The most visible symbols of the nation’s long-criticized, mile-wide, inch-deep traditional math standards are the 15-pound textbooks that students have been hauling back and forth from school for years.

New Common Core standards are designed to turn things around by presenting fewer math standards in greater depth — a streamlined, more rigorous approach that is used in higher performing countries.

So, how are these textbooks adapting to the new standards?

Not well, according to a pair of researchers who are studying the new textbooks. Publishers are marketing all kinds of new textbooks they say align with the Common Core standards.

In reality, “they do not look that different from the previous versions,” said Morgan Polikoff, an associate professor at the Rossier School of Education at the University of Southern California.

In a study debuted last weekend at an Education Writers Association conference in Los Angeles, Polikoff analyzed three “Common-Core aligned” fourth-grade math textbooks adopted in Florida and one commonly used textbook that is not aligned to any particular standards.

He found that 15 to 20 percent of textbooks cover topics outside the Common Core standards, while 10 to 15 percent of the standards are not reflected in the texts.

What is missing? Questions and problems that get to the higher levels of cognitive demand, he said.

High-quality textbooks and instructional materials are going to be essential to the successful implementation of Common Core. Teachers are under tremendous pressure to adapt to the new standards, which are radically different from how they learned math.

William Schmidt, co-director of the Education Policy Center at Michigan State University, has analyzed more than 40 textbooks being used by 60 to 70 percent of students. He found that most textbooks that claim alignment include far more material than the Common Core calls for, which could discourage the more focused, sophisticated instruction of key concepts.

Many eighth grade textbooks are still 800 pages long, he said, with half of the pages devoted to subjects that are not even included in the new standards. It’s a “sham” to claim that these books are aligned, he said.

Teachers will need to chart their own course through this transition, researchers said.

“If they follow the book they will not be teaching the Common Core,” Polikoff said.