For the 62,000 D.C. students returning to school Monday, new standards are expected to bring some dramatic differences to the classroom -- new curricula and textbooks aimed at changing the way they learn some core subjects.

The new math curricula and textbooks are designed to help students from kindergarten to 12th grade master their subjects better by learning how key concepts apply to life situations rather than by using the age-old approach of relying largely on rote memorization, drills and worksheets.

The new literacy curricula and textbooks will allow teachers to keep readers of various skill levels together instead of having to separate lower-level students from advanced ones.

"Standards are the basis for the curricula," said Hilda L. Ortiz, the system's chief academic officer, adding that previously, classroom instruction often was unrelated to the standards and to the achievement test given to students.

"The only way we're going to get better test results is to make sure the textbooks, curricula and the professional development for teachers are all linked to the standards," Ortiz said.

The introduction of new textbooks is drawing much scrutiny -- and is causing controversy. The school system has ordered math and reading texts and supplemental material for all students. In years past, schools were not able to get all their textbooks in time for opening day, creating major problems for students and teachers.

But school leaders say they have taken steps to ensure on-time delivery this year.

"We have been guaranteed: They will be delivered by the start of school. If not, the publishers will face a [financial] penalty," said Wilma F. Bonner, assistant superintendent for curriculum and instruction.

"We now have a textbook team at the schools . . . to receive, inventory and set up distribution," Bonner added. "In the past, when the textbooks were delivered, no one was there to receive them, and they may have been misplaced in a room."

The Board of Education has selected the "Connected Mathematics" textbook for middle and junior high students and "Everyday Mathematics" for elementary students. The two books, as well as a variety of others selected for senior high students, are aimed at making math more relevant, school officials say.

"In the past, we used rote memorization to teach math," Ortiz said. "While that is still valuable, what's more important is that students will understand how [the math concepts] connect, how they apply to life situations."

With the new approach, she added, "those concepts are going to stay with the students."

But the changes are facing criticism from some math experts involved in a nationwide campaign against attempts by any school system to embrace what they consider ineffectual approaches.

"The real problem is that the core skills and key topics are not taught. They are touched upon but not given nearly the amount of time needed for mastery," said Bastiaan J. Braams, visiting associate professor of mathematics and computer science at Emory University. He has been pressing D.C. school board members to drop the textbooks.

Sue P. White, the system's director of mathematics, disagreed, saying that "kids don't come away loving mathematics with the traditional approach. We lose them; they get discouraged from taking advanced courses."

White added that she is seeing positive results from about five schools that have been using the books. "The research on the materials we adopted is excellent," she said. "Within two years, kids are turning around their achievement and liking math enough to go on to advanced courses."

The new reading materials will be provided by Houghton Mifflin Co. and by Holt, Rinehart and Winston. The new curricula and textbooks, school officials say, will help teachers instruct students whose English proficiency is low as well as low-level and accelerated readers in one class.

"If you're reading above me, I can read on the same subject with an adapted reader," said Elizabeth V. Primas, the system's director of literacy. "Every child learns and moves along without having to be separated out or isolated."

The school system conducted training this week to familiarize teachers with the new curricula and textbooks. Ortiz said schools soon will offer sessions to help parents understand how the new standards, curricula and textbooks fit together.