: Is Algebra Necessary?
 

I was thinking about this very issue about a week ago. I saw some sad statistic about high school math skills and it got me thinking about what the problem is.

One thing that I've thought about recently is: are the right things being tought in elementary school? It seems that the cirriculum is very antiquated.

One example: long division. Is this really a necessary skill for people in modern times? (See sidebar below) Part of the problem with teaching long division (in my opinion) is the law of primacy kicks in and screws people up once they get to fractions. You'd be shocked at how many high school students (as well as people beyond high school) that I talk to that still don't understand that a fraction means division. After elementary school, the concept of ratio, proportion, and fractions account for 99%+ of all division applications, yet people are screwed by primacy by learning long division first. Just watch the youtube video of the woman trying to explain miles per hour as a great example.

It seems that a lot of the curriculum is antiquated and the early part of math education could be replaced to better prepare students for algebra and problem solving. I'm not yet sure what the solution is.


Sidebar: There is only one application in the modern world for long division that I am aware of: checksum computation (as a part of polynomial division). In this case, shouldn't it be tought in classes about checksums or in an algebra class? Once you get to that age and level of math, you can learn long division in a matter of minutes. Is it really necessary that elementary students spend cumulative months on learning it? It seems the time would be better spent elsewhere. Not to mention that primacy would then ingrain in people's heads that division = fraction and long division is a special case (instead of the other way around).

Re: Is Algebra Necessary?
 

There are many interesting facets to this problem.

1. Our educational system was never designed to do what we expect of it now. In the early days of public education, the goal was to each basic reading and arithmetic skills to as many people as possible to make them adequate workers. At that time, it was expected than about 20% would complete elementary and secondary school with the rest dropping out to join the work force. Only about 2% were ever expected to finish four years of college, mostly to become ministers, lawyers, and doctors. We have far exceeded these expectations with about 80% graduating high school and 20% finishing a Bachelors degree. Algebra has always been part of the high school and college curriculum, but we have cut out Greek and Latin, which were once considered necessary. It appears that Algebra has passed the test of time as a valuable subject for all students.

2. When you look closely at nearly every subject, the argument can be made that we really don't need to teach it because it is difficult, boring, and never needed in life. History? Just a bunch of facts about dead guys. Philosophy? Well, my ideas are just as good as anything the philosophers of the ages have said. Literature? Hay, I read what I want. Music Appreciation? If I want to listen to music, I'll use my iPod; besides, most of what they talk about is stuff written by more dead guys. So with the possible exception of Reading, there really isn't much that can't be thrown out.

But I'm of the opinion that a core curriculum, taught to everyone, is a necessary part of our cultural identity--a common knowledge base we all draw on, sometimes subconsciously, in our everyday activities. Look at the cartoons in the New Yorker magazine, for instance. Nearly all require a vast common cultural knowledge base in order to understand. Likewise with things as mundane as T.V. commercials. Take away to core cultural knowledge and you become unable to function effectively in society.

3. Algebra, like all technical subjects has moved more and more from the practical to the theoretical in the past two decades. Personally, I don't like this move since it takes the recognition of the reason for learning away. If I have MY problem to solve, I'm much more interested in learning the theory. Otherwise, the phrase, "Why do we have to learn this, I'm never going to use it," becomes very true. But it is also true that if you don't learn it, you for sure will never use it. Math teachers at one of the school where I have mentored robotics say that the robotics students pick up math concepts quicker than their cohorts who are not in robotics because the robotics students have real world experience to tie the new math concepts to. Ratios for instance, confuse the normal students, while the robotics students see the concept as the theoretical construct they have used with gears and chain sprockets. We need more practical applications to drive the teaching of the theory. If people saw how algebra could help them, they world be more motivated to learn it.

4. Algebra is taught badly in many if not most schools. I've had friends say they were good at language, but not at Algebra. In reality, both math and language are functions of the left side of the brain, which is rational, sequential, linear, and organized. Algebra at its most basic level is the language of mathematics. When people tell me they were good at language and not algebra, I tell them that Algebra is a foreign language with facts and rules that they never learned. To illustrate this, I'll usually say something like this, "I'm thinking of a number. If you multiply my number by three and add four, you get 31. What number am I thinking of?" Most immediately reply with the correct answer, yet freeze up if I present them with the same statement in equation form (3x +4 = 31). Somehow a teacher never conveyed to them the shorthand language nature of Algebra. At the heart of all algebraic statements is the equal sign which should always be understood as "is the same as". If this isn't taught first, people will have trouble with Algebra for ever.

5. In actuality, most students start to fall behind in math with the introduction of fractions, not the introduction of Algebra. By the time many students get to Algebra, they are already hopelessly lost.

6. Should we keep Algebra? Probably so. It is and always has been part of what we consider knowledge common to all educated citizens. Sure, it's a gatekeeper to that Bachelors degree, but I really don't have much of a problem with that. If you want to be an Art Historian but can't pass Algebra does that mean you won't have a degree? Maybe. Does it keep you from taking art history classes to your heart's content? Probably not. Does it mean you won't be a fully educated person in society? Yep, afraid so. Would it motivate you to work harder in Algebra? Probably so, if you want that degree so you can be recognized as an educated citizen.

Well, enough of my ramblings. You might not agree with anything I've put on the table, but I've been thinking about this for at least 45 years and am now entering my curmudgeonly years. I vote to keep Algebra.

Dr. Bob

Chairman's Award is not about building the robot. Every team builds a robot.

Re: Is Algebra Necessary?
 

To graduate with a Michigan high school diploma, each student must have 4 credits of math, which includes:

1 full credit of Algebra
1 full credit of Geometry
1 full credit of Algebra II
and a math course (can be applied math, financial literacy, accounting, computer science, business related, etc.) as a 12th grader

Michigan defines a full credit as a learning experience which is a school year. It also allows for the math to be delivered in a Career Tech Education environment. Algebra II can be sequenced to be covered in two years, instead of 1.

Yes, this is tough - but it does not have to be delivered at "sit and get" in columns and rows of desks - but don't get me started on that!

Julia

Re: Is Algebra Necessary?
 

In my mind the difference between history/language and algebra (BOTH are important and should be taught, no matter how much I hate writing) is that algebra (and higher mathematics) literally defines the universe we live in and is the definition of many problems we come across in daily life. History and language are facets of our culture.

Re: Is Algebra Necessary?
 

Then I'm struggling to see how you could possibly think European history is not important. See artdutra04's post.

You're taking an out of context quote from the article and attempting to use it to state that's what the article's premise is. The article is not arguing to make high school easier, but rather to change what we're teaching to be more applicable to everyday life. A large portion of the third page discusses possible alternatives to algebra to help make it more engaging and applicable to students with varying passions.

Let me make this clear, I don't agree with the article. I don't want algebra removed from our essential curriculum. I just don't want the article's viewpoints being misrepresented and the debate coming down to gut reactions rather than informed conversation.

I don't disagree with the general premise laid out by you, Arthur, Karthik, and others about the ability to reason and critical thinking skills that are cultivated by algebra. In fact, I strongly agree. But what I meant by "discrete skill" was that algebra as a tool isn't particularly useful to a large portion of the population (though ManicMechanic makes a strong counterpoint to this). You don't need algebra to balance your checkbook or figure out your monthly finances. Most people are probably never going to balance an equation outside of an academic setting.

The problem, in my eyes, is not algebra or even how algebra is being taught. The critical reasoning and logic skills that are important behind algebra and that students should take away from algebra (even if they don't grasp algebra as a tool) don't start in high school. The development of these skills starts much earlier in life. By the time a student is in algebra is often far too late in their development to try and fix the issue.

Re: Is Algebra Necessary?
 

I just graduated from Michigan State University with a degree in Journalism. In school/the start of my professional career, there was no need to really utilize algebra or calculus. I took no math credits while at MSU because I had credit from AP classes, so I don't have a very good idea of what math classes are like in the college level.

In one of my entry level Journalism classes I was able to earn extra credit because I understood how a logarithmic scale worked and could explain it in class (we were discussing the Richter Scale). I have a friend who is currently working as a page and graphic designer for a major magazine who took several tries to pass college algebra.

I live with one student who is getting a degree in engineering and another getting a degree in horticulture. About six months ago we had a discussion about the Republican primary process, neither one of them could name two people who were running for the nomination (this took place when Herman Cain, Ron Paul, Mitt Romney, Michele Bachmann, Rick Santorum, John Huntsman, and Rick Perry were all still in the race). I found this just as frightening as people not able to do algebra.

Every single person needs a basic understanding of political science, math, biology, physics, and writing to be able to function in society. Having baselines for understanding across all fields can improve our communication and can make it easier for us to relate to each other. The US is become more sharply divided along economic, educational, religious and political lines maybe figuring out a common level of education could help us solve the problem.

Re: Is Algebra Necessary?
 

Because not once has anyone likened anything in a briefing to the Habsburg rein of Austria. Also, I used that in the sense that it has no real-life use outside of high school for most people.

I realize that isn't the full premise of the article (though a generous portion of the article is precisely that, complaining that math is too hard). However, his whole argument is based on the fact that students aren't doing well in Math. If students were able to grasp algebra easily, this article would have never been written in the first place. The author is a prime example of someone who advocates the "dumbing down" of America just like No Child Left Behind. Algebra is something that many middle schoolers (including myself) took. It's not too much to ask of someone in high school to be able to take it either. High school today is no longer about educating students, but giving them a degree to get them out of the door....a McDiploma.

Re: Is Algebra Necessary?
 

I agree with you. My question is, how often are the discrete skills we teach useful to a large portion of the population? Reading (at tax form and newspaper level) and addition (arithmetic), sure. But manual matrix row reduction and analyzing causes of corruption in the Janissary corps? The school algebra curriculum is made up of a lot of discrete sub-skills that themselves bare no real impact on daily life. The same way basically every other subject is. I can certainly expound on uses for and abilities cultivated by these*, but to argue that algebraic computations are unique in their uselessness seems inaccurate to me.


This is not to say it mightn't warrant additional attention, if only due to its relatively spectacular corruption from critical thinking skills and/or its supreme difficulty for many students. I'm not sure that this is actually true, but if it is, algebra reform (or scrapping and re-doing, as Lockhart would prefer) may well deserve priority*. It's the argument that the subject itself is any more or less valuable--in discrete skill form or otherwise--than any other school subject which I dispute.


*EDIT: In that way, I partially disagree with Michael Hill. I, too, see a level of disingenuousness in focusing on algebra as "not necessary" while really arguing in large part that it's hard. These are two entirely different issues. However, if one were looking for a place to start productive reform, one might reasonably start with the subject of most difficulty to the most students. (I haven't perused the statistics in the Hacker article nor read contrary arguments, so I haven't yet judged if algebra is actually that subject.) I'd venture that this is Hacker's actual argument here--perhaps without knowing it.

Re: Is Algebra Necessary?
 

I find the whole "look at this aspect of the course that I haven't used" argument very disingenuous. Most people do (or, in reality, should) use the knowledge learned in history classes in their political behavior. Even if certain pieces of information never come to fruitition, others (and more importantly themes and historical trends) most certainly will.

A large portion of the article is indeed spent on the fact that students aren't passing algebra. That portion of the article served to demonstrate that a problem exists. Unless you're advocating that high failure rates are the desired outcome, I don't see how you can take offense to that. The solution to that problem, however, was not to "dumb down" education or give out "McDiplomas," but rather to adapt our educational system. The article is not advocating easier classes, simply different ones. If anything, it's suggesting the opposite of "McDiplomas," as the author is calling for more specialized math courses that apply more directly to different career fields.

Re: Is Algebra Necessary?
 

In that case, you should definitely talk to them about flutter. 747 Wind Tunnel Flutter Test

It's been really interesting reading everyone's responses. I went to a magnet school, and for us Calculus AB was a graduation requirement. I thought that was pretty awesome, even my friends who said they were "bad at math" still got mostly 4s and above on the AP.

Spot on! I think Linear Algebra was probably the coolest class I took even if I liked it the least. I always get excited when something I thought was unrelated pops up in a new place, and Linear Algebra has this tendency to show up just about everywhere. But that sort of natural curiosity means that I would be okay with really any class so long as it wasn't pointless.*

*I can't think of a pointless class I took with a good teacher...

Re: Is Algebra Necessary?
 

Student: This has no application. I don't get it. How can I use this? I don't understand it. It has no meaning to life.

Teacher: Well, this is how it's used every day. And here. And here.

Student: But those are story problems. I don't like story problems.

... and so the cycle continues.

Re: Is Algebra Necessary?
 

One thing that I don't think was brought up earlier is what happens if Algebra is no longer made mandatory in school. Many of my peers are lazy and would cut corners in any way possible. If given the option to take a moderate-workload Algebra class or to take the relatively homework free class Art 1, many would choose Art 1.

As a result, they would not even try to take Algebra. And who knows? Maybe some of them really will not benefit from Algebra and skipping it was a great choice, but for others who do no know what they want to study later on, the skipped Algebra course also narrows their options further along the road(either not do something related to math, or confront Algebra years later).

In summary: many people are lazy, if given the option to skip Algebra for an easier course they probably will. This skipping will narrow their study options later on.

Re: Is Algebra Necessary?
 

One of my favorite quotes that applies to some of the discussion here:

"Culture is what's left over after you've forgotten the details of what you've been taught."

EDIT: Another quote applies also: "The purpose of computation is insight, not numbers."

Re: Is Algebra Necessary?
 

Isn't that exactly the argument for the importance of algebra? I really don't see the difference you're pointing at.

Re: Is Algebra Necessary?
 

"I never used the quadratic equation" vs. "I never used algebra."

Re: Is Algebra Necessary?
 

huh. ok. I see it more as "I never use American literature or algebra" versus "I never employ the themes and trends I learned in American literature or algebra" first statement true for both, second statement false for both. As far as actual information once told to me by a teacher that I then called upon and executed on in my daily life, algebra beats all my history and literature courses [distinguished from writing and foriegn language] combined by an underwhelming 2 to 0 (but it wasn't polynomial). As far as trends, understandings and thinking skills I learned in them being useful day-to-day, they're about tied approaching infinity. Do you not find yourself using the trends and themes from algebra in your daily life? Maybe I just think weirdly. Never mind then.

Re: Is Algebra Necessary?
 

Most people DON'T use algebra, but most people COULD, and if they did, it would make their lives better. I teach lower-level math (prealgebra through statistics), and I tell my students, "Not every formula or technique in this course will be used by everyone, but every formula could be used by someone, and you never know when the person who needs that formula could be you." I've always been able to think of a plausible useful real-life scenario for every formula I teach.

For example, one of the nastiest formulas from statistics is for the standard deviation of the difference of difference of means for 2 populations -- a 6-layered complex fraction. When would you ever use that? Well, I came across an article stating that some cholesterol drugs may be far less effective in women than in men, and that it wasn't certain whether more tests were needed for the women (but not the men). Two populations: men and women. Difference of means: cholesterol level before and after medication. Difference of difference of means: men's improvement is different from women's improvement. How to evaluate whether more studies needed to verify hypothesis: evaluate standard deviation.

One of my neatest classroom experiences was a student who, after hearing multiple tie-ins to formulas said, "I bet you could never find an application for the problem 1/(1+(1/(1+(1/1+1)))), our homework problem." As I thought about it, this formula is tied to the Fibonnaci sequence, whose real-life application has to do with the fractions that ensue: 1/2, 2/3, 3/5, 5/8. As you traverse these fractional increments around a circle and draw rays to the edge of the circle, this mimics a bird's eye view of a corn plant that shoots out leaves at these fractional increments, for maximum sun exposure. I suggested that this pattern could be used to optimize water coverage for certain patterns in the design of a sprinkler system. The student came the next day with a box of apricots -- his family is in the farming business -- they grow corn and design sprinkler systems, and this was something they could use.

It's our job as "math literates" to see these connections and help the people around us to use these connections to improve their lives.

Re: Is Algebra Necessary?
 

I found this NPR story this morning quite applicable to the conversation at hand.

http://www.npr.org/2012/07/31/157637...-bed-with-math

One of the points they make is that society accepts when an educated person says "I'm not very good at math" but would be appalled if and educated person said "I'm not very good at reading"

Re: Is Algebra Necessary?
 

The problem with algebra is that a large plurality of people today seriously don't know how much they can actually use it to improve their lives. Ignoring the time-value of money*, simple algebra can be used in many real life problems.

For example, do I buy a more expensive house closer to my job that lower commuting costs, or do I buy a cheaper house that is farther away but has a significantly longer and more expensive commute? At the simplest level, these are two linear y=mx+b equations that may or may not intersect.

All too often people fail to grasp the concept that things in life have both initial and ongoing costs/benefits (again, y=mx+b), and only balk at or support various things based upon their initial cost and ignore the annual costs/benefits. It's even worse when this mentality is used in the voting booth for public/government proposals/projects. "$X is too much money for a new highway interchange/light rail line/rebuild the schools/support robotics teams/etc" and ignore the long term costs/benefits ("it will collectively save drivers $50m per year and have a cost/benefit ratio well into the positive").

One of the greatest examples of this is the Clean Air Act; while this law annually costs the federal government about $50 billion to run/enforce, the benefits to the people and the economy from having cleaner air end up totaling over $1.3 trillion every year. In other words, the law has an insanely huge return on investment (about 26:1!!) that not even Berkshire Hathaway can match.

At the same time, most people also fail to grasp p=e^rt, and then they get screwed over on credit card debt, home mortgages, 401(k) and investment accounts, and anything else that involves interest. Many see the value of things rise but fail to account for inflation; for example if something is worth $100 now but will be worth $500 decades in the future, you lost value if the inflation-adjusted price ended up being $600.

Or if people had even the most basic understanding of statistics they would likely be more hesitant to gamble. Or at the very least, they would accept the cost of occasionally gambling as the price of a few hours entertainment that may have a small chance of ending up with more money than they started.

This list can go on and on and on.


* Which is never a good idea if you want accurate projections, but even simple analysis that has an interest rate of 0% is better than nothing.

Re: Is Algebra Necessary?
 

Wow - thanks for posting the link to that paper. This paper has triggered a rant.

Trying to come up with a good way to teach math or science can be extremely frustrating, because in some ways we have both hands tied behind our backs. We are given a curriculum and told to teach it. Never mind that the curriculum misses the point and kills curiosity and creativity in favor of teaching certain procedures because they can be tested easily on exams, and because that's what will lead students to the next procedures in high school or college or whatever. It's frustrating to exist within a system of standards/curriculum/exams that constrain what we're able to do. I'm very interested in trying completely new ways of doing things, but I have a list of topics that have been deemed important, and I'm required to teach those things*. They're on the tests that I'm required to give. Some of them fall under the category of teaching notation without actually letting the students tackle a problem (see the linked article), and it's tough to salvage that type of curricular material with clever tweaks in the way you teach it. A new approach is required, and it is necessary to let go of some of the things that we deem essential. I think that's what the author of article in the OP's post is getting at. If you're not actually teaching people algebra, then you're not actually gaining anything by forcing them to take it. (Trust me, I personally enjoy and value algebra.)

*That said, I prioritize trying to teach well over following rules or doing exactly as I am told.

What I find really tiring is that teachers are constantly presented with requirements and standards and demands to measure student progress in new ways, but the experts always stop short of writing (or funding the writing of) a good curriculum for us to use as a resource. No, I don't want or need a step by step guide, but a list of great problems and investigations to use would be a nice start. You'd think this would be out there somewhere, but I certainly haven't found it. The idea seems to be that teachers are supposed to read the standards (which are full of concepts I completely agree with), and then concoct our own curricula to satisfy all of the standards. I think I could go on a pretty long rant about why this is impossible, but here's a medium length one: creating a curriculum is a very large and intricate puzzle; to do it right, you'd have to interweave all of the subjects in ways that reinforce each other and provide context for the others; you'd have to make sure each year builds on previous years; you'd have to make sure it's challenging for fast learners and accessible enough for your struggling learners to still make progress; you need to interweave a lot of "soft" (and more crucial) concepts with the so-called "content" learning, including inquiry/argument/critque (including doing them in social studies AND science AND language, etc). So... what's the master list of interesting and challenging problems that I should include in a chemistry class that will not only pique student's curiosity and creativity, not only get them the procedural skills that will allow them to survive a test from an outside entity, but also make up for the various deficiencies and bad attitudes they've collected from their previous education? I'm not saying it can't be done, but what I AM saying is that this isn't the type of problem that an enterprising teacher is going to successfully tackle over the summer as a summer project that I decided to try for shiggles. It's a large puzzle with a lot of constraints and moving parts, and I don't even have a great list of really interesting problems and investigations to start with as raw material.

If I have a point, it's this: the curriculum in math (and science) is way wrong, and we need to start over and write something that does a better job. The emphasis on specific content (such as stating electron configurations, or writing arcane geometry proofs) should be scaled back, and the emphasis on general thinking skills (like critiquing an argument or suggesting possible explanations for a surprising result) should be scaled up. Teachers shouldn't be expected to wave a magic wand and create this curriculum in our spare time... smart people, like the people who wrote the National Science Education Standards, should help in this effort instead of copping out and saying that districts are supposed to do it. If a brilliant curriculum is created, it should be a freely available resource, not a set of rigid requirements - let teachers use better stuff if they are clever enough to come up with it. And... more effort should be placed on this type of thing than is currently placed on creating and administering ever more standardized exams that will, predictably and inevitably, prove that our current system is still, in spite of doing the same thing repeatedly over many decades, not working as well as we would like.

Re: Is Algebra Necessary?
 

Remove algebra - truly an american answer to an american problem.

After remembering how awful I was at math in high school, thanks to this opinion piece, I remember the times when math was easy for me - and those where the days where we were taught not "how to solve the problem", but "how problems are solved". By this, I mean instead of the teacher putting an equation on the board and explaining how to solve it, the teacher explained how the symbols were utilized. It was like, solving a sudoku or Rush Hour puzzle. We were taught how the parts work, how the parts are solved - it was a series of systems that could be pulled from a shelf of knowledge and then worked with to get an answer. Instead of learning how to solve a problem, I learned how to solve a series of individual puzzles and their connections to a larger puzzle.

Maybe this is why I like designing board games so much - I love to work with systems as puzzles.

Re: Is Algebra Necessary?
 

I wasn't going to post, but I wanted to highlight something.

I'm surprised no one else has responded to your robot simile* because its kind of awesome. Because you don't get rid of your intake system, you just make it better. So we don't remove math education, we just make it better.

GUYS, THIS MAKES SO MUCH SENSE.**

How do we make math education better? At a practical level, not just conceptually? Most people are saying very broad things that are easy to say, but hard to apply.

Personally, the best teachers I had taught relationships in concepts to make sense of things (like the relationship between the y-value of f'(x) and the slope of f(x); that blew my mind in high school, physics formulas and derivatives made so much sense)(calculus is why I love math). What are concrete ways for teachers to teach?

*akin means "similar to" according to google. Similes use phrases in the range of "is like a". Just in case anyone cared. I needed to justify it for myself.
**Sometimes I just want to talk like we're all facebook friends, you know?

Re: Is Algebra Necessary?
 

That article was certainly illuminating. Although I never thought of it that way, the author certainly has a point. The fact that are students are falling behind compared to their international peers is hardly surprising considering how they waste their time studying needlessly abstract concepts. When will they ever need to solve for x or use a quadratic equation? We should abandon algebra in order to concentrate on real, concrete gains such as on test scores.

In fact, the view portrayed in the article can and should be applied to many other subjects. Most students will never play the clarinet or tuba outside school, and learning these useless skills takes up valuable time in the classroom. While they could be working to achieve real and positive gains on their SAT scores, they are spending time chasing the rather silly goal of learning to make music and express oneself.

On further consideration of the article, I realized that it could be applied to science as well. A car salesman or an advertising executive will not need to know what chromosomes are or the properties of gallium. They would benefit far more from working towards higher test scores, which would allow them to be admitted to the all important top college. Going to Princeton or Yale will take them much farther in their careers than attaining any meaningless "scientific" knowledge.

In fact, why pursue equally abstract and silly "educations" in the liberal arts or the humanities? Except for the all important Five Paragraph Essay, the mainstay of the SAT and several APs, learning literary analysis or many historical facts will not create more productive, higher testing citizens. These subjects should probably be eliminated as well.

I concluded that nearly all subjects should be eliminated from high schools in favor of concentrating on the holy trinity of tests: the SAT, the ACT, and the AP. Only these will allow the high school student to attain the true purpose of high school: the Ivy League School. Although some weak, liberal intellectuals may whine about the value of an "education" or "creativity," most schools are in fact already slowly coming around to this pragmatic view.

Re: Is Algebra Necessary?
 

From the article:
If only 5% of American entry level workers are proficient in algebra in 2022, I'm moving to Canada. Maybe only 5% of those jobs will require the knowledge what with the rise of technology, but I think it would be a considerably less innovative and and independent workforce, as Algebra and the math that comes after it really can help students learn how to think better.

Re: Is Algebra Necessary?
 

What does the populace of CD qualify as Algebra?

Its been my experience that while Mathematics instruction has changed due to testing mandates it also no longer covers all the concepts that an entry level Physics course expects.

One of my favorite quotes from a student from this past school year "...Physics is like Algebra if you take away all of the numbers."

The author of the article does have a point there is a large section of the workforce that does not "need" to have an understanding of "advanced" math.

Re: Is Algebra Necessary?
 

*This is my sole opinion, and I understand/respect all opposing opinions. This does not reflect the thoughts of Team 256 as a whole, but a majority of us (I asked around)*

*Start rant*


Wow, is this really happening? Are people actually debating over whether or not we need Algebra? I never thought it would come to the point where my education is being questioned.

Looking at the opposite side of the argument, it does make a lot of sense, though! Why teach kids skills they'll never use? If I'm a grocery bagger at a supermarket, I won't use the information I learned about the Great War. When I graduate college with my masters degree and take on my lifelong dream of digging ditches, will I use the Calculus I learned? Why even waste my time learning how to use correct grammar in my AP English class when my boss says I'll never have to write anything during my job as a janitor? We don't need all of this useless information if we're going to have really low standards for ourselves, strive to do very little and not try and accomplish things in our lives!

In case your haven't found out, that entire last paragraph was sarcasm. That's what I'm seeing from this article and those who agree with it. These people are seeing an obstacle in their lives, and instead of working hard to pass over it, like the good old American way, they want to eliminate it so they don't need to deal with it at the time, which just shows the laziness and low standards people want these days. We should be striving for the high level careers that change the world, and better humanity, not for a low-leveled job, and those world-changing careers use math. KrazyCarl's simile comparing a broken ball harvester mechanism to the kids failing Algebra was one of the best things I've heard on this topic. It's time to get the engineers in here, because these people are fixing the wrong problem. Students are failing. Is it because the subject is too hard and useless to them? Seeing as that there are still many students who pass Algebra can say it isn't too hard (My friend Carlos hated math, but understood Algebra and passed easily), and Algebra is used very much in the world today, so I'd say, No, Algebra itself is not the cause of the failing students. So taking away Algebra is just about the dumbest thing someone can try and do to fix the problem. I fail to comprehend why there are people in this world who are so blindingly unintelligent that they seem to think this is even a possible solution to anything. You might as well just take out the school system completely, because that's the exact same as taking out Algebra. If you don't want to do something because you don't think you'll ever use it, then you're doing things wrong. I am disappointed that this subject even came up.

You want kids to pass Algebra? Get a better curriculum! Teach so that kids will understand! Invest money in our school systems! Don't pass students who fail to reach the requirements! I can name over 20 things that we as a nation can do to fix this problem, and if I actually put some thought into it, I could probably think of 20 more. There are excellent ideas on this thread on how to raise the pass rate of Algebra, and I'm half tempted to send it over to the people who wrote this article.

You get what you celebrate, and in today's culture a positive attitude towards math and success in it isn't celebrated.

*End of rant*

Re: Is Algebra Necessary?
 

The rest of your post is reasonable, but this section is of note. I agree, but I must point out that "get a better curriculum" is unfortunately very hard without more money, and that doesn't seem to be coming. Again, failing students means keeping them in school for another year, costing more money. The government also seems to think that the embarrassment from being held back is not worth learning the material.

I expect some of those solutions would be related to spending, but the students themselves are much to blame. We need to change schooling at the elementary level, so students are not so averted to high school. Kids need to love school early, so they stick with it the rest of the way. That would take care of a large part of the problems with students failing classes, because General Education classes are not too hard to pass for those students who care, regardless of natural ability.

Re: Is Algebra Necessary?
 

Very true. I agree 100% with everything you've said. For those who fail Algebra at my school, a lot of the time it's the student's fault, and it's always students who have a negative attitude towards the class.

Re: Is Algebra Necessary?
 

Perhaps these students have a negative attitude because they believe that the knowledge is unnecessary, and have been taught by previous teachers that they are "bad at math."

(My own opinion is that any truly great student can succeed with any teacher, and any truly great teacher can succeed with any group of students. The problem is that both of these occurrences are quite rare.)

Re: Is Algebra Necessary?
 

I would argue that it is quite common for a good student to succeed in spite of poor teaching or poor curriculum. Kids with good parents can show up to school already interested and curious about everything, and that's half the battle. A lot of these kids are so good that you almost can't screw them up unless you try to.

The presence of a bunch of those kids probably causes some unwarranted complacency. "The system is working great for some people."
"Johnny works hard and does well - what's your problem?" etc.

Re: Is Algebra Necessary?
 

The easy way to fix 'No Child Left Behind'.

Just grade based on the ability to walk, talk and take orders.

See it's all fixed.

:ahh: < this smiley misplaced it's dentures.

BTW, I was not the model math student (several of my teachers were fond of gloating over that point). However, I oddly retain quite a bit more than many of my fellow students I still know and more importantly I know where to look if I can't remember a transform into the s-domain. I have these things and they have paper in them. Good for the retention of knowledge until the paper rots or the ink fades. We used to call them books and unlike media today you need to provide external light (I know archaic). Next I might suggest the use of holes in paper for programming. Wobbles away on my old man cane and when I was in school our robots went up hill both ways.

Here's a little point: A well learned individual is not the total of their ability to recall information like a teleprompter. A well learned individual knows themselves and how to collect and use the tool of knowledge.

Re: Is Algebra Necessary?
 

Your first point, I completely agree. Your second point, I agree, but there is an important caveat - "given an appropriate group size."

Being smart isn't necessarily knowing the answer to everything; being smart is knowing how to find the answer to everything. Rote memorization is a critical skill to have, and it's easily tested - in fact, I would argue that most standardized tests focus on memorization of facts. However, critical thinking, problem solving, understanding of processes, creativity, and being able to find material that isn't already between one's ears are arguably more important, but these aspects aren't commonly measured and evaluated. When rewards are evaluation- or merit-based, teachers are generally forced to teach toward memorization of facts, terms, and rules rather than investigate their use.

Re: Is Algebra Necessary?
 

First, I want to apologize for my previous incomprehensible post. Looking back at it, it's pretty confusing. Anyway...

I think this is what the author was getting at in the first place. Algebra is a wonderful skill to have, but if students are taught only "these are the steps to do something algebraic..." and don't gain any actual skills, algebra loses its importance and becomes just a family of rules to remember. At that point, it doesn't help most people to have even "learned" algebra (I wouldn't call it learning, because it is only memorization), because it doesn't apply to their daily lives.