Yes, I admit, the editorial at the New York Time entitled "Is Algebra Necessary?" pushes my buttons. Hacker makes some valid and relevant points, and I'll get back to that. However, the core of his argument is the ultimate in anti-intellectualism. What's worse, it's the kind of anti-intellectualism that you get from intellectuals, the sort of thing that sprouts from those on the math-ignorant side of the "two cultures" identified by C. P. Snow.

Andrew Hacker's argument against making algebra necessary for high school and college students is essentially: Math Is Hard. Having to do it gets in the way of people who could be amazing at other things, because they will drop out of high school because Math Is Hard. So, rather than stop them from achieving all that they might achieve, we should just remove algebra from the high school curriculum. He points out that failing math is one of the main reasons students leave school. Now, I might think that this is a reason to look at our educational culture, at how math is taught, at the fact that it is somehow deemed acceptable and indeed normal to find basic math impenetrable. But, if you're on the other side of the two cultures, evidently this means that we as a society should just give up on the general teaching of basic algebra. Evidently, it's OK that the elites who understand the simplest things about science become that much more separated from the general educated public, and that the generally educated public know that much less about them.

There's one particular part of the argument I want to highlight:

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” Even in jobs that rely on so-called STEM credentials — science, technology, engineering, math — considerable training occurs after hiring, including the kinds of computations that will be required.

So, because algebra isn't what's needed in jobs, we shouldn't be teaching it. This is absolutely the wrong way to think about a lot of education.

If you accept that argument, we need to reevaluate the entire high school curriculum, and the entire core curriculum of all colleges and universities. I think most people would agree that you need to be able to read and write in order to function in today's society. Do you really need to be able to interpret themes in literature, however? Honestly, is anything that you do in high school or college English classes really *necessary* in the workplace, any more than algebra is? The kind of reading and writing that most people *need* is something that students should already know by the time they're out of middle school. Likewise, history, biology, all the rest: everything that they study in high school is not going to be necessary for their jobs. And, really, if the purpose of high school and college is to train people to function like good little Betas and Gammas within our economic system, why is Andrew Hacker singling out algebra for attack? If we're going to dumb down the curriculum because we don't like that right now some people aren't mastering it, why don't we just dumb it down all the way?

The simple fact is that a college or university education is *not* job training. In recent decades, it's become conflated with job training, at least in North America, and this is too bad. A liberal arts education is all about expanding your mind, all about being able to think. It's not about gaining skills that you are then going to use in a job. Too many of us professors tend to not have any clue what somebody is supposed to do to earn a living after a liberal arts education other than go to graduate school (so that your liberal arts education *is* "training" for what you do next). That's because that was our own life trajectory, and it's what we know. Liberal arts education is to make people into good citizens, not into good workers. They are to acquaint you with the intellectual achievements of humankind. *That* is why we read the *Iliad*, why we watch a performance of *Hamlet*, why we learn about the history of ancient Greece, and, yes, why we study algebra. Because we want people to be educated so that they understand the intellectual achievements that have made our society what it is today, and that will drive our society in the future. We're training people to be *members of civilization*, not *employees*.

I will say that Hacker makes some good points. There are other kinds of quantitative reasoning, which too many of those coming into college and too many in our society completely don't grasp, that people should learn. A better understanding of basic statistics may at this point be more important to the citizen of a democracy than an understanding of algebra. So, yes, I would agree that we could and perhaps should de-emphasize algebra in favor of making time for statistical awareness, and perhaps in filling in the basic number sense that students failed to get out of elementary school. However, to me this is a bit of a red herring. Yes, we should always be evaluating what the subject matter of mathematical high school education is. But, right now, the problems are bigger than that. That so many people through high school without basic quantitative reasoning skills is *not* a reason to throw out algebra. We do, however, have to figure out why it is somewhere around fifth grade that individuals and society both get the "Math Is Hard" meme so firmly embedded. Why it becomes normal not to "get" math and indeed a little weird to actually understand and like those classes. Why it becomes OK to not like and not try at math and just do what's necessary to get by without actually learning anything. I strongly believe that there are serious problems with a lot of the math education that's done at the later elementary, middle school, and high school level. But that's not a reason to give up. We might as well point at various studies of how little so many people know about the state of the world to say that teaching geography and international history just isn't worth doing any more.

Perhaps the problem, or part of the problem, is that we *have* conflated vocational and liberal arts education. Anybody who is interested in a liberal arts education does not deserve a degree if they are completely ignorant of algebra, and any society that values liberal arts education cannot neglect algebra. However, perhaps not everybody *needs* such a liberal education. If we have the problem right now of too many people failing out, it may be that we're pushing them through the wrong kind of education. This does *not* mean that a liberal arts education needs to jettison those parts of it that are hard for people on the wrong side of C. P. Snow's divide!

Algebra is fundamental to nearly all of "higher math". Even if you want to do more than the most basic of things with statistics, you need to know some algebra. To give up on that would be right on par with the giving up on the teaching of history as anything other than memorizing the occasional date, and to give up on the teaching of English literature as anything other than being able to read a short document for simple surface content and to put together a simple declarative sentence. If you want people to be educated beyond elementary school and beyond "job training", then algebra is one of the intellectual foundations of our civilization that simply cannot be neglected.

Great perspective. I would further challenge Hacker's argument on the basis of option value - we don't actually know what career direction most students will take, and they often do not, either (even if they think they do). As a biologist, I was hammered with the "Math is Hard" doctrine regularly during my training, even at the collegiate and graduate levels. The expectation is that a student interested in biology will probably end up in mainstream cell biology, etc where mathematical manipulations are relatively rare (though statistical analysis is common). Fortunately, I ignored those lines of argumentation, and now I use algebraic manipulations every day (I ended up in biomechanics).

Yes, training for a specific job is fine, but it's not something you should spend four years and a whole lot of money doing, unless it's a REALLY special job. Given how much time and effort people put into college, they had damn well be getting something more than training for a job of their choice out of it. Most people will have multiple careers, and even if they just have one career, as you note that career may take a direction that hadn't been anticipated.

I've heard similar stories about neuroscientists... who avoided math, but nowadays there are parts of neuroscience that are extremely numerically intensive.

If you want to train for a specific job, go to a vocational school. College is not this and is not to be confused with this. It is about the broad training of a mind in many different facets of knowledge.

On my website http://www.fordham.edu/academics/programs_at_fordham_/mathematics_departme/what_math/index.asp

you will find an essay "What is Mathematics" that is very relevant here.

You wrote a good essay. Let me highlight a passage:

> Perhaps the problem, or part of the problem, is that we have conflated vocational and liberal arts education. Anybody who is interested in a liberal arts education does not deserve a degree if they are completely ignorant of algebra, and any society that values liberal arts education cannot neglect algebra.

This is indeed a terrible problem. As an experienced mathematics professor, I see this all the time, and can clearly see how this trend has grown over the last thirty years.

It may well be that we need to frankly acknowledge this (that education is not training) as a society, and understand that many people should be directed to post-secondary training, as opposed to college. This training should be called "training" or "technical school" or whatever, not "higher education" or college. Quite frankly, that's the way it was fifty years ago, except then the high schools provided enough training for most people.

"> Perhaps the problem, or part of the problem, is that we have conflated vocational and liberal arts education. Anybody who is interested in a liberal arts education does not deserve a degree if they are completely ignorant of algebra, and any society that values liberal arts education cannot neglect algebra."

I have worked as a professional artist as well as an environmental tech and in construction . Other than basic math I have never used algebra except in school. I have found that in fact algebra is nothing more than basic math written in a way meant to either confuse, or to be hypothetical. After all any variable is nothing more than a hypothetical number . AxB=C or AB or a thousand other things. It is empty, hypothetical. Even in higher forms it can be interpreted the same. Essentially they could ditch the concept and use real numbers and teach formulas instead which people would at least be able relate to and find useful.

Love your thoughtful and passionate response to the New York Times' opinion piece, "Is Algebra Necessary?"

As a science educator, the challenges AND motivations are very similar to those you outline-the goal for me is not students who can memorize chemistry facts and use algorithms to correctly solve equations used in chemistry. My goal (perhaps better called a vision at this point, not fully realized) is to help students develop the critical thinking skills and scientific literacy skills to fully participate as a citizen in the world whatever career path they follow.

I would like to suggest we could even search/replace "math" with "math and science" and your observations still hold:

"We do, however, have to figure out why it is somewhere around fifth grade that individuals and society both get the "Math (and science) Is Hard" meme so firmly embedded. Why it becomes normal not to "get" math (and science) and indeed a little weird to actually understand and like those classes. Why it becomes OK to not like and not try at math (and science) and just do what's necessary to get by without actually learning anything. I strongly believe that there are serious problems with a lot of the math (and science) education that's done at the later elementary, middle school, and high school level."

Do you see answers and solutions in the cognitive science of Daniel Willingham (critical thinking requires domain knowledge and practice) and the research of Carol Dweck (Growth Mindset=I thrive on challenge-I throw myself into difficult tasks-I am self-confident)? From your experience, how might these two ideas help eliminate the "success gap" in math and science that begins to widen for students in elementary school, certainly by middle school?

I am exploring the ways to practically implement their ideas, successfully, within the framework and time constraints of a broad NYS Regents Chemistry curriculum in an urban HS setting. I'd be very interested in hearing your ideas. Thank you.

I'm not familiar with Daniel Willingham -- I'll have to look into it.

I have to admit that there are times when I despair that "nobody learns anything ever." Teaching is *hard*, if you're doing anything else than drilling for memorization. Figuring out what people have really learned is tough.

In physics, the subject I know best, you generally don't have more than a passing understanding of something until you've seen it a few times, and have seen it deeply. I think the same is true of Calculus (which, after all, was partially invented to do physics with 🙂 ). What that means is that I should not despair that students are still fuzzy on their ability to apply the conservation of energy to physical situations after just one class where they've had to deal with it, but it's tough to know if they learned enough such that next time the grapple with it they'll really learn it faster.

Teaching is hard, assessment is hard. Which, of course, does not mean we should give up on either!

I sent you an e-mail with the link to the specific book..."Why Don't Students Like School: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom."

Susan,

I'm very interested in how you're implementing Willingham and Dweck's ideas into your teaching--would love to hear more.

Thanks for your swift and cogent reply to Hacker's article. There were so many flaws in his reasoning and use of statistics that I had palpitations by the end of almost every paragraph. (A linguistic hyperbole. Vs. a mathematical hyperbola.)

Why Algebra? Crucial to kids' understanding of things like their initial monthly cell phone fee + additional fees per text. Or why personal debt (credit card, student loans, mortgages) increases exponentially.

Algebra as a content area isn't a problem. Rather the way it's taught: memorizing algorithms. Maybe if algebra were taught from a problem-solving perspective with real world implications more students would see its value.

Oh, and did you notice that Hacker's answer as to the equivalence of (x^2 + y^2)^2 is totally (pun intended)...wrong!

I agree about the comment with how it is taught. But there is quite a bit of value in learning it properly even without an eye to real world applications. The sorts of skills one builds by starting with precise yet simple starting points and working out the implications of them in a rigorous way, I imagine, is much more valuable than learning how to balance one's checkbook. There are few other ways that I can think of in which one can begin to gain the clarity and rigor of thought that mathematics provides. In this sense, what may be most useful to one's ability to think well is precisely the bits of algebra which are most abstract. The value in studying Gallois theory, or symmetries, or the like, at least for non mathematicians, is not in anything practical one can do with such bits of algebra, but the transforming effect they have on one's intellect. Or at least so it seems to me. But I'm doing my phd in in of the humanities, so what do I know?

Somebody who's doing a PhD in the humanities ought to have some sense of the value of transforming one's intellect due to deep study of things that most people wouldn't think about 🙂

Did Hacker believe Barbie when she said: http://tinyurl.com/Barbi-On-Math

I was lucky enough to spend a fair amount of time in college with a senior citizen who was aiming for a fine arts degree in painting. As in most colleges, this does not require algebra which she thought was a shame as she had been home schooled and had a thorough background in mathematics as was expected of a young lady of her class and social standing. That 'woke' me up to the decline in education standards in the second half of the 20th century. Not only in this country but around the world. If you think I'm wrong, just compare the textbooks available now with what was available in say 1910! Would you even be allowed to use a text book by Hilbert? I doubt it. I will grant you that she was exceptional and typically excelled in any endeavor she chose---she was I believe the first American woman to be allowed a role on stage at the Abbey Theatre in Dublin as an example. Decline and Fall are us I guess...

As a senior in high school in 1986, I was taking calculus, preparing for the AP exam (Calculus AB -- the easier one.)

One of the things that the teacher did for the last couple of months of the class was give us the old APs that had been publicly released as tests, starting back in 1968 or thereabouts. The tests got noticably easier as time went on. Now, there is an observer bias here: due to practice, we were all getting better at Calculus as time went on. But, I couldn't shake the feeling that the tests were getting easier....

Thanks for your post - I appreciated seeing why you felt that algebra was important. I feel the same way and wrote my own response and identified what I think causes students so much problems with algebra. I hope you have time to check it out - http://pinojo.com/2012/07/29/is-algebra-necessary-absolutely/

To be fair, I haven't read the cited editorial. My understanding of its core idea is derived from a reading of this blog. And on one level, I am in agreement with Mr. Knop's opinion that a liberal education is essential for the furtherance of a civilized democracy.(my words) Learning not only to think, but to think critically, produces a citizenry able to fully participate in this process. I also believe that exposure to the historical milestones in the arts, sciences, and humanities results in folks grounded in the common knowledge necessary for community identity.

I might slice the apple in a slightly different way at this point. In my experience learning to think critically can be achieved in a variety of ways, and through many academic disciplines. Higher math can be included in the mix but is by no means a necessity. One of my sons was a mediocre math student, but a stellar debater. Now an adult, he has become a skilled computer systems engineer. His college major was English Rhetoric and Composition. One of his favorite elective courses was Fundamentals of Philosophy, where he was formally introduced to the art of logical thinking. I suspect his critical thinking skills were better served by studying philosophy than through the long list of math courses he was forced to take while in school. He learns specific and relevant math skills now as they are needed.

My other son, a PhD chemist, was/is a brilliant math student. His problem solving ability and critical thinking skills are natural and readily available when needed. For him, math is like daily bread, a necessity for his survival. He certainly never needed to be forced to take algebra.

You may argue that anecdotal evidence is of little value in this discussion. I would argue that my boys are emblematic of a simple truth; Algebra, while highly important in specific jobs, is not essential for the education of productive, and responsible citizens.

This is the 80th anniversary of Brave new World. Prof Hacker is very sly. Almost got me.

You've missed the point entirely. Look at the equation Hacker mentions, as just one example. Yes, we use algebra all the time in many areas, but not the abstruse version which is taught as part of math courses. The math we teach is ill conceived. People who like it, who love the math for math's sake will claim, as you do, it's all part of proving what an intellectual star you are. But that's just mental masturbation. If you like doing it, fine. Just don't push it on everyone else. A meritocracy ought to be based on true merit, and the defenders of calculus and abstract algebra don't know merit. You would not pick a football team by insisting everyone who tries out has to pole vault 16 feet. Why insist on this absurd machination for students who want to study medicine, history, sociology or even economics? Read Moneyball--you'll recognize yourself as one of those talent scouts who forever looked for the wrong attributes in the players they assessed.

obadiah -- in fact, you've missed *my* point entirely. In your comment, you're focusing on what it is that people *use*, on what people *need*. I answered Hacker's assumption that that was the primary criterion on which we should judge our math education when I was talking about how a liberal arts education is not job training.

If you want to be liberally educated, if you want to know something about the intellectual basis of human society, then an ignorance of algebra is as bad as an ignorance of the basic course of history, an ignorance of the basic ideas of biology, or an ignorance of human literature.

It's not about talent scouting to build a baseball team that will win. That's stuck in the mode of thinking like an employer trying to get the employees trained in the right skills.

Duh. Algebra is far more necessary than high school.

You can't de-emphasize algebra in favor of making time for statistical awareness, understanding algebra is essential to understanding statistics. If you don't understand that then you do not understand statistics.

The problem begins with elementary math where number facts are not learned because the calculator will do it faster. Move forward a few grades where formulas enter, and answers (and cheating) are more important than process. You can ace a class if you have good guessing skills (standardized tests are mostly multiple guess) but don't have a clue how you got there. By Middle school, word problems are about how many cupcakes Johnny will need if everybody gets 2.5 cupcakes. I interviewed for a math supervisor position and suggested changing questions to shopping skills and checkbook skills. I was told it was not "the way it was done". I was a HS biology teacher, and taught environmental skills using fish tanks and plants with lights and fertilizer balance. Because some students have "allergies" the tanks & plants are gone. We sterilize education, put it in little boxes and then are surprised that students cannot apply skills to the real world. Most teachers are locked into the way they were taught even as the world changes more and more rapidly. Until we can connect basic skills learned in school to the real world, school will appear pointless and learning ends at the test. It is not the details that count, but the process of reaching those details. There is far too much information to cram into the head of any child. We should stop trying, and begin to teach learning skills, using details that will be necessary later. Very little in HS or college is pointless, but we are mistaking memorization for learning. I suggest the change starts there.

It's a critique of teaching. As was described Aldous Huxley in tne Brave mew World. Readit again. And read his other works. Maybe too subtle , but the wrongness of the equation gives it away. Sigh....

You're saying the whole thing was a troll? (Or, to dignify it, a satire?)

If so, definitely too subtle. It come across as a straight argument.

Also, where's the wrong equation?

May be providing an option of either taking Algebra or not would benefit most students, especially those who do not want it. I think this would at least map the gap of "Liberal" of Liberal Arts and Choice. What do you think rknop?

If they don't want to take algebra, they shouldn't go to a liberal arts college where the graduation requirements clearly state taking a math course is necessary. So clearly they have the choice.

Of course, if their math is so bad they cannot understand algebra and their reading comprehension is so bad they don't understand the student handbook, maybe it's good that they don't get a degree.

Robert Moses and Charles Cobb, in the book, _Radical Equations: Civil Rights from Mississippi to the Algebra Project_, say flat out, "In today’s world, economic access and full citizenship depend crucially on math and science literacy." Whatever one's educational level, whatever one's specialty, understanding the mechanisms - the 'cause & effects,' the relations of dependent variables with independent variables, and actions with motivations - remains the primary requirement for understanding of the subject under discussion.

I'm sorry if someone doesn't like thinking about those relationships, and the math/algebra behind them. But they don't get my sympathy if they are unable to understand the reasons for what happens in their life, then and later.

For more interesting discussion on the article (as if the 475 comments weren't enough, and I only read a few), google "Fermat's dilemma". The JREF thread is quite interesting, and leads me to think you were too soft on the writer. This thought is reinforced by seeing Hacker's position as stated in Wikipedia, professor of political science. I have an engineering background (electrical, not locomotive), and I don't know what kind of science is in political science, but mathematics has often been called the language of science, and Andrew Hacker doesn't appear to know the language.

I entirely agree with Andrew Hacker, and I think this post misses the point. I should point out that I was a math geek who studied math through advanced calculus but ended up studying history and economics, and worked in finance and economic development. I used lots of algebra in my career and understand its usefulness and importance to critical thinking. But when my own son was in high school, struggling through algebra, the amount of utterly irrelevant mathematics came flooding back and I struggled to remember or even invent a real world application for most of the high school math curriculum. Of course on a website like Scientopia, people are going to valorize advanced abstract math. But just because something is beautiful doesn't mean it's necessary to teach it. As Hacker points out and this post fails to grasp, algebra is different from quantitative reasoning. This catastrophe of algebra is all the more appalling when you consider its impact -- which is Hacker's point. I happen right now to be writing a proposal for a nonprofit education organization, looking at school graduation stats for a certain low/moderate income mostly minority community. These are not bad/poor kids. They pass state standards for things like English, history and science at like 80%, but fall off a cliff with high school math meaning that the overwhelming majority are simply barred from going to college. Sure it would be nice if everyone learned algebra but it's a cost benefit analysis Hacker is making. Is it worth destroying the lives of millions of kids to make sure they all learn how to multiply binomials when they won't ever need it again? How many non-math career success stories are foreclosed because of the gate keepers of algebra and trig? Andrew Hacker isn't saying don't teach math; he's saying do we really need this particular gatekeeper curriculum?

I am really sorry to point this out but when you say you work in finance and that you think the above way what comes to mind is our current financial situation. Perhaps if you and your colleagues did learn more advanced math and more liberal arts and human values, we might have never ended up in such a mess where people lose their savings because of bankers. You seem to only value profit making or at least you sound like that.

Lastly, to Hacker's point. We are talking about a subject where people learn basically nothing difficult at all. Most problems in high school algebra are at the level of just straightforward step-by-step manipulations and people just have to memorize it or find another way of learning it. It cannot be that American kids are genetically modified so they cannot do it while all European and and Asian kids seem to not have any problem with college or high school algebra. The problem is the way algebra is taught in school, a bigger problem is teachers salaries (can you really expect someone on that salary to put considerable effort into teaching math semester after semester?) yet even bigger problem is the intellectual values in America. If you tell your kids that they need to learn math in order to be intellectuals and that this is just as valuable as being rich they might just might put enough effort into simple manipulations and be able to do it. They might able to understand that when you push a button on a remote control it does what it does because someone used a lot of that algebra they learn in high school to build such a machine. Or you might be able to explain them that cash machines are secure only because of the kind of math, in fact very basic algebra, is used in those transactions.

Lets stop math or change the curriculum. How do you exactly propose we find the next generation of talented mathematicians? Are we supposed to look at their eyes to find the next math geeks that will discover the next internet or the machines that will lead us to space or that will prevent disasters? You need to teach math, algebra in particular, to identify the next person, and yes the next Feynman might be your son, except we will never know that as you already taught him that some part of math is useless. Part of the reason we teach these classes and invest in good schools is so that this is the only way to discover the next generation of scientists, without schools we have no way of doing it. Weaken curriculum and make it less and less abstract and more and more practical, you will see more and more generations going after finance instead of science and as a result we will get a generation which has no clue how to deal with climate change.

Connecting math with practical applications is fine, but how do you propose we do this uniformly? It just cannot be done. You seem to think that the only part of math that is useful is the part that you used. Well, there is a part that is used in internet security, there is a part that used in physics and engineering, there is a part that used in biology, there is a part that used in city planning, there is a part that used in medical research, there is a part that used in finance, how do you propose we design a subject, one subject that deals with all. It is highly impractical and it is bound to fail, as all of these applications have stuff in common (namely the algebra and calculus that we teach) and stuff that is very different from each other. It is like teaching million english classes, one for those who want to work in academia, one for those who want to work in finance, one for those who want to astronauts and etc and etc.

The way the problem is solved is by developing foundations in those subjects and when people become college aged they have a choice of either going into vocational school or into intellectual school. Those who go for practical professions use their background as foundations for practical information they know. Anyway, I am tired of explaining stuff to people who have no idea what they are saying.

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Great post. Thanks for clearly pointing out that a college degrees (specifically from a liberal arts school) is not intended to provide direct preparation for getting a job.

Recently employers have been using degrees in lieu of on-the-job training and have been pushing changes in the curricula at schools to help accomodate this cost-saving measure by making courses more "applicable to the real world".

As a working mother without a BA, I find the BA degree in lieu of on the job training very frustrating. A high school diploma is the basic qualification for an administrative or bookkeeping clerk position. Traditionally, a working woman advanced to higher level administrative positions without a BA. Today, I am continuously disqualified from employment and advancement without a BA. Who the heck gets a business degree to be a secretary? Great, now I am constantly "reinventing" myself to further my career. Thanks for furthering the institutionalization of the Glass Ceiling.

On another note, I do appreciate that some schools are restructuring business classes in order to reflect the "real world." I am (on and off) in attendance at Western Governor's University. I find the classes to be quite progressive and relevant, and I hope to finish an accounting degree at that school within 2 years. However, the classes certainly lack a liberal arts perspective. I have yet to pass a business ethics course. My primary public education in the 80s and 9os trained me in philosophy and civics. In my experience, business/working ethics taught in primary and secondary schools are grossly lacking in humanitarian ethics. I keep dropping out of that class because I have this persistent optimism that I will finally find a teacher who reveres the classical definition of ethics.

I agree with Hacker: he is not asking that we get ride of algebra because it is hard, but because it is useless. There are much more thought provoking and useful kinds of mathematics to teach, and they are much, much harder than algebra.

But there is value in learning algebra, if we regard it as a verb, not a noun: you can read my take at http://www.bltm.com/blog

Robert, have you ever scaled up a recipe or tried to build anything? I used a lot of alg and a bit of trig as a carpenter.

Algebra useless? You can't be serious! Nearly everything you own or use is the result of some application of algebra. You can't even calculate the proper length of a bicycle chain without using algebra!

Forinstance: L = 2 (C) + (F/4 + R/4 + 1)

Where L is the chain length in inches.

C is the length of the chain stay in inches

F is the number of teeth on largest front chainring.

R is the number of teeth on the largest rear cog.

Without this algebraic formula you'd have to guess the length of your chain! Algebra useless! My foot!!!

Hacker's opinion didn't offer a math alternative. He clearly stated that young students should become better end users than problem solvers.

The more time I read Hacker's essay, the less sense it makes. But kudos to Rob for ignoring the many many specific errors in the essay and focusing on the underlying assumptions instead.

However I've decided there is one specific item from Hacker's essay I wanted to pull out. "For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia." Here are the numbers I found. Oklahoma has the EOI (End Of Instruction), and the 2011 proficiency rates were English 86%, Algebra 75%. West Virginia has the WESTEST (not clear if it is an exit exam) and the 2011 Grade 11 mastery rates were English 44%, Math 44%. In my home state of California we have the CAHSEE and the 2011 Grade 10 pass rates were English 84%, Math 84%. Now a snapshot of test results doesn't necessarily mean much, but you can see that it is far from clear that algebra is especially problematic.

What saddened me however was this bit from the CAHSEE Summary Results documentation, where somebody thought it was necessary and helpful to describe what was meant by "percent":

"Percent Passed – This represents the percentage of students who received

a passing score. The percent passed is calculated by dividing the number

passed by the number tested and multiplying by 100."

I loved Algebra. But, then again, I went to grade school in the 80s. We learned logic and problem solving in 3-8th grades with PCs - specifically BASIC programming. I was a poor kid in public schools, but a nerd none the less. Thanks to my grandfather, a Ukrainian immigrant who studied mechanical engineering, I got the coolest gadgets - Commodores and Vics. We had type-in games magazines at the corner stores!

I'm almost 40 (still a poor nerd) and my only son just became a teenager. His public school education has been horribly disgraceful. I am daily involved with deprogramming the "be a good worker/user" ethic that inundates his schooling. He graduated from 5th grade without knowing his multiplication tables nor able to write a paragraph. ("Mom, I don't like memorizing multiplication tables every day. It takes away time from learning higher math.")

For 6th grade, he attended a science and math middle school. One of his in-laws lent him an old TI-83. Suddenly, he was a math superstar. He consistently scored 20% higher than his peers in math assessments. After every computer adaptive test, he announced the math concept that finally stumped him. First, "What is (f)?" Then, "What is log?" He is perpetually driven by curiosity. Good for him. Bad for education administrators. I remember asking my own 9th grade Algebra teacher these questions. He was very offended that I wasn't following the syllabus (even more offended when I my homework grade was 0% but my quiz, midterm and final exam grades were 100%).

Thankfully, I live in Michigan. Our homeschooling laws are quite permissive thanks to the bible-belters. Basically, I can sign a piece of paper that states he graduated from high school. So, I'm dropping him out of school. I think it's the only way he will be able to learn how to write an essay and experience art and music. I have no worries about his math, science, history, and civics education. He is years beyond his peers, and has enough ambition to direct his own learning. He already has jobs lined up as a computer/systems technician. If the US is concerned about our knowledge economy readiness, then why do I have to take myself out of the workforce in order to secure my child's future?

I am horrified by the state of public education standards. Math is everywhere. Why don't our practices reflect this? Children learn math in the garden, in the garage, in the kitchen, in the stores, and especially in private. Public education and work environments stress group think and productivity. This ethic completely contrasts human nature. We need private space and time to solve problems. (And I believe that this is where discovery through reading is an admirable academic effort particularly in early childhood.)

Perhaps we need to create a publicly funded incentive to encourage math majors to teach. I also hope to see courses that help introverts communicate and navigate through school systems.

"Public education and work environments stress group think and productivity. This ethic completely contrasts human nature. We need private space and time to solve problems."

In part I made this point to the Dean of the school of science (and various others) at my university. I completely agree with you. Hopefully some day Sudbury valley and Montessori schools will be available options for everyone.

[...] Knop at Galactic Interactions. Liberal arts education is to make people into good citizens, not into good workers. They are to [...]

"If we have the problem right now of too many people failing out, it may be that we're pushing them through the wrong kind of education."

I came here through the Huffington post.

Have you heard of Louis Benezet's experiment with eliminating mathematics education in K-6 grades? He effectively replaced it with the trivium (in his words "to read, to reason, and to recite.... And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language.") and had great success. The kids who didn't formally learn math through the sixth grade did better at mathematical reasoning than did those kids who had three or more years of formal math. http://www.inference.phy.cam.ac.uk/sanjoy/benezet/index.html

[...] via When Andrew Hacker asks “Is Algebra Necessary?”, why doesn’t he just ask “Is High School Nec.... [...]

Rob, Thank you for your blog and the responses generated! I agree that algebra is essential to a liberal arts education, to critical thinking, to civilization. But Hacker raised good questions that got me thinking, too.

I have just finished teaching two sessions of 5th to 6th grade transition math. You are so right that this is a critical time in math education! Each session was three weeks, 8:30 to 12:00. Many of the students signed up because they were struggling in math. Most were girls. What a joy to be able to teach math in depth, with enough time to play! For a few, my best hope was a change in attitude to the "growth mindset" Susan Townsend talks about. For some, I helped them realize that they were fine in math already. I taught about learning, about how many times you need to learn something to really "get it," using the athlete/musician performance analogy, about the learning curve, about anxiety and performance. I showed them the research about brain development and how variable this is, how they are "not done yet." I showed them that the brain "does math" in different "modules" than language, and that it is necessary to learn to communicate math understanding. I taught them that being able to "teach" math requires knowing more than the answer and encouraged them to think like (good) teachers.

My curriculum included review of four operations with whole numbers, decimals, fractions and integers. It included the fraction-decimal-percent relationship. We did some basic geometry (angles and inscribing polygons with compass and straightedge). Yes, I introduced basic algebra. These students have been thinking algebraically all along, e.g. 7x = 21, so they wanted to jump straight to "the answer," which most could do. I wanted them to understand the process and communicate their ability to use it. Only a few of them seemed developmentally able to solve algebra problems with more than one step and even then, a/2=12 presented a bigger challenge than the other operations, never mind with negative values. There are developmental factors at play!

I think it's OK to think "Math is Hard" as long as you also think "and I like a challenge." The ones who find math too easy may eventually hit the wall. The struggle is part of the good game and is part of learning to solve life problems!

My concerns about math education: 1) Too much too soon for most kids, given what we know about brain development. 2) Too much emphasis on answers, not enough on the process - and that's where the fun is. 3) Too wide, too shallow.

We are only now coming to understand math cognition. Research on language learning the last three decades told us a lot and changed reading curriculum. The same thing is SLOWLY happening with math.

Yeah, Glen Van Brummelen, math prof here at Quest, says some of the same things. Different people have the right brain development to be able to handle algebra at different times somewhere between grades six and eight or thereabouts, but we foist it on everybody at the same time. People who aren't ready for it yet then develop "math coping skills", from which they never escape-- the skills that let them figure out how to pass their classes without learning things. Even once their brains are developed enough that they *could* learn the math, they're already trapped in first the idea that they just can't do it, and second the habital coping skills.

[...] slamming Prof. Hacker include patheos.com, Rob Knop at Galactic Interactions, Andy Soffer’s blog. If you’re looking for something a little more in-your-face, try [...]

We are now designing HS & college curricula for what students want to learn. My response has always been, "After you have a year of college (or a year in the real working world), come back and tell me what I should have done differently." The answer has always been, "If you knew how hard life was, you should have pushed us harder." Experience is a wonderful teacher, but school is supposed to prepare you to think, and give you the basic tools to do it. It does not prepare you for the skill of a job, but for ways of making that job better or more efficient. You are supposed to learn to think. Advanced schooling should lead to deeper thinking. That skill will allow you to adapt to more situations in life. The purpose of education is not to fill the vessel but to light a fire.

[...] against Hacker, rknop makes an interesting argument in his Galactic Interactions blog—but one I suspect Hacker would agree with. He defends algebra on the basis of the importance of [...]

Thank you for this piece. It points toward a larger problem: the American penchant for "big ideas" coupled with an aversion to abstraction. What a strange combination! For the past century there have been cries for "real-life" learning, as though learning that involved the intellect and imagination were insufficient.

You made many important points. I hope this one doesn't get lost in all the noise:

"Too many of us professors tend to not have any clue what somebody is supposed to do to earn a living after a liberal arts education other than go to graduate school (so that your liberal arts education is "training" for what you do next). That's because that was our own life trajectory, and it's what we know."

Indeed. I went to graduate school in Russian literature because I wanted to continue my studies, not because I saw myself on a career trajectory. When I made plain that I had no intention of entering academia, professors and fellow students showed puzzlement, even concern. When I look back, I see that they were working from what they knew. Some would ask me, "isn't it a shame to let your studies go to waste?" They never went to waste. I carry Gogol around everywhere. I continue to memorize Russian poems. I don't consider myself a model by a long stretch, but I do wish that liberal education made room for itself.

On a side note, I'd be interested in knowing what you think of recent changes to physics instruction--for instance, at MIT with its TEAL program. It seems reckless to me to replace the lecture with workshops. Perhaps workshops have a place--but should the lecture go? When listening to a lecture, you can see how a scholar distills and organizes a topic. You start putting it together in your mind. This is not trivial. True, you can find such distillation in the textbook as well, but the lecture offers another version, in real time. Of course, the lecture is not in itself sufficient; you may also need recitations, study groups, and labs. But that is no reason to treat it as obsolete. Should you wish to comment on this, I would welcome your insights.

It seems reckless to me to replace the lecture with workshops. Perhaps workshops have a place--but should the lecture go? When listening to a lecture, you can see how a scholar distills and organizes a topic. You start putting it together in your mind. This is not trivial. True, you can find such distillation in the textbook as well, but the lecture offers another version, in real time.I agree with you that there is some value in lecture, but there is physics education research out there that shows that just lecturing alone is not really all that effective a way to teach physics. To really learn, students have to engage with the material, interact with it. It's easy to be passive during a lecture. I suspect that the students who learn best from lectures are the ones who engage with it -- but they're then learning sort of in spite of the format, rather than because of it.

To be sure, there is information that needs to be transferred. But, I think that practice is a lot of what's really needed. When I teach classes, I try to engage the students back and forth all the way through. I give them reading questions on the textbook reading, both to force them to think about it, and to allow me to gague what they're getting out of the reading. ("Just In Time Teaching" is the buzzword name for that.) I also try to make my lectures as interactive as possible, with questions and problems embedded within the lecture.

Rob Knop write: "Yes, I admit, the editorial at the New York Time entitled "Is Algebra Necessary?" pushes my buttons." and I sign with both hands under this statement. And I fully support Robb's point of rethinking the whole curriculum rather than just focus on a single piece. We did it more than once, and we can do it again. We started with The Trivium: Grammar, Rethoric and dialectic - who takes such courses now? And we expanded it to Quadrivium: Arithmetic, Astronomy, Geometry, and Music. And then we changed the curriculum again to include College Algebra and, yes, the dreaded Calculus. So we can do it again. And we are ready to do it now. So lets just do it!!!

Now lets talk about how to do it in a rational and thoughtful way rather than by emotional reaction.

Yes, Andrew Hacker makes a good point that we should not be teaching useless things. And yes, Rob Knop agrees but makes a point that some things should be preserved. And this is where I disagree! What I worry about is that perhaps with all this emphasis on arithmetic, subconsciously we might be turning the education back a couple of centuries, reintroducing the Quadrivium again. And I worry that all this focus on algebra, just because so many people have trouble with it, is just a trick of a demagogue, not a voice of reason. Because yes, people may support elimination of something they found hard and useless. But this does not really solve the problem of wasted time, as most of the wasted time is elsewhere.

Just think how many hours of algebra are there in the curriculum, as compared say to writing, or reading, or arithmetic? Do you really want to save 10% when perhaps it is the other 90% that is also the waste?

Here is the list of the three most useless skills taught to students, and thus offered for elimination, with appropriate justification. This list is in the order of uselessnes - the first item is the one considered most wasteful, as it takes most time.

So here is my proposal for the list of three most useless courses/skills to eliminate first from our education. This list starts with the most useless skill, and continues to other slightly more useful skills.

1. writing

2. reading

3. arithmetics

Why writing is useless? Because nobody needs to write when you can speak/record your message. Because it requires fine motor skills that many people lack. Because I never got a good grade back in the times when the writing was still given a grade.

Why reading skills are useless? Because any message can be now spoken or recorded. And any text can now be read by a machine, by Acrobat Reader if in PDF, or by Kindle if its a book bought from Amazon, or on many other similar devices. And because English has no consistent rules of pronunciation so what are we teaching when we are teaching kids to read? (If you are visiting Cincinnati, ask for directions to "Reading Road" to hear a Cincinnatian laugh if it is me, or to politely explain to you how this is pronounced if it is someone else than me.)

Why arithmetic is useless? Because a calculator does it better, and faster. Because the only people who do arithmetic by hand are teachers and students. Because even the teachers do not know why you do things the way you do (try to get a teacher to explain to you why cannot you add fractions by adding numerators and denominators. Chances are that his/her only explanation is that you just cannot do thay because it gives wrong answers. So if I convince enough people to do it "my way", then it is the teacher who will be getting wrong answers. So who is right and why? And since I am a math professor, you better not dare to tell me that I do not know how to add fractions!)

Now once we have saved lots of time by eliminating writing, reading and arithmetic, we can spend all this time on teaching children how to count, how to sing, how to draw, and generally how to be a better and more understanding human beings. I would also add a class on how to start fire without matches, how to locate a suitable cave, which berries are edible, which mushrooms are poisonous, which herbs cure which illnesses, and also how to track animals. It is obvious to any intelligent human being (if you disagree, please do not get offended! Just retake an IQ test!) that all of these skills are extremely useful, and each of them alone is more useful than reading, writing, and arithmetic together.

Eventually, this education program will improve how we live in the word. It will eliminate all the machines (except guns and cars, of course) and we will return to natural organic living (in caves, if the classes on how to find caves are taught well enough).

Utopia? Well, maybe. But so is the world without algebra...

And since we are on this topic, why is it a Utopia? Well, simply because I have not yet met yet a person who can start a fire without matches! I have met many people who can read how to do it but none of them could do it. (Incidentally, this is another example of why reading is a useless skill!!!)

So unfortunately all of this is Utopia simply because we cannot really teach classes on how to start a fire without matches. We do not even know how to teach teachers how to teach such classes. We do not even know how to teach professors how to teach teachers how to teach such classes.

And yes, thanks Mr/Mrs Sinan for reminding all of us that "This is the 80th anniversary of Brave new World." Utopia it is, but it makes us all so much more happy, and and so be it.

Dislaimer: These are Mu thoughts. Any resemblance to real thinking is unintended and purely accidental .

I think really we're supposed to teach self-esteem in school.

Enjoyed this greatly. Can't resist the challenges you pose.

The reason you can't add fractions by adding numerators and denominators is that if you could, life would become absurd.

One half plus one half would equal two fourths--that is, one half. Just think of the consequences. You and a friend would each pay half the bill at a restaurant, and your combined payments would come to one half the bill. To rectify this, you'd each pay half of the remainder, and only end up paying half of that remainder. You would sit there all night and still be puzzling over that half penny that seems to split and split into ever finer filaments of copper.

So how do we create (or preserve) a world that isn't absurd? Well, for one thing, when you add one positive quantity to another positive quantity, you should get a sum that's greater than either of them. Better still, it should be the size of both of them combined.

For this to work, when the denominators are like, you don't add the denominators--you just add the numerators. After all, you're adding like units, which are the only things you can add, if you want to end up with a single quantity as your sum. The denominators give you the size of the fractional units. The numerators just tell you how many of them there are.

In such a world, one half plus one half would be two halves, that is, one, and you'd be able to pay the bill and get out of the restaurant.

But then what do you do when you have unlike denominators? How do you add units that are unlike? Well, to preserve a world that makes at least a little sense, you'd have to make these denominators like. How do you make one half and one third have like denominators? Two and three are not the same. But ah... wait... one half is the same as three sixths, and one third is the same as two sixths. So, when you add one half to one third, you get five sixths.

Again, this is absolutely necessary as a bulwark against absurdity. If one half plus one third didn't equal five sixths, then you'd see half an hour go by (30 minutes) and a third of an hour go by (20 minutes) and then find something other than a sixth of an hour (10 minutes) remaining. That would suggest that between the time that you started calculating and the time you ended, the length of an hour had changed. This would make it impossible to catch flights on time. It would make the very flights precarious. How can you tell your passengers that you really aren't sure what time it is below, that it all depends on how you define an hour? They'd get very upset. Also, you might end up planning the in-flight movies badly. The hours might suddenly shorten, so that the flight would end before you even got to the movie's climax.

As to your other point, it's easy to start a fire without matches (just use a magnifying glass), but I don't recommend it.

[...] op-ed incited a passionate response, with astrophysicist Rob Knop writing a rebuttal on his Scientopia blog in which he takes issue with Hacker’s point that because algebra is not required for most jobs, [...]

[...] exercise of memorising poems or dates? It’s not what you’re going to need for a job. This post over at scientopia blogs sums up my thoughts on why thinking of high-school and college education [...]

[...] contention, including Evelyn Lamb , who studies the mass media at Scientific American; Rob Knop, a professor and physics blogger; Valerie Strauss, a professor and psychologist, and RiShawn [...]

[...] see blogs by Rob Knop, Daniel Willingham and RiShawn [...]

[...] see blogs by Rob Knop and RiShawn [...]

[...] Hacker’s column already. I highly recommend these posts by Rob Knop, Daniel Willingham, and RiShawn [...]

[...] Much has been written about the recent editorial by Andrew Hacker in the New York Times. Prof. Hacker asks if we really should by demanding that proficiency in algebra be a condition for graduating from high school, or even college. This seems to fly in the face of accepted wisdom. Accordingly, the reaction from the scientific community has been overwhelmingly negative (some interesting examples are here, here and here). [...]

[...] more sophisticated discussions about why this columnist was wrong, see Galactic Interactions and Good Math, Bad Math. Tags: [...]

[...] science-math crowd certainly seemed to be in a feisty mood because all week I’ve been reading response after response after response and sort-of response. All are taking the opposite position from [...]

[...] Rob Knop commented in his response to the Hacker article, “So, yes, I would agree that we could and perhaps should de-emphasize algebra in favor of [...]

[...] When Andrew Hacker asks “Is Algebra Necessary?”, why doesn’t he just ask “Is High School Nec... by Rob Knop [...]

I believe that Hacker makes a lot of points (although some of his data is a little mystifying.) However, this does not abdicate our responsibility to teach "algebraic thinking," which contrasts with the stuff put down in textbooks. You can read more about my distinction between algebra the noun and algebra the verb at http://bltm.com/blog/?p=139

Warning this post is not for the faint of heart or mind, this is not for you simple minded people who would never change your minds.. this is for the people who want a better school sysytem better world in general;

if you say algebra is needed in schools to promote and teach better reasoning / thinking skills You are right..

if you think that algebra and all other classes teach you are help you in any way deal with a job mostl likely your wrong unless your becoming a teacher or a job that pools from a specific or correlation of classes ...

if you are one who beilives that schools are not ment to prepare you for a job your dead wrong and pig headed simple minded cowards, have none of your teachers ever caught u late and said hey are you gunna be late when you get a job, have one of your algebra teachers ever said your gunna need this later in life? so wrong thinking there.

i think that the people misunderstand andrew hacker hes simply saying we do we not update our school system if it keeps failing students, a evident sign that our school system is not up to par. but what you guys seem to misunderstand is that algebra like other courses is ment to have high fail vaules so that most fail and become losers , poor people and some (few) have better chances at getting rich. that hole is there so that the economy is kept going people struggle for money as politicians, mayors and other high value people make money and never have to work. i mean take a look at the forrest to support a class which many people fail is not showing any intelliect only showing blindness because you passed. well put your self in their shoes oh wait you cant because it pisses you off to think of youself as a have not, even then you'd say oh id study oh but if you were a have not or person who didn't pass or understand algebra despite your best efforts whould you still (rep) support algebra and any classes that most people fail in schools. esp seeing as to how a diploma is so important to job owners and hiring staff managers at jobs .. reconsider if your as smart as you claim to be in the way to talk in your post people above in below me in this post page chat room etc..

xoxo dave "keeping it real until my lungs give out"

Our author writes: "So, because algebra isn't what's needed in jobs, we shouldn't be teaching it...If you accept that argument, we need to reevaluate the entire high school curriculum, and the entire core curriculum of all colleges and universities."

I do, and yes, we do.

Caveat: It's not necessarily because algebra isn't useful. It's more that the *actual curriculum* - what somehow passes for mathematics, and has come to be known for some reason as 'algebra' - is not only unnecessary, but fails miserably to achieve its purpose, which is to scaffold further learning and develop higher order skills.

What we're teaching now in mathematics, we absolutely shouldn't be teaching, because it doesn't do what it's supposed to do. Get rid of it. Scrap the whole damn thing. There is so much more we could be teaching that might both help students in their real future lives *and* act as practical scaffolding and effective mental exercise.

We need to systematically re-evaluate high school and core college liberal arts curriculum for whether or not it actually helps develop the intellectual skills and habits of mind we value. Tons of research (see: Academically Adrift) suggest that our most treasured traditional educational practices are failing. We are holding on to the topics and texts we grew up with out of what looks like blind nostalgia, sacrificing our students' academic well-being and ultimately the mental health of our society in order to satisfy our own conservative desire for the good ol' Eurocentric-Heteronormative-Patriarchical-Way-Things-Should-Be.

To address L.Q.C.M.'s point, the school reading and writing curricula differ from the math curriculum in one important point - that they actually work.

I am appalled by Andrew Hacker’s ramblings, but not surprised by them. I have seen mathematics professors denouncing the inclusion of literature, history, and other liberal arts courses from the high school and undergraduate college curricula. I have also seen literature professors claiming that mathematics should be dropped from high school curricula and be replaced with simple arithmetic only. Since free speech and conflicting viewpoints should be encouraged, we need to live with such personal opinions.

I believe that the goal of high school and undergraduate college education is to provide the students with a broad base of knowledge in both arts and science subjects so that they can pursue career paths of their individual choice and can change a path if it is either unavailable or not to a student’s liking. The curricula can NEVER be sheer employee training manuals. I speak from my own experience. After getting my Ph.D. in mathematics from Lehigh University in 1971, I could not get a teaching job in a college or university. For a single vacancy there would be some 300 applications. As a foreigner with a green card only I had no chance. So, I had to take a non-teaching job as a computer scientist in industry. As I moved from one company to another and from one vertical segment to another, I found that each company had its own version of performing work. A general college curriculum prepares students to handle and survive in different work environments – academia, industry, government, but it cannot train students in each company’s individual work methodology. Hacker has a very twisted view of college education, which, in my opinion, is anti-intellectual. He wants to teach only those tools that the students will use as future employees. Then, by his criterion, political science should be banished from curricula since it has no influence on running an assembly line in an auto shop. He also wants to drop those subjects from the curricula that the students find difficult. What a prposterous idea!

Now I want to address another issue raised in the chain of e-mails – the lowering of standards in courses taught and the progressively lower caliber of the students that we get today. I have heard from my friends in academia, both at Lowell and elsewhere, that, for example, the notes that they gave eight years ago have to be made easier to suit students today, that the newer editions of the same textbook are made easier than their earlier editions, etc. Are we then collectively contributing to the dumbing down of American education? That is precisely Hacker’s objective – if at least half of the students find a subject difficult, then drop that subject from the curriculum instead of pushing the students to work harder and learn the subject. In academia the faculty and the administrators are at the preparation and delivery end of education and the students are at the receiving end. With the exception of a very small percentage (perhaps 5% or so) of students, an overwhelming majority usually wants to pass courses and get their degrees via the path of least resistance. Therefore, they prefer easier courses and more lenient professors. But why do the faculty and the administrators succumb to the students’ demand? I remember when I took the qualifying examination for the Ph.D. degree in January 1969 at Lehigh, 18 of us appeared but only four passed. I was the only one who passed at the first chance. Why can we not continue that tough standard? Let me give a personal experience. I admit that this is just anecdotal.

I worked in industry throughout my career. But I like teaching immensely. So, I taught part-time in the evening in the computer science departments of several colleges and universities in the greater Boston area during 1981 to 1997. I was and still am a harsh grader. I gave Ds and Fs without any reservation. The chairpersons and deans were supportive of my grading principle initially. In the early 90s, however, they started to oppose my grading policy and siding with the students who clamored for higher grades since my students would not get reimbursed by their employers if they received below C in undergraduate courses and below B in graduate courses. I objected and argued with the chairpersons and deans defending my grading policy. But gradually I got fed up and decided to stop teaching part-time. I remember that the chairwoman of the information science department of the last college where I taught regretted that she could not stop teaching on the same principle as I had since it was her full-time job, while I could quit since it was my part-time job.

[...] inability to cope with math is not the main reason that students drop out of high school.” Rob Knop asked why we’re not getting to the bottom of “why it becomes normal not to ‘get’ math,” and [...]

But what if the student is suffering and can't pass it just because he should "know" about it as a part of society?? a student like me who is math anxious will never choose any field related to mathematics so why it's part of high school education just because expecting me to change my mind one day,Why will a student who is suffering from math anxiety will change his mind and select mathematics in the future??U said why not to "get" mathematics i say why not to "teach" it well,who wants to fail??? no one.You said we should teach everything generally we all have learnt Basics of Math is our childhoods so why do we need such "high" math so that means we should even teach "high" biology,high chemistry,high physics,etc

Mathematics should be elective not mandatory,if anyone wants to learn it,can learn it.

[...] course, no major article like that is going to go unchallenged. My favourite of the rebuttals is this one by a BC physicist who emphasizes the idea that we are “training people to be members of [...]

I was searching for "Another Reason", to explain the need for algebra to my 4th grade daughter. In the 1980's it seemed like everyone in highschool, whether the grasped algebra or not, always asked "Why do we need to learn this, it's useless!". Wow, the world has changed so fast since then. I'm not an intellectual and worked in the court system until I retired from an injury. I never aspired to be a Court Officer, and as Civil Service Tests go, it was a very difficult one. I married very young and did not finish college. This was an oppurtunity to gIt in the system and when you're in, study for tests to become clerks, who actually make quite a bit of money. The tests are harder but, a great oppurtunity for intelligent people who have the extreme disadvantage of a higher education.

I'm off point! My 4 eldest children asked about algebra also. I told them that in this "Tech World", algebra will be your friend! That was all I could come up with. They struggled and I wasn't online yet, so I bought all the math reference books I could. One of my eldest daughters is very intelligent with a measured I.Q. Of 142. I know, I.Q.'s have been a controversial subject lately. I'm just trying to explain that she had a grasp of algebra in grade school. She told me that algebra helped her in other subjects, it helped her reason and solve problems easier. I know everyone is different and what helps one person to learn may not help another student. To me, even though I'm in my 40's and retired on a disabity pension, my limited knowledge in algebra allowed me to help my 6 children learn or at least help them with homework. Math is a subject that makes students not only concentrate, when they start to understand it, it gives them a real "Tangible", pride. When a 5th grader starts to understand the basics if algebra I feel and observed more inspired young students. It isn't a subject that can be taught by teachers that might disagree with your term paper or your opinions of a literary character. Math is what it is period! Algebra is so CRUCIAL because it's so much more than a math subject, it can inspire children to challenge themselves and possibly help them when trying to solve other problems, even life issues! Your child maybe a Genious, but without inspiration and the confidence that passing an Algebra Test gives them early on, in my opinion and experience, they might not reach their full capacity. This is why I believe Algebra is vital for students to learn. To put my opinion in perspective, I just wanted to say that while my eldest daughter just became an R.N. and wants to keep learning, I don't have the money it takes to put 6 kids through college and they knew how important school was from an early age. They're not all going to college and a couple learned a trade, I even have my musically gifted 10yr. old son learning a brass instruments along with the instrument he WANTS to learn in the hopes of maybe one day obtaining a scholorship they offer for the School's Marching Band. Sorry that sounds awful, but when you aren't "rich", your children have to find their strengths to obtain the dreams/