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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

The study found that the rate of improvement on math tests for high-achievers slowed in those schools that previously placed students into different classes based on ability level.

"When eliminating remedial math classes, schools are likely to put lower-performing students in algebra classes together with high-performing students," says the study

She suggests that what may be happening is that teachers are adjusting instruction to the "middle students" in a classroom, and so the declines in peer ability levels could result in "less-challenging content and slower-paced instruction."

the study wades into some touchy terrain in examining issues of tracking and mixed-ability grouping.

other points to keep in mind. First, she notes that the study is not saying that mixed-ability grouping will inevitably harm high-achievers, if other interventions are supplied.

it was not accompanied by additional supports for struggling students to master algebra, or professional development for teachers around how to effectively teach the subject in mixed-ability classrooms. (However, in 2003, the district instituted a new policy to provide additional algebra support to low-achieving students.)

Also, prior research by Ms. Nomi and several colleagues at the University of Chicago concluded that the algebra-for-all policy wasn't necessarily much help to low-achieving students either. That earlier research found that although more low-achieving students completed 9th grade with credits in Algebra I and English I, failure rates increased, grades declined slightly, test scores did not improve, and students were no more likely to enter college.

two other recent studies, one focused in California and the other in North Carolina's Charlotte-Mecklenburg school district, came to a similar conclusion, finding that placing struggling urban middle schoolers into algebra not only fails to improve their achievement on state math tests, but also reduces the likelihood that they will take and pass higher-level math courses in high school.

current evidence suggests that the policy led to mixed ability grouping and this, in turn, negatively affected high-achieving students," she said.

The study concludes by offering its findings as a cautionary tale about making changes in course mandates without other assistance.

simply mandating a college-prep curriculum for all students is not sufficient to improve the academic outcomes of all students."

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."