
How I faced my fears and learned to be good at math - mxfh
http://www.niemanlab.org/2013/11/matt-waite-how-i-faced-my-fears-and-learned-to-be-good-at-math/
======
Smudge
I hit a wall in college where math just stopped being something I intuitively
"got". I'm sure that given enough time and motivation, I could have continued
being "good at math" even at the higher levels, but these were luxuries I did
not have, given everything else on my plate at the time.

My biggest problem with math, especially once I got into academia, was how it
was taught. So many professors would scribble what seemed like nonsense on the
board (symbols that change from professor to professor, or even from lecture
to lecture) and then go on to say things like "...and the proof is trivial" or
"...it obviously follows that...", and I'd sit there wanting to shout "NO, NO
it's not obvious!"

Finally, I'd find a tutor to explain to me what it was I was missing, and it
really WAS obvious. If only it had been taught that way in the first place!

Admittedly, not everyone has the same learning style, but the classes I took
seemed really tailored towards the students who already had the intuition that
I lacked.

~~~
ChuckMcM
You have hit upon my biggest gripe with mathematicians, their love of
'notation', or more precisely their love of writing in symbology that makes
mathematics seem more arcane than it actually is.

When ever I've run up against "impenetrable" math I often ask "So how would
you use this?" and connecting it to the real world helped tremendously.

~~~
zenbowman
Notation is not a bad thing. What is bad is an inconsistent, ethereal form of
notation.

Computer science is also essentially about notation and vocabulary, but we
have to make our notation understandable to the computer, which is a much
higher standard than what mathematicians have to adhere to.

We are in a field that demands a much higher level of rigor than
mathematicians are accustomed to, as much as they'd hate to hear it.

~~~
krakensden
There was some point in my education where I was taking three classes, each
with their own definition of phi. It drove me nuts.

Coq notation, lisp-style notation, even python-style notation- anything would
be better.

~~~
drivers99
I remember taking three classes: informal logic (philosophy) which ended up
talking about formal logic anyway, electrical engineering, and a math class.
It make the logic class really easy, already knowing it from EE. They all had
different notation for 'implies', 'not', 'and', 'or', etc. You could argue
that the computer languages have a 4th notation, but I won't.

------
Millennium
One thing that worked well for my wife was a series of games from Nintendo
called Fire Emblem.

This isn't a series of educational games: it's actually turn-based strategy.
But the mechanics are all derived from very simple arithmetic, and although
they don't give you the actual formulas, they give you, up front, every single
number that goes into them formulas. Use a FAQ to get the small number of
formulas involved, and the randomness all but vanishes: for any given unit on
the field, you can always tell exactly which other units can attack it, how
many times those units can try to attack, how much damage they'll do if they
hit (and the exact odds of them hitting), how much damage you will do in
response if your counterattack hits, and so on. The game will do this for you,
but only for units that are directly in range at any given moment. With the
numbers, you can calculate for any unit on the field, and that lets you start
thinking multiple moves ahead.

The end result is that if you work out the math in your head, you can Neo your
way through the games, and this is exactly what my wife did. I have never been
the math-head in the family, but before she started this, I was still handier
with numbers than she was: now it's the other way around. I should look into
this myself.

~~~
011011100
Some people are very good at chess. Similar idea. Are these people also good
at math?

"One thing that worked well for my wife was a series of games from Nintendo
called Fire Emblem."

So are you trying to make a scientific claim? This is starting to seem like an
anecdote supporting brain training games.

~~~
Kiro
What are you even arguing about?

~~~
011011100
There are a lot of feel good nonsense posts in this thread. The parent gave no
indication he was referring to motivation. It sounded like he was saying his
wife suddenly became better at whatever he considers math to be by just
playing a video game. That's basically claiming that brain training works. I
may have a slightly different definition of "brain training", but it doesn't
really matter because it's just as unscientific. There is no evidence to
support the idea that playing video games somehow makes you better at "math"
(where "math" is referring to those activities that require deductive thought
and understanding of mathematical structures, not number crunching).

~~~
Millennium
Not even so much "brain training works" as "practice makes perfect". It was a
fun way to practice, and I thought it might be helpful for other people
looking for a way to brush up on the basics.

~~~
011011100
She's practicing number crunching and maybe some other cognitive tasks that
probably can't be related to mathematical thought, unless you squint really
hard. I can identify at least one cognitive task: holding configurations in
your head (I have played Fire Emblem). From my experience, I would say that
this has nothing to do with the type of thought that goes into mathematics.
Like I said in my first post: good chess players can do this well. Does that
mean good chess players are also good at some part of math?

And, you know, one would have to show that there is some "mathematical
thought" that can be trained to begin with. I'm not entirely sure there is.

I don't disagree that "practice makes perfect". I disagree with the statement
"practice in fire emblem makes perfect in math (not number crunching)".

People want to share stories. I get it. But if we're not being rigorous about
it, then we're just fooling ourselves. And then the conversation devolves into
a circlejerk where everyone thinks they're brilliant.

~~~
Millennium
We were all newbies once, and newbies have to start somewhere, even if it is
not the most "pure" of beginnings. The kind of proof-snobbery you're
displaying here likely bears a large part of the blame for driving people away
from math in the first place.

Yes, there is more to math than number-crunching, but to claim that number-
crunching is not math is to forget the very roots of the discipline. This is
where it begins, and it's where people who have been out of practice for a
while return. Give it some respect.

------
melindajb
I aced all my high school math classes including calc. Because my school was
small and rural they didn't have any more classes for me. So senior year I had
no math.

Got to college, took a math placement exam and bombed out, so upset. Then as I
was leaving knocked a chair down and everyone stared at me.

I ended up with a BFA in Drama.

Fast forward 10 years and like the author I worked my ass off to get into a
top MBA program and not only that, major in finance.

So yeah, it can be done. Hard work, and not accepting the bullshit line "oh
I'm not good at math." And without attacking my own gender, women tend to be
let off the hook more easily with this excuse, as if we accept that girls
can't do math.

Fuck that.

This post rocked. Thanks to the HN community for bringing it to my attention.

~~~
hackinthebochs
What was your path to an MBA? I'm assuming a degree in drama doesn't exactly
prepare you for an MBA in finance. What happened in between that gave you the
motivation and whatever prereqs necessary to even be considered for a spot?

~~~
obstacle1
There are no real academic requirements for an MBA program other than you have
an undergrad degree and did well in it. Prerequisites would be nil. On that
note, most adcoms likely value work experience _more_ than undergrad
experience.

You don't jump right into advanced topics, most streams give you an intro
sequence first assuming you know little to nothing about the topic.

That said coursework is like < 50% of the value of an MBA, it really isn't the
point of the degree.

Plenty of smart but somewhat wayward humanities/soc sci majors end up
graduating into a random office job, find out that surprise! they perform well
and enjoy business, and proceed to do an MBA.

Disclaimer: I'm not an MBA, this is second-hand from MBA'd friends and
acquaintances.

~~~
melindajb
it's true that there are intro sequences in some programs, but due to Cornell
Johnson School's unique structure, we did an entire semester of accounting in
six weeks; ditto for finance. I'd passed everything I learned in a semester of
accounting in 4 days.

agree about coursework not being the point, networking is; but coursework to a
point is a factor for many things: career changing, or in my case, burrowing
into math and finance so deeply you can hold your own with the best and
brightest in the world. (for example you learn when to recognize when you are
not the smartest person in the room, so it's time to shut up and let other
people teach you)

------
mathattack
For whatever reason, I hit a poor grades stretch in math for my first three
years of high school. It was just boring, and high school had distractions. My
school almost blocked me from taking calculus. When I hit Calculus, I had my
"Aha, I get it now" moment, and had great grades in math ever since.

Some students don't need to be motivated to work hard. Others do. Some in the
latter camp are led to believe that they're not good at math, when the reality
is that they're just not motivated for it. I'm glad that I ultimately found my
motivation.

The OP seems to have found this moment too.

~~~
FLUX-YOU
>Some students don't need to be motivated to work hard. Others do. Some in the
latter camp are led to believe that they're not good at math, when the reality
is that they're just not motivated for it. I'm glad that I ultimately found my
motivation.

Approaching it without other academic pressures and plenty of confidence from
being successful in other areas also helps. Plus the article gave no hint that
he was taking a full schedule. Personally, I would likely get bad math grades
if I had to go back and study math and other things.

Perhaps for these students that "didn't get" or were "bad at" math, maybe they
just need to be given some time to only focus on math to raise their
confidence and abilities. I had similar results as the author when all I was
doing was working and doing some math during the day. I also barely graduated
high school.

~~~
bglazer
I'm currently going back and learning linear algebra from the excellent MIT
OCW course [1]. I somehow didn't have to learn linear in the course of a CS
degree at a big state school. Focusing solely on learning this one subject has
allowed me to get the subject at a much deeper level than learning enough to
pass a test.

I'm hoping to move on to statistics, which I slept through because I was an
immature shit-head my sophomore year.

Then a review multivariable and diff-eq, and the end goal is to do the full
Stanford Machine Learning class, taught by Andrew Ng [2]. I also really want
to tackle "Underactuated Robotics", which is another MIT OCW course.[3]

[1] [http://ocw.mit.edu/courses/mathematics/18-06sc-linear-
algebr...](http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-
fall-2011/Syllabus/)

[2]
[http://see.stanford.edu/see/courseinfo.aspx?coll=348ca38a-3a...](http://see.stanford.edu/see/courseinfo.aspx?coll=348ca38a-3a6d-4052-937d-cb017338d7b1)

[3] [http://ocw.mit.edu/courses/electrical-engineering-and-
comput...](http://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-832-underactuated-robotics-spring-2009/)

~~~
mathattack
It's amazing how motivation increases once you know what it's useful for. :-)

------
danso
Like the OP, I also went to journalism school and can confirm that, while
Statistics 101 is sometimes a highly recommended elective, math is seen as not
needed, especially for those who want to tell "stories with impact."

I would've agreed back then as a student, but I also happened to be studying
computer engineering so I took math for granted. In the professional world,
it's astonishing how hard it is to explain ratios and basic enumeration to
those who didn't try math, and how that greatly affects the range of story
ideas you can conceive of.

And I say that as someone who still has to look up the quadratic
equation...something virtually all college grads learned at least in high
school. But there's a huge chasm between knowing that the quadratic equation
_exists_ and is applicable and not remembering that it exists at all.

~~~
swalkergibson
> [I do not] carry such information in my mind since it is readily available
> in books. ...The value of a college education is not the learning of many
> facts but the training of the mind to think.

\-- Albert Einstein

Source:
[http://en.wikiquote.org/wiki/Albert_Einstein](http://en.wikiquote.org/wiki/Albert_Einstein)

The above quote seems to be the genesis of the folk trope, "Never commit to
memory that which can be looked up in a book." To me, what you describe above
is why people think they are "bad at math," because they cannot commit to
memory long equations with foreign-looking symbols. Even the function sheets
provided during some math exams are needlessly obtuse, for the sake of proving
whether or not somebody can remember exactly what the different constants or
inputs into the functions are. It would be like encountering a function in
somebody's code that had cryptically-named parameters without comments or
documentation.

------
MatthiasP
"The difference between good at math and bad at math is hard work. It’s
trying. It’s trying hard. It’s trying harder than you’ve ever tried before."

-while that's certainly true, when people say they are "bad at maths" they usually mean exactly that they have to put in a lot more effort (=trying harder) to reach the same level of math skills as the "gifted" guys.

~~~
DerpDerpDerp
I was one of the "gifted" math students in high school, and I highly doubt
anyone "bad at math" put in nearly the effort I did.

The ease of doing it in class or breezing through homework assignments was
backed by hours a night of looking at high level concepts and talking about
math with people more advanced than me, including teachers during lunch breaks
and after school - a habit I'd had since late elementary school.

At the end of the day, they weren't "bad at math", I just put a lot more
effort in to my practice - and it showed on game day, as it were.

Just like the guy in my school who was "gifted" at basketball spent hours a
night practicing since early elementary school.

~~~
011011100
Except... just because you haven't observed it doesn't mean it isn't true. And
just because you believe you're gifted doesn't mean you are. It's really easy
to be a big fish in a small pond. It's also possible to think you're a big
fish in a big pond when you swim in a pack with smaller fish.

edit: I just realized you said high school.

~~~
DerpDerpDerp
I also put "gifted" in quotes for similar reasons.

I picked high school though because most of the comparisons about being "bad
at math" start around then. The reality is that I just put in more work than
many people and was a class or two ahead of the average student up through the
start of university, where I went on to study math (and was at a similar
starting point with most other math majors at my particular school).

At the end of the day, I'm just an average fish in the math pond, but it's
easy to think you're not as good if you don't see the work backing my talent
in high school and base your comparisons for life on that (or even the first
year of undergrad).

------
eloisius
Jim Fowler's calc II course on Coursera[1] is wrapping up right now, and I
think he's the most engaging math professor I've ever had to please of
learning from. Highly recommend.

He's also a maintainer of an OSS MOOC platform, MOOCulus[2], built with Rails.

[1]:
[https://class.coursera.org/sequence-001/class](https://class.coursera.org/sequence-001/class)
[2]:
[https://github.com/ASCTech/mooculus](https://github.com/ASCTech/mooculus)

~~~
ics
Even if you're not interested in doing the course work (though really, it's
only six homeworks) everyone should take a second to watch some of his
videos... definitely some of the most entertaining, engaging, and _clear_ math
lectures I've ever seen. I also highly recommend it.

~~~
kisonecat
(I'm Jim Fowler.) Thank you---I certainly appreciate it.

The Calculus One videos are available at
[http://youtube.com/kisonecat](http://youtube.com/kisonecat) and the new
Calculus Two: Sequences and Series videos will be posted soon.

------
scott_s
I feel this applies to programming, too. I do not buy that some people can
"just program" and others cannot.

~~~
Someone
Very few people invent math or learn programming on their own without any
help, but there are huge differences in innate ability.

I don't agree with the author's claim _" The difference between good at math
and bad at math is hard work."_

I have a M. Sc in math, but never worked hard at it. I went to the classes,
paid attention to what was told and visited most of the exercise classes, but,
except for the first few weeks, never prepared for either of them. That left
plenty of time to spend on other things, such as sport and reading the art of
computer programming, Compute! Magazine, Byte, etc. (partly because of that, I
am not that good at math)

IMO, it is the same with about everything else. For example, there are people
who just throw a baseball well, and there are those who can learn to throw a
decent one through hard work.

~~~
_delirium
I think you would at least need to take a fairly broad view of "innate" that
extends past the literal moment of embryo fertilization. How someone's raised
in childhood can have a huge impact on what seems innate by the time they get
to their teenage years. I've been "good with computers" since a young age, for
example, but I also had an Apple //c in my house since I was 3 years old, and
parents who encouraged me to use it. I don't think my teenage computer
proficiency would have been the same if that had not been the case.

------
verteu
> [The claim that] "bad at math" was a thing — probably even genetic... was
> all a lie.

I disagree. Math ability is highly genetic:
[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2913421](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2913421)

------
arethuza
At first, I was _terrible_ at maths at University and indeed had to retake a
year due to my awful attitude. Oddly enough after almost flunking out
completely I came to really enjoy the more abstract mathematical aspects of CS
(e.g. lambda calculus) and even in the mainstream maths classes I ended up
getting rather splendid marks which eventually led to me getting a 1st.

At a post-grad level I then ended up working in an Electrical Engineering
department with Control Engineers - rather ironic for someone who started off
almost failing because of maths...

Maths went from something I had no interest in, and therefore did terribly, to
something I loved.... maybe it was age/maturity or just plain getting a scare!

[NB I'm very happy we had the UK style degree grading system rather than GPAs]

------
columbo
I know he mentions people doing their own googling, but I'd like to recommend
this coursera course:
[https://www.coursera.org/course/maththink](https://www.coursera.org/course/maththink)

It's one of my favorite MOOCs of all time, a fantastic intro to mathematical
thinking.

------
smithbits
I think the author is making an excellent point about needing better math in
journalism. An article in the NY Times yesterday about online shopping China
had this line (pulled from a press release) "Tmall.com, one of Alibaba’s
shopping sites, said Chinese bought...two million pairs of underpants, which
if linked together would stretch 1,800 miles..." Why should I believe the rest
of the article when the author is quoting someone saying that underpants are
57 inches wide?

~~~
BlackJack
To cross check your claim about the author, I did:

1800 miles ~ 2000 miles 5280 ft/mile ~ 5000 ft/mile So 10M ft / 2M underpants
= 5 ft/underpant. 12*5 = 60 in/underpant, which is close to 57, so I trust
your statement :)

I think this sort of "back of the envelope" calculation is something that just
comes by practice/habit and is not some innate ability. I love this article by
Jon Bentley on the topic: [http://www.csie.fju.edu.tw/~yeh/research/papers/os-
reading-l...](http://www.csie.fju.edu.tw/~yeh/research/papers/os-reading-
list/bentley-cacm84-envelope.pdf)

~~~
sveme
Sorry, but you Americans need to get rid of that imperial system: 1800 miles ~
2000 km = 2,000,000 m. Each pair is around a metre. Simple, isn't it? Okay,
admittedly, 1800 miles is definitely more than 2000 km...

------
AndrewKemendo
This is great and needs to be said more often. I feel as though I am the
opposite. I absolutely love math, but I am terrible at it. I have taken tons
of math, both formally in undergrad (up through diff eq) and on the side on my
own. I struggled like hell through Calc 2 because I just couldn't visualize
the transformations. I still feel like I want to take two years off and just
start over from scratch.

~~~
blktiger
I have the exact opposite problem in math courses. I can visualize the
transformations and what the math means, I can know the exact approach to take
to solve a problem, but I can't seem to get all the way through without making
stupid mistakes. "Partial Credit" for showing work never really helped me
much.

~~~
SamuelMulder
You are good at math and bad at calculation. There are branches of math where
calculation is not so important... also, use a computer for the calculations
:)

~~~
spenuke
What branches of math are good for people who are bad at calculation?

~~~
SamuelMulder
Abstract algebra, number theory, geometry, logic, topology, graph theory - off
the top of my head.

------
SamuelMulder
Good for you!

"The difference between good at math and bad at math is hard work. It’s
trying. It’s trying hard. It’s trying harder than you’ve ever tried before.
That’s it."

I love this quote. I think that nails it. When you see someone run a marathon,
you don't think they are just naturally good at exercise, you recognize that
they've put in a lot of hard work.

I think the value of hard work is under appreciated. Thanks for writing this.

~~~
dwaltrip
I think the main problem is kids aren't taught abstract problem solving, and
don't learn how to process the deep concepts that you find in math. This is
largely due to our rigid, rote memorization math teaching methods (here is
formula x, here are the type of problems formula x can be applied to, now do
this pracitce set with 100 of them, and so on).

The majority of math currently taught k-12 is also largely useless to most
students who don't go into hard sciences. This time would be better spent
learning math as an art. They could struggle with problems without knowing the
formulas ahead of time. They could modify the axioms and see where that leads.
And so on, working their way through the different areas of math, and actually
internalizing the concepts. In high school, the curriculim would include a
life skills: arithmetic/statistics class, to ensure that day to day practical
math skills are learned.

There was a really good paper on HN a few months about math as an art form
which influenced my thinking in this regard.

~~~
SamuelMulder
I agree completely. I'm working on a curriculum just like this :)

------
bridger
Working hard at math might be necessary, but it doesn't have to be painful! I
have found learning about the history of math has me puzzling over difficult
concepts on my own time because it is fun.

The book I am reading (Journey Through Genius) is really good, but not very
advanced math. I would love to find some self-study math courses that approach
math not as a bunch of symbol-pushing but as an art with a history.

~~~
SamuelMulder
I've thought a lot about this and haven't found many good resources. I finally
gave up and started reading history of math books. Unfortunately, most of them
are aimed at grad students in history or grad students in math.

It has frustrated me enough that I've started developing my own versions. I
taught a history of ancient mathematics class to homeschoolers locally and now
I'm writing a book that works through Euclid while placing everything in
historical context and focusing on the story of its development.

~~~
gshubert17
I found Lancelot Hogben's "Mathematics for the Million", originally published
in 1937, to combine history and biography, concepts and calculations,
explanations and illustrations, in a very engaging manner.

------
nextos
There are some great books to build up some intuition and rigor in all
branches of math, with no prior knowledge:

* How to Prove It (Velleman)

* Algebra; Trigonometry; F&G; The Method of Coordinates (Gelfand)

* Geometry (Kiselev)

* Calculus Made Easy (Thompson)

* How to Count without Counting (Niven)

* Introduction to Probability Theory (Hoel)

* The Little Schemer (Friedman)

The proceed to more advanced texts like:

* Naive Set Theory (Halmos)

* Linear Algebra Done Right (Axler)

* Geometry Revisited (Coxeter)

* Infinitesimal Calculus (Keisler)

* Concrete Mathematics (Graham)

* Information Theory, Inference and Learning (MacKay)

* SICP (Abelson)

~~~
tokenrove
All of these are great. I'd like to add, maybe not for everyone, Calculus by
Spivak. For me, it was the calculus book for which I had been looking for a
long time.

------
mtdewcmu
I always thought of myself as good at math, but I had an unexpectedly hard
time in required freshman calculus courses en route to a CS degree. I think
the source of all of these paradoxes is that math is too broad a thing to be
simply good or bad at. The objective in first year calculus seemed to be to
practice basic techniques until they became rote. If you were an engineer,
you'd have much more calculus to do and the early stuff was like learning to
tie your shoes. I didn't encounter any really mind-bending concepts (I
actually had to retake some calculus I originally took in high school and
placed out of); the problem was that I couldn't do the problems fast enough on
the tests, and I had to devote way more energy than expected to practicing
doing them fast, which felt sort of like learning to play a musical instrument
-- training muscle memory so the mind didn't have to be involved. I figured
that calculus wasn't for me and I stopped after I met the degree requirements.

My point is that different scenarios involve different "math." For
engineering, math is a hill to climb on the way to the interesting part. For
CS, math is not about learning math per se, it's about learning to prove
things and think rigorously. For math majors, it's about deep concepts in math
itself. You could be good at proofs and bad at adding numbers in your head,
and be good and bad at "math" at the same time.

Dividing people into good at math and bad at math is pretty meaningless. If
you were truly bad at all math, you could probably not function in any job,
because everyone needs to do something that could be called math. On the other
hand, hardly anyone is just plain good at math, because you would have to be
good at pretty much every hard subject that exists (statistics, economics,
physics, and so on). If anyone is that smart, there can't be more than a
couple of them.

------
Spoom
My wife has dyscalculia[1]. She might take offense at the statement that _"
Bad at math" is a lie you tell yourself to make failure at math hurt less._

1\.
[http://en.wikipedia.org/wiki/Dyscalculia](http://en.wikipedia.org/wiki/Dyscalculia)

~~~
thatswrong0
> Estimates of the prevalence of dyscalculia range between 3 and 6% of the
> population.

I think this article is targeting a much larger audience than the small
percentage of the population that has genuine problems with math.

~~~
acuozzo
All the author needs to do is reword a bit: "Bad at math" is a lie _that some
people tell themselves_ to make failure at math hurt less.

~~~
Spoom
Indeed, that's what I was going for.

------
ivan_ah
Part of what makes (re)learning basis math difficult is the lack of math
textbooks written for adults. Most math books are either too advanced (assume
prior knowledge) or too basic (assume reader is retarded). In both cases, an
otherwise intelligent adult with some gaps in their knowledge will get
discouraged.

I wrote a math textbook which starts off from the very basics (numbers,
equations, functions) and proceeds all the way to university level topics like
calculus and mechanics.

Check out the "No bullshit guide to math and physics:"
[http://minireference.com](http://minireference.com)

~~~
bobbles
This is what I tend to struggle with when reading maths textbooks.

Example from your page:

Sup­pose that you monitor the file size dur­ing the en­tire down­load and
ob­serve that it is de­scribed by the func­tion:

f(t)=0.002t2[MB].

\- 'Supposed that it is described by the function' \- Where does this function
come from? Is it derived from something else?

~~~
ivan_ah
I understand your unease. In this case I totally pulled this equation
f(t)=0.002t^2 out of nowhere. It is just "some" function that satisfies f(0)=0
and f(600sec)=720MB.

I basically skipped (invented) the modelling step. In practice you would
observe the download size f as a function of time t, and then ask yourself
"which function f(t) correctly describes what I see." I wanted to describe a
download that gets faster and faster with time, so I picked a quadratic
function f(t)=At^2 as a template, then chose A=0.002 so the function matches
the problem statement.

Suppose instead I wanted the download rate to be uniform (constant download
speed), then the function which describes the file size would be of the form
f(t) = m _t+b. More specifically, the function would be f(t)=720 /600_t+0=1.2
_t. (You can check that f(0)=0 and f(600)=720, as in the problem setting).

In general, once you become familiar with the main function families
f(t)=mx+b, f(t)=ax^2+bx+c, f(t)=Aexp(k_x), f(t)=ln(x), f(t)=Asin(kx-ϕ), etc,
you will be able to describe real-world phenomena by using one of these
equations. This ability to "model" the real world through mathematical
equations is one of the super-powers that comes with math knowledge, but my
download example doesn't quite manage to communicate that. I will have to
rework it...

For a slightly better example of "modelling" using equations, check out page
26 in the PDF preview:
[http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#pa...](http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#page=26)

------
DanBC
I'm especially interested to hear from HN readers about good methods for
teaching math to children.

My son is 3, so at the moment we're just counting everything and making little
groups to add them together.

~~~
aethertap
I have been researching this for a couple of years and can recommend a couple
of books that I thought were particularly good:

* Good questions for math teaching ([http://amzn.com/0941355519](http://amzn.com/0941355519))

* Young Mathematicians at Work ([http://amzn.com/032500353X](http://amzn.com/032500353X))

* Number Sense Routines ([http://amzn.com/1571107908](http://amzn.com/1571107908))

* Dr Wright's Kitchen Table Math book (there are three) - [http://amzn.com/0982921128](http://amzn.com/0982921128)

I haven't finished these next two, but they look promising:

* Fostering Geometric Thinking ([http://amzn.com/0325011486](http://amzn.com/0325011486))

* Fostering Algebraic Thinking ([http://amzn.com/0325001545](http://amzn.com/0325001545))

I also like the approach of the Art of Problem Solving curriculum, though it
doesn't currently have elementary school material. I haven't used it on my own
kids yet because they're still too young, but I did buy the set and I think it
looks good. If you read "Good Questions for Math Teaching" you will probably
modify the way the problems are presented to make them more open-ended, but I
like that topics are introduced with a problem that is later explained,
instead of explaining then drilling.

[http://www.artofproblemsolving.com/Store/curriculum.php](http://www.artofproblemsolving.com/Store/curriculum.php)

Finally, I thought that this online course was a nice introduction to the
approach. It's a pretty short course, but I just put the audio on an mp3
player so I could listen while working on other things and there were only a
couple of places where I couldn't tell what was happening in the video.

* [https://class.stanford.edu/courses/Education/EDUC115N/How_to...](https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about)

For a more general book about early childhood education, I really liked

* "Engaging Children's Minds - the Project Approach" ([http://amzn.com/1567505015](http://amzn.com/1567505015))

* Making Thinking Visible ([http://amzn.com/047091551X](http://amzn.com/047091551X))

* Learning Intelligence: Cognitive acceleration...([http://amzn.com/0335211364](http://amzn.com/0335211364))

Sadly, most of these books are pretty pricey for the page count, but the
material I thought was quite good. If you were to get only two, I'd say go
with "Young Mathematicians at Work" and "Good Questions for Math Teaching"
because they will probably give you the quickest jump start, especially if you
can get the "How to Learn Math" course.

If you're interested in where my evidence for the approach outlined here comes
from, my main sources are the following books:

* Effectiveness In Learning (cognitive load theory) [http://amzn.com/0787977284](http://amzn.com/0787977284)

* Visible Learning (synthesis of 800 meta-analyses) - [http://amzn.com/0415476186](http://amzn.com/0415476186)

 __Edited because I put some of them in the wrong spots and forgot links...

------
auctiontheory
The curriculum for Math 101 looks like something that would be taught in the
ninth grade in a reasonable school district.
[http://bulletin.unl.edu/undergraduate/courses/MATH/101](http://bulletin.unl.edu/undergraduate/courses/MATH/101)

It is alarming (for our country) that this needs to be offered at the
university level, and even more alarming that most students are (according to
the OP) failing it.

------
nachteilig
Math didn't really "stick" for me until Calc 2. I'm not sure why--perhaps just
maturity?--but at that point it really clicked.

------
DonPellegrino
The thing about math is that you don't know what you're missing until you
learn more. It sometimes lets you solve hard problems in an incredibly obvious
and simple way because you knew a mathematical solution existed. Ignorance of
the existence of that solution would have lead you to build a complicated and
clunky chunk of code.

I recently was able to apply a few math techniques in a project to solve a
problem elegantly[1][2]. It is useful in my career as a software developer.

[1] [https://github.com/SGrondin/map-
reporting/blob/master/src/ge...](https://github.com/SGrondin/map-
reporting/blob/master/src/geometry.coffee) [2]
[https://github.com/SGrondin/map-reporting](https://github.com/SGrondin/map-
reporting)

------
gtani
I thought i was bad at math, but compared to people in my high school calculus
class, of whom one is an econ prof at a top university, one a MD/PhD, and they
weren't even the best student. The best student was so delighted to solve a
problem that he would bust out laughing (he was one of the 2 top math students
in the whole state, according to competition results). You never forget when
you see somebody that's so entertained by studying math.

________

As with learning to program or play piano/violin, you can:

\- take private lessons

\- take group classes

\- join some kind of study group or peer teaching. I've seen meetups, google
groups for that, and here's a subreddit for Bishop's ML text, which takes a
decnet amount of concentration:
[http://www.reddit.com/r/mlstudy](http://www.reddit.com/r/mlstudy)

------
droopybuns
My math career turned a corner when I started exercising in college. I would
take flash cards of all the formulas I needed to memorize and just burn
through them on my runs. I found that that was one of the best situations for
me to learn the tools I needed to approach problems.

It was kind of by accident. I knew I needed to memorize the formulas, but I
couldn't find a situation where I could sit down and do them without becoming
anxious and distracting myself.

On a run, there is no alternative. The eventual runner's high helped me
memorize things even more, and I found I'd associate the mental high that
comes with working on a math problem for a long time with a runner's high.

I'm super exited to share this wisdom with my kids. I wish I knew this secret
when I was in high school.

------
InclinedPlane
It's so sad how many things are taught so terribly in formal education and end
up turning away many people from things like literature, math, and science.
One of the things I'm looking forward to with the proliferation of mobile
computing devices is the opportunity for interactive self-directed learning
through educational applications. Not only will it allow for people to learn
at their own pace and to take the time to focus on aspects that they are
having a hard time getting (rather than being driven over like a speed bump
the way conventional learning works) but it will allow for a diversity of
teaching/learning styles.

I have a feeling that in a century people will look back at formal education
today and view as barbaric and ineffective.

~~~
SamuelMulder
The number of us who look at the school system today and see it as barbaric
and ineffective is growing rapidly...

------
mattivc
I told myself i was bad at math all the way through high school. I realize now
i was just lazy. Thankfully, through game development i discovered how cool
math can be when you actually do stuff with it.

Now i find really enjoying differential equations.

------
phaus
>Journalism's problems aren't with journalism.

Journalism has many problems, but make no mistake, this certainly is the
biggest. Journalism hasn't been a respectable profession for at least a
hundred years. Sure, there are examples of good journalism, but sadly they are
the exception. The overwhelming majority of journalism today is either
meaningless pop-culture drivel, or hyper-politicized, sensationalist
propaganda.

Its not even the journalism industry's fault. Its just a sad fact that
unbiased, factual articles are incredibly hard to write, and nearly impossible
to make interesting to the average person.

~~~
FedRegister
The problem is that journalism, as a bias-controlled profession, is only just
one hundred years old.

The National Press Club, founded in 1908, is seen as the beginning of
professionalism in journalism. They were built upon promulgating a set of
ethics and standards for journalism, including a focus on the facts, accuracy,
and bias-control.

Before that there was very little focus on what we consider bias-control. In
the early years of the United States up through the 1890s, newspapers were
most often owned by political parties and were explicitly for slinging
innuendo, suggestion, rumor, and scandal at the political opponents of that
party. So if you think it's a new problem or that it's bad now, history has
shown that it has been worse.

~~~
phaus
I didn't say that it was a new phenomenon, that's why I said its been
journalism's biggest problem for AT LEAST 100 years.

------
austinl
I've been wanting to write something similar for a long time. I left high
school feeling very "bad at math", and now I'm a CS major with a math minor.

I think the biggest problem in my approach to learning was my refusal to
practice. From other classes, I was used to reading the textbook and
understanding immediately. That meant to study for math exams, I would read
the chapters, try to learn principles, and memorize some formulas.

I later realized that I would never get any better without doing practice
problems - and lots of them. The best advice I've gotten is to start with the
problem, and then learn.

~~~
khyryk
I find this more difficult to do as I progress. My calculus book was full of
difficult example problems so that I was prepared to tackle the problem sets
whereas my number theory book has some proofs and trivial examples, leaving me
almost completely unprepared for the problem sets without hours and hours of
struggle.

------
mrchucklepants
I just sent this link to a friend of mine. He just crammed enough high school
pre-algebra to get his GED. He is terrified of math, but realizes he has to
learn it. I worry for him if he doesn't. He's 36.

------
RaymondRamone
Thanks for this post! I'm 36yrs old and now I'm even more pumped to get better
at programming and start reviewing my MATH.

I just wanted to share to you guys that this morning I really feel bad on my
way to work (I'm an iOS developer). I told myself if only I'm really good at
math maybe I could have use a lot more algorithms for my apps that I was
making. All I can think of until I got to the office was math math math math.
And I admit I was envious of other people who are really good at math.

Now I'm not envious anymore! Thank you Mr. Matt Waite!

------
jebus989
This article confuses statistics with (at least on my assumption) pure math.
He talks about the use of math by journalists in data analysis and
visualisation, when that's purely the realm of the statistician, who need not
necessarily know any calculus. Similarly I've met super intelligent pure math
PhD candidates that are working at the precipice of their (very esoteric)
field but wouldn't know where to start with applying "data science" stats/ML
techniques some interesting slab of data.

~~~
upquark
If you think a statistician need not know calculus, I sure as hell hope you're
not a statistician :) This is a central concept in stats:
[http://en.wikipedia.org/wiki/Maximum_likelihood_estimation](http://en.wikipedia.org/wiki/Maximum_likelihood_estimation)

~~~
jebus989
Your assumption being that I don't know calculus? Anyway I stand by my
original statement, if you're working in data analysis (even as a frequentist)
you should be able to see the truth in it; "data scientists" aren't deriving
MLEs for wacky distributions and using the mean to parametrise a Gaussian
doesn't require calculus. Thanks for the link, I guess?

~~~
tokenrove
If you read any classic text on statistics like Feller you can't get past the
first chapter without hitting calculus. Any statistician will be very, very
familiar with the Central Limit Theorem, for example.

~~~
jebus989
Yea of course they will. That doesn't mean they spend their days explicitly
enumerating limits of functions, and limits are pre-calc anyway. The point
isn't that calculus isn't /integral/ in mathematics, just that it's not
_necessarily_ (I did say necessarily) the workhorse of the applied
statistician.

------
MLfan
It’s a really great and inspiring article as I’m thinking of taking a Maths
course myself. After being a straight A student in school, I graduated a
Linguistic department and here I am thinking I can barely add sufficient sums
in my head. I guess the disadvantage of Not knowing Maths is different
thinking from tech guys who I need to communicate a lot to. The thing that can
cross the bridge of misunderstanding should be Math thinking. So thank you for
a kick to get the ball rolling.

~~~
jebus989
Basic arithmetic isn't math in this context, sitting through a multivariate
calculus MOOC isn't going to help you with addition.

------
southphillyman
Can anyone here recommend a good resource for learning discrete/computer math?
I'm a self taught developer doing well in the CRUD/Enterprise arena. But
whenever I try to delve into books about things like algorithm analysis I
usually have to tap out after the first few chapters, which are usually heavy
with mathematical explanations and proofs. I need to dedicate some time into
learning the basic comp sci math foundation.

~~~
nisa
My high school math teacher used to say math is like handcraft. I'm a lousy
student but if you have the discipline and will to learn something I'd look at
where you tap out in the chapter and try to learn that. Math is based on a lot
of concepts. You have to solve the problem sets in order to grasp a lot of
concepts. A lot of books are very dense and theoretical. Start small. Read the
college textbooks for the algorithm courses and try to solve the problem sets
on your own. If you are stuck join some communities. There are subreddits and
forums dedicated to math. If you ask there kindly with a concrete problem and
your efforts you'll get an helpful answer. That's the only thing that works
for me: Solve the problem sets on your own. Everything will be easier. And
don't take shortcuts. That's at least my experience.

There is:
[http://en.wikipedia.org/wiki/Introduction_to_Algorithms](http://en.wikipedia.org/wiki/Introduction_to_Algorithms)
which is pretty readable.

And there are a lot of MOOCs:

[https://www.coursera.org/course/algs4partI](https://www.coursera.org/course/algs4partI)

[https://www.coursera.org/course/algs4partII](https://www.coursera.org/course/algs4partII)

[https://www.coursera.org/course/algo](https://www.coursera.org/course/algo)

[https://www.coursera.org/course/algo2](https://www.coursera.org/course/algo2)

If you work yourself up from there and solve one problem after another you'll
be quite good at these things in a few months time.

------
bloaf
>Young man, in mathematics you don't understand things. You just get used to
them.

John von Neumann

The only way to get used to things is to work with them regularly!

------
zasz
I feel like a tool for saying this, but getting a B in a calculus class
doesn't qualify as "good at math." I was hoping this would be a story about
someone bad at math ending up majoring in it. If the author had to put _this_
much effort into it, well, no, they're probably not that good at math.

~~~
trentlott
You should.

C is the average grade. B is above average. A is excellent. You think he's not
"good" because he's above average while learning calculus at _37_?

------
CurtMonash
There's a foolproof way to learn math -- find somebody to coach you through
enough problems until you "get it".

Alternatively -- and this is much more common -- self-coach. But then you're
in the hard work territory that the author speaks of, since you'll be banging
your way through a number of walls headfirst.

------
barbs
_I sat in the front row. I asked questions non-stop. I did all the homework. I
did extra practice problems. I raised my hand to answer questions so much the
instructor asked me to stop._

Oh no, you're THAT person.

[https://twitter.com/MatureAge](https://twitter.com/MatureAge)

------
jisaacstone
I used to think I was 'bad at spelling', I realize now it is the same.

I was 'good at math' but 'bad at spelling' and that was normal and natural.
Except I found out it is just as much a lie as the opposite thought the author
had.

~~~
meowface
It's funny, because I don't think it's the same. And I think this is a good
example of why I don't agree with the article.

Even in 2nd and 3rd grade (American elementary school system), any time we had
a "spelling test" I got 100%. The first time I looked at any word, I
remembered how to spell it perfectly. To this day I still have the ability. I
can read a 5,000 page essay and immediately notice every typo and grammar
misusage; and when writing anything myself, the only reason I ever misspell a
word is due to an accidental typo, not a result of forgetting the correct
spelling.

I saw many classmates struggle with trying to remember the correct spelling of
various words, and I never had to do any of that.

However, in contrast, I've always had to put in much, much more effort than
some of my peers to properly grasp math concepts. Some people could basically
be introduced to a concept once. I wonder if this may be due to dyscalculia on
my part, becuase the math I struggle with the most is basic arithmetic and
algebra; I'm ok with the more advanced concepts, generally, except when I have
to do the real number crunching.

------
mrleinad
TL;DR: Study harder

------
kimonos
Wow! That is great! Math is one of my fears too and I wish I had done the same
when I was still in school.. (",)

