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A new set of 鈥減ublishers鈥� criteria鈥� crafted by the lead writers of the common core in mathematics is intended to help reshape K-8 instructional materials nationwide by spelling out what it means to align faithfully with the math standards adopted by 45 states and the District of Columbia.

The document blends general guidance with some real specifics, such as suggesting how long textbooks should be鈥攆ewer than 200 pages at the elementary level鈥攁nd at what grade level it鈥檚 appropriate for chapter tests to address particular topics.

A key mantra is the standards鈥� push for focus鈥攃overing fewer topics in greater depth鈥攚hich the authors acknowledge 鈥渃an seem like hard medicine for an educational system addicted to coverage.鈥�

Some in the education and publishing fields have offered generally favorable reviews of the 24-page document, which has been endorsed by several prominent organizations that provided feedback on early drafts, including national groups representing governors, chief state school officers, state boards of education, and large urban districts, as well as Achieve, a Washington-based nonprofit organization that managed the process for developing the Common Core State Standards.

A for the common English/language arts standards鈥攆irst issued last year and endorsed by the same five organizations鈥攚as revised this spring.

鈥淚 believe that, in general, publishers will welcome the deeper level of clarification represented in the [math] criteria,鈥� said Charlene F. Gaynor, the chief executive officer of the Wilmington, Del.-based Association of 91制片厂视频al Publishers. 鈥淢uch of the document sells the overarching pedagogy of focus, coherence, and rigor, which, for most publishers, is like preaching to the choir.鈥�

Diana L. Kasbaum, a math consultant at the Wisconsin education department and the president of the Association of State Supervisors of Mathematics, agreed: 鈥淚 think it鈥檚 very good. ... It鈥檚 exactly what we need to move forward.鈥�

Linda Gojak, the president of the National Council of Teachers of Mathematics, said the document aligns 鈥渧ery nicely鈥� with the standards and offers helpful guidance, such as the emphasis on ensuring coherence in materials across grade levels to build knowledge over time.

However, Ms. Gojak said she was disappointed that the NCTM and other math groups were not invited to provide input before the document was published.

That point about broader input was made more bluntly by Robert C. Calfee, a professor emeritus at Stanford University鈥檚 school of education.

鈥淭he process really bothers me; no public input into any of this, no indication that they consulted extensively with publishers, and just a document that has come down from Mount Sinai, at times almost arrogantly so,鈥� said Mr. Calfee, the vice chairman of a California standards commission in the 1990s.

Jason Zimba, a co-author of the criteria and one of the lead writers of the common-core math standards, said the document will be revised early next year to reflect input from across the field.

鈥淲e do expect NCTM and others to provide feedback on the substance of the document,鈥� he said.

Criteria for high school math are also expected to be issued early next year.

鈥楩ixing the Market鈥�

Called , the document also explicitly seeks to guide states and districts in evaluating and selecting curricular materials or revising existing ones.

鈥淭hese criteria were developed from the perspective that publishers and purchasers are equally responsible for fixing the materials market,鈥� the document proclaims. 鈥淧ublishers cannot invest in quality if the market doesn鈥檛 demand it of them nor reward them for producing it.鈥�

To that end, one endorsing group, the Washington-based Council of the Great City Schools, recently signaled that more than 30 of its member districts鈥攊ncluding Chicago, Los Angeles, and New York City鈥攚ould use the criteria in math and ELA to guide their decisions in selecting materials.

The goal of the criteria, the document cautions, is not to dictate acceptable forms of instructional resources. Instead, it says that 鈥渕aterials and tools of very different forms鈥� can be deemed acceptable, including digital and online media.

The document speaks at length about the need for focus, coherence, and rigor in materials aligned to the common core, and wades into specifics that may raise eyebrows, such as the proposed 200-page limit for elementary math books.

Ms. Gojak of the NCTM, a former elementary teacher, argues that the limit will help teachers meet the goal of increased focus. 鈥淚f you were to line up the traditional elementary math books over the last 15 years, they have grown thicker and thicker.鈥�

For middle and high school, the document says page lengths should not exceed 500 pages.

But Ms. Gaynor from the publishers鈥� association questioned the value of limiting page counts. 鈥淚 don鈥檛 think good curriculum is driven by that kind of directive.鈥�

In addition, the criteria say that at any given grade level, approximately three-fourths of instructional time should be devoted to the 鈥渕ajor work鈥� of that grade. To illustrate, at the K-5 level, the 鈥渕ajor work鈥� generally consists of arithmetic and the aspects of measurement that support it, Mr. Zimba explained.

The document also spells out when it is appropriate for certain topics to be assessed in textbooks, such as through chapter or unit tests. Probability should not be assessed until grade 7, for instance, the document says, and statistical distributions until grade 6. That timing, it notes, is pegged to when those topics are first introduced in the common core.

Mr. Zimba said wading into the particulars of curricular decisions rather than being overly vague was a deliberate strategy.

鈥淪ome of these specifics are going to attract comment,鈥� said Mr. Zimba, a co-founder of , a New York City-based nonprofit working with states and districts on common-core implementation. 鈥淏ut if we weasel out of limits and specifics, then we鈥檙e actually not pushing things forward.鈥�

The other two co-authors of the criteria (and lead writers of the math standards) are William McCallum, a math professor at the University of Arizona, and Philip Daro, an education consultant who is working on a common-core project for the Pearson Foundation. Mr. McCallum and Mr. Daro also are advisers to Student Achievement Partners.

Carrie Heath Phillips, a program director at the Council of Chief State School Officers, in Washington, said the criteria will be a vital resource. 鈥淲e鈥檝e heard loud and clear, especially from district-level curriculum specialists or supervisors, that they need that guidance,鈥� she said.

Need for Coherence

On the issue of 鈥渃oherence,鈥� the criteria make clear that this is not simply across topics but across grade levels. 鈥淢aterials cannot match the contours of the standards by approaching each individual content standard as a separate event,鈥� the document says. 鈥淣or can materials align to the standards by approaching each individual grade as a separate event.鈥�

Also, the criteria emphasize three aspects of rigor at each grade level: conceptual understanding, procedural skill and fluency, and applications. 鈥淭o date, curricula have not always been balanced in their approach to these,鈥� it says.

W. Gary Martin, a professor of math education at Auburn University in Auburn, Ala., gives the document high marks for 鈥渉itting the right notes,鈥� though he raised a few concerns, including treatment of the eight standards for mathematical practice, which range from making sense of problems to constructing viable arguments.

鈥淢y biggest surprise was that the math practices were as buried as they were,鈥� he said, noting that they are not dealt with in any depth until more than halfway through the document. 鈥淭o me, that is a central issue with textbooks. That鈥檚 where textbooks are not even in the ballpark.鈥�

Peggy Brookins, a high school math teacher in Ocala, Fla., who served on an American Federation of Teachers team that provided feedback on the common math standards, said she鈥檚 pleased by the document.

鈥淭hey captured a lot of what teachers were thinking,鈥� she said. 鈥淭he big part of the standards that it talks about that I like the most is having problems worth doing.鈥�

Ze鈥檈v Wurman, a former education official in the George W. Bush administration who has been an outspoken critic of the standards, said the document 鈥渞epresents a reasonable effort to translate the standards into textbook criteria.鈥�

But he had several concerns, including the absence of language stipulating that instructional materials should have indices and glossaries and should support 鈥渟elf study鈥� by students.

鈥淪ome popular current textbooks ... do not support self-study and some do not even contain an index or glossary,鈥� he said in an email. 鈥淪uch textbooks make teachers the sole gatekeepers to content and create extra difficulties for transfer students or students absent due to illness.鈥�

Question of Affordability

A variety of observers say it鈥檚 hard to know how influential the criteria will prove to be.

鈥淗ow are the publishers really going to use this?鈥� said Auburn鈥檚 Mr. Martin. 鈥淎re they actually going to redo their materials in light of this, or simply retrofit a bit?鈥�

Brad Findell, the associate director of math teacher education at Ohio State University, in Columbus, said publishers may balk at some criteria because of the cost.

鈥淸Some] misinterpretations are going to be business decisions,鈥� he said. Publishers will say, 鈥淲e can鈥檛 do that. That鈥檚 going to cost us $450,000,鈥� Mr. Findell said.

At the same time, the criteria document says it鈥檚 not just publishers who need to respond, but also those who select textbooks.

鈥淎s a publisher, we respond to market demands,鈥� said Stewart Wood, Pearson鈥檚 editorial chief for mathematics.

Mr. Wood called the criteria a 鈥減ositive step,鈥� but said there鈥檚 more to come that will shape the materials market.

鈥淚 expect a series of events that will change expectations of common-core materials: these criteria, their final version in early 2013, assessment items released in the spring of 2013, actual tests released in 2014,鈥� he said. 鈥淓ach of these events will place new demands on common-core materials.鈥�

Coverage of the implementation of the Common Core State Standards and the common assessments is supported in part by a grant from the GE Foundation, at