Material to discuss is here. (A NYT Opinion Page)
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.
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.
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.
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…”
It’s also necessary for people to earn the standard of living they think they deserve in the future.
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…”
You stole my thunder. Well said.
The problem is not Algebra. Failure to pass Algebra, poorly taught or otherwise, is the symptom of a far greater cultural problem.
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.
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.
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.
“kids seem to not be doing so well in school…lets get rid of school”
That is essentially what I get from this article.
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.
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.
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:
The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.
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.
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
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.
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.
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
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.