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The Stereotypes About Math That Hold Americans Back
JO BOALER
NOV 12 2013, 11:51 AM ET
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Mathematics education in the United States is broken. Open any newspaper and stories of math
failure shout from the pages: low international rankings, widespread innumeracy in the general
population, declines in math majors. Here’s the most shocking statistic I have read in recent
years: 60 percent of the 13 million two-year college students in the U.S. are currently placed into
remedial math courses; 75 percent of them fail or drop the courses and leave college with no
degree.
We need to change the way we teach math in the U.S., and it is for this reason that I support the
move to Common Core mathematics. The new curriculum standards that are currently being
rolled out in 45 states do not incorporate all the changes that this country needs, by any means,
but they are a necessary step in the right direction.
I have spent years conducting research on students who study mathematics through different
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I have spent years conducting research on students who study mathematics through different
teaching approaches—in England and in the U.S. All of my research studies have shown that
when mathematics is opened up and broader math is taught—math that includes problem
solving, reasoning, representing ideas in multiple forms, and question asking—students perform
at higher levels, more students take advanced mathematics, and achievement is more equitable.
One of the reasons for these results is that mathematical problems that need thought, connection
making, and even creativity are more engaging for students of all levels and for students of
different genders, races, and socio-economic groups. This is not only shown by my research but
by decades of research in our field. When all aspects of mathematics are encouraged, rather than
procedure execution alone, many more students contribute and feel valued. For example, some
students are good at procedure execution, but may be less good at connecting methods,
explaining their thinking, or representing ideas visually. All of these ways of working are critical
in mathematical work and when they are taught and valued, many more students contribute,
leading to higher achievement. I refer to this broadening and opening of the mathematics taught
in classrooms as mathematical democratization. When we open mathematics we also open the
doors of math achievement and many more students succeed.
In mathematics education we suffer from the widespread, distinctly American idea that only some
people can be “math people.” This idea has been disproved by scientific research showing the
incredible potential of the brain to grow and adapt. But the idea that math is hard, uninteresting,
and accessible only to “nerds” persists. This idea is made even more damaging by harsh
stereotypical thinking—mathematics is for select racial groups and men. This thinking, as well as
the teaching practices that go with it, have provided the perfect conditions for the creation of a
math underclass. Narrow mathematics teaching combined with low and stereotypical
expectations for students are the two main reasons that the U.S. is in dire mathematical straights.
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The Myth of 'I'm Bad at Math'
This summer I taught a course through Stanford’s open online platform explaining research
evidence on ability and the brain and on good mathematics teaching, for teachers and parents.
The course had a transformative effect. It was taken by 40,000 people, and 95 percent said they
would change their teaching or parenting as a result. Hundreds wrote telling me that the ideas in
the course had been life-changing for them. Teachers and parents are open to research, and new
technologies are finally providing a way that important research evidence, on mathematics,
learning, and the brain, can reach the audiences that need them.
Conrad Wolfram, cofounder of Wolfram-Alpha, one of the world’s most important mathematical
companies, has spoken widely about the mismatch between the math that people need in the
21st century and the math they spend most of their time on in classrooms: computing by hand.
The Common Core helps to correct this problem by embracing broader mathematics and
requiring the use of advanced technology, such as dynamic geometry software. Students in the
Common Core will spend less time practicing isolated methods and more time solving applied
problems that involve connecting different methods, using technology, understanding multiple
representations of ideas, and justifying their thinking.
For example, consider the following two published test questions. The first comes from
California’s old standards, the second from the Common Core.
1. Which of the following best describes the triangles shown below?
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A both similar and congruent
B similar but not congruent
C congruent but not similar
D neither similar nor congruent
California Standards Test, released test questions, geometry, 2009
2. Triangle ABC undergoes a series of some of the following transformations to become triangle
DEF:
Rotation
Reflection
Translation
Dilation
Is DEF always, sometimes, or never congruent to ABC? Provide justification to support your
conclusion.
Common Core Smarter Balanced Grade 8 Sample Item, 2013
The second question, from one of the Common Core assessment teams, does not simply test a
mathematical definition, as the first does. It requires that students visualize a triangle, use
transformational geometry, consider whether different cases satisfy the mathematical definition,
and then justify their thinking. It combines different areas of geometry and asks students to
problem solve and justify. It does not offer four multiple-choice options. Common Core
mathematics is more challenging than the mathematics it will replace. It is also more interesting
for students and many times closer to the mathematics that is needed in 21st-century life and
work.
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An important requirement in the Common Core is the need for students to discuss ideas and
justify their thinking. There is a good reason for this: Justification and reasoning are two of the
acts that lie at the heart of mathematics. They are, in many ways, the essence of what
mathematics is. Scientists work to prove or disprove new theories by finding many cases that
work or counter-examples that do not. Mathematicians, by contrast prove the validity of their
propositions through justification and reasoning.
Mathematicians are not the only people who need to engage in justification and reasoning. The
young people who are successful in today’s workforce are those who can discuss and reason about
productive mathematical pathways, and who can be wrong, but can trace back to errors and work
to correct them. In our new technological world, employers do not need people who can calculate
correctly or fast, they need people who can reason about approaches, estimate and verify results,
produce and interpret different powerful representations, and connect with other people’s
mathematical ideas.
Another problem addressed by the Common Core is the American idea that those who are good at
math are those who are fast. Speed is revered in math classes across the U.S., and students as
young as five years old are given timed tests—even though these have been shown to create math
anxiety in young children. Parents use flash cards and other devices to promote speed, not
knowing that they are probably damaging their children’s mathematical development. At the
same time mathematicians point out that speed in math is irrelevant. One of the world’s top
mathematicians, Laurent Schwartz, reflected in his memoir that he was made to feel unintelligent
in school because he was the slowest math thinker in his class. But he points out that what is
important in mathematics “is to deeply understand things and their relations to each other. This
is where intelligence lies. The fact of being quick or slow isn't really relevant.” It is fortunate for
Schwartz, and all of us, that he did not grow up in the speed- and test-driven classrooms of the
last decade that have successfully dissuaded any child that thinks deeply or slowly from pursuing
mathematics or even thinking of themselves as capable.
The new Common Core curriculum gives more time for depth and exploration than the curricula
it has replaced by removing some of the redundant methods students will never need or use.
Sadly it does not go far enough in this regard, and the high-school grades in particular are still
packed with obsolete content. But educational progress is rarely fast and the changes
implemented in the Common Core are a step in the right direction.
The U.S. does not need fast procedure executors anymore. We need people who are confident
with mathematics, who can develop mathematical models and predictions, and who can justify,
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with mathematics, who can develop mathematical models and predictions, and who can justify,
reason, communicate, and problem solve. We need a broad and diverse range of people who are
powerful mathematical thinkers and who have not been held back by stereotypical thinking and
teaching. Common Core mathematics, imperfect though it may be, can help us reach those goals.
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Jo Boaler is a professor at Stanford University's Graduate School of Education and the CEO and cofounder of
YouCubed, which provides math-education resources for students, parents, and teachers.
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CCSSIMath
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1/3/14, 8:36 PM
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2 months ago
There are too many unfounded statements in this ramble to respond to all of them, so we'll
choose one substantive issue:
>Students in the Common Core will spend less time practicing isolated methods and more
time solving applied problems that involve connecting different methods
That's the theory, but there's nothing in Common Core's a la carte menu of standards that
actually ties concepts together. The theory, instead, is being distorted in classrooms, where
students are being required to practice, not one, but a multitude of ways to perform simple
operations, such as multiplying two numbers together, as if that will lead to a deeper
understanding of multiplication.
To understand the true complexity that is entailed in pulling concepts together to solve
problems, one only need look at a world-class caliber high school mathematics problem of
the sort that will never make its way into a Common Core classroom:
http://fivetriangles.blogspot....
This particular example pulls together triangle area, ratio, linear functions and quadratic
functions, 4 concepts that in American classrooms rarely overlap, if only for the reason they
are taught in different years.
In contrast, here's PARCC's rendition of Common Core high school math:
http://ccssimath.blogspot.com/...
We do agree that K-12 mathematics education in the US is broken, but Common Core is not
the complete rethink that it needs to be.
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99Luftballons
CCSSIMath • 2 months ago
CCSSIMath, how do you claim "K-12 mathematics education in the US is broken" in
other than the sense that it produces too many who are good in mathematics?
Given only 2.5% of the pool of high schools grads get a STEM job and many of those
jobs require no knowledge of quadratic equations (other than plugging some info into
the computer program), assuming they aren't eliminated by programs like
Mathematica or by off-shoring, it seems odd to train more than 2.5% of K-12 in
quadratic equations or anything more sophisticated, let alone worrying about deep
thinking.
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thinking.
Under 1% of college students major in Math and they are relatively poorly paid. Math
PhDs are generally poorly paid. They get paid less as 4-year college Instructors than
their counter-parts in Home Economics.
There is a surplus of domestic Mathematical knowledge and a large world-wide pool.
Most people can't do their 8th grade math after a few years, why should they? Why
shouldn't Math end for 97.5% at the 8th grade?
This way the 2.5% might get a Mathematical education the objective of which “is to
deeply understand things and their relations to each other" that might result in better
Scientists and Mathematicians, keeping in mind they will still be relatively badly paid.
There is no STEM shortage. There is no Math skill shortage.
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Nick
99Luftballons • 2 months ago
The problem solving and relational competencies that mathematics teach are
skills that go well beyond STEM fields. These are critical thinking skills, not just
technical knowledge of mathematics.
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99Luftballons
Nick • 2 months ago
Nick, you write, "The problem solving and relational competencies that
mathematics teach are skills that go well beyond STEM fields."
But that only applies to the 2.5% of students and they probably had the
competency to start with, which is why they do well in STEM because
they understand instead of "turning the crank." Most mathematics
education currently teaches and rewards "turning the crank". The
minority who understand play the game and progress through the
system.
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EnderTZero
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99Luftballons • 2 months ago
You aren't listening. The core components of mathematical competency
are useful beyond the '2.5%' of STEM fields, and help people succeed
in a number of other occupations, including many trade occupations.
Understanding how the world works mathematically, understanding how
mathematical concepts define personal finance, understanding social or
political issues through math, are all universally beneficial.
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Unfortunately, the institutional focus in re: math here in the United States
focuses less on core components than on memorization of formulas and
algorithms, from the simple to the complex. Thus we lose many of the
potential benefits of teaching people to use math in the world rather
than separate the two. That is the conceit of the entire above article.
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99Luftballons
EnderTZero • 2 months ago
EnderTzero, just because I'm not swallowing the proposition doesn't
mean I'm not listening. I'm not hearing evidence and logic, I'm hearing
brazen assertion. I don't see mathematical proof. How ironic!
Let's compare the skills of race drivers and mathematicians on the race
track. Provide the evidence of "many trade occupations." Birds fly
without understanding math or physics.
When you write "conceit" I read the definition "excessive pride in
oneself." But I also think it's one in a list of deceptions.
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Flatley
99Luftballons • 2 months ago
Do airplanes fly without understanding math or physics?
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99Luftballons
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Flatley • 2 months ago
Flatley, actually "airplanes fly without understanding math or physics" or
do you believe they have understanding? People, animals and inanimate
objects also fly within them without understanding.
Now, the aerospace engineers (who count as STEM) who design them
do have some abilities in those areas, but with CAD/CAM tools like
CATIA fewer of them probably do with much great understanding.
The extensive use of flight simulators for pilots suggests academic
training is insufficient. But Air Force pilots certainly get Math and
Physics courses, along with Engineering courses. All nicely fit within my
2.5%.
Most people learn how to walk, run, skip and swim without knowing the
Math, Physics or Biology behind the processes. Some can also chew
gum and walk at the same time.
You comically wrote, "Do airplanes fly without understanding math or
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You comically wrote, "Do airplanes fly without understanding math or
physics?"
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Flatley
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99Luftballons • 2 months ago
First of all, computer tools don't replace an engineer's need for
mathematical competency. That's how people die. (As an engineer
myself, I can assure you that there is no "probably" attached to this
statement).
Secondly, and more importantly, your view on the importance of
mathematical education is pernicious, though not unique. You, like the
educational establishment at large, would prefer that people fit into neat
little boxes, sorted by their perceived capabilities on timed, fill-in-thebubble examinations. Turns out not all students work like that. Who
cares if only 2.5% percent of students will need mathematical skills,
that's no reason to dissuade the other 97.5% from giving it a shot to see
if they like it. Our schools should not be a caste system.
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RobertSF
Flatley • 2 months ago
Actually, computer tools are already de-skilling occupations in which
people die. Flying airliners is one such occupation. Several accidents in
the last few years have been traced to pilots who failed to respond
correctly in emergencies because the auto pilot has dumbed flying
down.
On the other hand, it could be argued that, without the reliance on auto
pilot, an even greater number of people would have died because
humans are more fallible.
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badphairy
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RobertSF • 2 months ago
Indeed, there is no "good" and "bad" side, there are only competing
tradeoffs.
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99Luftballons
Flatley • 2 months ago
Flatley, and you seem to want to keep people ignorant and exploited.
You seem to want to deceive the young. You want to worsen a caste
system that exploits the mathematical.
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You wrote, "Who cares if only 2.5% percent of students will need
mathematical skills"
Well, I think that students would like to know 2.5%, instead the
propaganda shoved down their throats. They ought to know in advance
that only 2.5% of the high school pool get STEM jobs (the number
requiring extensive math is less, let alone the Schwartz level thinking).
They should know how poorly colleges pay Math/Stats Instructors on up
compared to Home Economics. They should know that it is hard,
determined, persistent work that gets you ahead in STEM. Why do you
want them to be ignorant of these things?
I reject your lies and distortions. You write such outrageous rubbish like:
"You, like the educational establishment at large, would prefer that
see more
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darklordmeow
99Luftballons • 2 months ago
By your train of thought, we should cease educating 97.5% students in
literature and English or civic studies because they're not going to
become authors or civil servants. Some people are just innate "grammar
people" and some aren't.
I implore you to examine the past 300+ years of human civilization.
Mathematics is part of our culture and civilization and history. All citizens
are entitled to that privilege, not just 2.5%, and they are all capable of it.
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99Luftballons
darklordmeow • 2 months ago
darklordmeow, actually, your train of thought is rubbish, not mine. Most
are citizens or will be, so need English and civic studies. The right
choice of literature can make English and civic studies much more
effective and enjoyable. I have written elsewhere about Animal Farm etc.
You bizarrely wrote:
"By your train of thought, we should cease educating 97.5% students in
literature and English or civic studies because they're not going to
become authors or civil servants."
But running with your ridiculous claim. We should not pay students to
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But running with your ridiculous claim. We should not pay students to
get English Lit degrees and MFA degrees whether or not they become
authors. We should not pay people to get degrees whether or not they
become civil servants -- especially not Homer Simpson's sisters Selma
and Patty at the DMV.
Once you have learned English you can read about civilization. The
Egyptians, Archimedes and Euclid date back further back than 300
see more
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99Luftballons
EnderTZero • 2 months ago
EnderTZero, to illustrate the lack of market value of deep mathematical
knowledge we can see at a 4-year college or university the average
Instructor salaries (which tells us nothing about the % of PhDs that
succeeded in landing these jobs instead of remaining as adjuncts or
how many years it took) for 2010-2011 were:
* English Language and Literature/Letters $41,733
* Math/Stats $42,538
* Parks and Recreation $43,503
* Physical Sciences $43,980
* Communication, journalism, and related programs $45,070
* Home Economics $45,247
Actually, Home Economics is now called "Family and consumer
sciences/human sciences"
see more
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frank T
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99Luftballons • 2 months ago
Instructor salaries are a subset of the argument. Why not strip away the
background noise caused by statewide, largely union-driven, universal
pay scales, and institute a pay scale based on demand? Instructors
have very little variance in salary based upon the skill's demand; and
this is not natural for the market of such skills as there is a much larger
disparity between teacher salaries and industry salaries for technical
(physics, chemistry, math) vs non-technical disciplines. Much has been
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(physics, chemistry, math) vs non-technical disciplines. Much has been
written on this, but state legislatures continually are reluctant to act.
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99Luftballons
frank T • 2 months ago
frank T. but if "union-driven" pay scales dominated you wouldn't see
these large differences between fields. But even with them, you see the
difference and Home Economics continues to beat Math/Stats all the
way to the full professor level. If there was great demand for Math/Stats
there would soon be no Math/Stats professors left. If there was high
demand then they wouldn't even bother with grad school and would go
to work in industry.
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Flatley
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99Luftballons • 2 months ago
Unlike in many non-technical fields, though, a math or science PhD is
actually of value outside the university. Technical graduates are, in
general, more employable than non-technical, and will come with higher
starting salaries. A faculty survey hardly tells the full story.
Of course, the specific faculty numbers you chose to post hardly tell the
whole story, either. In particular, the engineering salaries are
conspicuous by their absence:
Full professor: $114,365
Associate: $87,664
Assistant: $75,822
New Assistant: $76,518 (market price rising faster than wages for
tenure-track faculty)
Instructor: $57,768
So there's a dominant market advantage there, competitive even with
the lucrative business fields. Not quite the narrative you're pushing, eh?
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99Luftballons
Flatley • 2 months ago
Flately, you are being quite deceptive again, as seems your habit of you
and that of others who follow your line.
We are discussing Mathematics so the comparison of Math/Stats is
precisely the best comparison to be making.
The next closest proxy for mathematical knowledge would be Physics,
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The next closest proxy for mathematical knowledge would be Physics,
which wasn't in the list so I used Physical Sciences.
Now the sharp difference in average salary for Engineers demonstrates
that Mathematical knowledge is not the key factor because if it was
then Math/Stats and Physical Sciences would be paid at least twice
what Engineering profs made.
But no, that isn't the case because Mathematical knowledge is not
prized in the marketplace. Not only to do Engineers get paid better as
professors, they get paid better with just a bachelor degree and thus
they have a lower rate of going to grad school.
So you have conclusively proved my point that mathematics talent is not
see more
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Flatley
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99Luftballons • 2 months ago
An engineer without a mathematical background is just a bad concept
artist. All that you have "conclusively proved" (here and elsewhere) is
that you are deliberately being disingenuous and not making statements
in good faith. There's no problem with that, (this is the internet, after all),
it's just important to point out.
What's truly entertaining, though, is your final paragraph. Let's break
this down:
1) You point out the fact that industry pays well for engineering/comp sci
grads, even at the bachelor level. True.
2) You point out that many engineering grad students will choose
industry over academica, because industry pays better than even the 6figure professor salaries I quoted. Also true.
3) You conclude that mathematical talent is not valued. (Admitting, along
the way, the point I made above - engineering is well within the realm of
"mathematical" professions).
see more
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99Luftballons
Flatley • 2 months ago
Flatley, no, "All that you have 'conclusively proved' (here and elsewhere)
is that you are deliberately being disingenuous and not making
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is that you are deliberately being disingenuous and not making
statements in good faith."
Because you cannot accept that the best comparison of the market
value of mathematical value is Math/Stats not engineering. Math/Stats
is the "pure play." You can't seem to distinguish between Engineering
talent that makes use of mathematics and Mathematical talent.
But then a few engineers did give us the O-Rings, the second Shuttle
disaster and the Tacoma Narrows Bridge. Now, a physicist (Richard
Feynman) did use a glass of ice water to illustrate the problem with the
O-Rings, but some ignored his minority report and were able to kill
again. Actually, I'm not sure they actually did much about the O-Rings
either.
But I knew you were a liar and deceiver when you comically wrote:
"Do airplanes fly without understanding math or physics?"
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Flatley
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99Luftballons • 2 months ago
A "liar and deceiver?" That's cute. I didn't think the intent of that
statement was quite so mystifying, I apologize for having confused you.
Challenger was a disaster that is best not used to score points with, we
are better off respecting the dead. I'd suggest, however, that you read
up on Roger Boisjoly. He knew full well that problems with the o-rings,
and was ignored by NASA management. Feynman's after-the-fact
demonstration hardly had priority.
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99Luftballons
Flatley • 2 months ago
Flatley, avenging the dead would make more sense to protect the living.
Remembering how the dead were killed and why, would make more
sense to protect the living.
"Remember the Alamo!"
to pick an analogy.
Feynman did report that some people would slip him info or lead him to
info to get at the real story.
Some Engineers have different views than some others.
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"Tufte's point is that the engineers' failure led to the
death of the astronauts. Had the engineers presented their data clearly,
he claims, Challenger would not have been
launched."
http://www.onlineethics.org/To...
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99Luftballons
Flatley • 2 months ago
Flatley, I see that Boisjoly writes:
"I hope the suits send a serious and significant message to MTI in
particular and to executives of other companies and government
agencies that they cannot make arbitrary irresponsible decisions that kill
people and ruin the lives and careers of their employees without
accountability. In my opinion, there has been zero accountability to date.
Everyone involved with the decision to launch Challenger at MTI and
MSFC has been either transferred or taken normal or early retirement
without any penalty for his actions. Further, MTI has not paid the $10
million penalty in their contract for their hardware being responsible for
the disaster and loss of seven lives and the destruction of over $2 billion
in hardware. "
http://www.onlineethics.org/To...
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99Luftballons
Flatley • 2 months ago
Flatley, more about Boisjoly
"Yet, those are not apt images for Roger Boisjoly's heroic action. What
he did that branded him as a whistleblower was to tell a Presidential
Commission after the disaster his story of the events that had led to the
disaster. The tragedy he had warned against had already occurred. In
the face of strong opposing pressure from top officials of his company,
he gave the commission his history of the O-ring problems and the
decision to launch. Generally, the whistleblower's action is forward
looking. While Boisjoly's account had implications for the redesign of
the shuttle in the future, it served chiefly to explain how the terrible
failure, both technical and moral, had occurred. It seems that the high
visibility of that very serious failure and of Boisjoly's disclosure helped to
put his report in the category of whistleblowing."
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put his report in the category of whistleblowing."
"Boisjoly suffered retaliation from Morton Thiokol. The head of the
Presidential Commission was moved to bring Morton Thiokol's
treatment of him to national attention. In spite of this public reprimand,
or maybe because of it, Boisjoly's situation did not improve. Retaliation
see more
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99Luftballons
Flatley • 2 months ago
Flatley, to provide another counter-example to the claimed general
wonderfulness of deeper Mathematics learning we have this report on
teach Math in school, which could be interpreted as meaning that
learning Math in college stunts the mind or alternatively teaching Math in
school stunts the mind.
"And although the TFA teachers were less likely to have
majored or minored in math, they scored significantly higher on a test of
math knowledge than their teacher counterparts."
"The bump in their test scores is equivalent to an additional 2.6 months
of school for the average student nationwide."
"Study: Students Learn More Math With Teach for America Teachers"
http://www.theatlantic.com/edu...
Of course, other interpretations are possible, but the clear message is
that in teaching school Math a college Math education is not
demonstrably helpful, especially when the lack of teacher training and
experience among the TFA teachers is considered.
• Reply • Share ›
99Luftballons
Flatley • 2 months ago
Flatley, I have a slightly improved version of my post on how playing
baseball is not actually Math and Physics problem solving, that was
here, here:
http://www.theatlantic.com/edu...
• Reply • Share ›
darklordmeow
99Luftballons • 2 months ago
Wow, your shallow interpretation and crude abuse of statistics sure
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illustrates the whole point of this argument - way to be the poster child
of a poor understanding of math. To say that having a thorough math
education in HS only applies to kids who major in math or physical
sciences in college is a childish conclusion. Surely, a math foundation
counts for many other majors that aren't captured in the stats you have
laid out.
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dwight mannsburden
darklordmeow • 2 months ago
not just college track, but also there is a shortage of people who are
capable of working in skilled technical positions
http://www.huffingtonpost.com/...
math understanding is critical to doing many modern factory jobs. the
stereotype of the assembly line worker who can be trained in 5 minutes
is not valid anymore
6
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99Luftballons
darklordmeow • 2 months ago
darklordmeow, thank you for illustrating the degraded state of education
and your inability to mobilize evidence and logic to make a case, not
even a deceptive one like the article does.
I enjoy how you make insults and assertions without backup.
As an example of your lies, you wrote:
"To say that having a thorough math education in HS only applies to
kids who major in math or physical sciences in college is a childish
conclusion."
I didn't say that, you did. You Replied to my post that starts:
"to illustrate the lack of market value of deep mathematical knowledge
we can see at a 4-year college or university the average Instructor
salaries"
Thank you for demonstrating that this article and its supporters should
be treated as deceptive at best.
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darklordmeow
99Luftballons • 2 months ago
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darklordmeow
1/3/14, 8:36 PM
99Luftballons • 2 months ago
well, it's settled. i'm 99.9% confident (know what that means?) that
99Luftballoons is actually some high schooler who probably failed
remedial math twice. I'm done with this "debate." i resign myself, i'm
gonna get some coffee. peace, all
1
• Reply • Share ›
99Luftballons
darklordmeow • 2 months ago
darklordmeow, you comically wrote:
"well, it's settled. i'm 99.9% confident (know what that means?) that
99Luftballoons is actually some high schooler who probably failed
remedial math twice. I'm done with this "debate." i resign myself, i'm
gonna get some coffee. peace, all"
I love it. If it were true, it would truly be embarrassing for
darklordmeow and the rest. It would reveal how pathetic the
claimed benefits of math are, at least for the more vocal hypers
Be ashamed! Be very ashamed! When a supposed high schooler can
quote numbers and sources and darkloadmeow can't, it shows how
degraded college has become.
Priceless!
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emin0413
• Reply • Share ›
99Luftballons • 2 months ago
You have this notion that the only value something has is material
market value. Knowledge of advanced mathematics has a much greater
value in understanding the fundamentals of our own reality. Isn't that
what humans have been trying to do since the beginning of conscious
thought anyway? There is more to a persons education than learning the
minimum required to perform their job. We need an intelligent society,
and math is key to making that a reality.
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99Luftballons
emin0413 • 2 months ago
emin0413, I have this well supported notion that most students, parents,
taxpayers and politicians "only value something [that] has is [a] material
market value." Or at least would like to know if there is one prior to
making decisions and spending money. So I think they should know the
facts. You are certainly free to tell people to ignore the relative poor
risk/reward prospects.
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But you are not free to claim "math is key to making it a reality" in terms
of an "intelligent society". Unless you are going for a tautology where
"intelligent society" is defined as one where deep math learning and
understanding is held by all. Well, actually, you are free to make that
claim, since you are free to lie and deceive.
You really are quite comically when you write:
"Knowledge of advanced mathematics has a much greater value in
understanding the fundamentals of our own reality. Isn't that what
humans have been trying to do since the beginning of conscious
thought anyway?"
see more
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stichmo
• Reply • Share ›
99Luftballons • 2 months ago
Funny, I thought Home Ec involved things like cooking, including
knowing how to halve the ingredients in a recipe that calls for 1/3 cup of
milk or sugar. I could be wrong, but I think that takes a little bit of math
reasoning.
Not to mention other family and consumer math skills like family
budgeting, understanding a mortgage loan, understanding car loans and
credit card purchases, and understanding compounded rates of return
on savings and investments.
• Reply • Share ›
99Luftballons
stichmo • 2 months ago
stichmo, funny, I think they have cups with the amounts engraved on the
side. Funny, I think they should have learned interest (percentages) by
grade 8. Funny, since the time of fire people have been able to cook.
Funny, crows, chimps, human babies, and the illiterate all engage in a
"bit of math reasoning."
None of this involves understanding quadratic equations or more
advance math.
And recent events show that many claimed not to know much of what
you talk about, but that just shows they don't know their material up to
grade 8. They should not have passed high school let alone be admitted
to college. But then they were called Liar Loans, that's one thing that
people seem very good at, along with excuses. So maybe they just are
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people seem very good at, along with excuses. So maybe they just are
lying when they say thy didn't know.
It illustrates a lack of standards or maybe just that what is taught is how
to make excuses. Funny, I don't think it takes much to realize that not
paying off your credit cards at the end of the month is kind of foolish at
25+% interest compounded.
It pleases me that this is the best you come up with. But it reinforces the
message that very rudimentary math for Home Economics is better
rewarded by colleges and universities than Math/Stats. Thank you.
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stichmo
99Luftballons • 2 months ago
Good luck finding a measuring cup for 1/6 of a cup. (half of 1/3) I don't
have one in my kitchen.
In case the problem is too difficult, 1/6 cup = two Tablespoons plus two
teaspoons.
• Reply • Share ›
99Luftballons
stichmo • 2 months ago
stichmo, "funny." And your solution requires knowledge that isn't really
mathematical, in the sense that you need to know what the relationship
is between the 3 quantities. I'd have similar problems with guineas,
groats, crowns and shillings.
"1/6 cup = two Tablespoons plus two teaspoons."
And I'd be curious to test Home Economics grads on this one.
1
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Jeremy Kun
99Luftballons • a month ago
You do know that not all people who use math become math teachers.
How about finance, economics, software, ALL ENGINEERING. I could
go on and on.
• Reply • Share ›
99Luftballons
EnderTZero • 2 months ago
EnderTZero, to illustrate the falsehood of your claims I refer to my reply
to Nick in which I use data from Academically Adrift
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mtbr1975
1/3/14, 8:36 PM
EnderTZero • 2 months ago
I would have to disagree. I know many people who work in fields that
traditionally required a very strong understanding of mathematics such
as architects, structural engineers etc. And all of them said they learned
all the math in college and haven't used it since. THey have computer
programs that figure it out and they have reference materials that also
state all the formulas, etc that are required. These days, unless you're
going to be a mathematician the background is only good to have so
you understand what's going on - you no longer have to actually be able
to do any of it.
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RobertSF
mtbr1975 • 2 months ago
Exactly. About the only people who use math on a daily basis are math
teachers.
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dormilon
mtbr1975 • 2 months ago
I am one of those people who have worked in various fields that
"traditionally required a very strong understanding of mathematics," and
I assure you that those among us who blindly rely on merely plugging
numbers into SAS, STATA, or other mathematical software have very
poor reputations. Their failure to understand the underlying concepts
impede them from a clear interpretation of results or even correctly
setting up analyses based on the unique circumstances of their
problem.
Your secondhand understanding of how professionals appropriately
leverage analytic tools ("computer programs") reveals your own
ignorance of the complex understanding actually necessary to succeed
in these careers.
Have I memorized Bayes' Theorem? Maybe not, but I better damned
well understand how and when it is appropriately employed, how to set
up the problem and code it, and how to interpret the results in order to
make or recommend the right downstream decision.
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JeffHenster
mtbr1975 • 2 months ago
Interesting comment, and one I have had issue with before. I am a
mechanical engineer, and certainly have had access and have used the
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mechanical engineer, and certainly have had access and have used the
spreadsheets, applications, etc to assist in analysis. I also have found it
necessary to write my own at time, finding what's available either
insufficient, or not clear enough about its basis. The idea of using math
aids without knowing what makes them tick, mentioned a couple of
times here in this thread, implies that engineers may use these programs
without understanding the math that underlies them. This is scary to me,
and I have seen it happen. They don't have to manually do complex
conjugates or cross-products every time they do an analysis, it's true,
but they had better understand how this stuff works on the inside before
they use any program, in my opinion.
In industry, I have had disagreements with managers who want exactly
the opposite, that is, a preference for computer jockeys who are not
required to demonstrate a firm grasp on reality and the math we use to
describe it, usually learned by hard study and experience. This stance
taken by management (or, worse, HR personnel who don't have a clue
what this entails) often boils down to lower requirements and less
training to save money, but I don't think it serves the public good.
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dormilon
• Reply • Share ›
99Luftballons • 2 months ago
I wonder.
Most people could certainly get by on a vocabulary of less than 5,000
words to communicate the majority, if not, entirety of their
communication needs. I wonder if you feel similarly about the
dispensable nature of literature in a world where only media
professionals require "anything more sophisticated."
Similarly. Why would secondary school students waste their time on
social studies? Or world history? How often will more than 2.5% of
Americans actually remember or need to remember who Charlemagne
was?
Indeed, as a bilingual American, ask me how often any of the multiple
professions or industries I have worked in required Spanish-language
proficiency. I wonder what percent of Americans are in professions that
demand foreign-language capability? Perhaps less than 2.5%? I
suppose, following your argument of economic efficiency, we should
limit foreign-language requirements for only those who seek
employment within this limited range of jobs.
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Indeed, I cannot fathom why anyone bothers to learn anything more
than he will need to employ DIRECTLY in his professional career. Every
thing else is superfluous, or simply "surplus."
Brilliant!
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99Luftballons
dormilon • 2 months ago
dormilon, you have to remember that I am going after the various
deceptions in the article. A key one is the title:
"The Stereotypes About Math That Hold Americans Back"
They in no way "Hold Americans Back" in any meaningful economic
way.
You wrote, "How often will more than 2.5% of Americans actually
remember or need to remember who Charlemagne was?"
Do you actually believe more than 2.5% over 30 do? Do you think that
there was a time when it was different? What problems do you think this
causes?
You wrote:
"Why would primary students waste their time on social studies? Or
world history?"
see more
1
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dormilon
• Reply • Share ›
99Luftballons • 2 months ago
You wrote, "I believe that you need to get the basics right before moving
on. But I also believe that some literature helps in the learning of basic
vocabulary and in the role of citizenship."
But, as you've clearly gleaned from the myriad responses, most similarly
believe that "the basics" includes some advanced
mathematics...particularly "in the role of citizenship."
Bottom line: Your initial premise that "... it seems odd to train more than
2.5% of K-12 in quadratic equations or anything more sophisticated, let
alone worrying about deep thinking" is based on the faulty premise that
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one should only study that which is explicitly necessary for one's
chosen profession, presumably decided by one's high school freshman
year. Aside from the illogic of your proposition, it also undermines the
breadth of a citizen's "basic vocabulary," which should include
mathematical analysis and problem solving.
No need to double down on your argument here. You are simply
defending an opinion that is resoundingly unpopular. For most, myself
included, reading and understanding "Brave New World" is as critical to
a well-rounded education as geometric proofs.
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99Luftballons
dormilon • 2 months ago
dormilion, the "myriad" just mean I've gored the ox of a motivated
subgroup.
You wrote:
"You are simply defending an opinion that is resoundingly unpopular."
That's the best you've got? Especially when I can quote statistics and
sources and you cannot?
It would be interesting to see how many over 30 actually understand
Brave New World let alone the way you do. But geometric proofs which
should be pre-8th grade are less critical, but more likely to be forgotten,
but note that I didn't preclude them.
And this talk about "well-rounded education" is somewhat alien to this
article.
Have you noticed you decide "faulty premise" and "illogic of your
proposition" simply because you have different opinions. You aren't able
to justify them because to use a poor analogy they contradict the
axioms that you have arbitrarily picked or the tautological definitions
that you have already picked.
2
dormilon
• Reply • Share ›
99Luftballons • 2 months ago
I see you're only capable of doubling down. I wonder if you criticize the
same behavior from our most intransigent politicians.
Anyway. Sticking only to the "illogic of your proposition," I will point out
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that your proposal requires that "sophisticated" study of mathematics
be predicated on having first decided upon a STEM career. In practice,
you appear to suggest that all rising eighth-graders first decide upon a
STEM career before their study of advanced mathematics could be
justified. And then limiting that study to only the 2.5% that will
(somehow) actually be employed in those roles, no career changes
allowed. For everyone else, study of advanced mathematics has no
value.
And, I missed the statistics (and sources) that prove that the study of
advanced mathematics is uniquely superfluous for "the role of
citizenship." Please forward the whitepapers that point to how effective
citizenship is predicated on advanced literature studies or advanced
studies in social sciences, but not on the study of advanced
mathematics. Fascinating premise.
Outside of investigating your sources, I will not entertain you any longer.
I already concede a difference of opinion; I disagree with you, and that's
the best I got.
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99Luftballons
dormilon • 2 months ago
dormilon, I just would cite those against the British at Lexington,
Concord, Bunker Hill etc. I would cite the lack of appeals to
mathematical reasoning in Common Sense, The Declaration of
Independence and the Constitution.
1
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