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Topic: [ncsm-members] Seizing the Moment for Mathematics [Wm. Schmidt]
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Jerry P. Becker

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Registered: 12/3/04
[ncsm-members] Seizing the Moment for Mathematics [Wm. Schmidt]
Posted: Jul 23, 2012 5:36 PM
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From Education Week [American Education's Newspaper of Record],
Wednesday, July 18, 2012, Volume 31, Issue 36, pp 24-25. See

Seizing the Moment for Mathematics

By William Schmidt

For years now it has been clear that the U.S. mathematics curriculum
is a mile wide and an inch deep, and that the fragmented quality of
mathematics instruction is related to our low ranking on
international assessments. Nearly a generation after the first Trends
in International Mathematics and Science Study, the nation's
governors and chief state school officers, in concert with other
stakeholders, have fashioned the Common Core State Standards for
mathematics that may finally give American students the high-quality
standards they deserve.

These new math standards have attracted some criticism, however.
Aside from more abstract arguments, a number of specific claims have
been leveled against them, including that they are untested; that
they are not world-class; and that some existing state standards are

As part of our ongoing research, [see
] Richard Houang and I recently concluded a study of the math
standards and their relation to existing state standards and the
standards of other nations. Drawing from our work on the 1995 TIMSS,
we developed a measure of the congruence of the common core to all 50
state standards in effect in 2008-09, as well as to an international
benchmark. We also examined the relationship of each state's math
standards to the common standards and how each state performed on the
2009 National Assessment of Educational Progress. Although, we can't
project the success of the common math standards with certainty, it
would give us reason for optimism if states whose standards more
closely resembled those of the common core performed better on NAEP.

What did our research uncover?

The common-core math standards closely mirror those of the world's
highest-achieving nations. Based on the 1995 TIMSS, we identified
common standards from the best-performing countries, which we call
"A+ standards." We found an overlap of roughly 90 percent between the
common math standards and the A+ standards. If the standards of the
world's top achievers in 8th grade mathematics are any guide, then
the common standards represent high-quality standards. Of course, as
a nation, we shouldn't just slavishly replicate whatever we find
other countries doing. But when we look across a number of very
different countries-all of whose students do better than ours-we find
the same curricular characteristics over and over again. The only
sensible course of action is to take a close look and see if
important lessons can be learned.

In doing this, we find three key characteristics in the curricula of
the highest-performing countries: coherence (the logical structure
that guides students from basic to more advanced material in a
systematic way); focus (the push for mastery of a few key concepts at
each grade rather than shallow repetition of the same material); and
rigor (the level of difficulty at each grade level). The common core
adheres to each of these three principles.

Unfortunately, when one hears that a state's existing standards are
better than the common core, it usually means that those standards
include more-and more advanced-topics at earlier grades. But this is
exactly the problem the common math standards are designed to
correct. It is a waste of time to expose children to content they are
not prepared for, and it is counterproductive to skim over dozens of
disconnected topics every year with no regard for student mastery. As
it stands today, we simply hope that students will somehow "get it"
at a later grade, and yet we know that far too many students never
do. The disappointing reality is that, while improved from a decade
ago, most state math standards fall below the common standards in
both coherence and focus.
SIDEBAR: "The essential question is not whether the common core can
improve mathematics learning in the United States, but whether we, as
a nation, have the commitment to ensure that it does."
In debating the utility of the common core, it is very important to
recognize that standards are not self-executing. For example, states
with very strong standards but very low thresholds for "proficiency"
on the state assessments are, in effect, sending a message to
teachers and districts that their standards aren't to be taken that
seriously. In that way, proficiency cut points can serve as a rough
measure of implementation. After including both cut points and how
far away a state's standards are from the common core (controlling
for poverty and socioeconomic status), we found that the two in
combination are related to higher mathematics achievement-an even
stronger relationship than was the case when only the measure of
similarity was included. In the final analysis, however, the key
ingredient in the implementation of standards is whether districts,
schools, and, most importantly, teachers, deliver the content to
students in a way that is consistent with those standards.

As it stands in many classrooms, teachers are forced to pick and
choose among the topics as laid out in the textbook, items on state
assessments, and the content articulated in state and district
standards-expressions of the curriculum that frequently clash with
one another. In our recently completed Promoting Rigorous Outcomes in
Mathematics and Science Education, or PROM/SE project-a research and
development initiative to improve math and science teaching and
learning at Michigan State University-we found tremendous variation
in the topics covered in mathematics classes within states, within
districts, and even within schools. In fact, the content coverage in
low-income districts had more in common with the content delivered in
low-income districts in other states than with that of the more
affluent districts in their own states. [ ]
Given how haphazardly standards are implemented, it shouldn't be much
of a surprise if the relationship between state standards and student
achievement is modest. What's remarkable is that the relationship is
as strong as it is.

The essential question is not whether the common core can improve
mathematics learning in the United States, but whether we, as a
nation, have the commitment to ensure that it does. The adoption of
the common core doesn't represent a success, but an opportunity. It
remains to be seen whether the right kind of common assessments and
supporting instructional materials will be developed. It is very much
an open question whether states will devote the energy and planning
required, especially in a time of fiscal constraint. And, most
urgently, we don't yet know if teachers will receive the preparation
and support they need to teach mathematics in a fundamentally new way.

The common core offers the opportunity to revolutionize math
instruction in this country, to improve student performance, to close
the gap between the United States and its competitors, and to ensure
that every American student has an equal opportunity to learn
important mathematics content. But it is only a chance, and it is
imperative that we seize it.
William Schmidt is a Michigan State University distinguished
professor and co-director of the university's Education Policy
Center. He holds faculty appointments in the departments of education
and statistics. He is a member of the National Academy of Education
and a fellow of the American Educational Research Association.
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

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