Non-Traditional Mathematics Curriculum Results in Higher Standardized Test Scores

Sept16, 2013 — For many years, studies have
shown that American students score
significantly lower than students worldwide in
mathematics achievement, ranking 25 th among
34 countries. Now, researchers from
theUniversity of Missouri have found high
school students in the United States achieve
higher scores on a standardized mathematics
test if they study from a curriculum known as
integrated mathematics.
James Tarr, a professor in the MU College of
Education, and Doug Grouws, a professor
emeritus from MU, studied more than 3,000
high school students around the country to
determine whether there is a difference in
achievement when students study from an
integrated mathematics program or a more
traditional curriculum. Integrated mathematics
is a curriculum that combines several
mathematic topics, such as algebra, geometry
and statistics, into single courses. Many
countries that currently perform higher than
the U.S. in mathematics achievement use a
more integrated curriculum. Traditional U.S.
mathematics curricula typically organize the
content into year-long courses, so that a 9 th
grade student may take Algebra I, followed by
Geometry, followed by Algebra II before a pre-
Calculus course.
Tarr and Grouws found that students who
studied from an integrated mathematics
program scored significantly higher on
standardized tests administered to all
participating students, after controlling for
many teacher and student attributes. Tarr says
these findings may challenge some long-
standing views on mathematics education in
the U.S.
"Many educators in America have strong views
that a more traditional approach to math
education is the best way to educate high
school students," Tarr said. "Results of our
study simply do not support such impassioned
views, especially when discussing high-
achieving students. We found students with
higher prior achievement scores benefitted
more from the integrated mathematics
program than students who studied from the
traditional curriculum."

Tarr and Grouws' papers, which were recently
published in the Journal for Research in
Mathematics Education, come from a three-
year study measuring educational outcomes
for students studying from different types of
mathematics curricula. Tarr says improving
American mathematics education is vital for
the future of the country
.
"Many countries that the U.S. competes with
economically are outpacing us in many fields,
particularly in mathematics and science," Tarr
said. "It is crucial that we re-evaluate our
school mathematics curricula and how it is
implemented if we hope to remain competitive
on a global stage."
Tarr and Grouws' longitudinal study is funded
by grant of more than $2 million from the
National Science Foundation.

Story Source:

The above story is based on materials provided
by University of Missouri-Columbia.

Journal Reference:

1. James E. Tarr, Douglas A. Grouws, Óscar
Chávez, and Victor M. Soria. The Effects of
Content Organization and Curriculum
Implementation on Students’ Mathematics
Learning in Second-Year High School
Courses .
Journal for Research in Mathematics.

Photo maths

Some maths articles :  only image,  just like topic.

Arresting Model Stops Cars

Sep. 5, 2013 — Researchers in China have
developed a mathematical model that could
help engineers design a flexible vehicle-arrest
system for stopping cars involved in criminal
activity or terrorism, such as suspect car
bombers attempting break through a check
point, without wrecking the car or killing the
occupants.

Writing in a forthcoming issue of the
International Journal of Vehicle Design, Pak Kin
Wong and colleagues in the Department of
Electromechanical Engineering at the
University of Macau, in Taipa, Macao, explain
how common vehicle-arrest systems used by
law enforcement, the military and in anti-
terrorism activities, usually cause serious
damage to the vehicle and maim or kill the
occupants. A more positive system for bringing
a car chase to a halt or stopping a car-bomber
in their tracks is needed if perpetrators,
witnesses and evidence are to be protected.

A flexible system would increase the stopping
distance of a vehicle involved in criminal or
terrorist activity and allow its kinetic energy to
be dissipated without the complete destruction
of the vehicle as otherwise occurs with solid,
immovable barriers and equipment currently
used. The team's mathematical model of
vehicle arrest with different flexible materials
and designs bears up to theoretical and
experimental scrutiny and offers engineers a
new set of variables to embed in their design
program in the development of new, effect
vehicle arrest systems. Moreover, the system
could allow the design of an "intelligent"
vehicle-arrest system for roadblocks and
checkpoints that could respond differently
depending on vehicle speed and type and allow
for greater control in bringing a vehicle to a
stop

Story Source:

The above story is based on materials provided
by Inderscience Publishers , via EurekAlert!, a
service of AAAS.
And ( science daily magazine ) .

Note: Materials may be edited for content and
length. For further information, please contact
the source cited above.

Journal Reference:

1. Pak Kin Wong et al. Modelling and testing of
arresting process in flexible vehicle
arresting systems. Int. J. Vehicle Design ,
2013, 64, 1-25

Generosity Leads to Evolutionary Success, Biologists Show

Sep. 2, 2013 — With new insights into the
classical game theory match-up known as the
"Prisoner's Dilemma," University of
Pennsylvania biologists offer a mathematically
based explanation for why cooperation and
generosity have evolved in nature.
Their work builds upon the seminal findings of
economist John Nash, who advanced the field
of game theory in the 1950s, as well as those
of computational biologist William Press and
physicist-mathematician Freeman Dyson, who
last year identified a new class of strategies for
succeeding in the Prisoner's Dilemma.
Postdoctoral researcher Alexander J. Stewart
and associate professor Joshua B. Plotkin, both
of Penn's Department of Biology in the School
of Arts and Sciences, examined the outcome of
the Prisoner's Dilemma as played repeatedly by
a large, evolving population of players. While
other researchers have previously suggested
that cooperative strategies can be successful in
such a scenario, Stewart and Plotkin offer
mathematical proof that the only strategies
that succeed in the long term are generous
ones. They report their findings in the
Proceedings of the National Academy of
Sciences the week of Sept. 2.
"Ever since Darwin," Plotkin said, "biologists
have been puzzled about why there is so much
apparent cooperation, and even flat-out
generosity and altruism, in nature. The
literature on game theory has worked to
explain why generosity arises. Our paper
provides such an explanation for why we see
so much generosity in front of us."
The Prisoner's Dilemma is a way of studying
how individuals choose whether or not to
cooperate. In the game, if both players
cooperate, they both receive a payoff. If one
cooperates and the other does not, the
cooperating player receives the smallest
possible payoff, and the defecting player the
largest. If both players do not cooperate, they
receive a payoff, but it is less than what they
would gain if both had cooperated. In other
words, it pays to cooperate, but it can pay
even more to be selfish.
In the Iterated Prisoner's Dilemma, two players
repeatedly face off against one another and can
employ different strategies to beat their
opponent. In 2012, Press and Dyson "shocked
the world of game theory," Plotkin said, by
identifying a group of strategies for playing
this version of the game. They called this class
of approaches "zero determinant" strategies
because the score of one player is related
linearly to the other. What's more, they
focused on a subset of zero determinant
approaches they deemed to be extortion
strategies. If a player employed an extortion
strategy against an unwitting opponent, that
player could force the opponent into receiving
a lower score or payoff.
Stewart and Plotkin became intrigued with this
finding, and last year wrote a commentary in
PNAS about the Press and Dyson work. They
began to explore a different approach to the
Prisoner's Dilemma. Instead of a head-to-head
competition, they envisioned a population of
players matching up against one another, as
might occur in a human or animal society in
nature. The most successful players would get
to "reproduce" more, passing on their
strategies to the next generation of players.
It quickly became clear to the Penn biologists
that extortion strategies wouldn't do well if
played within a large, evolving population
because an extortion strategy doesn't succeed
if played against itself.
"The fact that there are extortion strategies
immediately suggests that, at the other end of
the scale, there might also be generous
strategies," Stewart said. "You might think
being generous would be a stupid thing to do,
and it is if there are only two players in the
game, but, if there are many players and they
all play generously, they all benefit from each
other's generosity."

In generous strategies, which are essentially
the opposite of extortion strategies, players
tend to cooperate with their opponents, but, if
they don't, they suffer more than their
opponents do over the long term.
"Forgiveness" is also a feature of these
strategies. A player who encounters a defector
may punish the defector a bit but after a time
may cooperate with the defector again.
Stewart noticed the first of these generous
approaches among the zero determinant
strategies that Press and Dyson had defined.

After simulating how some generous strategies
would fare in an evolving population, he and
Plotkin crafted a mathematical proof showing
that, not only can generous strategies succeed
in the evolutionary version of the Prisoner's
Dilemma, in fact these are the only approaches
that resist defectors over the long term.
"Our paper shows that no selfish strategies will
succeed in evolution," Plotkin said. "The only
strategies that are evolutionarily robust are
generous ones."
The discovery, while abstract, helps explain the
presence of generosity in nature, an inclination
that can sometimes seem counter to the
Darwinian notion of survival of the fittest.

"When people act generously they feel it is
almost instinctual, and indeed a large
literature in evolutionary psychology shows
that people derive happiness from being
generous," Plotkin said. "It's not just in
humans. Of course social insects behave this
way, but even bacteria and viruses share gene
products and behave in ways that can't be
described as anything but generous."
"We find that in evolution, a population that
encourages cooperation does well," Stewart
said. "To maintain cooperation over the long
term, it is best to be generous."

Story Source:

The above story is based on materials provided
by University of Pennsylvania , via
EurekAlert!, a service of AAAS.