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Probability should not be assessed until grade 7, for instance, the document says, and statistical distributions should not be assessed by materials until grade 6.

In a sign that the new math document will be taken seriously, it has the endorsement of several prominent organizations in the education sphere, including the National Governors Association, the Council of Chief State School Officers, the Council of the Great City Schools, the National Association of State Boards of Education, and Achieve, a national nonprofit that managed the process to develop the common standards. Both the NGA and CCSSO spearheaded that undertaking.

In fact, a group of 20 big-city districts, led by the Council of the Great City Schools, served notice to publishers last month that any materials they purchase must reflect the priorities of the publishers' criteria.

Jason Zimba, a co-author of the document and one of the three lead writers of the math standards, said he anticipates some disagreement.

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 to states and districts. Both McCallum and Daro also are advisers to Student Achievement Partners.

To be clear, this is not the final word from the standards writers. An "updated" version of the publishers' criteria for math, taking into account feedback, is expected out early next year. In addition, a separate document for high school math will be issued around the same time.

Zimba argues that the single most important element to ensuring the common core's success in improving math education is the emphasis on focus—essentially the idea of covering fewer math topics, but in greater depth.

The criteria document acknowledges upfront that it may be hard for math educators and experts to let go of some topics. "During the writing of the standards, the writing team often received feedback along these lines: 'I love the focus of these standards! Now if we could just add one or two more things,' " it says. "But focus compromised is no longer focus at all. ... 'Teaching less, learning more' can seem like hard medicine for an educational system addicted to coverage."

the new criteria are also aimed at helping to shape professional development pegged to the common-core standards.

The goal of the criteria, the authors say, is not to dictate acceptable forms of instructional resources, suggesting that "materials and tools of very different forms" can be deemed acceptable, including digital and online media.

the guidelines are not binding.

"Ultimately, it's still up to people at the local level. We think it's better to have something to react to than to have nothing out there, ... with people guessing on what they're supposed to do."

Using ASSISTments, the student goes through assigned questions in sequence, working out the solutions on a sheet of paper and entering the answers into the computer. If the student gets the right answer, the program moves to the next question. If the answer is wrong, the program tells the student to try again. If the student struggles with the question or gets stuck, he or she can ask for a series of hints that will lead to the right answer.

Before students come to class the next day, teachers can look at a table, which shows whether the students got the answer correct and whether they requested hints to get to the answer. The table also breaks the statistics down into percentages. If 95 percent of the class gets a question right, there’s little need to spend time on it in class, but if only 25 percent get it right, the teacher might decide to review that topic. The program also tells teachers how long it’s taking students to complete their assignments.

“We don’t shop the same way we did 30 years ago. We don’t communicate the same way we did. So why do we teach students the same way?” Heffernan said

Heffernan said his goal is to evolve ASSISTments into something like Wikipedia,

ASSISTments users will help build an expansive bank of textbook questions, which teachers will dip into to select assignments. Only teachers and educational institutions, such as textbook producer Pearson, will have access to add to or alter ASSISTments entries.

There are similar homework and tutoring programs available, but ASSISTments is unique in that Heffernan provides it for free.

ASSISTments is a prime example of “formative assessment,” which allows teachers to observe student performance and adjust their teaching plan or techniques to help students better retain the material.

ASSISTments doesn’t restrict the role of the teacher, but rather it crunches numbers and presents statistics so teachers can do what they’re trained to do — teach

covers the development of the two pieces of the test that will yield students' summative scores in mathematics and English/language arts and be used for accountability purposes: a computer-based end-of-year test and a performance-based assessment given toward the end of the year. The scope of work also includes developing midyear formative assessments that are part of PARCC's system but are optional for states.

A preliminary blueprint of PARCC's English/language arts exam shows that the performance-based assessment, spread over two days, would involve a "research simulation" that asks students to read a suite of texts, including an "anchor" text such as a speech by a prominent historical figure. They would have to answer questions that require them to cite evidence from the text for their answers and write an essay. Another aspect of the performance-based test would require students to "engage" with literature (grades 3-5) or conduct literary analysis (grades 6-11) using a combination of shorter and longer texts. The end-of-year exam would employ six literary and informational texts and ask students to respond to machine-scorable questions, including ones that demand comparison and synthesis of the readings. The end-of-year test in English/language arts would yield at least half of a student's points in that topic. One-third to one-half would come from the performance-based test, according to the preliminary blueprint.

ARCC's math test will include three types of questions: "innovative," machine-scorable, computer-based items; items that call for written arguments or justifications; critiques of mathematical reasoning, or proof that students "attended to precision" in math; and items involving real-world scenarios. The performance-based assessment in math will count for 40 percent to 50 percent of a student's points in that subject, and the end-of-course exam will yield 50 percent to 60 percent of the points. The math exams will focus on solving problems in the "major content areas" at each grade level, as well as demonstrating conceptual understanding, fluency and mathematical reasoning, and applying knowledge to real-world problems. At the high school level, PARCC will develop two series of end-of-course math tests: a traditional one—Algebra 1, geometry, and Algebra 2—and one that integrates those topics. Those parallel pathways reflect choices educators can make about how to design math courses from the common standards. The solicitation document answers a question that had been circulating among some educators of young children. PARCC said that its tests will be given by computer to students in grades 6-11, but those in grades 3-5 will answer questions with pencil and paper because of concerns about younger children's keyboarding skills.

PARCC has contracted with the Dana Center at the University of Texas at Austin to build prototype assessment tasks in math, and with the University of Pittsburgh's Institute for Learning to generate such items in literacy. Those items are slated for release this summer.