

"I can't do math" (2001) - mejakethomas
http://faculty.umf.maine.edu/michael.molinsky/public.www/iaq/mmm001.html
My favorite professor's take on the ever-increasing "I can't do math" statement.
======
mjn
I see his larger point, but the conflation of "understanding math" and "being
able to do simple arithmetic" is something of a pet peeve. The latter may be a
useful life skill, but is not very closely related to understanding
mathematics. In fact it's not only non-technical office workers who can be
proud of not being able to do it: if you walk into any _math department_ you
will find accomplished mathematicians almost gleefully recounting how bad they
are at doing simple arithmetic. They can prove things about topological spaces
but can't balance a checkbook!

That makes the comparison to literacy more complex. Clearly mathematicians
think mathematics is important, or they wouldn't be studying it. But many of
them consider ability to do arithmetic, as a skill, essentially irrelevant, to
the point where they don't even learn it themselves. Then a question might be:
what _is_ the relevant literacy-like skill? I think it comes closer to logic
and analytical thinking than specifically mathematics, although understanding
of statistical arguments fits into that category.

~~~
Derbasti
I think being able to interpret common mathematical writing in your area of
expertise is a valuable skill. I think this is what is meant by "understanding
math".

I don't know much about anything but signal processing, but I am able to read
and understand vector/matrix notation and differential equations. This enables
me to read most papers published in signal processing. Just like being able to
at least roughly read most C-derived programming languages, this is a valuable
skill.

I have seen coworkers "not understanding" my work because it involved problem
descriptions in mathematic notation. Frankly, it annoys the hell out of me.

~~~
ebiester
How about I write my comments in Turkish? It's your fault you don't understand
them, after all.

The art of programming, and of comments, is the ability to communicate to
another human, and incidentally to computers. (I believe that was a paraphrase
of Knuth.) If the terminology gets in the way of their understanding, then use
a different terminology.

(I can fight my way through a mathematics paper, myself. But why be obtuse in
your communications?)

~~~
jarrett
Mathematics offers a standardized, internationally accepted notation for its
various problem domains. Turkish is not the standard language of software
comments. So I don't think the analogy holds.

~~~
frenchy
Neither is math. My guess is that you will find many more Chinese programmers
who understand English comments than those that understand high-school
mathematics symbols.

~~~
jarrett
I would venture that any such programmers ought not work on a math-intensive
domain like signal processing. Sure, not every programmer has to know high
school math. You can, for example, do great work with HTML, CSS, and
JavaScript without knowing high school math. But there are certain fields
where math is unavoidable. Signal processing is one of them. And the
internationally accepted notation for such math is part of what you're
expected to know.

BWT, I assume you're not saying China uses different mathematical notation. I
wouldn't know about that. If so, then that does undermine my argument.

------
Irregardless
People who say "I can't do math" are lazy? Sorry, but I think that's a gross
oversimplification of the issue (which is also evidenced by the comparison to
physical exercise) and the two assumptions fundamental to that opinion are
just plain wrong. Namely:

> _So what do people actually mean when they say that they can’t “do” math?
> Usually they are really stating one of two things. First, that they don’t
> like mathematics. Secondly, that mathematics is more difficult for them than
> other subjects, and that it takes a great deal more effort on their part to
> learn it._

He conveniently chose the two reasons that are easiest to dismiss (irony,
anyone?). What he fails to account for is the fact that math education is so
poor that many people don't truly understand _what math is_. Beyond arithmetic
and algebra, they think it's some really complicated stuff with big numbers
and funny symbols that geeky people with glasses do -- it's practically a
foreign language to them, except it has a reputation for being much harder.

Why is this? If I had to guess, I'd say it's based on the fact that math
involves a lot of critical thinking and critical thinking is very difficult to
teach. Those who attempt to do so often do it very poorly, which leads
students to the false belief that math is extremely difficult. On the other
hand, it's very easy to teach someone to memorize formulas and plug in
numbers, so that's what we're most often taught in math class. That's good
enough to get us through the standardized test so we can graduate from high
school, but memorizing formulas and plugging in numbers is not "doing math".
So I believe many people are completely justified in saying "I can't do math".

What's more, people who "can do math" should be taking the blame for those who
say "I can't do math" rather than using pointless semantics to wag a finger at
them.

~~~
lenazegher

        What he fails to account for is the fact that math 
        education is so poor that many people don't truly 
        understand what math is. Beyond arithmetic and algebra,
        they think it's some really complicated stuff with big 
        numbers and funny symbols that geeky people with glasses
        do -- it's practically a foreign language to them, 
        except it has a reputation for being much harder.
    

I can attest to this. Academically, I am a reasonably able person, but I found
math simply baffling at school. Arithmetic and algebra were fine. Rudimentary
geometry made sense. When we got to trigonometry, things just fell apart for
me. We were taught sine, cosine and tangent in the context of how they could
be used to derive angles from other angles, not what they _were_ and how they
_worked_. They were presented as tools that could be used in particular ways
that had to be memorized. To me, it felt like trying to teach an alien from
another dimension to use a hammer without the alien having any intrinsic
understanding of mass or momentum or kinetic energy or friction.

In fact, if I'm totally honest, I'm not 100% I completely understand the sine
function now. And it wasn't just math. In physics, current, voltage,
resistance etc. were taught as inputs to formulas. I know it must be
challenging to teach about these kinds of principles that lack concrete
macroscopic analogs, but I can't help but feel they could have done a better
job than they did. In chemistry too, I remember being taught about valency and
how you could work out the valency of an element by its position on the
periodic table. I asked what valency actually _was_ , either didn't understand
or wasn't satisfied with the answer, asked again, and the teacher brushed off
my question and carried on the with the lesson. "Oh well," I thought, "I guess
I don't understand chemistry." That was when I was about 12 years old, and I
didn't study chemistry after that. I studied biology until I was 16 because I
had a teacher who took the time to actually explain things.

The worst part is, I went to a pretty good school. It must be absolutely
dreadful at bad schools.

Most of this happened before I had regular access to the internet and the
chance to learn about these things for myself. I can't help but feel the whole
course of my schooling and advanced education might have been different had I
had better (or at least different) teachers of hard science and math at an
early age.

~~~
SiVal
It's the phrase, "I'm just no good at math" that breaks my heart. Most of the
time, the student is taking the blame that belongs to the education industry.

Last week, my son had a "Chapter 9" math test here in a top-ranked Silicon
Valley public school. His teacher pointed us to an official study guide PDF,
which we went over carefully. I was not at all surprised to find that it
covered a random grab bag of unrelated topics: sorting a half-dozen fractions,
each with different denominators, two different silly algorithms for
multidigit multiplication, how many $2.30 widgets can you buy for $9.00, and a
few others.

This incoherent, random presentation of unrelated topics within a single
chapter is totally characteristic of the "reform math" so beloved by our
"progressive educators." They despise the approach of methodically working
through a small number of carefully sequenced topics, making sure that the
foundation of layer N is solid before getting to work building the closely
related layer N+1 on top of it. They call it, "drill and kill," "soul-
crushing," and "creativity destroying."

Instead of mastering a few closely-related concepts each year and
systematically building expertise, they prefer "exposing" kids briefly to lots
of unrelated math ideas, trusting that some kids will get some of it, and
telling the rest to "trust the spiral," meaning trust that when they hop,
skip, and jump over multiple topics the following year and the year after
that, most of them will eventually "get" most of the stuff.

The result is that many parents just teach their kids real math outside of
school. Many in our neighborhood send them to Chinese school, which teaches
them math in addition to Chinese. The Chinese school buses line up in front of
all of our local elementary schools at the end of each school day. (A lot of
blond kids board those buses.) Some send them to Kumon, which is getting to be
as common a sight around here as McDonalds or Starbucks.

I teach mine myself, using non-US curricula (Chinese, Japanese, and
Singaporean in my case.) I feel terrible for the kids who don't have parents
doing the schools' job for them, whose math skills are limited to what they
can pick up from their classmates in "group discovery" sessions, since the
"professional educators" have now decided that kids learn best what they
discover for themselves and now serve merely as "guides on the side" in edu-
speak.

My son took his Chapter 9 test and reported to me that, with the exception of
testing the two different, useless multiplication algorithms, the test was a
DIFFERENT grab bag of unrelated math topics, bearing little resemblance to the
study guide. Totally typical of "reform math." He did fine, but only because
he had learned all of it outside school. His friends who rely on what they
learn at school think he's a genius.

So kids go through this ridiculous joke of a math education and can't do math.
The school points at their friends who did just fine (because--shh!--they
learned math elsewhere), the school takes credit for having taught them so
well and tells the others and their parents, "well, not all kids are equally
good at math, but many of your classmates learned quite well," clearly
implying that the kids who didn't are somehow defective.

The result is that those kids will soon be saying, "I'm just no good at math."
What a disgrace.

~~~
mikevm
Any chance you could link me to the non-US curricula materials you use to
teach your kid?

I found a lot of the things you talked about in this school's approach to
education: <http://www.russianschool.com/about-us/our-approach>

~~~
SiVal
I can't link you to the Chinese or Japanese materials, because I bought them
in Shanghai and Tokyo. Also, they aren't written in English. The Googlers next
door use Russian materials from Moscow, also not written in English.

It's hard to do better than Singaporean materials, which are in English and
modified (not in a bad way) for the US market, which you can find at
SingaporeMath.com. Their Primary Mathematics series is superb. I use the
Standards Edition, which is said to track the California State Math Standards.
That sounds ominous, but actually the state standards are excellent. The
districts essentially ignore them by using a ridiculous "reform" curriculum
that, being "a mile wide and an inch deep," will always include a checkmark
every year for any topic you can think of, thereby covering anything mentioned
in the state standards (superficially and in random order).

Note that for these Asian curricula, you REALLY need to know how to teach the
math. The textbooks only provide visual aids and example problems, not the
tutorial text (paragraphs of explanation) typical in US books. If you go for
Singapore Math, you should get the Home Instructors Guide (at least for a few
levels), which teaches you how to teach it.

And DON'T start a kid at too high a level. Use the placement tests
downloadable from singaporemath.com to decide where to start. It's all about
carefully building up from the bottom, mastering each level before moving on.

~~~
mikevm
Thank you very much!

------
R_Edward
I had a trig/pre-calc teacher in high school who I really respected. He had a
catchphrase in his classes, especially in the earlier math classes. "In my
class, there are only two kinds of people: those who love math, and those who
are going to learn to love math." I only had the one class with him, but he
left a huge impression on my life. He was convinced that computers were going
to become essential to education, so he spent his department's entire budget
for a year on two spankin' new Apple ][+ computers. Just set them on carts in
his classroom and didn't touch them. He knew he didn't need to. Eventually, a
handful of us approached him to ask if he could teach us to use them. "No," he
responded. "I don't know anything about them myself... but they came with a
tutorial, so maybe you could teach yourself how to write programs, and then
maybe help me out."

That changed the course of my life. I was planning to be a lawyer, catering to
artists and performers. My time spent learning to write programs led to my
taking a number of computer science classes in my undergrad, for the easy
grades they represented, which then led to majoring in CS, and, eventually,
opting for a career in software development.

All of which is just to say that, if someone feels that they cannot "do" math,
maybe they missed out on the right math teachers; those who understand kids
and know how to motivate them and who have their own love for the subject
matter and are able to infect others with it. If their math teacher(s)
couldn't be bothered to make personal connections with their students, nor
find any way at all to make math relevant to their lives, it shouldn't come as
a surprise if they wind up being uninterested in "doing" math.

~~~
duopixel
What a wonderful person. I sometimes take the time to contact teachers that
have made an impact in my professional/personal life and thank them for
setting me on the right course. It's a really simple gesture but they are
always thrilled to hear they've made a difference.

------
wtvanhest
The key problem with math is that the learning keeps going and at some point,
every single person fails to either have the ability or time to learn more
math. Everyone becomes "bad at math" relative to other people. This same thing
doesn't happen with reading because once you are a pretty good reader you feel
like you have mastered it.

3 examples: 1) Kid who never completes pre-calc. "can't do math" 2) Adult who
gets through calc, but doesn't go any further "can't do math"... like an
engineer 3) Math PhD. who gets stuck on something they can't solve.

Person 1 and 2 are both stating they can't do math, and both people are
relatively right. Relatively being the key word.

If we rephrased the way math is taught, it would never be labeled as math at
all. This would box people in to saying things like "I don't do calculus"
which would be correct in many cases, whereas it would be alarming if someone
said "I can't add".

Really, whether people say "I don't do math" or "my bad" doesn't really matter
and being stressed over it is probably just as ridiculous as saying those
things.

~~~
CamperBob2
This can't be overemphasized. My favorite (apocryphal) Einstein anecdote is
the one where a society matron approaches him at a party and exclaims, "I
don't know how you can deal with all that math. I have _so_ much trouble with
math." Einstein replies, "Lady, you can't imagine how much trouble _I_ have
with it."

s/math/computers, and that line comes in very handy in my own social life.

------
jpwagner
Indeed there is something wrong with someone saying "I can't do math..." but
it is not what the author identifies.

In blunt summary, the author says "you may not be able to do the specific math
you claim, but don't worry I'll teach you." In my experience this is not at
all what the complaint is saying and the solution "I'll teach you" is not at
all what they are looking for. The comparison to illiteracy is completely off-
target.

In my experience, "I can't do math" is simply "I don't know" in disguise. Ask
most children: "what's 300 times 248" and you get a knee-jerk "I don't know".
Ask also "what's a balloon made of"; "I don't know". Same goes for many other
questions that appear to them to have a definite answer. We excuse children
for saying this, but it becomes less and less acceptable as an answer because
we learn of tools for finding the correct answers.

The real lesson that needs to be taught is:

Your worldview of can/can't do math is wrong. Doing math is learning what
tools to use after we've broken down our question to its core...kind of like
everything else.

~~~
chrisdone
Saying “I don't know” is a fantastic skill that children are born with but
have it beaten out of them into adulthood and the beating never stops. I have
deep respect for people who can say “I don't know.” That person is one step
away from learning something new.

~~~
jpwagner
It's great when adults who do not usually say "I don't know" can admit to not
knowing something. Other than that, I cannot agree with anything else you say.

------
a_p
My favorite story about how Ernst Kummer [1] did arithmetic, from Hoffman's
_The Man Who Loved Only Numbers_ [2]:

"One story has him standing before a blackboard, trying to compute 7 times 9.
"Ah," Kummer said to his high school class, "7 times 9 is eh, uh, is uh...."
"61," one of his students volunteered. "Good," said Kummer, and wrote 61 on
the board. "No," said another student, "it's 69." "Come, come, gentlemen,"
said Kummer, "it can't be both. It must be one or the other." (Erdos liked to
tell another version of how Kummer computed 7 times 9: "Kummer said to
himself, 'Hmmm, the product can't be 61 because 61 is a prime, it can't be 65
because that's a multiple of 5, 67 is a prime, 69 is too big-that leaves only
63.' ") "

[1] <https://en.wikipedia.org/wiki/Ernst_Kummer>

[2] [http://www.amazon.com/The-Man-Loved-Only-
Numbers/dp/B004R6HX...](http://www.amazon.com/The-Man-Loved-Only-
Numbers/dp/B004R6HXRQ/)

~~~
fyi80
> Erdos liked to tell another version of how Kummer computed 7 times 9:
> "Kummer said to himself, 'Hmmm, the product can't be 61 because 61 is a
> prime, it can't be 65 because that's a multiple of 5, 67 is a prime, 69 is
> too big-that leaves only 63.'

That's how I do problems like that, too (I am not a genius mathematician), and
it is exactly the sort of thinking that kids should be doing all through K-12.
Estimation, intuitive reasoning, analogy, pattern matching, logic, etc.

~~~
rimantas

      > Estimation, intuitive reasoning, analogy, pattern
      > matching, logic, etc.
    

Alas, most of the things on your list require a pretty solid foundation to
work. You need patterns already committed into your brain to do pattern
matching and to see analogy, you need to have internalized experience for
intuition to work, you need to have previous exposure for any meaningful
estimation. All to often people forget foundation when they move to the upper
layers and sadly sometimes this leads to thinking that foundation is not
necessary. And now matter how you look at it there will always be bits of the
foundation that require rote learning.

------
pfortuny
It is not that people can't do math. It is that other people (who supposedly
can but in fact cannot OR will not do them properly) insist on them doing the
math they do not need (like computing the second derivative of the
unemployment rate) or doing wrong the math they DO need (like with their
mortgages).

As long as people can add, subtract, multiply and basically understand what a
division is, they can do math. The problem is they are scared at what other
people tell them 'math' is.

I am a mathematician, a professor of mathematics and witness to what I have
said.

Of course people cannot do 'math' when 'math' means being able to compute
multiple integrals or roots of third degree polynomials. That is not 'math'
that is UTTER RUBBISH EXCEPT FOR PROFESSIONALS in all caps. Really.

You do not expect the average man to be able to write a sonnet with
alliteration, second order metaphors and in iambic, do you? And they call
themselves "literate".

People are not lazy, they are scared. An the blame falls on BAD MATHS
TEACHERS, in all caps. Really.

~~~
piato
Hi, I'm a former (high school & middle school) math teacher. I taught various
ages, but was only ever responsible for curriculum with age 10-11.

We studied a lot of fractions, decimals, percentages & converting between
them. There was a bit of angle stuff mixed in there, too.

I love mathematics, so I think I'd be the sort of teacher you could see eye-
to-eye with. What should I be doing differently?

~~~
pfortuny
Hi! That is exactly what they need: fractions are just a way to explain
division and it helps them a lot (actually they are the basis for the "rule of
three" which is the "fifth rule").

Proportions. Trying to start with square (?) triangles and the idea of
similarity of triangles so that they can later (when 12-13) understand
trigonometry (the basics) which, once again, is PROPORTIONALITY. There is
little more to 'maths' than that.

What I object to is the unnecessary abstraction. Getting 10-11s to perform
correct computations is hard but exactly what they need: lots of exercises (no
sweat no learn or whatever).

You are a HERO. Really. In all caps My respect. I teach undergrads and this is
way easier.

~~~
piato
Aw! This was super kind, and I like the idea of stressing proportionality.
It's nice to be told that the abstraction can wait - I've felt like I should
be abstracting more at times, but it's not my natural instinct, so it's nice
to be told I'm doing things right on that front! I feel the same way about
anyone who can teach older (or younger!) mathematicians - keep on keeping on.

~~~
pfortuny
[A night later]

Oh, I really mean it. Teachers to children (and especially maths teachers) are
essential for our society, and have one of the hardest job.

Focusing on proportions you can teach almost anything: from basic triangle
geometry, including elements of what later they will know as 'trigonometry',
to interest rates -even letting the best get the scent of 'compound
interests'-, to areas & volumes to the notion of 'speed' as a ratio, to how to
save money for the future... There is little more a normal 'literate' person
needs to know, as I see it.

However, it takes quite an effort getting them to actually perform the
computations. This is where 'good' -appealing- exercises and problems are
required, and this is where the teacher's craftmanship comes into play. A good
craftman will find the correct and 'fancyful' exercises, according to the
class, the student, the time... You know, this is where the 'heroism' takes
place.

All the best.

------
btilly
The underlying problem is two-fold in my opinion.

#1 We focus on teaching procedures rather than understanding. Most people
therefore view math as a list of memorized fixed procedures, and that's
intrinsically very hard to remember and become good at.

#2 Math is simple in a way our brains are not wired to be good at, yet we have
a mistaken belief that simple is easy. It is not. Adding 1000 numbers by hand
and getting the right answer is very simple, but hard. Recognizing my voice is
very complex, but easy. Be aware that your brain is working in a way it is not
designed to work and have patience with it. Otherwise you'll get frustrated,
and mistake "It took me this long to understand something THIS simple?" for,
"I'm stupid!"

The result is that most people understand math in a way that is hard, and
their experience of math is an experience of repeatedly confirming the message
that they are stupid. Is there any wonder that they take that frustration out
on the entire subject of mathematics?

------
speeder
I only think the author forgot that there are people that REALLY cannot do
math.

It might sound bizarre and weird, but I met more than once person, that did
their best to learn, and were intelligent with many other things (one of these
persons had a degree in law, another in international relations, and was doing
a masters in international law), yet could not do 29/3 without a calculator...

Or even worse, I knew people (in that case usually working with more low level
work, like burger flipping) that even trying, or even if needed (ie: cashiers)
cannot do it right even with a calculator, their grasp of math is so weak
(even if they want to have a grasp) that they cannot even use the correct
operations.

Also the same apply to many other fields, I knew intelligent people that could
not read, or that could not grasp history, or geography, and so on...

People keep forgetting that brains CAN be very specialized, and be great with
something, and terrible with other, and I personally believe that the old way
of teaching professions (ie: throw the kid to work with a Master in that
profession) was better because of that, currently you throw kids on the
school, and the ones that might excel at some things that are not on school
(like Music) reach adulthood thinking they are dump and they don't make a
effort even in thinks they do have a talent to do.

~~~
com2kid
> It might sound bizarre and weird, but I met more than once person, that did
> their best to learn, and were intelligent with many other things (one of
> these persons had a degree in law, another in international relations, and
> was doing a masters in international law), yet could not do 29/3 without a
> calculator...

There are multiple ways to learn even something like arithmetic.

Some people can naturally juggle a lot of numbers in their head and can
basically brute force problems.

Others can break problems down into component pieces, work out each individual
piece, and reassemble them into an answer. This requires a different type of
mental juggling than the above.

And then there are those who just have to memorize a lot of problems.

When I was in school, we started off with memorization (multiplication tables
and such), which requires a _large_ time investment that I am sure many
students did not make. (My peer group tended to stay inside during recces and
practice our multiplication!) After that I think we were supposed to
"naturally" progress to breaking problems down into parts, but that was never
really covered all that well. From what I understand, other countries make
this part of learning arithmetic very explicit.

A good deal of this involves training ones working memory. Right at the end of
college my working memory for numbers was amazing, I could do 3 digit divides
in my head, and at one point I could even do a binary search to find
logarithms down to a decimal place or two!

But as with many other skills, they degrade from a lack of use.

29/3? I have a minor on mathematics. If you give me that problem, I'd honestly
type "win-r calc 29/3 enter".

Now days I have problems just adding up large strings of numbers, I play a
bunch of D10 games and I have to actually do math rather than it coming to me
instantly!

> People keep forgetting that brains CAN be very specialized, and be great
> with something, and terrible with other,

Well yes of course, but we choose what to specialize in! I really do believe
that anyone can learn math if they put the time and effort into it. My math
classes took 2-3 hours a day of studying a good 4 days a week in order for me
to completely grasp the concepts being taught.

Repetition of hundreds of problems, as much as I hated it, was the only real
way to burn technique into my head, and even then most of those techniques
have fallen by the way side! A few still bounce around inside my skull, but it
has been a good 8 years since my last math class, so the amazing feats of
mental gymnastics I could perform are long gone.

On the flip side, ask me to design a test infrastructure for code sometime,
and I'm right on it! How about a custom memory allocation scheme? No problem!
Specialization indeed.

------
egutesman
Seymour Papert (<http://www.papert.org/>), inventor of Logo in his seminal
work Mindstorms (1980) did a very good job on analyzing this phenomena.

Not only he did a great analysis on children but also came up with Logo, one
of the best paradigm-changing environments for teaching math.

On his second book, The Children's Machine (1991), almost 11 years later he
went deeper into the issue of computer's at schools and what should or
shouldn't be taught at school on math lectures. There's a nice section on an
experiment involving hat he called "Kitchen Math" which served to evidence
that a constructivist approach is inevitably better than memorizing formulas,
rules and formal stuff.

I recommend both books to anyone interested in this topic.

Here is a link to an essay written by Dr. Papert in 1996:
[http://papert.org/articles/AnExplorationintheSpaceofMathemat...](http://papert.org/articles/AnExplorationintheSpaceofMathematicsEducations.html)

------
swinnipeg
I went through this exact issue with a junior employee moved to my team to do
some analysis that required a basic understanding of medians/means and a
little intro stats.

It took about 8 weeks of tasks with incremental mathematical challenges to
overcome this, and at least reach the point where he could do his work, and
apply the fundamentals learned to solving more complex problems.

In the end he "could do math", the real issue was he had never "put any work
into math".

------
brudgers
Telling people they can do math because they can add is disingenuous at best.

"Ciphering" is the term that used to be used for figuring sums and such.
Nobody pretended that was math. At the school house it was called
"arithmetic". It was one of the three "R's" not something with it's own Phd
granting departments at universities.

People who say they cannot do math are speaking with the knowledge that they
are looking up toward a massive intellectual edifice containing ideas they do
not understand - whether they are looking up to high-school trigonometry or
differential equations or Bayesian statistics is irrelevant.

What is relevant is that they are not looking up to ciphering as unobtainable
- at least not those people likely to be conversing causally or academically
with a tenure track academic.

------
e3pi
When `she' said "I hate math".

Read as: I hate the public school/university mathematics rote droning
pretentious pedagogy ecosystem.

I personally still retain a enthusiastic thread of the childlike wonder and
delight 15 contiguous years in classroom minefields attempted to lame, but its
`opportunity cost' has been expensive.

Today's increasing autodidact free materials eliminates this cost.

------
edtechdev
It traces back to cultural and educational issues.

Math has typically been taught devoid of any context or relevance to our
everyday lives. Even in college, you just mindlessly plug and chug formulas to
get by. Some students don't see the use in it, beyond perhaps the parts needed
for basic financial literacy (which many do not have, either).

Better and more engaging and relevant and effective ways to teach math have
already been developed, such as Realistic Mathematics Education.

But people actually say things like "I can't do math" in regards to all forms
of literacy, I believe. It depends what standards you are mentally comparing
yourself to, I guess, such as professional vs. social standards.

"I'm not good with money, or I'm not good with the business stuff" - financial
literacy

"I can't write" - as in, I can't write books or novels or easily do other
professional writing tasks. Again, there are pedagogical techniques that can
help students write more, write better, and have more interest and confidence
in writing.

"I don't read" - most folks nowadays don't really read books or novels
anymore, what with TV, movies, and the Internet.

"I don't know computers" - how often do we hear that - that's computer
literacy. I hear it less and less though nowadays.

To tell you the truth, maybe it will be nice when one day people feel forced
to admit "I can't code." Because that would mean that programming and
computational literacy is something taught in most schools.

~~~
derleth
> most folks nowadays don't really read books or novels anymore, what with TV,
> movies, and the Internet.

Reading off of a screen is still reading. I don't know why some people think
paper is magical.

~~~
will_work4tears
Sadly, most of what is on the internet counts as reading the same as watching
a spongebob episode and "The Stand" both count as watching a 'show.'

It's telling when writing a 3-4 paragraph article requires a ;TLDR section.

Usually when a person says they are a "reader," or the like, are specifically
talking about long works, not articles in Maxim magazine.

~~~
derleth
> It's telling when writing a 3-4 paragraph article requires a ;TLDR section.

You mean humans are still lazy mammals as opposed to being industrious
insects? Say it isn't so!

The rest of your post has nothing to do with the Internet. People read Maxim
both online and off. We haven't changed.

~~~
will_work4tears
My post was, in context, not about the Internet, it was in response to your
comment in reference to:

"most folks nowadays don't really read books or novels anymore, what with TV,
movies, and the Internet."

Comparing reading a 3-4 paragraph article on HN (or elsewhere) as being the
same as reading a book or novel, the "rest of my post" was an anology.

True, those people that don't read ebooks or longer articles propably were not
reading books or novels to begin with, so it is a win for literacy, but its
just as likely they just shifted to that because it's easier to read an
article off their phone while shitting than turning the pages of a physical
magazine.

So TLDR; Reading articles online isn't the same level of effort as reading a
book, which your comment seemed to support.

------
sbashyal
This reminds me of my experience with people in China when I was there. My
friends there told me that many young people in China do understand English.
But every time I approached them with "Do you speak English?" They usually
took two steps backward and replied "no". They hesitate speaking English
(because they find it difficult) despite knowing enough to serve my purpose.

I have had similar experience with "Do you know maths?" in the US.

------
ltnately
Really good book on the subject that deals with why/ramifications of a society
that's okay with "I can't do math" as a reasonable thing for an otherwise
educated person.

Innumeracy: Mathematical Illiteracy and Its Consequences John Allen Paulos
[http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-
Its...](http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-
Consequences/dp/0809058405)

------
piato
One fun parallel - not to literacy, but to another skill at which artsy types
are often better than mathematicians - is the oft-repeated, and completely
acceptable, "I can't read minds".

Lots of people can read minds. Not literally, of course, but they've put in
the work (and perhaps it was work that they found easy and pleasant, much as
many programmers found math) to be able to essentially tell what people want,
don't want, are implying, will be offended by, etc. Yet I've certainly heard
plenty of people, and especially STEM-types, making a point of pride about
lacking this skill: "I'm a straight-shooter" and the like. There's aspergers
and there's dyscalculia, but many STEM types who happily admit to lacking this
skill are just like those whom the author bemoans - they find it difficult and
uninteresting. And that's okay! But it's no truer, really, than "I can't do
maths".

------
jcampbell1
When I hear, "I can't do math...", it gets immediately translated in my head
to, "My math skill are on the level of a typical 5th grader, and I don't want
to be asked to do math because it will expose an embarrassing ignorance." The
author's approach to people that feel this way is likely to humiliate them
further.

------
300bps
This sounds like an extension of the recently widely covered practice of not
telling your kids they're smart. Basically, studies have shown that praising
your child for intelligence as opposed to hard work can cause them to
undervalue effort. They start to separate subjects into things they are "good"
at and things they are "bad" at. They then avoid the things they've labeled
themselves as bad at doing.

On the contrary, praising a child for their hard work seems to not be
associated with this same negative behavior.
[http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-
should...](http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-shouldnt-
tell-your-kids-theyre-smart/)

------
cupcake-unicorn
Yeah, I didn't like this article. It's overly harsh and doesn't take into
account other situations. I have dyscalculia, the math version of dyslexia.
People generally don't say "I can't do English" if they have dyslexia, but
they can say, "I can't spell" which I wonder would be assessed as harshly by
the author as this article.

Also, it was pointed out that what math is can be fuzzy - I always thought I
was BAD at math, when I was young and it was still adding numbers together and
stuff, which I only can do with great difficulty. Once I got into algebra, I
was already devising my own ways to solve equations and acing the class
(although they told me to stop solving the equations in my own way...)

------
forrestpitz
I feel like the sentiment of "I can't do math" stems mostly from the way math
is taught. To contrast we can look at how reading is taught to elementary
students. Students read books at their "level." Once they are comfortable with
the words and concepts in a given level then the difficulty of the content is
scaled up appropriately. In math, students are often pulled along with the
rest of the class. It is very difficult to understand division when you are
still struggling to understand subtraction. This happens for a number of
reasons but mostly because it is more difficult to teach math on an individual
level the way reading can be though. I think that the solution to issues like
this will/would look similar to the reverse model that the folks at
KahnAcademy are creating. It's clear that it is difficult to teach math of
every student is at a different point and understands a different amount of
math. By transferring the teaching onto prerecorded videos the students are
able to learn at their own pace and rewatch the lessons for more difficult
concepts without exasperating the teacher. Salman Kahn has stated that his
cousin (that he first started making videos for) told him that she liked
learning from him in his videos more because he wouldn't get frustrated when
she didn't understand a concept. She could just watch it again. This also
frees the teacher to help the students who are learning at a slower rate or
have gotten stuck with a difficult concept.

------
6d0debc071
We seem to accept what's essentially illiteracy in all the subjects that
require more precise thinking as the status quo. Most people don't seem to
understand much about chemistry, physics, logic or computers either, and that
doesn't get them in for a lot of stick.

If people are poorly taught and have gaps in their understanding that are
never adequately addressed, then I can see how they'd think that the problem
was them - that they couldn't do maths. Couldn't make the connections that
were expected of them and portrayed as normal functioning for maths.

Maths is different to history, and many other subjects, in that regard. If you
don't understand something in history, it probably doesn't have a massive list
of dependencies that you're going to fail a lot of stuff in the future on. If
you don't understand something in English, the worst that's going to happen is
you have an esoteric interpretation of the text. You can still do those
subjects if you don't really understand them, as long as you use the right
buzzwords and hook them off the right things.

I suspect part of the answer may just be that admitting you can't do history
or the like is different to admitting that you can't do maths in that it's
unclear what someone would even mean by claiming that they can do history.
Certainly the claim that someone knows a lot about the broad strokes of
history would rarely be justified these days.

------
akiselev
I do like the author's comparison to illiteracy. Language, just like
mathematics, tries to solve the problem of communication but while language is
more about the expression of emotions, thoughts, and feelings, mathematics is
meant to describe precise ideas and abstractions in a quantified way. While
language can be ambiguous in how it relays our true intentions, mathematics is
anything but. It is the only method humanity has that, through experiment and
observation, can help us reach for and perhaps even attain absolute truth.

Just like reading/writing, you don't learn mathematics (real maths, not
arithmetic) to be able to scribble symbols on a piece of paper. You learn it
to develop a way of thinking that promotes certainty and helps you develop and
understand complex abstract ideas that describe how the world works. When you
dive deep into math (or programming for that matter), you don't just learn a
subject, your brain actually reconfigures itself and fundamentally changes how
you act and think. This effect, called neuroplasticity, functions pretty much
until you die so it's never too late to learn math.

When someone says that they can't "do" math it says nothing about their
intellect. All it says is that they didn't like the mathematical equivalent of
"The Cat in the Hat" taught in primary school and are now going to live (many
quite proudly) without the mental faculties to express and grok abstract and
complicated ideas and systems. Sadly, now more than ever, we need each and
every human to have these faculties if we are going to survive and thrive as
individuals and as a species.

------
pshin45
> _But many people feel the same way about, for example, physical exercise:
> they don’t enjoy doing it and find it to be very hard work when they try.
> But it would be strange indeed to say that you can’t “do” exercise. You may
> not want to do it. You may be unwilling to invest the time and effort into
> doing it. But you aren’t incapable of doing it. And the same is true, in my
> experience, in mathematics._

I think a more apt comparison might be to sports, rather than to exercise.
Everyone can get reasonably good at "exercise" i.e. be able to run a mile in a
reasonable time, but I think we can all agree that there are certainly many
people who simply "can't do" a sport.

For example, I am pretty bad at baseball. I was a terrible batter and an even
worse fielder. I "persevered" and played Little League Baseball for several
years, eventually realized I didn't have much if any aptitude for it, and
stopped playing altogether. Does this mean I'm lazy or that the Little League
coaching system is broken? No, it just means I'm not that good at baseball and
probably never will be, and I don't think any amount of great coaching would
have changed that.

Are there some people who could have been good at a given sport but "slip
through the cracks" due to laziness or bad teaching? Maybe, but I doubt it's a
significant number.

It's easy to take mathematics ability for granted on a focused forum like HN,
but perhaps being good at math is no different from being a great sports
athlete - Some people are really good at it, but most aren't and it's pretty
unrealistic to expect everyone to change their expectations and opinions on
the matter.

------
ssw1n
Totally relevant: <http://www.phdcomics.com/comics/archive.php?comicid=1356>

------
Detrus
_> But many people feel the same way about, for example, physical exercise:
they don’t enjoy doing it and find it to be very hard work when they try. But
it would be strange indeed to say that you can’t “do” exercise. You may not
want to do it. You may be unwilling to invest the time and effort into doing
it. But you aren’t incapable of doing it. And the same is true, in my
experience, in mathematics._

The way physical exercise is often presented to people, it's no surprise they
give up on it. A lot of gimmicky exercise programs and contraptions designed
to take money from you in exchange for no visible results.

And even time tested exercise programs like P90X won't teach you the
fundamentals. You'll spend a lot of time doing crunches which is the least
effective and most time consuming way of working abs.

The same is certainly true for math and when people say they can't do any
moderately complex math, they're saying "fuck you" to the establishment that
wasted their time while teaching them nothing. They also do just fine without
complex math, just like most people who never exercise.

------
timmm
Neil Degrasse Tyson made this point.

He basically said that imagine if instead of people saying at cocktail parties
"I can't do math" they said "I can't read..."

~~~
zecho
Sure, but "I can't do math" is a shorthand for "I can't do math beyond
arithmetic, and even then, I often can't do that in my head." That is not
equivalent to "I can't read." It is more equivalent to "I can't read Proust
without getting bored and confused."

The author in the OP acknowledges this substitution of "I can't" for "I
currently struggle with." It's complaint about semantics that misses the
point, I think.

Rather than complaining when people say they can't do math, we should find out
why they feel that way. I suspect a large part of the reason is that math
education is pedantic and boring (memorizing axioms and doing rote
calculations, when we should prove them, for example, or apply math in ways
that doesn't involve trains leaving stations) and when people do speak their
minds about their difficulties with mathematics, they often face snooty
responses like this one in the OP, rather than a lighter touch.

~~~
hudibras
One of the OP's main gripes is that many people will gleefully, happily tell
you that they can't do math. Nobody will ever admit to a stranger at a
cocktail party that they're illiterate but being bad at math is, for some
reason, a conversation starter.

------
pvaldes
> So what do people actually mean when they say that they can’t 'do' math?

That I "can't". That my brain is differently "shaped", simply, and that this a
common variation.

Personally I think in spatial 3d structures, classify images, read superfast
recognising words by the shape of the contour of the letters, learn at a good
rate and can accurately drawn what I see in the real world...

But in the other hand I find deadly boring to express, in a unnecesarily
complicated formulae drawn in 2d with many arcane symbols, a simple concept
that could be introduced and expressed instead in two or three simple
phrases... or logically, graphically...

The "atoms" of my thinking process are shapes and relationships between
shapes, not abstract quantities. Is as simply as this. Other people "think in
sounds" and are very good at music, and other "think in mathematical
structures". I'm not blaming nobody, not excuses... I'm just a perfectly
normal human with an intelligence basically visual

(... And I prefer not spend much time with this when a machine can do the math
part for me in the blink of an eye).

------
skittles
I believe that lots of people really can't do math. Most people are fine until
fractions. Many people never gain any intuitive feel for what "2/5 * 7/8" even
means. It only gets worse with algebra. They can often learn the mechanics of
fraction arithmetic and solving equations, but they will never understand how
to apply the knowledge later in life.

------
gyardley
"I can't do math" actually means "I both don't like to and don't believe I
really need to do any math, so I'm going to say 'I can't do math' to cut you
off before you propose I do any."

Of course college-educated people _can_ do a little math - but they don't like
to, so they don't.

------
nnq
I sympathize with the OP on all he says, but what does he mean by this, aren't
these expressions synonymous, the only difference being the tone?:

> although saying “my bad” when you mean “my mistake” comes close

...and going further on the linguistic ambiguity route, most people saying
"can't do" actually mean simply "I hate it / I'm not good at it, and because
it's so much effort for met o do it I'd rather not have to do it"... and the
only bad thing in it is the uberannoying implied "I don't want to learn it,
don't try and teach it to me"...

~~~
ameister14
'My bad' is a foolish thing to get upset about people saying. People have said
it for thousands of years and they're going to keep saying it. See: "Mea
Culpa"

------
haubey
I think these people mean "I can't do arithmetic" which is much more
acceptable, in my opinion. If you asked me to find a derivative, I could
probably do it faster than I could find 123*26. It's not because the
multiplication is harder, but because I don't have to do it in my head that
often anymore. I have a calculator, and I use it. However, I have to do
derivatives in math class everyday and at this point I'm probably faster at
it. Not being able to do arithmetic is fine by me, I can't do it.

~~~
learc83
That's just because there are fewer steps for finding a simple derivative.

If you evaluate 123 _26 in your head, most people probably end up thinking
through something like this

    
    
        123 * 20 + 123 * 6
    
        123 * 20 
        123 * 10 * 2
        1230 * 2
        2460 Now remember this part
    
        123 * 6
    
        100*6 + 20*6 + 3*6
        100*6 = 600
        20*6 = 120
        3*6 = 18
        600+120+18
        738
    
        2460 + 738 = 3198
    
    

Now compare that to taking a simple derivative.

Although I could ask you to take the derivative of 123x^26.

------
mberning
There is an idea that pervades their rant that all people are more or less
equally educable in all subjects. In my experience this is simply not true.

------
gridmaths
I think part of the problem is we don't teach Math in a way that is
visual/obvious enough, which means early math is experienced as 'mechanics'
not 'understanding'.

For example, we should explain commutative rule [ a(b+c)=ab+ac ] by drawing
the rectangles.

My efforts to help this in some way : GridMaths.com [ sample pics + blurb :
quantblog.wordpress.com ]

------
tempire
Math is just another word for structured thought. When people say they're not
good at math, what they really mean is that they attempted learn something
without understanding the underlying principles, and therefore found it
difficult.

They're not lazy, they're just ignorant to the process because they were
taught incorrectly.

------
droidist2
Yeah, it's interesting that people will proudly admit "I can't do math" but
you don't nearly as often hear them say "I don't understand politics,
government, or world affairs." People will do their damnedest to appear
knowledgeable about those things.

~~~
chrisdone
That's true. “I don't really understand national politics in any deep way,” is
something I've said many times and has been responded to often with “me
neither”, but I'm quite sure had I not said it, the person would've kept quiet
about their ignorance and feigned insight in other conversations.

------
Tycho
Maybe they should teach it as 'modelling' instead of 'mathematics.' When you
start thinking of it in terms of interpreting real world dynamics and
relationships, curiosity takes over and it becomes a much more compelling
subject to learn. IMO.

------
mathiasben
Surely if effort and attention to detail were applied most of these people
could work their way through whatever math task was set before them. What they
should instead be saying is; "I don't do math".

------
devgutt
But If a person says "I can't \"do\" mathematics" also could imply that the
person would like to like it, or maybe the person at least respect the subject
as important.

~~~
easy_rider
how did these added slashes slip in?

~~~
fyi80
Java/C++ programmer who observed that English lacks Perl's qq operator or
python's r''

------
RobotCaleb
I never learned how to do long division by hand. That doesn't mean I can't do
math, though. I could, of course, learn how, but I haven't needed to.

------
tokenadult
As I did the last time I posted a reply about mathematics education, I read
the original post and the comments here before posting this reply.

First things first. Mathematical notation is now universal. A student in China
learns in middle school (junior high) most of the mathematical notation that
an American is expected to learn by graduation from high school. I know a
large number of Chinese people who have taken the GRE test for admission to
United States graduate schools. All of them, even those pursuing graduate
studies in humanities, deride the GRE math section as "junior high math,"
which it literally is in terms of the standard school curriculum in China. Not
all people in China have access to schooling beyond junior high, but through
junior high the instruction in mathematics is generally excellent, and the
United States could learn from the methods of mathematics teaching used in
schools in China.

[http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles...](http://stuff.mit.edu:8001/afs/athena/course/6/6.969/OldFiles/www/readings/ma-
review.pdf)

<http://www.ams.org/notices/199908/rev-howe.pdf>

Second things second. There is indeed a distinction between doing the kinds of
calculations in arithmetic that may be tested in elementary school, are often
done by adults with electronic calculators, and may or may not be a practiced
skill of professional mathematicians and the kind of mathematical reasoning
that makes up university-level study of mathematics and quantitative sciences.
But that is not to say that learning arithmetic is not important. W. Stephen
Wilson, a professor of mathematics at Johns Hopkins University, surveyed
mathematics researchers about a year after the webpage submitted here was
written, and asked them to agree or disagree with the statement

"In order to succeed at freshmen mathematics at my college/university, it is
important to have knowledge of and facility with basic arithmetic algorithms,
e.g. multiplication, division, fractions, decimals, and algebra, (without
having to rely on a calculator."

<http://www.math.jhu.edu/~wsw/ED/list>

His colleagues around the world unanimously agreed, answered him in terms such
as

"I am shocked that there is any issue here. I absolutely agree with your
statement."

"That it is even slightly in doubt is strong evidence of very distorted
curriculum decisions. I do not know even one university-level teacher of
mathematics who would disagree with it. I would be truly astonished to meet a
person who disagrees."

The charming story about Kummer is one I tell my own students, but I also tell
them that the mathematics I teach them (prealgebra mathematics, in a class for
self-selected elementary-age pupils looking for a challenging mathematics
course) is based on their doing their own calculations with their minds alone,
or with pencil and paper, never with a calculator.

Other mathematicians point out that learning the long division algorithm is
itself a basis for the development of mathematical understanding.

<http://www.csun.edu/~vcmth00m/longdivision.pdf>

The late mathematician W. W. Sawyer spent decades thinking about how to teach
mathematics effectively.

<http://www.marco-learningsystems.com/pages/sawyer/sawyer.htm>

Back in 2004, when I joined the Art of Problem Solving forums, I chose the
screen name "tokenadult" (which so annoys some people here, chosen there
because many participants on the forums are much younger than I am), and also
chose a tagline quotation from Sawyer:

"The proper thing for a parent to say is, 'I did badly at mathematics, but I
had a very bad teacher. I wish I had had a good one.'" W. W. Sawyer, Vision in
Elementary Mathematics (1964), page 5.

Sawyer didn't want parents to give their children an excuse for thinking "I
don't have a head for mathematics." Instead, a learner can keep searching for
an effective teacher, and learn more than at first seems possible. The
curriculum expectations in much of the English-speaking world are meager. In
both Singapore and Taiwan (and in some other countries), every seventh grader
is expected to learn algebra, and a fair amount of geometry--even all of the
below-average students. That is possible. Not everyone in those countries is
brilliant in mathematics, but many, many people in those countries have a day-
by-day correct understanding of mathematics that helps in their daily life
activities. My wife received that kind of mathematical education back when
Taiwan is wretchedly poor. Taiwan is no longer poor, in part because it has
developed rapidly through its educated workforce.

~~~
lenazegher
I was educated in the UK and given (in my estimation) very poor maths
instruction. I stopped studying maths at the earliest opportunity. My
undergraduate degree was in the humanities.

Even for me, someone who identifies as being very bad at math, the math
section of the GRE was not challenging in the least, even though I had done
literally no preparation. (I was applying for a course that required all
applicants to take the GRE, even though it wasn't considered at all in the
entry process. Apparently it had something to do with funding.)

I guess my point is, I find it difficult to imagine _anyone_ who had completed
a degree and was sitting the GRE would find the math section anything beyond
elementary.

------
shawndumas
"I can't do math [at a university level]..."

------
Derbasti
Indeed, it is often beneficial to state your preferences up front instead of
sputtering nonsense trying to be "diplomatic".

Everyone can interpret what I have to say about text editors much more
usefully if I state up front that I love Emacs. The same goes for programming
languages, frameworks, operating systems and math.

------
Kekeli
I wish i could do math

