
Abandoning Algebra Is Not the Answer - tokenadult
http://blogs.scientificamerican.com/observations/2012/07/30/abandoning-algebra-is-not-the-answer/
======
jeffdavis
"Math certainly is incomprehensible to many students, but from where I sit,
poor teaching is often the reason."

I'll paraphrase what I said in the last thread: algebra isn't harder than
other subjects, it's more objective. Therefore, it tends to make educational
fraud more visible. People rarely fail algebra and succeed in other subjects;
they fail in all subjects and algebra is the only one where it can't be
ignored any longer.

~~~
mrxd
In the humanities, you are taught how to understand what people are trying to
do with language, so I can't help reading your comment from that perspective.

You say people rarely fail algebra and succeed at other subjects. To put that
another way, let's assume that there are four sets. Set A consists of a group
of people who are successful at one or more subjects, and Set B consists of
people who are successful at no subjects. Set C consists of people who are
good at math, and Set D consists of everyone else. Your statement implies
that, for the most part, A = C and B = D.

Thus you seem to be arguing that excellence at math is the sine qua non of an
educated person -- it is a defining characteristic.

What might you be trying to do with this line of reasoning? It seems fair to
assume that you yourself are skilled at math, so really you are making a claim
about yourself and other people who are similar to you. Your model of an
educated person is based on yourself. In society, educated people are people
whose judgments should be trusted and listened to, so we can conclude that the
purpose of your argument is to try to get those benefits for yourself and
people like you. Conversely, we can also conclude that you are trying to have
those benefits removed from people who are different from you.

~~~
einhverfr
Exactly. I have a liberal arts degree and studied math basically only through
first year calculus. The strange thing is, compared to most people around me,
I am relatively skilled at math. I can do algebra, some calculus perhaps at
least pulling some estimates of integrals and derivatives, but my real love is
in humanities.

The reason why algebra is important has nothing to do with the GP's idea that
it is the most objective of studies. Algebra is _useful._ That's it. People
who know basics of algebra can use it constantly. I could see replacing
geometry with a deductive logic class since that's all one studies with HS
geometry anyway. I could see teaching less plane trig and more spherical trig
too (I tried to teach myself spherical trig in order to better follow some
writings of Ptolomy and others, and failed). But these aren't going to happen.
But if you don't know algebra these doors are all closed.

~~~
rimantas
Skills in math are skill in seeing patterns and operating abstractions. Those
are very very valuable skills, no matter what are you doing.

~~~
einhverfr
This is true, but when you look at geometric proofs all you are doing in HS
geometry is deductive logic using an abstraction which is a general
approximation of the real world. That's why I could see getting rid of HS
geometry and just having a deductive logic class too, perhaps with a unit of
Euclidean Geometry included in it.

Algebra and calculus are different though. They are tools for finding unknown
information and thinking about changing values.

------
comicjk
This essay is still buying into the idea that algebra is "higher level," or
that only people who identify as mathematicians would be affected by this.
There are 1.5 million engineers in the US and 3.1 million programmers, and
without algebra they would be as helpless as lawyers who couldn't read.

This essay says "Hacker is probably right that very few people use high-level
math directly in their work." If algebra is counted as high-level, then no,
Hacker is dead wrong. His position does not deserve even the modicum of
respect which this essay gives it.

------
WalterBright
My accounting prof used to be a used car salesman. I was talking about that
with him one day, and he said that a car dealership doesn't make money selling
cars, but makes it selling financing.

The people who really pay through the nose for financing are people who do not
grasp mathematics. He said it wasn't just a matter of them being taken
advantage of - even when he explained the lower cost option, they'd insist on
the higher cost one, based on faulty notions about math.

If you don't learn math, it's going to cost you plenty your whole life, and
you won't even realize it. Math is necessary, even if you don't go on to get a
STEM degree.

~~~
theorique
_a car dealership doesn't make money selling cars, but makes it selling
financing._

This also scales to the production level. Prior to the recent troubles, GMAC,
the financing arm, was larger and more profitable than GM, the auto maker.

------
ak217
Stupefying.

With friends like Andrew Hacker, does this country need enemies?

On the other hand, perhaps we can take this as an opportunity to discuss the
accessibility of math education, the level of engagement and hands-on examples
that teaching materials give, and how this can be improved with modern
teaching aids (tablets). I know I certainly struggled with engineering-grade
math in college (math was one of my majors, but not a favorite one), and I
blame the combination of my laziness, poor professors (rewarded for
publications, not teaching), and poor teaching materials (far removed from
practicality).

I'm really excited by how much better kids' aptitude and quantitative
cognitive skills will improve over the coming years for the ones who have
access to tablets. New apps are popping up that make learning elementary math
a joy... apps that can keep a kid's attention without adult help - starting at
age 4. This will be a serious boost to whichever nations/groups emphasize it.

~~~
rimantas

      > I'm really excited by how much better kids' aptitude and quantitative cognitive skills
      > will improve over the coming years for the ones who have access to tablets.
    

I say we will see zero improvement caused by tablets (or any other technology
of this kind). This is not a technological problem it cannot and wont be
solved by technology. Technology might aid a tiny bit with it, but just that.

~~~
darkestkhan
This is much more complicated. Technology may add a lot, not just a tiny bit,
but it has to be used in such way. While certainly apps are being created [and
soon they may reach much harder topics, like indefinite integrals] the core
issue is in using them - there is no point in technology alone if it is not
used. It depends heavily on parents so that they can enable and encourage
children to use the app but it also depends on children to use [or rather
play] the app.

Technology is not solution to the problem per se - Technology only enables us
to solve the problem.

------
rossjudson
I'm not going to defend removing some of the math. What I will say is that
improving understanding of statistics, generally, is something that most
democratic countries desperately need.

------
zarify
From the article, I particularly liked the bit about math being useful to
doctors so that they can learn to succeed in the face of a challenging
subject... as if medicine isn't enough of a challenge in itself.

I would certainly like to see more statistics in high school math, since
people are bombarded with bad stats every day through the media and just
swallow it up without thinking. It's hard to agree that other aspects should
be dropped though (although I am in favour of repurposing some math courses to
better meet the needs of the students).

------
imgabe
The real problem I think, or at least part of it, is that it's considered
acceptable for kids to be declared "just not good at math" and left at that.
It's presented as a skill that you're either born with or not, instead of one
that can be improved with practice. We wouldn't find it acceptable to declare
a kid "just not good at reading" and give up on teaching him to read, so we
shouldn't do the same for math.

~~~
mangodrunk
It's a little different though. I think a better analogy would be writing, and
I have seen people claim to not be good at writing as others do with math in
general. Reading would be like counting in math, and most people can do that.
I agree though, that with practice many would probably benefit from it for
either math or writing. But there will be some people, who will just be not
good at math short of some upgrades to their brains.

------
jinfiesto
This was an interesting read. I think the author of the original paper though
has some valid points and that this response labeling the original paper
"anti-intellectual" is dishonest in that regard.

In my opinion, the problems we have with Mathematics education in this country
stem more from how the curriculum is structured than from particularly bad
teaching or lack of natural ability. Looking back, it seems bizarre that all
of elementary school gets devoted to performing arithmetic and then Algebra is
suddenly introduced sometime in middle or early high school. In my opinion,
arithmetic can be taught much faster than it is (Trachtenberg system et alia)
and basic Algebra should really be introduced concurrently.

The problem with this approach is that you can no longer sell neatly
compartmentalized textbooks labelled "Addition," "Subtraction," ... ,
"Algebra" etc...

The other thing that bugs me is the bizarre choice of topics taught in Algebra
classes. I remember, I was forced to memorize the binomial theorem. At the
time, it really made no sense. I'm now of the opinion that you shouldn't be
taught math you don't have the machinery to develop on your own. Knowing
arithmetic, you can build Algebra (not very rigorously, but the idea seems
pretty obvious.) It's a much bigger leap to develop the binomial theorem,
which requires more advanced machinery, which is generally not taught.

Of course, once I could derive the binomial theorem on my own, it made much
more sense.

I did very well in math throughout my academic career, but didn't ever really
feel like I had very much mathematical skill. Only now that I've developed an
interest in doing math in a recreational capacity that I really feel like I've
developed any sort of substantial mathematical ability. I'm really now
convinced that the problem solving approach is the way to go and that this is
how early math should be taught.

~~~
mangodrunk
Now that you mention it, it does seem that too much emphasis and time is spent
on counting and calculations. A symptom may be how some people equate doing
fast calculations with being good at math.

~~~
jinfiesto
It's funny how that escapes detection. I only realized looking back how
baroque that was. I think people do equate doing fast calculations with being
good at math. While I think everyone should certainly know how to add,
subtract, multiply and divide without error, there's really no reason to be
able to do so obscenely quickly, given the wide availability of calculators.
If you did want to be able to do very fast mental math, there are much better
systems than what are typically taught in schools.

Really though, my point was that the school system spends far too little time
on solving substantial problems in Math classes. I think an integrated problem
solving approach that touches on many of the important branches of Math (graph
theory, number theory etc...) would serve most people much better than the
current system, where we spend 8 years building up to Algebra and then engage
in a smattering of Geometry and Trigonometry.

In the current system, if you're smart, you do AP Calculus, which is obscenely
dumbed down. If you want to proceed to study Math in college, you'll almost
certainly have to re-teach yourself calc to be successful.

------
numeromancer
The original article is another iteration from the ancient and venerated
Academics with Inferiority Complexes Society. Here is an article discussing an
earlier effort from this time-honored society:

<http://www.sourcetext.com/grammarian/newslettersv06/6.1.htm>

This article is by the late malcontent newsletter The Underground Grammarian,
a diabolical work which has cleverly trapped me into spending entire nights in
the wicked attractions of its addictive prose.

An à propos quote from another part of the site:

 _However, while the retreat from the measurable provides comfort for the
educationist[and, apparently, the occasional “political scientist”], it makes
it hard for him to claim, as he would so dearly love to, that "education"[...]
actually is a body of knowledge and that his Faculty Club card should not be
stamped: "Valid only when accompanied by an adult." What a dilemma._

------
tsotha
>Hacker’s first main point is that math is difficult, and the poor grades that
result prevent too many people from graduating high school or college.

Yeah, great plan. Dumb down high school and college even further so even a
monkey can end up with a BA. Then we'll all have great jobs.

------
385668
Hacker sounds like kind of an idiot. I really liked the point made that being
able to analyze "The Old Man and the Sea" doesn't come up very often in day to
day life, but is still a good thing to be exposed to. Additionally, I
appreciate the valid opinion that most teachers, particularly elementary, and
to a lesser extent, middle school teachers have little to no math education.
My mother actually changed majors and became a teacher because she did not
have the prior education to pass calculus, and did not think she would ever be
able to pass it. She's a very good teacher, and very smart, but it's for the
best that she teaches HS English, and isn't required to teach math.

------
wikkiwa
Let's just have the chinese do our math and then pay them with the money we
borrow from them.

------
natep
As he says, Hacker's essay had so many flaws it's hard to know where to start.
On the other end of the spectrum, this (and the linked) essays raised so many
_good_ points that it's still hard to know where to start.

------
ctdonath
The biggest un-addressed problem is sheer lack of will. A significant
percentage of students _will not_ do the work. They'll show up, they'll go
thru motions, but will not do the actual _work_ required. Telling them they'll
fail won't help: they either don't care or don't comprehend. Punishments won't
work because punishments are forbidden. Offering more assistance and resources
won't help because those are tools, useless if unused. They do nothing, life
goes on in an acceptable manner. They have no reason to do the work, so they
will not do the work, and thus will fail.

------
alberthartman
Math, especially algebra, is essential to all technology. Counting and
measuring and projecting forward are foundational skills. The thing is that
there are two basic aspects to algebra, one is conceptual and the other is
mechanical. The conceptual part is interesting and worthwhile to most people.
The second thing is what drives people off - the long detailed mechanical
aspect of accurately doing long equations, perfect transcriptions, looking for
simplifications and cancellations. But it is precisely this laborious
mechanical aspect that has been drastically improved with modern symbolic math
software like Mathematica and Mathcad, et al. Factor a twenty term formula, do
any integral, or differentiate a messy equation in about, oh, half a second?
The failure is that we don't teach these software skills right at the start.

How boring would writing be if we didn't let students use word processors with
their perfect erasers, spelling checkers, scissors, tape, carbon paper, and
endless new blank sheets? Or if we forced all architects and engineers to use
rulers, pencils, Leroy lettering guides, and E-size paper on drafting boards
every time they wanted to design something for others to build, not allowing
them to use Solidworks or Autodesk, or equivalent modern tool to help? Ditto
for movie making, or pretty much everything else.

Algebra is great. Teach it along with teaching the modern symbolic math tools
that go along with it.

------
nyrulez
Instead of getting all riled up, it's fair to realize that there is such a
thing as free market, demand and the corresponding motivation to supply. Folks
write all sort of controversial opinions (there was this essay a few months
back from a UCSD professor in Bloomberg about how CS education is overrated
and the folks in CS don't make enough money).

My response to these kind of articles is: everything is fair game. If someone
or some community thinks CS or math is not for them, it's their right. It's
just that the demand will be filled up by folks who do believe in it (like
folks from outside US which constitute a significant portion of most CS/tech
firms inside US). Ultimately, if some folks in US realize they are losing too
much potential out there by refusing to raise their bar, they might re-orient
towards the demand. If they don't realize this/stuck in their
stubbornness/incompetence, then they didn't probably deserve it anyway (or
don't care).

Agreed that there is short term pain for folks who get effected by these kind
of policies outside their choice.

~~~
retrogradeorbit
Free market. Seriously? There are no free markets anywhere in the world today.

------
ctdonath
As a counter to any complaint about how hard algebra is: recall the recent HN-
featured app DragonBox. It strips away the boring/confusing irrelevancies of
the subject, replacing the appearance with cute tiles and animations -
creating a game where a kid learns the core concepts. If my 4-year-old (and
even my 2yo) will sit there for prolonged periods playing and picking up rules
& techniques on her own, then surely high school students can grasp the
subject - if they choose to.

[http://www.hnsearch.com/search#request/submissions&q=dra...](http://www.hnsearch.com/search#request/submissions&q=dragonbox&start=0)

------
dougabug
Sad that the march to abandon reason has reached this far, where even the most
rudimentary mathematical knowledge is scorned. Maybe degrees should be given
out based on attendence and self esteem. Without algebra, people could not
evaluate even at a broad level the tenability of a scientific or technical
claim, they would be denied any form of meaningful understanding of
probability, algorithms, complexity, physics, chemistry, biology, astronomy,
even linguistics has deep roots in algebraic notions. To abandon the teaching
of algebra would be to condemn the public to a life of ignorance and obedience
to crowd think.

------
thisrod
Forcing rooms of teenagers to factor cubic polynomials for hours on end is
pointless, of course; these essayists fail to consider that pointlessness
might be the point of school, as it is of boot camp. Read John Gatto instead.

------
tpr1m
For years and years I've wasted time in the classroom with Algebra, a skill I
will _never_ need in my lifetime. As a computer science major, I find it
perfectly equatable to make my math teacher sit through the same amount of
time in some of my major-specific classes, since he will get just as much
value out of them. Not to mention I have to pay for it.... difficult or not,
most math classes simply are not useful. This differs from other "general"
classes, such as English.

~~~
jinfiesto
I find this to be short-sighted. I also program, and have found Algebra to be
very useful. Solving a problem trivially with Algebra can sometimes save you
lots of programming work. Granted I don't use Algebra in my day to day, I'm
glad I know how to do it and have found it useful often enough to say I'd be
less of a programmer without it.

------
alter8
> Eliminating abstract math education in the early school years, or allowing
> young students to opt out of rigorous math classes, will only serve to
> increase the disparity between those who “get it” and those who don’t. Those
> who have a grasp of mathematics will have many career paths open to them
> that will be closed to those who have avoided it.

This is currently true on programming, which is (was?) left out of the basic
curriculum.

------
scotty79
USA already abandoned knowledge of evolution as visible here:
<http://www.youtube.com/watch?v=UkBmhM0R2A0>

Now it's time for math as imagined here:
<http://www.youtube.com/watch?v=9QBv2CFTSWU>

------
johnx123-up
Site crashes my Chrome and IE. Probably as Xdm.swf is pinging for every
second.

Safe URL:
[http://viewtext.org/article?url=http://blogs.scientificameri...](http://viewtext.org/article?url=http://blogs.scientificamerican.com/observations/2012/07/30/abandoning-
algebra-is-not-the-answer/)

------
dinkumthinkum
So, the answer to people failing at _basic_ mathematics and being unable to
pass high school or college is to simply lower the standards? Why stop at
mathematics? Why not stop short of anything beyond being able to write Tweets
or just figure out where the signature box on a loan application is (but not
understand all those funny things that come before it)?

Many want to say college degrees aren't necessary. I say fine, great that's
awesome. For this NY Times article, I say, well of what utility is a high
school education? I think it benefits society for people to be able to read at
least enough for Google to sell people text-based advertising that most
citizens can modestly understand so we should have training to a fourth grade
level or so. But really, once you know "1+1" then just leave it that and it's
time to go to the Nissan plant.

This just seems like someone saw the movie Idiocracy and decided "that's a
good plan."

We have a bad education system in some ways in the U.S? Much of it is probably
related to poverty and, perhaps, to some extent, parental irresponsibility.
This is just pathetic. The idea that we should just throw away any standards
is hard to take serious. For many people in this audience, it would probably
benefit us greatly, financially, but if you care about society as whole, it
doesn't sound very appealing.

~~~
rimantas
I am not that knowledgeable in US education and policies, but there is/was
some "no child left behind" thing going on and I may be completely off, but my
impression was it has something to do with all this. My (again, possibly
completely wrong) understanding of it, that the end effect was "let's pretend
we don't have dumb students" instead of "let's help the bright students".

If someone can shed more light on it I'd appreciate that a lot.

~~~
stinky613
I may not be much better suited to answer your question than you, but my
understanding goes more like: the intent was "let's use standardized testing
to identify and then help weak students and to support schools that yield good
overall students (according to the test results)" and the result was schools
trying to game the tests to maintain/gain funding.

------
cafard
I buy the "no bad students, only bad teachers" argument--though I must say
that might teachers from 8th through 11th grade were good to very good. I buy
the "more objective" arguments I see here and elsewhere. The "push-ups for
your brain" maybe not so much.

------
biggfoot
When you start defining education & learning 'objectively' you can kiss
progress goodbye. That we don't directly apply most of what we learn is a bad
way to look at why we learn stuff in the first place.

------
retrogradeorbit
I found the late George Carlin had an even better explanation of the New York
Times piece.

<https://www.youtube.com/watch?v=9dY4WlxO6i0>

------
scrame
Innumeracy should be treated like Illiteracy.

------
tkahn6
Any discussion about mathematics that fails to distinguish between
computation-based and proof-based mathematics is not going to be a very
informed discussion.

There's a reason that so many would-be math majors switch out when they reach
Intro to Proofs. Up until then it's just memorizing formulae and recipes;
you're just a glorified TI-89.

------
ten_fingers
Let's see: The author of the essay is in political science. Here notice
'science'!

Now, I have to wonder: (1) In political polling, could he give a solid
definition of a simple random sample? Could he suggest how to select one?
Could he explain just why we often want a simple random sample? (2) Could he
explain why in political polling we average to estimate a population
proportion? That is, the average is a statistical estimator. Just why is it
the estimator we want? (3) If he is to estimate variance, does he know which
of the two common algebraic expressions is biased and which is unbiased? Can
he define a biased estimator? (4) A common topic in political science is
principal components analysis, and key there is orthogonality in vector
spaces. Can he suggestion how to give a solid description of that topic
without algebra? (5) Political science likes to construct quantitative
measures, and there two important issues are 'reliability' and 'validity'. Can
he give solid discussions of these two issues without algebra? (6) Political
polling reports results with an 'margin of error'. Could he define that? The
usual calculation is based on the central limit theorem; could he describe
that? (7) One of the more important research tools in political science is
statistical hypothesis testing, especially nonparametrics. There the core
concepts are Type I error, Type II error, power of a test, and a most powerful
test. How can he describe this material without algebra?

Uh, a first course in algorithms commonly described heap sort and points out
that its execution time, on sorting n items, is O( n log(n) ) in both worst
case and average case and, thus, is best possible in that it meets the Gleason
bound. Without algebra, how is a student to understand the significance of
that material?

The world is moving on to more in automation. The main approach here is
computing where we describe what we want and how to get it in terms that are
essentially mathematical -- e.g., stiffness of arbitrary space frames, finite
element analysis in solid mechanics, Reynolds number in fluid flow, sines,
cosines, and exponentials in A/C circuit analysis with passive components,
force, torque, energy, power, and momentum in mechanical engineering, etc. All
these subjects commonly assume first and second year algebra, plane and solid
geometry, trigonometry, analytic geometry, calculus, and ordinary differential
equations.

For political science, we should include linear algebra and multivariate
statistics.

That author wants less algebra but more statistics? That's like saying he
wants to lose weight but eat more!

Yes, to too great an extent, public K-12 is more about babysitting, i.e.,
keeping the kids off the streets, than about education. Moreover, really, math
is too difficult for essentially all of the US K-12 educational community.

