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tatee
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Topic: What's Wrong With Math Education in the U.S.? Posted: Feb 26 2014 at 1:13pm 
What's Wrong With Math Education in the U.S.?
Answer by Alon Amit, Ph.D. in mathematics, math circler:
This is (obviously, I hope) a complex and controversial question. It
is also geographically diverse: Whatever problems exist in math
education in the U.S. are very different from those in India, Mexico, or
Mongolia. I'll focus on the U.S.
My understanding is based on the following ingredients:
 I have been regularly teaching in math circles around the San
Francisco Bay Area for the past five years, and through that I've
gathered some knowledge of what those children who are really interested
in math know and what their unfulfilled needs are.
 I have been regularly speaking at math circles for teachers, where
I've worked with middleschool and highschool math teachers who are
interested in expanding their understanding of mathematics. I know
something about what teachers tend to know and not know.
 I have spent my career working with software engineers, data
scientists, economists, and other "knowledge workers" who rely, to
varying degrees, on mathematical training and mathlike problemsolving
skills. (I've been a researcher and engineer myself before succumbing to
the irresistible allure of product management.)
 I have a Ph.D. in math, so hopefully I know a little about what mathematics is.
 I've held official positions at the Mathematical Association of
America (the Northern California, Nevada, Hawaii and section) and have
had some exposure to the challenges facing an organization dedicated to
exciting students about mathematics.
 I have two children in elementary school in the U.S. (and another little waif who isn't quite there yet).
 I've read lots about the issue. I care.
Those are my credentials, such as they are. I don't purport to
understand the issues completely or even reasonably well; the following
are my personal opinions based on my experience and observations.
First, there are two metaproblems: 1) The lack of consensus around
the goals of K12 math education. Many people have strong opinions, but
they are often at odds with one another. 2) The lack of consensus around
the proper way to define and measure the success of the math education
system. Not everyone agrees that there is a problem, and among those who agree, many disagree on its specific form.
Beyond these two higherlevel issues, I think the following are true as well:
 The vast majority of the people who teach mathematics in schools
know very, very little mathematics. They are not to blame—many are
intelligent, caring, wonderful people—but they severely lack training
and skills. This includes not just exposure to higher mathematical
content; for the most part, they're not even aware what mathematical
problem solving is, let alone how to go about solving problems.
 People who do have the skills and even the passion for teaching math
are not often excited about the career prospects of being a math
teacher. Compensation is part of this; public perception and prestige is
another. And I am aware of at least anecdotal evidence that the arduous
certification process is not helping either.
 The textbooks are horrendous. They are massive, confusing,
uninspiring, incredibly inefficient, and stupefyingly boring. I lack the
expressive skills to describe how awful and misguided they are.
 The recent adoption of the Common Core standards is actually a
positive and promising move, but as of this writing, both the teachers
and the textbooks are unprepared to actually teach students to those
guidelines.
As a result, many children are led to hate the subject and lose all
confidence in their ability to excel at it. This is an oft repeated
cliché but it is, unfortunately, true.
Despite all of that, some people do become software engineers or
physicists or mathematicians, having developed a taste for mathematical
thinking, acquired problemsolving skills, and dove into deeper
training. This is often done outside of the school system, but not
entirely—there are certainly some great teachers and some useful
resources within schools. Not all mathematical teaching in schools is
broken; but much of it is, and many naturally talented and curious minds
are turned off by the broken parts and face an uphill battle as they
seek to nurture their talents and interests.
Those are some of the problems as I see them. How to solve them is an
even harder question (but I do have a few opinions on that, too).
I was a seventh and eighthgrade math teacher. From my experience,
it seems that the basic problem with math ed is the lack of focus on the
fundamentals.
Let me give you an example: Most teachers taught 2(x+y) using
dolphins. They would draw two dolphins traveling from the 2 to the x and
the y. This was meant to indicate that we distribute the 2 to get 2x +
2y.
Teaching this way allows kids to answer that specific construction of
problem, integer(variable + variable) = integer * variable + integer *
variable, but not much else. What happens when the kid sees (x+y)2 or
(x+2)(y+2)? The dolphins can only allow a child to guess at what to do
in these new circumstances.
Rather, if the teacher had taught that 2(x+y) = (x+y) + (x+y),
therefore giving the students some insight as to how and why the
distributive property works, then kids might be more able to approach
new circumstances and prevail by force of logic rather than speculation.
A student facing a new construct—say (x+2)(y+2)—has a shot at
realizing that the (x+2) can be seen as its own number, thus (x+2)y +
(x+2)2. The kid didn't have a shot with the dolphins.
Moreover, this drilling approach that is commonplace in schools is
very inefficient. Think about it: The above two examples take up the
better part of two quarters over the course of two years in most schools
using the drilling method. Is that really necessary? And imagine you
are the student. How boring! Three to four months of what?
The drilling approach requires that the teacher drill almost every
new circumstance with the same ferocity as the first circumstance.
Rather, when teachers focus on fundamentals, new circumstances still
need to be taught, but usually not drilled to the same extent.
Perhaps the worst consequence of the drilling paradigm is that
students and adults have no ability to use the math they learned in
school outside of the boxes within which they were drilled. The value of
math is in its predictive powers. You combine math with economics, or
math with biology, or math with physics, even with law (see Coase) etc.,
and suddenly you can predict the future. But these uses of math require
extremely strong fundamentals, which most people were never taught.


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carolina cutie
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Posted: Feb 26 2014 at 1:20pm 
"The textbooks are horrendous. They are massive, confusing,
uninspiring, incredibly inefficient, and stupefyingly boring. I lack the
expressive skills to describe how awful and misguided they are."For me Imo Ijs Imho, many teachers didn't make it relevant to the real world which makes it a little harder to follow. Geometry was fun because you could use it and you knew it was practical. With advanced algebra...not so much. I knew it was useful for computers or bio science but it was never taught in a manner I could relate too and that's how I learn best.


JoliePoufiasse
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Posted: Feb 26 2014 at 2:49pm 
Don't know how your math books are in the U.S. but some people simply do not have a head for math. I never did, much to my parents' chagrin. My brother was really good at it, though.


iliveforbhm
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Posted: Feb 26 2014 at 2:50pm 
Math is the language of the universe is the best way to show someone how important math is. We can communicate through numbers vs words.


JoliePoufiasse
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Posted: Feb 26 2014 at 2:54pm 
iliveforbhm wrote:
Math is the language of the universe is the best way to show someone how important math is. We can communicate through numbers vs words.  Oh, I understand the importance of math. I'm just saying that some people are not naturally inclined to do well in math. Must be a right brain, left brain thing, I don't know. I always excelled at literature and languages but math and physics always were a stumbling block. For some people, it's the opposite and math comes easy to them.


Random Thoughts
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Posted: Feb 26 2014 at 2:58pm 
I remember in 2nd or 3rd grade we learned our times tables with a rap song that the teacher would play. Was about the last time math was ever fun for me.


SamoneLenior
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Posted: Feb 26 2014 at 3:00pm 
my father was a math major in undergrad, got a MS in IS, and was a computer programmer
my brother sucks at math and I'm a B math student lol
trying to do math homework with my father was a struggle every single time....talk about tears
only reason I do as well as I do when it comes to math is constant studying
I have to have it fresh in my head otherwise I lose it
I can always get back to where I left off after awhile, but it takes some effort


OoDles O
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Posted: Feb 26 2014 at 3:02pm 
math "eww".
thats about all I got for this thread
sorry


JoliePoufiasse
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Posted: Feb 26 2014 at 3:03pm 
SamoneLenior wrote:
my father was a math major in undergrad, got a MS in IS, and was a trying to do math homework with my father was a struggle every single time....talk about tears
 Man, I can so relate to this. My dad studied engineering and he was always exasperated with me when it came to homework. I was mediocre at it. I would pass with a lot of studying, though.


AshBash89
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Posted: Feb 26 2014 at 3:09pm 
My dad is naturally good at math. It isn't naturally easy to me but I'm decent with lots of studying...but I hate studying.

