Education Week - April 17, 2013 - 9

EDUCATION WEEK

Common-Core Writers Offer
‘Publishers’ Criteria’ for Math
Guide designed to influence high school curriculum materials
By Erik W. Robelen
With educators on the lookout for
instructional materials that fit the
content and vision of the commoncore standards, a new set of “publishers’ criteria” aims to influence
decisions by both the developers
and purchasers of such offerings
for high school mathematics.
Crafted by the lead writers of the
math common core, the 20-page
document issued last week seeks
to “sharpen the alignment question” and make “more clearly visible” whether materials faithfully
reflect both the letter and spirit of
the math standards adopted by 45
states and the District of Columbia.
Also, revised K-8 criteria were issued, with changes to a version first
put out last July based on feedback
from the field. For one, an earlier
call to limit the length of textbooks—to no more than 200 pages
at the elementary level and 500 at
the secondary—was removed.
Both sets of criteria attempt to
drive home three core dimensions
of the math standards: focus, coherence, and rigor.
The high school document drew
a generally favorable review from
W. Gary Martin, a professor of
mathematics education at Auburn
University who has helped develop
tools for assessing the alignment of
instructional materials to the new
math standards.
The criteria, he said, “provide a
vivid picture of how effective instructional materials could support the [math standards]. If those
adopting and developing materials
really took these criteria to heart,
the face of high school mathematics could significantly change in
very positive ways.”

‘A Key Resource’
The publishers’ criteria are endorsed by several prominent organizations that provided feedback,
including national groups representing governors, chief state school
officers, state boards of education,
and large urban districts, as well as
Achieve, the Washington-based nonprofit that managed the process for
developing the Common Core State
Standards.
In fact, one of the endorsing organizations, the Council of the Great
City Schools, signaled last year that
more than 30 of its member districts
would use the criteria in math (and
a companion set for English/language arts) to guide their decisions
in selecting materials. Also, California recently used the K-8 math criteria as part of its work to develop
guidance for districts on selecting
math materials.
“The states who do play a role in
[reviewing] instructional materials
are really looking at these as a key
resource,” said Carrie Heath Phillips, a program director at the Council of Chief State School Officers.
On the issue of focus—address-

ing fewer math topics in greater
depth—the high school document
signals that materials should have
a clear eye on readying students for
postsecondary education.
“In any single course, students
using the materials as designed
spend the majority of their time developing knowledge and skills that
are widely applicable as prerequisites for postsecondary education,”
said the document, which will be
revised next fall.
A table spells out domains and
specific standards that deserve special attention in five areas: number
and quantity, algebra, functions, geometry, and statistics and probability. For example, the table spotlights
all three specific standards in a
section on reasoning quantitatively
and using units to solve problems.
In algebra, it highlights every domain in the standards as containing
widely applicable prerequisites, but
identifies as “especially important”
the first domain, focused on “seeing
structure in expressions.”
“Materials must give especially
careful treatment to the domains,
clusters, and standards in Table 1,
including their interconnections and
their applications,” the criteria say.
Jason Zimba, a co-author of the
criteria and one of the lead writers of the common-core math standards, said attention to postsecondary education is key and reflects the
common-core focus on preparing
students for college and careers.
“Students deserve to spend the
majority of time on what will prepare them for the actual work of
postsecondary education,” said Mr.
Zimba, a founding principal of Student Achievement Partners, a New
York City-based nonprofit working
with states and districts on common-core implementation.
But Mr. Martin from Auburn said
that was one dimension of the criteria that gave him pause. “They almost seem to be redefining the standards,” he said, “[suggesting] ‘what
we really meant was [this].”
J. Michael Shaughnessy, the immediate past president of the National Council of Teachers of Mathematics, said he found the items
identified in the chart appropriate,
“but I might include some other
ones, too.”

clutter in the curriculum.”
The criteria acknowledge it’s
sometimes helpful to isolate part
of a standard, but say an emphasis
on reducing standards to smaller
pieces, or “microstandards,” threatens their focus and coherence.
That message resonates with
Denise M. Walston, the director of
mathematics for the Council of the
Great City Schools. “In so many instances, you’ve seen math taught
as a set of discrete little facts,” she
said, “so you lose the unity.”
The criteria, she said, are helpful
to districts not simply in selecting
new materials, but also in evaluating existing materials and figuring
out where adjustments are needed.

Page Limit Scrapped
With the revised K-8 criteria,
the decision to scrap limits on the
length of textbooks came in response to feedback from curriculum
experts that this kind of cap was
not helpful, Mr. Zimba said.
The change was welcomed by
Dennis J. Slattery, the editorial
director for K-12 math at Pearson,
who said that while “the intention
is a good one” to focus on fewer
math concepts, simply counting
pages would be misguided.
“I don’t think they wanted teachers or schools to be evaluating
on that type of criteria,” he said.
Overall, Mr. Slattery said he was
pleased with both sets of criteria
and that his publishing house is
taking them to heart.
“We’re paying attention to it because our customers are,” he said.
Another change replaced language in the first version saying
“approximately three-quarters”
of students’ time should be spent
on the “major work” of the standards. The document now offers

APRIL 17, 2013

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MEASURING UP
New “publishers’ criteria” for the common
core in math offer guidelines for high school
instructional materials that align with the standards.
FOCUS
“In any single course, students using
the materials as designed spend
the majority of their time developing
knowledge and skills that are widely
applicable as prerequisites for
postsecondary education.”

COHERENCE
“Coherence is about making math
make sense. Mathematics is not a list of
disconnected tricks or mnemonics. ... A
special character of the mile-wide, inchdeep problem in high school is that there
are often too many separately memorized
techniques, with no overall structure to
tie them all together.”
RIGOR
“Educators will need to pursue, with
equal intensity, three aspects of rigor: (1)
conceptual understanding, (2) procedural
skill and fluency, and (3) applications.
The word ‘rigor’ isn’t a code word for just
one of these three; rather, it means equal
intensity in all three.”
PROBLEMS WITH PURPOSE
“Each problem or exercise has a
purpose—whether to teach new
knowledge, bring misconceptions
to the surface, build skill or fluency,
engage the student in one or several
mathematical practices, or simply
present the student with a fun puzzle.”
BEWARE OF ‘MICROSTANDARDS’
“A drive to break the standards down
into ‘microstandards’ risks making the
checklist mentality even worse than it is
today. ... If the standards are like a tree,

a range, saying materials should
devote “at least 65 percent and
up to approximately 85 percent
of the class time to the major
work of the grades, with grades
K-2 nearer the upper end of that
range, i.e., 85 percent.”

iStockphoto/Flugga

then microstandards are like twigs. You
can’t build a tree out of twigs, but you
can use twigs as kindling to burn down
a tree.”

MATH PRACTICES
“Over the course of any given year of
instruction, each mathematical practice
standard is meaningfully present in
the form of activities or problems that
stimulate students to develop the
habits of mind described in the practice
standards. These practices are wellgrounded in the content standards.”
MATCHING THE CONTENT
“Any discrepancies in high school
content enhance the required learning
and are clearly aimed at helping
students meet the standards as written,
rather than setting up competing
requirements or effectively rewriting the
standards.”
VARIETY OF TASKS
“There is variety in what students are
asked to produce,” including answers
and solutions, arguments, explanations,
diagrams, and mathematical models.
REASONING
“Materials provide sufficient
opportunities for students to reason
mathematically and express reasoning
through classroom discussion, written
work, and independent thinking.
Reasoning is not confined to optional or
avoidable sections of the materials.”
SOURCE: High School Publishers’ Criteria
for the Common Core State Standards for
Mathematics

Scan this tag with your
smartphone for a link to
the K-8 and high school
publishers’ criteria.
edweek.org/links

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Rigor and Coherence
When it comes to rigor, the publishers’ criteria document articulates a three-pronged definition
centered on conceptual understanding of key math concepts,
procedural skill and fluency, and
application of mathematics.
“Curricula have not always been
balanced in their approach to
these three aspects,” it says.
On “coherence,” the document
says high school coursework often
emphasizes too many memorized
techniques with “no overall structure to tie them all together. Taking
advantage of coherence can reduce

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Education Week - April 17, 2013

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