Both quoted for truth. Sad but absolutely true.
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
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).
There are many interesting facets to this problem.
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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.
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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.
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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.
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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.
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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.
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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.
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
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.”
Isn’t that exactly the argument for the importance of algebra? I really don’t see the difference you’re pointing at.
“I never used the quadratic equation” vs. “I never used algebra.”
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.
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.
I found this NPR story this morning quite applicable to the conversation at hand.
http://www.npr.org/2012/07/31/157637444/n-j-mom-puts-kids-to-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”