Why Algebra is Necessary: Rebutting Andrew Hacker

If your concern is that students will lose out on the critical thinking portion of math, why not remove the “useless” algebra, replace it with something most people will use, say (for lack of a better term) “life math”, critical thinking or programming class?

Actually, I remember lots of students complaining about how they didn’t need to learn about poetry, history, and many other subjects. Claims that math is singled out don’t really hold water in my experience.

Yep, my boyfriend is an engineer and it’s always complaining about having had to study Literature and what would be your English. It makes me pretty mad and it’s not even my main field (Medicine student), specially because it plays on the stereotype that science people can’t enjoy, be interested in or understand anything outside their field (like literature, …) that’s pretty prevalent around here.

I would agree that it’s all about how subjects are taught – teachers who can make the classroom lessons relevant to the real world are what our schools need.  This can be in the specific details of a lesson and/or explaining how the skills translate into life skills. 

I’ve always contended that being able to solve ‘word problems’ where you have to ferret out the pertinent details and determine how to put them together to reach an answer – first specifically encountered in math class –  is one of the most basic skills needed to succeed in life – since life throws word problems at us every day.

I was fortunate to have great algebra & geometry teachers.  Statistics, on the other hand, pretty much left me cold & most of the details of any given section were immediately forgotten as soon as the test ended.  But I did at least learn the basics – questioning statistics & studying how a number was arrived at rather than just accepting them at face value, and the important differences between average, median & mean (though I still sometimes have to look it up).

I blame poor mathematics education in the United States on crap like FOIL – it taught me the mentality of how to get an answer but NOT SOLVE A PROBLEM.

Also, I just plain hate the whole damn FOIL thing…frankly, remembering “first, outer, inner, last” seems to take more effort than to simply understand order-of-operation.

 Spanish teacher, here!  Each and every day I have to justify my subject  to my students.  I even have to justify it to their parents and some of my colleagues.  Every few years a former student stops by to tell me how something I taught  helped him/her with something in their studies or their life and it finally clicked for them that I was right.

 I see this as an argument to push for the jury to know math, not just you. If they can’t think logically because they never took math and science in school, then you are screwed, no matter how well you prove your point.

I teach physical sciences to undergraduates, mostly in humanities majors. I have had girls hyperventilate and cry when I ask them to use a very simple formula to rearrange and plug things into. The word “variable” seems to be terrifying. It’s baffling. But I come from a catholic girls school abroad, not the American school system. Those nuns did two things right: make me an atheist, and teach math.

 Did this guy just suggest we will do better on global aptitudes if we make the test a lot easier for us? Let’s hope the rest of the world continues real education so that they can continue making all the stuff we use. I used to like science fiction and dystopian stories until I saw I was living in one.

 (sorry that wasn’t meant as a direct response to Stev84)

First we take away math, then we take away literature, pretty soon school just becomes a place for parents to get rid of their kids for the day.

The country grows dumber every day.

when I get asked the inevitable “when are we ever going to use this in real life???” by my students, my stock response is to say “did you do jumping jacks in PE this morning?” “yes” “When are you ever going to use jumping jacks in real life?” “probably never!! but they are exercise and make us healthy!!” and I respond with “the math we are doing today is exercise for your brain, makes your brain healthy and helps you learn how to think and solve problems… not just math problems.”

They huff and puff a bit more, but tend to get down to it.

As far as using what we learn in school… for crying out loud, I have never used osmosis in my real life! but it’s still cool to know about it. We learned LOTS of things at school that we never use in real life. But it’s important to exercise your brain and teach it to take different pathways.

I have to say that I’m partially concerned with the desire that everything we need to learn be “useful.”  I’m a high school English teacher, and I do try to make sure students see the connections between “Romeo and Juliet” and their life (and human life in general), but I think it’s pernicious that everything around us, and everything we learn, must have a specific use. I think that’s part of the reason we have a country so invested in religion:  if we debase everything that doesn’t have a specific use for us, there’s very little importance in a life that is a cosmic blink of an eye, let alone a beautiful poem without a concrete meaning (say Mallarmé) or a fun mathematic concept like Kaprekar’s Constant that has little to no practical import.

I love that TED talk about statistics. I reference it in nearly every conversation I have about mathematics (been having a lot more on Facebook after this article came out)

I too think that we should focus on statistics more. It is absurd that we graduate high school students who have never had any education in basic probability and statistics, even if they’ve had advanced calculus.

I also agree that we should not do away with algebra. I think what should happen is some introductory algebra, followed by some probability and statistics, more algebra, more statistics, eventually into calculus. In a perfect world, there wouldn’t have to be strict breakdowns where one year is algebra, the next year is statistics, etc. Algebra and statistics should be blended seamlessly. Why is it that we teach kids how to graph the slope of an equation without explaining what that line equation is commonly used for? How many kids graduate and go on in life thinking the equation of a line was useless, never understanding that it’s used all the time in calculating those trend lines we see all the time? Then they move on to more advanced polynomial equations, never knowing that calculating probabilities is a powerful use of those tools.

Honestly, this killed me in math. We had Algebra, Geometry, Algebra II, Trigonometry, and then Calculus. I never made it through Algebra II, and a big reason was not that algebra is too hard, but that I was simply told that the solution to a certain equation was a certain curve and that was it. Not why the equation described that curve, not what it meant in the real world. Of course people think there’s no real world use for algebra, they have teachers and books that can’t seem to communicate the very obvious real world uses.

Then I went on to take two years of probability and statistics in college and it was like somebody turned on a light bulb. Why had no class ever linked this stuff before? I was playing catch up, but I had just enough algebra to get by and I learned so much, did well, and discovered that I’m not actually “bad at math” and that I could love and be fascinated by it. But I was too far behind. I didn’t have the fundamentals to go any further and would have to spend countless class hours catching up on Algebra II, Trig, and Calculus to advance my math education. Some of my computer science courses were made more difficult as well. So this is one more reason we need to teach algebra, on top of all your good ones: because we shouldn’t close the door on students. Algebra is a door to a wider world of knowledge, and you never know when a student will discover in their junior year of college, or even years later that they want to see where it leads. We shouldn’t take that away from them.

The answer is not to get rid of algebra, but to teach it better, and it seems to me that most of higher math is inextricably linked with statistics, separating it makes things that should be deeply meaningful seem utterly meaningless, and it is a huge mistake. What I don’t understand is how we’ve gotten here, how people who know far more about math than me didn’t work to link statistics and algebra from day one, and why more aren’t trying to reconnect them in curricula now.

I was one of the kids who said, “Pfffft, when am I ever going to use this in real life?” So I learned for the test, and promptly forgot it afterwards.

Then, a few years after I was out of college, I discovered 3D graphics; as the renderer I was using didn’t have a GUI modeller, but required the user to describe the geometry of all the models in text files, I ended up having to relearn all the geometry, algebra, and trig I had dismissed as something I’d never need.

Ironically, one of the few things that did stick in my memory – “FOIL” – I still haven’t found a use for. But I’m remembering it just in case.

Nicely done, Hemant.  

You’re right that Benjamin’s position is not too far from Hacker’s. In fact Hacker would say that some form of applied statistics (what he clumsily calls “citizens’ statistics”) should be required.  He doesn’t suggest that algebra should be eliminated, only that it is elective.  I think he’s wrong to think that one can understand statistical analysis deeply without some basic algebra, but that’s another story.

Re chemistry and Jane Eyre:  I think I disagree with you here.  A working knowledge of the periodic table and Bronte’s yawner really can facilitate ” more credible political opinions or social analysis. ”   For periodic table, one would have a deeper understanding of climate change, ozone depletion, and a jillion other things that should be informed by science.  Jane E. is chock-full of themes on morality, gender and class issues, and so on — what every child needs to be adept at social analysis! (And anyway, unlike Algebra, Chemistry is usually an elective–which is what Hacker advocates.)

But seriously, nice post…

 When I moved to Ontario, I heard a lot of people proudly state that they’d studied french for 5+ years and can’t speak a bit of it. In the next breath half of them claimed that everyone in Quebec speaks perfect english and they just don’t to make a political point.

(This is usually where I usually switch to french while explaining exactly why they’re idiots)

Yeah, this is absolutely huge. Do you want your life in the hands of a jury someday who don’t have the skills to work through a problem in a logical manner? (Well, maybe if you’re guilty you do). 

 Too long didn’t read.

And what’s with all the foreign words in that post anyway? I speak English. I don’t need to know any other language. Try using Google Translate next time kthx.

You can get very far in computer programming without algebra. You may be able to code up a simple web page, but as soon as you want to say, assign unique colors in a gradient based on some numeric property, you’ll need to figure out the algebra to create the code. You can forget writing anything like a decent video game without some algebra. Computer code expresses equations differently from an algebra text book, but it’s all about variables and algebra. I’d be all for folding some programming in with the algebra teaching, so kids learn something practical and get to approach the problems from a different direction, but you’d still be teaching algebra.

This goes along with the question of whether we should we have a one-tier or two-tier society.  The “one tier” argument would say to minimally educate everyone to at least a “basic education” where some people will be over-educated with skills they will never use in certain subjects.  This argument says that it is better to have a society where everybody is at least minimally educated to a certain level in a whole variety of subjects.   The two-tier argument says to only educate people for what they will actually use in life.     This argument says that we waste a lot of time and energy educating people for skills they will never use and everybody should be free to opt out of any education they don’t want.  This argument would say it is OK to have illiterate uneducated people walking around as long as they are able to do their job.

I’m for the one-tier approach.

I used to work in tech support, and when filling out tickets we had to use the “PAR” structure (state Problem, Action taken, and Result).  We made a game of being able to write our tickets in poetic forms — haiku, limerick, etc.  Usually we needed one haiku for Problem, one for Action, and one for Result, but I did manage to write an entire ticket (a simple password reset) as one Haiku:

P: User can’t login
A: Reset password in AD
R: Login now working.

(AD is Active Directory, the program we used to control user accounts.)

It actually takes more time to become fluent in French than it does to become fluent in English. French is a lot more complicated.

Though it’s really no excuse when you live somewhere where it’s spoken. The reason I forgot most of my French is because I never had a chance to use it.

What? Long division? If anything, it is silly long arithmetic that has
become completely useless in life, ever since calculators were invented.
Although you can treat it as a good mental exercise.

Being against proving things sounds to me like the typical trend of
wanting to remove science from class rooms. You just learn your
divisions, you will never learn to doubt on a lemma until you know a
proof. Our modern world is built on algorithms like long division, but I
wonder if so much people have bothered proving why it is correct to
split the problem like that.

That Hacker’s article, it boils my blood and comments are now closed. Just about all of school’s subjects are not going to be used by the majority of people in their lives.  Historians won’t get to use calculus. Engineers won’t get to use History. But that’s the whole point. For starters, how are kids ever going to find out they like Maths, or they like Calculus if they don’t get to it?

And Americans supposedly struggle with Algebra. Isn’t it a reason to make it a more important subject rather than to delete it? If such a basic skill is not as easy to learn, then we need more education for it.

Statistics replacing other things baffles me. How are you going to learn statistics without calculus or algebra?

I think there has to be made more game theory and optimization and the such. The moment you start seeing that with some math and creativity, you can really get better results. Spend less money, spend less time. Win more often than lose. It tells you, the reason you are not using math knowledge to improve your life, is because you never learned it well enough.

Where does the savage fit in?

Thanks for this post. I totally agree with you and was completely offended when I read this article in the NYT this past weekend. I am so sick of the dumbing down of America. As someone for whom math was always a struggle, I am grateful for that fact that I retained some geometry and algebra because I use it almost every day. In the business world I often find myself shocked when people can’t even create a simple formula in Excel.

The U.S. would be absolutely stupid to remove Algebra from the curriculum. Not only would it increase the general dumbing down of our population, it would decrease our ability to create and be innovative. Another issue is jobs and people capable of doing them. Yeah, we’re still recovering from the recession and unemployment is high but just look at some of the professions in which we don’t have enough skilled workers: Medical doctors (The same issue of the NYT included an article noting the the U.S. will face a shortage of 5,000 medical doctors by the year 2014) and software/computer engineers. Both of these professions require mathematical skills far beyond Algebra. We might as well just hand over our economy to Asia because Algebra still matters there.

I’m appalled at how short sighted the Hacker article was.

Alpha children wear grey. They work much harder than we do, because they’re so frightfully clever. I’m really awfully glad I’m a Beta, because I don’t work so hard. And then we are much better than the Gammas and Deltas. Gammas are stupid. They all wear green, and Delta children wear khaki. Oh no, I don’t want to play with Delta children. And Epsilons are still worse. They’re too stupid to be able to read or write. Besides they wear black, which is such a beastly colour. I’m so glad I’m a Beta.

 Pretty sure that’s not Italian, I bet it is French or Spanish.

One of the things I try to explain to my students (I tutor all subjects through elementary school, and math/physics/literature through high school) is that every subject – every one, from mathematics to fine arts – is the same subject. Knowing more about one thing helps to understand everything else. The artist and the theoretical physicist both do the same thing – they observe the universe, grok it, and demonstrate why and how it is or is not amazing.

 I’m not convinced that lack of programmers is due to the dumbing down of America(or Canada, for that matter). In fact, I view it as a smartening up of the population. Kids growing up over the past 20 years or so have witnessed the absurd upheavals of this industry and decided, en masse, to forgo it. That’s actually smart. Why enter professions that the corporate world values so little and has no problem with simply shipping wholesale overseas, and in fact searches day and night for the slightest reason to do so?

 Ah, Kodachrome 25. Now there was a slide film.

The four blondes go to Starbucks and the bill comes to $28.
They can’t work out how much that is each so they call the cute waitron guy
over to help them.

He decides that they are as blonde as they look, and says “That’ll be
$25 each.”

The one blonde who’s a bit sharper than the others says, “How
did you get that number?”

He says, “Easy if you know long division.” He takes pen
and paper and writes:

   ________

4 | 28

“Now 4 doesn’t go into 2, but 4 goes into 8 twice, so we
write it like this:”

         2

   _________

4 | 28

“2 times 4 is 8, so we have to subtract it from 28, and that
leaves us with 20.”

         2

   _________

4 | 28

         8

    _________

     20

“But 4 goes into 20 five times, so we write it like this:”

       25

   _________

4 | 28

         8

    _________

     20

     20

    _________

       0

“And so $28 divided by 4 is $25.”

Well all the blondes think that he’s not only seriously
cute, he’s really clever too, so they happily give him $25 each.

But after he’s gone, the one blonde who’s a bit sharper than
the others says, “Something doesn’t seem right. I wanna check that.”

So she writes down,

    25

    25

    25

    25

 ________

“Right, so 2 plus 2 plus 2 plus 2 is 8.”

    25

    25

    25

    25

 ________

    8

“Then 5 plus 5 plus 5 plus 5 is 20.”

    25

    25

    25

    25

 ________

    8

    20

 ________

    28

“And 8 plus 20 is 28. He was right.”

On a point of note: Required reading for anyone old enough to masturbate is Simon Singh’s “Fermat’s Last Theorem” (USA title: “Fermat’s Enigma”) which is an awesomely brilliantly written book which will keep you riveted for each of its 300  odd pages.

Read the reviews here: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622/ref=sr_1_1?ie=UTF8&qid=1343752001&sr=8-1&keywords=fermat%27s+last+theorem

I’ve read his “The Code Book” and “The Big Bang” and both are real examples of science writing at its most gregarious… I’d even score him a half a point above Dawkins!

There were times when I learned French that most of our time seemed to be taken up with memorizing irregular verbs. For months on end. English has maybe 300 irregular verbs that you actually need, but they only have three forms. In French it’s more tenses (for English it’s only two past forms) and of course more genders. So although there may be less irregular verbs in French, a lot more time needs to be spent learning them.

Yeah French grammar is consistent, but it’s also a lot more extensive than English. English has one of the most simple grammars.

HS math class probably taught me the most “real-world” lesson in school.

  I was great at understanding math and did well on tests, but I was disorganized and lazy.  The math teachers at my school formed some sort of cabal where they all required that we keep a “math folder” with sections for our notes, turned in assignments, a running total grade, etc.  This stupid thing made up like half our grade, and I was always trying to put it together right before grading, and getting upset that they marked down my notes because I wrote down what I needed to remember, not exactly what they wrote down on the board.  I was furious and frustrated that so much of my grade had nothing to do with my actual ability to do math (at which I was very good at) but my organization (which I sucked at), and consequently my grades suffered.

I have found this is the most work–like experience I had in school.  People don’t care so much that you can do the job, but that you do the job the way they want it done-including things that you don’t think are important and aren’t a part of your job title.  

While people balk at learning math at the high school level, at the university level STEM  (science, technology, engineering & math) classes are the least threatened to but cut due to budget cuts.

My wife was someone that was scared of math. She could calculate a 20% tip but did it the hard way. I showed her that dividing by 10 and multiplying by 2 was quick and easy. I also showed her how Algebra can help in daily life by showing how to check her speedometer. I showed her the math involved in rate x time = distance came to simply dividing whatever number of seconds it took to go a mile into 3600. She still doesn’t quite grasp that and thinks that I am some sort of savant but I believe that anyone can learn simple algebra and apply it to things in everyday life.

Why would an educational establishment that gets a lot of it’s funding from lotteries want a public that understands math?

Clearly LESS MATH is the solution to our country’s personal credit debt crisis.

IMO..

Every high school in the US should have 4 years of Math, 4 years of science, 4 years of Econ, and 4 years of Social Studies (not effing history, i mean social issues like white privilege, civil rights, etc..).

Maddox makes a terrific point. Every dumb ass in my class was ecstatic to read Shakespeare but cringed at the thought of doing Trig.

Or, on the other hand, consider the fact that Hacker is a professional writer, and still can’t manage to express his argument without making a lot of the people who he most needs to reach if he wants to seriously implement his ideas think that his main argument is that math is hard. Maybe it’s the fact that he essentially says as much in the very opening of his piece.

If it wasn’t for the genders, I think I could have continued with German. I was always excellent at grammar and decent at remembering new words. The genders were just impossible for me to learn though because there was no logical reason why some words were male, female, or neutral. It was very inconsistent which words were which.

cutting a cake correctly for an odd number of people?

bollocks! then there’d be no extra slice left over for me!

“Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.” Wonderfully summed up Hemant!

In Singh’s book (to which I linked above) you can read how elliptic curves are related to modular forms via the Taniyama–Shimura conjecture.

Two totally different areas of mathematics that were found to be inextricably linked! 

The beauty of this discovery is that problems (of elliptical curves, for example) could be solved using the techniques of other mathematical disciplines (modular forms).

Sexy stuff. 

http://en.wikipedia.org/wiki/Modularity_theorem 

I didn’t take Spanish in school, but after working for 9 years with a group that was mostly Hispanic, yeah,… Spanish is a handy thing to know. What some people don’t understand is that it never hurts to know things, just for the sake of knowing it… never mind there comes that time when ya DO wish you really had paid attention in class.

so I sucked at math when I started high-school. my elementary teacher told my parents I would never ever make it to university. (my parents laughed and gave me the freedom I needed.I really want to see her again and show her the PhD I got last year) My first year in high school, we had a math teacher who told us that some of the stuff was hard but he was teaching us in small steps because small steps are easy, only the big leap is “hard”. I don’t remember anyone complaining and the class average was a B+ . in high school. in math.  I still remember that. It has helped me through a lot of statistics in university. Maybe this anecdote helps. I tell my student that a lot of statistics problems are fear, not that it’s really hard.

Generally I agree with you here, so I’m just gonna jump in on one point you made.

“We also have to revise our teaching because we live in a world with graphing calculators and Wolfram Alpha — and we want students to use them. So let’s teach them when and how to use those tools. Again — less regurgitation of skills, more critical thinking.”

Back in my Junior year of high school, I argued (successfully, in the end) that I should be allowed to use TI-BASIC programs during tests, provided I had written all the code for them. By writing the software, I was giving myself a much stronger understanding of the methods of solving complex equations. If I didn’t fully understand an equation while writing the code, I’d end up with wrong answers on the test day, and it would be my fault.

As it turned out, I ended up falling in love with programming after being able to use it in such a practical way, and it has driven my course through life from that point onward. I use math every single day, even though I work with numbers very rarely. Math is simply the logic underneath the flow of information.

And I really wish that was what we’d been taught in class.

 I speak Spanish, so you can find out what was my post about :).

I was one of those kids that struggled with math. The first time I took Algebra I, well, I barely passed. Know what I discovered? The teacher wasn’t teaching very well (he was there 20+ years and really didn’t care anymore). Most students barely got a C in his class. A few of us got a student teacher as a tutor that summer, came back with new skills (our tutor is now a math teacher at my old school, the kids are lucky because he knows how to teach well) and most of us ended Agebra II with Bs and As. We even helped other students understand things.

I think it’s less to do with the subject and more with how it’s taught. Teacher taught it in vague abstracts and told us to read the book, tutor taught us the same abstracts and how they may apply in our lives later. I know which method worked best for me and many others.

Good teachers and relatable lesson plans. It can be done.

And sorry, Hemant, I still don’t care for geometry. ;D

“Show me a student who can’t find x and I’ll show you a student who needs an iPhone app to calculate a 20% tip.”

Really, Hemant? Really?

You are so very wrong. I’m sure you wouldn’t make a similarly sweeping generalization about, oh, let’s say,
atheists. So I’ll make one for you, even though I am an atheist myself:
“Show me someone who doesn’t believe in gods, and I’ll show you someone
who’s incapable of feeling love, expressing joy, and creating great art .”

Ever heard that one? I have.

Here’s the thing: I have zero aptitude for math, and zero interest. But I’m
very good at foreign languages. Nevertheless, I was forced to take
Algebra I twice in high school, but couldn’t take French III or IV as a result because my schedule was full. I can
make an extremely strong argument that, as a writer, I would have gotten far
more value out of French than I have ever gotten out of Algebra. The idea that you can’t learn critical thinking skills anywhere but in a math classroom
won’t wash, either. I learned them — far better than my own father, a mechanical engineer who tithes 20% to
his megachurch every single week.

Do I use math everyday? Of course. We all do. Is it math I learned in 4 semesters of basic Algebra? No. I learned how to make change, figure a tip, do my taxes, figure
out how much paint I need to cover my walls, and all those other “life
math” skills you need to function in society, by seventh grade. I can’t
“find X” to save my butt. Nor do I care to. Believe me, I’d love to
be good at everything, just like all of you clearly are. But I’m not, and I
never will be.

So how about we drop the whole “STEM careers are the only ones that smart
people go into” and “Algebra was easy for me and you’re just a lazy thinker” crap, and realize that people are different. That doesn’t mean that
the non-mathematical among us are stupid. Let’s meet our students where
they are, help them find their aptitudes, nurture their interests, and send
them out into the world armed with the practical skills they need to function every
day and the passion to excel in their chosen fields, whatever those may be.

Finally, this whole discussion reminds me why I have cut down dramatically on my reading of atheist blogs and websites. Most of them display a bias towards STEM readers and professionals that goes completely unquestioned. I would remind you all that it is very possible to be an atheist, a skeptic, and a critical thinker without knowing how to solve for X. It saddens me that, as an artist, there is clearly still no place for me here.

Try manufacturing just about anything without a good working knowledge of math.  It won’t happen.

Yes, yes, and yes! Your experience of math is almost identical to mine — although I never made it to Trig. I had to take Algebra I twice in order to take Geometry I, which was ridiculously easy for me. But because I could never have passed Algebra II, I wasn’t allowed to take Trig. Which was probably just as well. I took one math class in college — Finite Probabilities, same as you — and passed with a C- only because my then-boyfriend was a Physics major and coached me through it.

The problem in high school wasn’t my teachers, either. They were, by and large, good teachers who did the best they could with me. No one could understand why someone as bright and inquisitive as I was simply couldn’t cut it in that one subject. When I look back on my high school math classes, I still get the feeling I had then: This teacher is speaking a foreign language, and NOT one of the ones I know!

I have a teenage daughter who also struggles with math now, and I hate it that I can’t help her. My husband is a bit better, but not much. At 13, though, my kid already knows how to do just about every “real-life” equation she will ever need. She’s also a great critical thinker and a skeptic. It kills me that she will have to continue to struggle through useless math classes for the next 5-9 years in high school and college, when all she really wants to do is study Linguistics. What a waste of time for her, and for her future math teachers.

I don’t think we should stop teaching math, either. But I also don’t think we should equate achievement in math with overall school success and intelligence. My husband the accountant is completely tone-deaf. Should his school have forced him to stay in choir throughout school anyway? Of course not. Once you get past the point of basic life skills and music appreciation, there’s no reason for non-musicians to take music if they don’t wish to. But that’s exactly what happened to me. I was forced to take and re-take a math class that bewildered me. My constant questions and requests to go more slowly were a nuisance to teacher and students alike. I knew by age 12 that I wanted to be a writer. Advanced math was and is useless to me. I had acquired all the math skills I will ever need by 7th or 8th grade, from figuring a tip to reviewing a freelance contract for fairness. But I was forced to take more math classes anyway, because of some misguided “value” placed on those classes and applied uniformly to all students, regardless of aptitude and interest.

Good point, Rebecca.  My high school introduction to critical thinking and making structured arguments was presented mainly in honors English and history courses, and never touched in math.  The idea was barely touched in non-honors courses of any kind. 
I don’t think Miko’s suggestion is in any way helpful.  In my experience, taking related subjects completely separately only makes it seem like more work, and makes later integration of skills more difficult.  What good is a whole class on making a structured argument if you’re not going to apply it to subjects where stuctured arguments are actually used?  Sure, we could take out more classes to make room for every high school student to take the equivalent of college level philosophy and Intro to Logic classes, or we could fold more general subjects into more specific subjects and help learning actually be interesting.      

Although I never had a very hard time with math, it was presented in the most boring and dry ways possible in high school, hard to absorb and impossible to remember or any length of time.  I would have loved to have had math classes that were more integrated with other related subjects.  I barely passed Algebra 2 because I could barely keep my eyes open and my brain focused, yet I flew through chemistry and college level astronomy because the math was applied to interesting and more concrete subjects instead of just being page after page of numbers with no obvious context.  I know that students should be able to appy math skills generally, and we don’t want to tie them down to  few applications, but a I think more students would learn to enjoy math if we at least tried to make it relevant to something else that interests them.   

You’re making sweeping generalizations that simply aren’t warranted. Hemant’s point is correct: you need an understanding of how to solve for x (at least to a degree) to be able to do your own calculation of a tip. He’s also suggesting that knowing how to do such a calculation is a good thing for any person to know, not just a “mathematical” person. That’s not unusual; we generally have lots of things that we think are standard in a well-rounded education.

You just strike me as taking these things too personally. Maybe it’s the fact that I have long had an interest in science and math, despite pursuing careers in the arts and humanities, but I don’t find that there is any such bias against non-STEM people, of which I am one (I teach high school English). I have never gotten the impression on any of the atheist blogs I read (and I read a lot of them) that I’m not intelligent because I didn’t become a scientist or engineer. Loosen up a bit, would you?

I struggled with math throughout primary and secondary school; while I could usually eke out a B, it took constant work, and a great deal of relearning basics that I had forgotten. By basic I mean multiplication, adding large numbers: BASIC. I also had a hard time distinguishing left from right, selecting between greater and lesser amounts, and telling time. The only exception was geometry, which I somehow breezed through.
It wasn’t until I applied to college that I learned that I had acalculia. The admissions office saw my ACT scores (12 in math, upper 30s in everything else), and called to ask if I had ever been tested for a learning disability. I was floored. Even the teachers who realized that I was struggling never suggested that such a thing was possible. I have since learned to work around my problems, although this entails NEVER using cash, using my iPhone for calculating tips, and forcing all financial decisions on my already-overworked engineer husband who, having bullied me through college algebra (the last required math I had to take), is very supportive. Luckily, I chose my major according to my strengths rather than job prospects, and am currently rocking the perpetual English grad student lifestyle.
I still am grateful that I took all those years of math classes, although at the time I hated every second of them. I may not have learned math, but I learned humility and the importance of hard work. I only wish that there was more awareness that such a learning disability exists, especially among educators in primary school. I always wonder whether there might be strategies I could have learned as a child, before I internalized my not-very-efficient work-arounds, which would have made it easier to do the things I need to use.

tl;dr – Math is useful, even for people who can’t do it. Learning disabilities suck.

For you math is the key to the universe. For me, it’s not even close. And my English degree is far, far, FAR from worthless.

No offense, but I hope you are better at art than logic, because your analogies aren’t that great.  You take great offense yet don’t even realize that you ARE using math and “finding X”, and to be honest it couldn’t hurt you or your art to know a little more. Or AT LEAST appreciate it, and all the wonderful ideas that make what you do in this life possible.

 I too have spent much more time in the arts than the sciences, but really- what are we supposed to do, just say that nothing matters except personal taste?  We encourge literacy in math and science because it’s important and necessary for survival and almost everything beyond survival.  Because circumstances change,  knowledge can fade, and a time could come where your own life, health, or ability to make a living are at stake, and how many people knw useful thiongs could become very important.  How much better would the world be if we just encouraged everyone who isn’t a math genius to ignore math and science, and to be proud of that ignorance, as too may already are?  It might be a world with some stunning art, but only because art can sometimes make great beauty out of suffering and misery.  I doubt there would be many enthusiastic fans though.  Most people who have lived without the many modern benefits of math and science didn’t have a lot of spare time, resources, or motivation to go around appreciating other people’s art, except maybe at church.

I’m a guy who learned critical thinking and basic logic in English and history courses, not math or science.  I’m a guy who depends more on visual artists, writers, musicians, and comedians than scientists (or preachers, of course) for keeping me humble, moral, and open-minded.  But your rant here, quite frankly, comes off as hyper-sensitive and missing the point.  If you think you knew everything you needed to know by the seventh grade in ANY area, AND were capable of deciding that fact for yourself in the seventh grade, you’re self-aggrandizing and dramaticizing to the point of delusion. 

Als0-I don’t know what kind of high school you went to or when, but how did repeating ONE math class make you miss out on TWO electives?  By my senior year, I had at least three electives, half of my class day.  If you couldn’t come up with another elective to cut out to make room, is the school just supposed to give you a pass on basic requirements?  There is no art our language class in high school that you can’t get privately or in college- but innumeracy, unfortunately, is often forever.  For a school to say “Oh, it’s okay, she’s wanted to be an artist since she was 13!” would just be stupid and negligent. 

You know, that would explain a lot.

“Every dumb ass in my class was ecstatic to read Shakespeare but cringed at the thought of doing Trig.”

And there’s the very questioning of intelligence that I was anticipating when I started reading these comments.

Trig is no more the answer to our debt crisis than Shakespeare, by the way. Although…a close reading of “The Merchant of Venice” might be illustrative.

Really good Economics and Consumer Math classes? Absolutely. Trig. Nope.

 Much like when the kids get rid of their parents in a retirement home!

I did the same thing way back in High School but in my case, I programed my HP reverse-Polish calculator.

I wrote a program that used numerical methods to home in on a solution through iteration to a problem and used it on a test. While it was cranking way, I went on and solved the problem analytically by hand in parallel just to have something to do while the program was running. We both got the same answer.   The teacher was impressed.  I got a good appreciation of the two different ways to solve such problems.

There was an Abbot and Costello routine that played with numbers like that.
https://www.youtube.com/watch?v=rLprXHbn19I
Someone else did a variation of it, too.
https://www.youtube.com/watch?v=omyUncKI7oU

Not a programmer, so not applicable.  I am an artist, and learning to draw involves a great deal of very pragmatic information about perspective, color and volumetric space.  The craft aspect of art is very learn-able, and used to be considered essential for gentlemen and their ladies (like penmanship).  But nobody expects everyone to draw, even though it is a useful skill involving logic, spatial and critical application problems.  It is really applied geometry, but seldom taught as such.  “I can’t draw” is considered a valid excuse (by many artists, as well), but I don’t get math is some kind of crime or deficiency?  I know how to find the information I need on the internet, and I have never needed algebra for anything but a grade in a class.  And I do make change instantaneously because I leaned the multiplication tables by rote up to 15×15 — now that has been useful.

Like like like like! x 1000!  🙂  Señora Friedman dice: Most of you aren’t learning Spanish to become Spanish speakers or to use Spanish in your job.  Some of you are.  That’s awesome!  For the “most” of us, we’re learning Spanish to get our minds to think about things differently, to express things from more than one point of view, to understand our *own* language better, to understand other people and cultures, and to give us a leg up when we start studying that *other* language that we really wish were offered in high school.  I don’t care if you never say more than “Hola” after graduating.  

If you want computer scientists to understand long division, make them write a program that is able to divide arbitrarily long numbers (or add them for simplicity). There are some algorithms that are more efficient than literally replicating the way you do it per hand, but hardly anyone will bother to look those up.

 …In basic Spanish you write basic logic by the end of 1st semester “Él es artístico porque le gusta cantar, dibujar, y pintar” (He is artistic because he likes to sing, draw, and paint).  In advanced Spanish you do the same expository writing essays that you do in language arts and have debates in the target language. 

…In art you defend your media and color choices based on precedence and artistic purpose

…In science you write lab reports that provide evidence for or against a hypothesis

Structured argumentation and critical thinking exists across the curriculum 🙂

Wow, what a nasty piece of work Maddox’s comment is.

Math is exactly like cooking: just follow the recipe. Symbols look confusing? Can’t figure out how to solve a problem? All I hear is, “Waaah! Boo-hoo! I didn’t read the introduction to the chapter that tells me exactly how to solve this generic category of problems!” Math isn’t some voodoo that only smart people understand. It’s something that people understand on their path to enlightenment, and it’s about as straightforward as thinking gets. … if you’re leading your life in such a way that you never have to do math, congratulations, you are a donkey.

A donkey? Seriously? This is a great way to make people who can’t do math feel even more inferior. Like I didn’t get enough of that in every single math class from second to twelfth grade. Being insulted certainly doesn’t give me warm-fuzzy feelings about the subject he’s trying to promote.

Maddox’s whole schtick is to say offensive things. I still think it’s hilarious. (My personal favorite is when he graded children’s drawings.)

Saying that atheist blogs don’t often focus on the arts and humanities is perhaps a fair point, but I think that just reflects the general interests of the community (so to speak) more than a bias against artsy people. I would recommend searching out arts blogs rather than atheist blogs for that kind of thing, and you might be more likely to find atheists writing about the arts than if you search for atheist blogs that are covering the material (if that makes any sense).

 To be fair, Maddox is an equal opportunity misanthrope.

I think even if kids don’t immediately grasp it, it doesn’t mean they never will. I really didn’t like math in high school and college, but I gained a new appreciation of it when I was already working. If I didn’t have at least some knowledge of it, I never would have had even that to refer back to. 
Re-learning math (and science, but its more difficult to understand that without math) was really important to me because it kind of shaped my worldview. I found it comforting and amazing that some things in the world could be expressed, explained and predicted using math.  It helped me have a deeper understanding of the world and be happier as a result.

I find it more problematic that he seems to think being able to do math is a matter of reading the chapter intro. It’s not that simple. Some of us read the instructions, and we still couldn’t figure out what to do because we couldn’t understand the symbols or the memorize the formulas. To me, it’s like looking at Japanese characters. No amount of poring over my textbook helped because I couldn’t understand what any of it meant and couldn’t remember what to do without copying directly from my notes.

I am always saddened by my own experience with math in school (no programming/computer science programs to have fun in because “it wasn’t in the budget” or “the students are mostly girls, so they aren’t interested, obviously”). Add to that teachers who would use sarcasm/insults/ignoring (plenty of rolling eyes and ignoring questions) to silence students who needed help, and I eventually gave up trying to enjoy math. The only exception to this rule was my Stats class, which I loved and did very well in. Even today, I enjoy pointing stuff about Stats on the news to my friends, and even correcting the news’ interpretation of graphs!

Despite my bad time with math in school, though, I agree that it is necessary. Especially proofs (which funnily enough, I enjoyed heavily because I was having to prove something), which lead to me being good in history debates in terms of organization of thought. 

I’m sorry, but it takes me a little longer to dig out the change due to being disabled. (I do indicate, however, that I have the change, and am digging it out, so please hold on just a moment, thank you.)

I loved “story problems” because they made more sense to me.

My brain just… locks up when you throw a bunch of numbers at it. I do understand that there are a lot of maths that we use on a near-daily basis, yes, even bits of algebra and geometry. I only question the necessity of the higher maths (calculus, trigonometry, advanced algebra, and the like) — we’re not all going to be engineers or programmers, and aren’t going to actually need those things. I think, in some respects, education should be tailored to the student, and for those not going into maths-intensive careers, the requirements should be lessened. I honestly cringe when I think of all the time I wasted struggling with concepts and equations I did not (and still don’t) comprehend, when I could have been furthering my education in other areas.

(Yeah, I’m a word nerd, and I really do wish I could have spent that time and effort on delving more into the forms and functions of language.)

BTW, I have friends who are practicing linguists. They program and use a lot of math beyond the high school level, so I can say this is incorrect. Those classes in math are quite likely to be necessary if your daughter wants to do linguistics at some point.

 When mixing colours for your paint, you do things like X amount of white tint added to the red gives you = Y, right?

Xwhite + Yred = Zpink.

 Didn’t she get by, though? She figured out the change (with some technological help)

Well that’s different. Plenty of people say they have change before they hand me their money and that’s fine. But here are lots of people who hand me their money, watch me enter it in and start to count out their change, and *then* say, “Wait, I’ll make this easier for you!” and hand me their change and they don’t realize that it actually makes things much more complicated.

 Yeah but like all the Greeks are extinct.

p.s. I Pie.

You wrote way too little for an English major.

Tell them that they can get paid more money at any job if they’re bilingual. That might help. I wish I remembered more of my high school Spanish.

I r
² a pie heart-er. 😀

I’m not sure about Japanese. While I was always excellent at languages, anything involving symbols throws me for a loop. It took me forever to decipher Roman numerals and learn how to read an analog clock. Impossible as a child, and even as an adult I still have to spend a lot of time working it out. I also can’t read music. I nearly failed my college music class because we had to learn to read music and compose a simple song, and I absolutely could not do it.

I absolutely agree that basic probability and statistics should be a standard part of the K-12 math curriculum in order to prepare people to be functioning citizens. I don’t know about “pinnacle” though. I took basic probability/statistics in 8th grade as an elective at my rural public school. It wasn’t the most rigorous class but that was mainly because I was the only nerd who signed up voluntarily and one of few who were grade-level proficient at math in the first place. Even so, it covered about the same content at the first couple of weeks of grad-level intro stats.

I am not a math educator but I am a fan of lumping all of the subbranches together and teaching them together. I was taught (7th-10th grade) with a series that included algebra, geometry, and trigonometry in each book and taught it very cumulatively so that we had problems on each topic for weeks and then off-and-on for the whole year. You had to figure something out or you got it wrong every set for weeks. To this day I still think of it all as “algebra” and I am glad that I do because I think if I had had to do trigonometry separately I would have developed a bad attitude about it. We switched for pre-calc, calc, and college algebra and even at the time I thought it was a poor choice. 

I was completely with you right up to the last paragraph of the Maddox quote. If you think students don’t complain that they’ll never need to know the stuff taught in high school English, sciences, etc., I can only conclude that you don’t teach those subjects. I work as a private tutor for kids in Grades 5–12, and they all make that complaint whenever they encounter something they find difficult. If anything, I find English gets the worst of it—kids complain about having to read poetry and Shakespeare and write essays long before they get to anything in math they’re convinced they’ll never need.

Your post is spot on about why math is so important and why the arguments for scrapping it are ridiculous

I’ve used geometry extensively to do things as prosaic as building a picnic table.  In fact I’ve used trigonometry, because I needed to work out such things as how far I needed the table off the ground, and how far out I wanted the feet to go, and how long to cut the legs.  In fact, I’ve used calculus (Taylor-series expansions of the trigonometric functions) because I didn’t have a calculator with me.

Bravo!  My first thought upon reading Hacker’s piece was what difficult subjects should be given the axe next. Writing? Critical thinking?

Algebra is often taught when kids are 13 and 14, far before they know WHAT they’ll be doing in college and beyond. Education is about giving people choices down the road — we help children develop a toolbox of skills that allow them to choose from the wide array of options of study and work. Omitting algebra eliminates options down the road.

Elementary math in this country is poor. It’s largely taught by people uncomfortable with math. Change needs to happen there, at the start. Poor mathematics education early turns kids off to math as well as poorly preparing them for higher math. Fix that, and more will find algebra enjoyable and interesting while keeping their options open.  Here’s my longer take on it: http://quarksandquirks.wordpress.com/2012/07/31/math-matters-a-response-to-is-algebra-necessary/

I don’t think math has a “pinnacle”.  In my experience, by the time you’re halfway through a decent undergraduate understanding of math, it just starts branching out like mad.  Then those branches start cross-connecting.

Sorry. Not true. 5+5=10, but 5 +5 is not equal to 1*x^1 + 0. 
It’s irrelevant, I know, but I just couldn’t resist the urge. 

In my view, mathematics should be studied for its aesthetic beauty. The fact that it has real-world applications is only a by-product.

I suggest you to read “A Mathematician’s Lament” by a school teacher, Paul Lockhart.
http://www.maa.org/devlin/LockhartsLament.pdf

It’s not that students don’t complain about them, but that it is socially acceptable to complain loudly about math and not so much about literature (being illiterate is connoted with being stupid, but not doing math is connoted with being normal) or a few other subjects.  It is true that certain aspects of each subject is allowed to be viewed as something for the elite only (some poetry, history, non-English languages in North America), but watching Jeopardy you’re more likely to see a trivia question based on any of those than you are about math.

That’s why the “math is singled out” argument is even stated.  In fact, my girlfriend was an academic advisor at a community college for a while and she came across more math-phobia than anything else.  

That’s great, really, it is. It’s just that some of us simply don’t (and in some cases can’t) grok the higher maths.

Call me weird, but I
use algebra in real life
occasionally

First you say, “For example, one of the things my department is working on this coming year is getting away from spending all our time on skills that just require mindless work — plugging and chugging — and spending more time in class on one or two problems that require a lot more thought.” and then you say, “But the students who don’t do well in algebra usually struggle precisely because they don’t know basic arithmetic.” Correct me if I’m wrong, but it sounds as if you are planning to try and teach skills through problem solving, and that methodology already has been proven to be ineffective. How do you expect students to be successful without the drill? They DON’T know the basics, and cutting them out of the curriculum is setting your kids up for failure. I have been teaching for 22 years and am an educational consultant, presenting workshops to teachers, so I have “been there and done that,” so to speak. This is not a good plan – there has to be a balance between drill and problem solving.

In regards to the article, the thinking skills you are talking about can be taught outside the parameters of algebra and geometry. I have been teaching since before the time that students could graduate without ever having taken Algebra I. Back then, Algebra I curriculum is what we teach in Algebra II today. Why? Because we have had to water stuff down so much so that everyone can pass and be successful, even though everyone doesn’t belong there. I agree that Algebra and Geometry teach problem solving skills that kids need no matter what field they go into, but do the really need college prep Algebra and Geometry, dragging the true college prep kids down to their level? No, I think there is a better way, and Statistics may be the answer. I have met Art Benjamin, and he may be on to something…

FOIL is just an easy way to make sure you’ve done all the necessary multiplications. What’s the problem?

 Maddox is known for his inflammatory writing. He doesn’t tiptoe around anybody’s emotions. He bulldozes right through them.

Algebra is just a technique for  understanding the relationships between numbers.   Things like:

When people drive more, what happens to gas used, and to gas prices.

 How much faster do you have to drive, if you need to get somewhere by 5 and you don’t want to drive fast over the 20 miles near the speed trap?

Calculus is just a technique for tracking how quantities change, and how those changes add up.