
My sister absolutely refuses to learn math - pmelendez
http://math.stackexchange.com/questions/416226/my-sister-absolutely-refuses-to-learn-math
======
tokenadult
A good starting point for this discussion might be this quotation from the
late Israel M. Gelfand, a pioneer of writing correspondence course materials
in secondary school mathematics in both Russian and English: "Students have no
shortcomings, they have only peculiarities. The job of a teacher is to turn
these peculiarities into advantages."

Thus far the Stack Exchange discussion includes a lot of complacency along the
lines of "some students just don't have the capacity to get it" that I never
found when I was living in Taiwan. Over there, even the below-average students
in seventh grade are all expected to learn quite a lot of algebra and
geometry, which they consolidate knowledge of during junior high school. By
the end of junior high, students in Taiwan and students in urban areas of
China and students in Korea, Japan, Singapore, and Hong Kong generally know
United States secondary school mathematics quite well. (I have heard Chinese
graduate students in the United States, students in nonquantitative subjects,
deride the mathematics section of the GRE general test used for graduate
school admission as a test of "junior high math," and that is literally true
in terms of the standard curriculum in China.)

So how about it? What creative ideas do we have here to help the young learner
learn how to solve proportions, an aspect of day-by-day reasoning that only
secondary school graduate might reasonably be expected to know? How to
reignite a spark of interest in mathematics after school lessons that may have
been a turn-off, may have been flat wrong,

[http://www.ams.org/notices/200502/fea-
kenschaft.pdf](http://www.ams.org/notices/200502/fea-kenschaft.pdf)

and at a minimum have left the learner with an excuse to not keep trying to
learn?

~~~
munin
> (I have heard Chinese graduate students in the United States, students in
> nonquantitative subjects, deride the mathematics section of the GRE general
> test used for graduate school admission as a test of "junior high math," and
> that is literally true in terms of the standard curriculum in China.)

this is true for students educated in the US as well! it's super frustrating,
because you're staring at trig identities that you last looked at ten years
ago.

~~~
dtparr
Agreed. I always assumed the GRE must have been designed to
accommodate/calibrated to humanities and social science grad students (or
other majors without a significant math component) more than STEM students.
Almost every CS friend I had either scored a perfect score or missed only one.
It was a little frustrating, as there's no room to differentiate students who
are average from those who are outstanding.

~~~
ekm2
You must be talking of the Old GRE.The current GRE Math section is computer
adaptive and getting a perfect score is no longer as easy as before.

~~~
dtparr
Admittedly I've not kept up with the GRE since I took it in 2004. It was
computer adaptive at that point, but I found it fairly easy (and had a perfect
score on the math section)

------
protomyth
I would hope the poster knows what things the sister actually likes to do.
Math is the one subject people will use to excess when it isn't seen as Math.
Watch any fantasy draft or craft and see how much math is going on. Find the
Math in the math she is already doing and work up from their.

We have the same problem with new students at the community college I
currently work at. I am at the "searching for sources" phase of trying to put
together a "just numbers" course to get students comfortable with numbers and
their uses.

Perhaps buying some of WeWantToKnow AS's software
[https://itunes.apple.com/us/app/dragonbox+-algebra/id5220691...](https://itunes.apple.com/us/app/dragonbox+-algebra/id522069155?mt=8)
[https://itunes.apple.com/us/app/dragonbox-
algebra-12+/id6344...](https://itunes.apple.com/us/app/dragonbox-
algebra-12+/id634444186?mt=8) for iOS if you have that.

~~~
anonymous
The first and hardest step is getting them to think of math as something other
than torture devices for teaching children obedience. (Un)fortunately, being a
mathematically-adept child from a mathematically-adept family, I've never
encountered that problem and can't offer solutions.

------
api
Mathematics is arguably the worst taught subject. I think this is entirely the
fault of the teachers and writers of the curriculum, who systematically fail
to explain their subject in an approachable way. I wrote a rant about it here:

[https://news.ycombinator.com/item?id=5819935](https://news.ycombinator.com/item?id=5819935)

TL;DR: This rant identifies a major cause: math is taught as if one should
magically be able to comprehend its language and syntax without explanation.

~~~
zephjc
Math uses symbols heavily as its own jargon, and someone approaching formulae
that have unspecified symbols, without knowing this jargon, is typically
fruitless.

That said, I agree that math is terribly taught. My mother and my wife both
hate math, and talking it out with both of them, I've been able to pinpoint it
to a single bad/discouraging (and sometimes straight out mean) math teacher
for both of them. Once the teacher is mean or otherwise bad about teaching,
they have not only failed as teachers, but have sometimes caused the students
to put up mental walls that can be hard to tear down.

I suspect the sister mentioned in the OP may have had such an experience.

~~~
api
I never got math or liked it until I had to do real-world things with it, at
which point I dug and managed to teach myself things that I needed. Nearly all
my math teachers were horrible. One or two of them seemed almost intentionally
obtuse... like they were trying to trick you and taking pleasure in your
failure to understand what they were teaching.

------
luisivan
I feel like his sister. I've been trained to solve math problems using
formulas, but I don't know the why. Some day, in a math class, the teacher was
talking about how to solve derivatives - and it required to know what infinite
means. I asked to all my classmates to put their hand up if they knew what
infinite means. Nobody did. But the teacher went on, omitting that basic
concept. I have just finished high school and I feel like I don't know why 2 +
2 = 4

~~~
akjetma
I feel the same way, despite being 'good at math' and having completed the
math curriculum for an engineering degree. I know how to use everything, I
understand what is being represented and the general structure of the tools I
use, but I feel like something is missing. Math used to 'flow' for me when I
was in grade school, but somewhere along the way, I think I lost the plot and
no longer think mathematically. I am quick to look up formulas rather than
intuiting them. I have moments where I completely understand gradient descent
for multi-dimensional logistic regression, but they are fleeting and pass with
some retarded thought like why does 2 + 2 = 4? I then give up and just
implement the parts of the algorithm without keeping track of the broad
picture and it feels... dirty. Guh.

~~~
primelens
I feel exactly this way as I am trying to teach myself some more involved
statistics. There are moments of clarity but the broad picture is too fuzzy.
And there was a time I could get really excited about math - still love the
experience of (re)learning it but it seems like several years of formula
grinding with the sole intent of passing entrance exams has taken its toll in
the worst possible way by diminishing some of the intuition and feel I seemed
to have.

------
AUmrysh
Having grown up in public schools in the southern US, I don't understand why
we focus so much on memorizing formulas but not the underlying concepts or how
they apply to other things. The power of math is the ability to abstract other
problems into math and then solve them with a standardized toolset. We spent
the first decade of our schooling learning very basic mathematics (up to
algebra), and I hadn't seen calculus until my second year of university.

It's no surprise to me that kids are having issues understanding the parts of
a circle, why the formulas do what they do, or how to do the related math.
I've been there. I think teaching basic physics and some of the more esoteric
math earlier (number type sets, limits, boolean logic, simplified of course)
would help with some of this. I always wondered how to do things infinitely or
how to calculate things certain ways in algebra, and it always seemed like
parts were missing. Calculus filled in so much of this for me, and I wish I
had known it earlier. Physics and video games (wiremod) gave me reasons to
learn some of the math.

Another thing I wish there had been more of is the history and practical
implications of this stuff. I never cared about the quadratic formula before I
learned about electric circuits or things falling in gravity. I didn't know at
the time it went back to Babylon, India, and Greece.

Kids don't get taught how to think critically and use the tools at their
disposal, and that's the largest problem with our education system. We learn
how to ask someone for the proper tool to use and then do the work ourselves
without thinking about it. It's probably an accurate representation of what
work in much of America has come to nowadays, busy work, but it's a shame that
we don't do something better for the next group coming along.

~~~
gohrt
When schools try to teach a holistic sense of numeracy to connect with average
students, with programs like Discovery, Tiger parents* revolt with stuff like
[http://wheresthemath.com/](http://wheresthemath.com/)

* Using Tiger parent as a trope here, not specific to any ethnicity.

~~~
ISL
Perhaps that's because the parents find that their kids can't compute
anything?

With the students that I've seen in college physics/math courses, ability to
solve real-world arithmetic/word problems quickly is limited at best.

------
fjdghsd
I tutored in uni for extra beer money and I've tutored children, teenagers,
fellow university students, grad students, and adults. What I learned from
this was that there was no one single best way to teach someone things. The
phrase sucks, but it really depends on the person. Some people you can teach
better by not giving them the answer and trying to get them to think and
that's great. On the other hand, some people actually do excel if they are
simply given the answer (of course one doesn't just stop after giving the
answer, you would then explain the answer, how we got there, etc, and then
knowing this, solve another similar problem to see how much of it they
understood). Figuring out your student's learning style is unfortunately the
hard part, and it looks like this guy in the link has not figured out his
sister's learning style. Even just reading that conversation he posted---he
sounds extremely condescending.

Just picking something out, he wrote:

"The circumference of the glass divided by the diameter gave me pi, what does
that mean?"

OK, first of all, he goes to say that she JUST now learned what a
circumference and diameter is and still doesn't know what a "pi" is. Why in
the world would you ask a question like this with unfamiliar words to someone
who just learned these words? He was making it unnecessarily difficult to
understand. Of course she said she didn't know and then he goes on and says
"WELL what if I divide 10 by 2?" Which is like comparing apples to oranges.

------
ceautery
I used to work at a phone center for Dominos Pizza. There would occasionally
be a need to give this basic size approximation: two 10" (diameter) pizzas are
about the same area as one 14". (50/49ths as big as one 14", unless you care
about toppings vs. crust, in which case the big pie is a better deal, but I
digress...)

Some people would balk at this for a second, and usually just throwing the
word "math" or "area" into the conversation would quell any doubts (or at
least any protests). But occasionally you'd get the "but two tens is twenty!!"
people.

Those conversations degraded pretty quickly into "ok, math is the devil, let's
just... what can I get you?" They wanted their incorrect view of the numbers
to be the right one, no matter what the rules of area were. Those people were
a drag...

...but the sister in the article, she's not. She wants it to make sense;
that's a great starting point. After getting past the "girls are cute and
stupid" indoctrination she's been listening to her whole life, there might be
a watershed moment where she "sees" it. Hang in there, try not to be
pedantic... and read Ittay Weiss' answer, good stuff there.

~~~
drzaiusapelord
I think its hard and maybe a little disingenuous to sell people on practical
everyday math while we shove trig, calculus, etc down their throats.

"Okay you like the pizza anecdote, lets talk derivatives."

I wonder if all this talk of no one but STEM majors taking advanced math
really is a problem. Not sure why someone who wants to get an English Lit
degree really needs to worry about anything past a practical level.

~~~
derleth
If you redefine 'practical level' to include basic statistics, which is almost
entirely ignored, I might actually agree with you. Basic statistics is
essential for the eminently practical purpose of not being ripped off and lied
to, and is, in fact, much more useful in that respect than trigonometry, which
is mainly useful if you're either going into calculus or becoming an engineer.

It's also a great way to introduce the mathematical mindset of breaking
problems down and figuring out which rules apply, which also has great
practical value but must be taught in context if it is to stick.

------
sehutson
I've tutored quite a few kids of varying ages over the years and in my
experience, there's no harder group to teach than teenage girls - and it's
doubly hard if the kid in question is fairly popular and active in other
areas. There are just so many things competing for a kid's attention that it
makes the most sense to (most of) them to quickly memorize a formula, get the
best grade possible with minimal effort, and move on to more enjoyable things.

The best method I've found for tutoring teenage girls (and I'm saying this as
a girl who hated math as a teenager in spite of a love of computers and
economics) is to start off by finding out what they enjoy. Put the lessons
aside, don't try to talk theory, and don't get all crazed trying to show her
how awesome math is. Eyes will glaze over and you will have lost before you
ever get started. You can't teach someone unless you first inspire an
interest.

What does she want to do as a career? What are her hobbies? What kinds of
things interest her? At that age, she's probably thought about a lot of
different careers, and in pretty much any career, you can tie things back to
math (especially junior high and early high school math).

If she enjoys cooking, you can talk about proportions and cross multiplication
and show how you can use that to adjust the number of portions produced by a
recipe. I know of one family where the parents had their daughter go on
Pinterest and find recipes for a family meal, then scale them up to fit the
size of their family.

If decor is her thing, you can talk about floor plans and usable area. Make a
diagram and figure out how much space an 8' circular rug will leave for a bed
and desk...the swing radius of a door is generally 1/4 of a circle, and you
can't put most things in that space.

Mathalicious.com is a good source of more real world lessons.

Take the time to walk through the logic and show how things relate back to her
lessons. It's not efficient, but in most cases, you don't have to do this for
every single concept. The goal is to (a) create interest, and (b) show how
math is relevant to her life.

Above all, be patient and understand that even with the best, most passionate
instruction...she might still hate math. The world needs many different types
of people, and not all of them have to have a deep understanding of math. She
can still be happy and successful even if she never learns to like math.

------
Eliezer
I still remember the shock of first encountering someone who was not naturally
good at math.

If I had one piece of advice to give, it would be, "Only ever try to teach one
cognitive motion at a time." Divide the circumference by the diameter? No.
First teach how to measure the diameter. Verify that this skill is being
practiced correctly. Teach how to measure the circumference. Verify that the
skill is being practiced correctly. Ask her to divide the two. Verify that the
skill is being practiced correctly. Then observe that the result is always pi.

------
grandalf
It's important to realize that jr. high algebra is largely syntactic
transformations.

 _a - 2 = 3_ is a syntactic transformation of _a - 1 = 4_.

Most of algebra is taught as a series of syntactic transformation rules. The
skill students acquire is learning to apply the right rules to solve a larger
problem.

If algebra were taught in a more abstract way, there would be an even more
pronounced stratification of aptitude, such that the educational system would
not be able to teach to the variety of different levels. At least when it's
taught as syntactic transformation, the best students are still largely
bounded by working memory rather than intellect.

------
altcognito
While not practical for all math, for the particular "mystery" of PI and
calculus, I find the story of Archimedes very useful.

Having _a_ concrete example of how PI was calculated was very easy to wrap my
head around:

[http://betterexplained.com/articles/prehistoric-calculus-
dis...](http://betterexplained.com/articles/prehistoric-calculus-discovering-
pi/)

~~~
jpwagner
ha! i mean, honestly, this is great, but would be so inappropriate for the
OP's sister that i had to laugh.

------
tixocloud
You can't really force someone to learn something they don't wish to learn.
And it's not about whether or not a person is capable or incapable. The value
of math needs to be communicated - try using examples that speak to the girl's
worldview. Show her the wonders of math and what it can do for her to solve
her puzzles in life.

I never got the hang of what I learnt in school until I began working and it
gave me so much reason to what I'm studying.

------
kryten
This is the distinction between education and training.

Training is what the poster's sister has.

Education is the bit that is missing.

Unfortunately education and training are confused these days.

I have the same battle with my children and mathematics. The teacher teaches
them the mechanics of mathematics but no meaning, reason or application.

~~~
prawks
This is a very important distinction to make, however issues with this style
of teaching (training rather than deep education) are difficult to see in
subjects other than mathematics.

At a high school level, I doubt any subjects really build on early learnings
as much as mathematics. History, biology, and chemistry for example are all
easy enough at the US high school level, as little actually builds on top of
early concepts. Sure, it helps to have insight into theory behind chemistry,
but I can still memorize some elements, molecules, and energy levels of
electrons. High school doesn't really go beyond that. Mathematics however, is
incredibly abstract, and without a framework of theory to encompass
everything, is just a vague sequence of techniques.

------
jloughry
This 'Foxtrot' comic is relevant:

[http://www.gocomics.com/foxtrot/2009/01/25/](http://www.gocomics.com/foxtrot/2009/01/25/)

------
DigitalJack
Sometimes the brain just isn't ready to understand at the time.

I struggled with math early on because why the fuck do I care what the
cicumference of a circle is? When things don't have some practical relevance,
they are harder to learn.

To motivate someone, you must find a way to tie in the subject to something
they are genuinely interested in.

~~~
genwin
Yep, memorizing formulas and tricks is the best choice absent some motivating
tie-in.

------
OnionChamp
From her perspective, this is literally like the following situation, where a
Haskell enthusiast is trying to explain monads to you, and after having told
you the technical definitions of a monad, an endofunctor category and a
monoid, which you think you maybe half-understood, he asks you

"Now, when we consider monoids in the category of endofunctors, we clearly get
something that reminds us of the definition of a monad. What does this mean?"

"er, I don't know"

"Well, what if I add the neutral element of a monoid to itself, what do I
get?"

"uhh, the neutral element?"

"Right! So if I apply return twice and then apply join, it's the same as
having applied return how many times?"

"..umm... none?"

"WHAT? Why none? That's not even the right type!"

"uhh... two?"

"Why two?"

"because a monoid means having a binary operation?"

"An operation acting on two what?"

"..two monads?"

...

And he looks at you irritated, like he thinks you're not even trying.

------
jackmaney
"How do you teach someone to understand math when they are capable but
unwilling to do so?"

You don't. Full stop. This is a lesson that I've had to learn the hard way.

~~~
mhurron
Basically this, you can not force someone to learn. By this point you're just
talking at them.

------
biot
For those who actually _want_ to learn more math, but find traditional
education lacking, I recommend this book:

[http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg...](http://www.amazon.com/Mathematics-Birth-Numbers-Jan-
Gullberg/dp/039304002X/)

It's filled with a lot of history on why things are as they are and it builds
up a substantial base of math knowledge from there. I can't comment on whether
the additional background information would help someone who is math shy to
"get it" but, from the parts I read, it certainly rounded out (and expanded)
my knowledge.

------
6d0debc071
Generally my advice would be to go back to the most basic set of skills you
can identify that she doesn't understand and work up from there - including
having her construct formula to solve problems (preferably ones that she finds
interesting.)

Though, honestly, if she doesn't want to learn maths she's not going to learn
maths. If you're really concerned for her and she doesn't want to do
something, then you're probably best off just teaching her the tricks and
cheats so that she can get a good result and then forgetting about the whole
thing - it's not like maths is likely to be a particularly important aspect of
her life.

#

With respect to pi in specific -

> Instead of giving her the c=πd formula she wanted so badly, I wanted her to
> understand that π represented the amount of times the diameter "fits" into
> the circumference and that this is the relation between the parts of the
> circle.

If she's never constructed formula to solve problems for herself, she many not
know that you can do anything with that sort of information. It's not a
trivial step if you don't already know what = and * and / and so on really do
to go from any particular instance to c = pi _diam.

> I measured as accurately as possible the perimeter and diameter of the mouth
> of a cup I had and showed her that dividing the numbers produced
> approximately pi. This unfortunately didn't provide the "ohhh" response I
> was looking for, which signified that she didn't intuitively understand
> division.

Try cutting up an apple or counting little blocks or something like that. If
she doesn't understand division then trying to use division in any capacity
with relation to more complex problems is a waste of time.

> "The circumference of the glass divided by the diameter gave me pi, what
> does that mean?"

I thought you werne't just giving her the formula? If she were able to
substitute letters in she'd have it. =p

Really though. It doesn't _mean* anything beyond that pi is the circumference
over the diameter. You need other knowledge to network it into before it
becomes meaningful.

------
vingt-2
What I don't understand is why the OP is even trying to teach stuff in which
his sister is obviously not interested. He is seeking a solution to the wrong
problem. "How do you get someone interested in math so he can develop the will
to learn it ?" is the problem he should solve before trying to teach her
anything. If he fails getting her attention on mathematics, then he's lost the
game and she'll have to wait until she gets interested, or just do something
else (which is fine, by the way).

What I think is most depressing on another note, is that even though she
clearly isn't learning maths, she'll probably stay in the average of her
class, and with this attitude eventually even get a university degree in
domains where comprehension of maths is the cornerstone.

I'm a software engineering student at what you'd call a "valued" university.
It is unarguably essential to understand basic university maths, and yet so
many of my friends would just give their faith into "applying formulas" with
little to no idea on what's going on in fairly easy topics like introductory
linear algebra, and they'll even sometime get As because the teacher gave up
when he asked for a little reasoning on the midterm (failing half the class)
and gives a silly final.

I think the issue is more that we force people into doing what they don't want
to do. Her sister doesn't have to understand maths at her age, she can wait
until she feels the need to (and she will for these simple maths problems, but
later).

------
chemcoder
I take engineering applied mathematics tuition part time for students in
Mumbai.

Certain things i learned from the students (opinions of students) after
discussing and inferring from their daily progress.

1\. Maths is dry and we have to be in different plane of imagination to study
it.

2\. In lecture hall they are mostly pondering about how the end result has
come into being.(instead of why it should come)

3\. Look for tricks emphasis on remembering things/patterns.

4\. When you think on how to solve a problem means solve the equation
according to the pattern learned. It's like they have put some identifiers on
the problems if they see something similar they will use the pattern.

5\. The textbook is the ultimate authority if it says so don't ask why because
-- "its printed there so it must work", trust issues are imminent.

I drew these insights because they recurred during tests, discussions,
question and answer sessions. Most of the time students would tell the
problems if someone asks them.

What i found difficult was to pin point the problems from the symptoms. Some
of the faults are with the books and others with the teaching system in India.
Students i found, are always eager to work hard if they feel they are
appreciated over minuscule achievements, so can't really blame them for
developing these conceptions.

------
MichaelAza
Seeing this is such a universal issue really saddens me. In Israel, High
School level math is divided into 5 point, 4 point and 3 point courses. 3
points is a very basic set of mathematical tools, "math for everyone" if you
will, which includes basic algebra, basic geometry and trigonometry, basic
statistics and what could possibly pass for the first lesson of a calculus
course.

4 points is pretty much what this guys sister is studying, conceptually, in
that it's a lot of memorization and very little to no understanding. This
includes higher level algebra, trigonometry in 3D space, calculus and some
other stuff.

5 points is where the problems start - students are required to do 4 point
level exercises with "twists" which make them harder and require actual
thinking. This sounds great until you understand that most 5 point students
have no idea about the underlying mathematical concepts and are just
memorizing the answers to thinking part as well. Instead of being elite
students who understand the internal workings of mathematics they are
distinguished by better memory and more cramming.

So yes - horrible math education is everywhere and no one seems to know what
to do about it. Three cheers for the human race...

------
danbmil99
> She doesn't have any learning disabilities

I would revisit this proposition. Whether it is native cognitive skill, an
unwillingness to focus, or what is typically called a "mental block" due to so
much negative attitude -- when someone can't learn, I think you have to call
that a learning disability.

Depending on where she goes to school, you probably can get her some
additional resources to help her deal with this problem. Don't assume just
because you took to Math and love it that she shares either your enthusiasm
(that's obvious) or your cognitive gifts. Let some professionals who have
dealt with kids for years tease out what ails her.

This kind of help is typically mandated in most states (for public education).
The problem is, districts are always tight for money, and they fail to offer
these services unless parents explicitly push for them. It's a form of
rationing -- the squeaky wheel gets the grease.

Your family needs to advocate for your daughter and get her the help she
needs. It is not just attitude or laziness, it's a legitimate disability if
she can't get herself into a frame of mind where she absorbs this stuff.

~~~
jamesaguilar
I dunno about that. "Learning disability" has, as far as I understand, some
kind of formal meaning that goes beyond mere laziness. It would be almost
impossible to deduce whether the sister has that from the evidence presented.

~~~
danbmil99
> It would be almost impossible to deduce whether the sister has that from the
> evidence presented.

Right, so why not have a professional, who is trained to figure this out, get
involved? The OP seems to just assume his sister must have the exact same
mental equipment he has, and is just "being lazy". Where is his evidence to
back this up?

~~~
jamesaguilar
Presumably knowing his little sister for his whole life? He's in a much better
position to judge than you are.

------
edtechdev
There are professionals and researchers out there whose job is dedicated to
this issue of improving math education (and the same with physics education,
computer science education, etc.). You can find great ideas and sample lessons
and great educational software.

Math is taught out of context, or completely decontextualized - that's why
people hate it, and that's why it's hard to motivate people to learn it. Math
knowledge is both situated and embodied. Look at mathematics education
research for ideas on how to teach math more effectively.

For example Jo Boaler's work. She is teaching a MOOC on this topic of how
people learn math next month:
[https://class.stanford.edu/courses/Education/EDUC115N/How_to...](https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about)
[http://joboaler.com/](http://joboaler.com/)

NCTM - National Council of Teachers of Mathematics
[http://www.nctm.org/](http://www.nctm.org/)

RUME - Research in Undergraduate Mathematics Education
[http://sigmaa.maa.org/rume/Site/News.html](http://sigmaa.maa.org/rume/Site/News.html)

As someone else mentioned, the app DragonBox helps with understanding algebra:
[http://dragonboxapp.com/](http://dragonboxapp.com/)

The Adventures of Jasper Woodbury taught math in context, in the form of
complex challenges: [http://viking.coe.uh.edu/~ichen/ebook/et-
it/ai.htm](http://viking.coe.uh.edu/~ichen/ebook/et-it/ai.htm)

------
r0s
So much advice here, and yet not a mention of psychology!

Where are the answers? How can learning behavior be quantified and understood?

I want nuts and bolts. I want hard answers to the problem of learning. I'm a
self-taught professional, I know for a fact different people learn in unique
ways. I'm heading back to school to learn the one thing that kept me out of
academia, how to learn.

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cupcake-unicorn
I agree with some of the other sentiment. I'm really uncomfortable with the
attitude that the poster seems to have that he needs to FORCE his sister into
being interested in math.

I was the exact same way with History. But, despite being surrounded by junky
grade school textbooks, I was still able to do extra research and get involved
in math, because I was _interested in it_. Is she like this in all her
subjects? She's not just some blank slate that you can mold into what you'd
like - she's a person with her own interests and passions. These may be
something that you might scoff at, I don't know, like posting makeup tips on
youtube, but that's what she's interested in. You shouldn't try to change it,
and doing so will end badly.

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prawks
Many people in society value practicality. Why should I do something if it
doesn't directly benefit me in the physical sense? How will this make me more
likable/valuable/wealthy?

Theoretical studies like mathematics serve no purpose to people who view the
world this way, except to qualify their earnings gained through other
pursuits. Theory is something some smart guy with a big head does. "Normal
people" are practical, and work with what is real.

This sort of viewpoint is one reason (in my opinion, the reason) why many
students give no effort in learning math, because it is "too hard", when
"hard" means "different", and "different" equates to "not concrete/tangible".

~~~
Shivetya
Sadly I am in this camp, I say sadly because part of me thinks that I should
care more about math yet I don't. I program every day and I could give a flip
about the math behind a circle. Business math for me is pretty much canned
routines. I know where to get the formula I need should anything advanced come
up, I don't usually care about why it works, only that it does work. I trust
it works because the sources I use are trusted.

There is a great benefit to teaching practical only, it engages people easier
when they can see the immediate benefit. There will never be a shortage of
those who want to know more on a give subject, maybe for this guy's sister he
needs to find what moves her. Not everyone likes math, and even of those who
do I wonder how many get to work with it

~~~
gohrt
One day you will start to notice that not every source can be trusted. And you
will need critical thinking skills and logic -- the underpinnings of
mathematics -- to separate truth from lies. The specific formulas and
structures of geometry and calculus math are irrelevant -- they are just
examples that are universal across all cultures.

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tiglionabbit
Have her play DragonBox.
[http://www.dragonboxapp.com/](http://www.dragonboxapp.com/)

I've played through it, and it's a really fun way to learn algebra.

------
mdm_
>Of course then most students will insist that 0.999⋯≠1 which shows how
ineffective this method is to understanding what the real numbers are.

Okay, you got me. Why is 0.999... != 1 incorrect?

~~~
saalweachter
Starting at the very beginning:

Stuff you write down aren't _numbers_ , they're _representations_ or _names_
of numbers. There is a number named "1", there is a number named "2". "2" is
not the number itself. You can't infer the two-ness of "2" by staring at the
symbols.

It turns out that our way of naming numbers isn't perfect. Each number has
multiple names. "2" and "2.0" are both names for the same number, as is
"2.00", "2.000", and "2.0000". It turns out that you can name "2" a different
way, as "1.9999999999999999999999999999999999999999999999999999...", where
there are an infinite number of nines. The names may be different, but the
numbers they name are the same.

------
gridmaths
You might find visual cues / diagrams helpful ...

I've been gradually doing a few of these as I bootstrap Gridmaths.com. You can
see some sample screenshots of worked problems in blogposts at :
quantblog.wordpress.com

I think we miss engaging with quite a few students, because we focus on
procedures and process rather than visualization in school [ I could be wrong,
this is subjective, but at least we should try and explore different ways of
presenting math ]

Khanacademy videos and GeoGebra might be useful also.

------
firesofmay
These two apps look really good for a kid -
[http://www.youtube.com/watch?v=1hHPCTV6KAw](http://www.youtube.com/watch?v=1hHPCTV6KAw)
[http://www.slatescience.com/](http://www.slatescience.com/) &
[http://www.dragonboxapp.com/](http://www.dragonboxapp.com/)

I have played with dragonboxapp, I loved it.

------
stcredzero
A fellow grad student told me once to, "Shut up and give me the answer! I'm
going to get my paper and go into management!" I never forgave her.

------
lizzard
A good tutor needs to be able to meet the student at their level, and be
patient and encouraging with confusion and lack of understanding and bigger
motivational problems.

Instead, this person seems disrespectful and judgmental of his student.
Perhaps she is on another forum, writing, "My sibling badgers me for hours and
acts like I'm stupid."

Good one on one discussions done with an open heart really moves mountains.

------
detcader
All this advice seems to ignore what sociologist Emily Kane calls "The Gender
Trap" (in her book by the same name), where females are _taught_ by their
parent(s) from their birth to prioritize things like appearance and social
status over intellectual pursuits thus making it impossible to gain an
interest at an older age. Try reading that book, highly enlightening.

------
aditgupta
First, not everybody will have interest in Math. And that's fine. Secondly,
you need to be creative for teaching math, especially at a junior level. I
think Lockhart gives a very good insight on this matter -
[http://www.maa.org/devlin/lockhartslament.pdf](http://www.maa.org/devlin/lockhartslament.pdf)

------
ExpiredLink
De-motivation wrt learning actually is a relatively well-researched field in
psychology. Essentially, you learn to become demotivated by a series of
aversive experiences with the subject. Unlearning your avoidance strategy is
hard work cannot be done by carrying out some tricks. I know from personal
experience that it can take years to unlearn an avoidance mindset.

------
pwenzel
Has anyone ever taken an integrated math course[1]? I grew up in Minnesota and
enjoyed those math classes when I was in junior high.

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

------
Datsundere
I think he needs to show his sister videos made by vihart to show how
beautiful mathematics can be.

------
johnchristopher
> What I do is define π as the circumference of the circle of diameter 1 or as
> the area of the circle with radius 1.

This is how π was made clear to me when I was younger.From there I understood
it was some kind of ΅natural and constant ratio" of circles.

------
auctiontheory
A good excuse to repost this marital math misadventure:
[http://www.youtube.com/watch?v=Qhm7-LEBznk](http://www.youtube.com/watch?v=Qhm7-LEBznk)

------
dmourati
People learn in different ways. Keep trying different ways until you find the
one that she gets.

------
bane
I was a very "challenged" math student in k-12. By 9th grade my experience had
been so poor that it turned into a virtual phobia and I simply zoned out of
the subject, scraping by with whatever remedial maths I could take until
graduation. I was _torture_.

After High school I took a break for a few years before going to college for
real. Once I had it in my mind to go to college, I signed up at my local
community college and retook all of my high school maths. When I made it to
Calculus I started signing up for other classes. I drilled, drilled, drilled
the problems in every subject until my hands ached from writing. Slowly some
patterns emerged and I started understanding more fundamental concepts about
math, started to think symbolically. Working problems became an exercise in
very careful symbol manipulation and not just arithmetic on steroids. It
trained me in the kind of very careful mental discipline needed for a STEM
degree.

I never really used much of the math I learned while studying Computer Science
(outside of a couple small subjects), but that discipline, the intolerance for
errors, and solving problems _did_ have a huge impact. I also use very little
of those maths in my day-to-day, but it's definitely left me with a rigor I
bring to the job.

It turns out that what I really enjoyed was logic and set theory that you just
have to learn when you start out in CS. I _wish_ that I had learned that first
instead of arithmetic tables or pointless long division. I use logic and set
theory all the time in critical thinking and daily reasoning...it's so useful
that it's practically automatic and subconscious at this point.

I think the real problem, and the one the original question is pointing out
is, math doesn't mean _anything_ to a youngster. There's literally no
application for it in their life beyond very simple addition and subtraction,
skills usually learned by 3rd or 4th grade. After that it's years and years of
absolutely pointless busy work (to them). I also think Maths education should
include more reading and math history.

Here's an alternative k-12 maths education route that I think I would have
taken to much more readily, since I could have started to apply it as a
reasoning and critical thinking skill immediately:

\- K, True and False, Counting numbers - reinforces concepts of True and False
they're already learning, teaches necessary basic numeracy (even Kindergarden
aged kids get why counting is important)

\- 1st and 2nd grade, T and F, AND, OR and NOT. More counting numbers, to 1000
and by 5s and 10s.

\- 3rd grade, More complex boolean equations, basic boolean algebra, truth
tables, implies -> operator. Negative numbers, count from -100,000 to 100,000
by 1s, 2s, 5s, 10s, 100s, 500s and 1000s.

\- 4th grade, more complex boolean algebra, binary arithmetic (using +, -, *
etc., it's the same thing but with new symbols!) Simple, boolean word problems
(teach rational reasoning! [1]), boolean laws (commutative, Associative,
etc.). Basic Set Theory.

[1] - The moon is in the sky and the moon is made of cheese. Is this statemen
true or false?

\- 5th grade, More Set Theory, boolean equivalency (T /\ F = F == F /\ (T \/
F)), base 10 arithmetic, more boolean word problems, set theory word problems,
critical thinking and reasoning. Read simple articles and determine if they
are true or false. Basic prepositional calculus.

\- 6th grade, various elements of digital circuit design (diagramming,
equivalency, etc.), more base 10 arithmetic, more set theory, more binary
math, half and full adder truth tables and diagrams, algebra

\- 7th grade, more basic algebra, fractions, decimals, digital circuit labs
(woah, application!, make a binary counter, and maybe a half and full adder)
maybe Karnaugh maps, more critical reading, deeper set theory (Jaccard
coefficients), base conversion

\- 8th grade, geometry, functions, more complex circuits, non-binary logic and
reasoning, basic statistics, maybe basic probability, logical fallacies,

\- 9th grade, more geometry and functions, more complex probability and stats
(non-calculus), deeper logic and reasoning topics, inductive and deductive
arguments, basic proofs, etc., end of year logic project, intro to abstract
mathematics, predicate logic

\- 10th grade, basic calculus, basic trig, more proofs and techniques, complex
inductive and deductive reasoning, complex set theory, end of year logic
project, more abstract mathematics, simple physics equations and labs!

\- 11th grade, more calculus, more Prob&Stats, vector algebra intro, mid-year
and end of year logic project, more proofs, more abstract mathematics, physics
equations and labs!

\- 12th grade, discrete math, vector algebra & calc, imaginary numbers,
abstract mathematics topics, etc. simple calculus physics and labs!

I'm of the opinion that most children can learn the mechanics of basic
calculus pretty simply. If you can do algebra, you can do basic calculus. You
might not understand the immediate application, but physics and physics labs
can be incredibly fun, calculate everything out and run an experiment.

I think logic should be taught before regular math because quite simply, the
student isn't getting hung up on all these _values_ and can focus on learning
what an operation is. Young children also are learning topics like "truth and
lies" anyways and this helps reinforce this and will come more easily to them.

Digital circuit breadboarding is fun and gives a nice application for logic,
it will engage tactile learners who tend to struggle with math subjects.

Reading and critical thinking discussions should be _central_ in the
curriculum. It reinforces the need to read, teaches rational thought and gives
application to the logic. The scientific method is covered as an application
of math in simple physics labs.

Also, by not focusing an entire year on a single subject (say a year on
Geometry), the student can flex as some topics will come more naturally than
others. So if they're great at probability, but terrible at geometry, they'll
get the slack in the year to get up to speed on their geometry.

Side benefits, a better understanding of critical thinking skills and rational
thought, the fact that there are different kinds of number systems, a good
transition from math into physics (and science), hands on with computer stuff,
they'll be set up to understand things like bayes theory and proofs, it
doesn't treat relatively simple subjects as "scary things only math priests
do" like calculus, word problems and logic go hand in hand, it eases them into
word problems and base 10 math as a matter of course instead of as a "special"
subject. Geometry just becomes another piece of the puzzle instead of a
different course, leading nicely into calculus. Probability and stats open up
lots of possibilities for practical labs and long term assignments and non-
binary logical reasoning. etc. etc.

At every grade, there's some way of spinning some of the subjects out into a
practical, hands on lab...teach and reinforcing the _applicability_ of math.
Which of course is the entire problem all along. Reading assignments will
bring along kids who are readers, I found math history unbelievably
fascinating, you can go from ancient history to the computer age easily.

It shows future STEM jobs as part of the course work.

I'm sure I'm missing some topics and in real-life things might be shuffled
around a bit, but I think I'm getting the basic gist across. There was no
reason for me to struggle in school except that I could understand the
application, and all of the adults around me seemed to get along fine with a
calculator and basic arithmetic. But with this kind of curriculum, I would
have been aware of a few dozen possible career paths in STEM (and elsewhere)
that I never even conceived of. It would have kept me interested and focused.

