e-book

Adding + It Up: Helping Children Learn Mathematics

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Public concern about how well U.S. schoolchildren are learning math-
ematics is abundant and growing. The globalization of markets, the spread
of information technologies, and the premium being paid for workforce skills
all emphasize the mounting need for proficiency in mathematics. Media
reports of inadequate teaching, poorly designed curricula, and low test scores
fuel fears that young people are deficient in the mathematical skills demanded
by society.
Such concerns are far from new. Over a century and a half ago, Horace
Mann, secretary of the Massachusetts State Board of Education, was dismayed
to learn that Boston schoolchildren could answer only about a third of the
arithmetic questions they were asked in a survey. “Such a result repels com-
ment,” he said. “No friendly attempt at palliation can make it any better. No
severity of just censure can make it any worse.” In 1919, when part of the
survey was repeated in school districts around the country, the results for
arithmetic were even worse than they had been in 1845. Apparently, there
has never been a time when U.S. students excelled in mathematics, even
when schools enrolled a much smaller, more select portion of the population.
Over the last half-century, however, mathematics achievement has become
entangled in urgent national issues: building military and industrial strength
during the Cold War, maintaining technological and economic advantage when
the Asian tigers roared, and most recently, strengthening public education
against political attacks. How well U.S. students are learning mathematics
and what should be done about it are now matters for every citizen to ponder.
And one hears calls from many quarters for schools, teachers, and students to
boost their performance.
During the new math era of the mid-1950s to mid-1970s, reformers
emphasized changes in the mathematics curriculum; today’s reformers want
changes in mathematics teaching and assessment as well. In the mathemati-
cian E.G. Begle’s laconic formulation, the problem is no longer so much teach-
ing better mathematics as it is teaching mathematics better. Almost every-
one today agrees that elementary and middle school mathematics should not
be confined to arithmetic but should also include elements from other domains
of mathematics, such as algebra, geometry, and statistics. There is much less
consensus, however, on how these elements should be organized and taught.
Different people urge that school mathematics be taken in different directions.
A claim used to advocate movement in one direction is that mathematics
is bound by history and culture, that students learn by creating mathematics
through their own investigations of problematic situations, and that teachers
should set up situations and then step aside so that students can learn. A
countervailing claim is that mathematics is universal and eternal, that stu-
dents learn by absorbing clearly presented ideas and remembering them, and
that teachers should offer careful explanations followed by organized oppor-
tunities for students to connect, rehearse, and review what they have learned.
The trouble with these claims is not that one is true and the other false; it is
that both are incomplete. They fail to capture the complexity of mathematics,
of learning, and of teaching.
Mathematics is at the same time inside and beyond culture; it is both
timely and timeless. The theorem attributed to Pythagoras was known in
various forms in the civilizations of ancient Babylon and China, and it is still
true the world over today even though systems of geometry now exist in which
it does not hold. Mathematics is invented, and it is discovered as well. Students
learn it on their own, and they learn it from others, most especially
their teachers. If students are to become proficient in mathematics, teaching
must create learning opportunities both constrained and open. Mathematics
teaching is a difficult task under any circumstances. It is made even more
complicated and challenging when teachers are paying attention simulta-
neously, as they should, to the manifold paths mathematics learning can take
and to the multifaceted nature of mathematics itself.

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

New York : National Academy of Sciences., 2001

Deskripsi Fisik

480 pages, 7 x 10

Bahasa

English

ISBN/ISSN

0-309-50524-0

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

PENDIDIKAN ANAK

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

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