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Topic: Stereotypes About Math That Hold Americans Back
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Jerry P. Becker

Posts: 13,744
Registered: 12/3/04
Stereotypes About Math That Hold Americans Back
Posted: Nov 12, 2013 2:20 PM
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From The Atlantic, Tuesday, November 1, 2013. See
http://www.theatlantic.com/education/archive/2013/11/the-stereotypes-about-math-that-hold-americans-back/281303/
*********************************
The Stereotypes About Math That Hold Americans Back

Speed doesn't matter, and there's no such thing as a "math person."
How the Common Core's approach to the discipline could correct these
misperceptions.

By Jo Boaler

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. [See
http://www.achievingthedream.org/sites/default/files/resources/PathwaysToImprovement_0.pdf
]

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 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. [See
http://www.amazon.com/Whats-Math-Got-Do-It/dp/0143115715?tag=vglnk-c53-20
]

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. [See
http://gse.berkeley.edu/sites/default/files/users/alan-h.-schoenfeld/Schoenfeld_2002%20Making%20Math%20Work%20ER.pdf
and http://uex.sagepub.com/content/30/4/476.abstract ] 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."[See
http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/
] This idea has been disproved by scientific research showing the
incredible potential of the brain to grow and adapt. [See
http://www.fil.ion.ucl.ac.uk/Maguire/Maguire2006.pdf ] 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.
---------------------------
SIDEBAR: Related Story ... The Myth of "I'm Bad at Math" --
http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/
---------------------------------
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. [See
https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about
]

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.[See
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html
] 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?




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.

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.
-----------------------------
SIDEBAR: The new Common Core curriculum gives more time for depth
and exploration than the curricula it has replaced
------------------------
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.[http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/
] Parents use flash cards and other devices to promote speed, not
knowing that they are probably damaging their children's mathematical
development. [See
http://www.amazon.com/Einstein-Never-Used-Flashcards-Learn/dp/1594860688
]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. [See
http://www.amazon.com/A-Mathematician-Grappling-His-Century/dp/3764360526
]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, 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.
-------------------------------------------
SIDEBAR: AP Photo of student explaining math problem.
-------------------------------------------
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.
********************************************
--
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244
E-mail: jbecker@siu.edu



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