From left to right, second-graders Sade Joyner, Axel Zelaya, Daymond Davis and Camila Joshua receive one-on-one help May 8 from their teacher, Elise Carter, at Galway Elementary School, as they work through math problems. (Nikki Kahn/THE WASHINGTON POST)

In Elise Carter’s second-grade class, some students still write their numbers backward or look at their fingers to add. Others race through multiplication tables or search the Web to teach themselves about negative numbers.

She does her best to challenge all of them, dividing her class at Galway Elementary School in Silver Spring into thirds and customizing a series of rotating lessons for the students. Each group takes a turn at the teacher’s table at the sound of a little brass bell.

Experts call it differentiated instruction — in essence, adapting lessons for kids of different abilities within a classroom. Teachers have always had to juggle disparate student needs. But pressure is rising to do it more often and with better results.

The practice of “tracking” students — isolating the high, average or low performers in different classrooms — is falling out of favor. Inclusion is in. Schools are expected to push all students to graduate ready for college. At the same time, new teacher evaluations being developed in many states and ever-higher testing goals make it even more critical to meet the needs of every student — those who speak limited English, those with special needs, those way behind and those far advanced.

“Each year, it seems like the expectations and the demands get a little bit higher,” Carter said.

The 27-year-old teacher arrives at school each day two hours early. Before the opening bell, she prepares three math lessons and five reading lessons for her 19 students. Some of her readers are still sounding out basic words while others are analyzing themes in chapter books. Eleven are learning English as a second language.

Last year, Carter sent her more-advanced students down the hall to learn third-grade math. This year, in a switch that reflects a new Montgomery curriculum, all of her students stay together.

The shift in math instruction in Maryland’s largest school system is the latest example of a move toward more mixed-ability classes that is mirrored in Fairfax and Arlington counties and across the country, with greater inclusion of special education students, more open enrollment in Advanced Placement classes and the elimination of some honors-level courses.

It’s all part of an effort to lift the performance of all students and overturn a legacy of sorting children into perceived ability tracks that often divided along racial lines. But some parents wonder if it is really possible to meet everyone’s needs in one room, or if their kids will get lost in the shuffle.

“With a single teacher dividing her time, I don’t know how it’s benefiting the kids who are struggling or the ones who are ready to move along,” said Alice Caponiti, who is concerned that her child, a second-grader at Sequoyah Elementary School in Derwood, is not being challenged.

Montgomery’s curriculum, which reflects new national academic standards and is being taught this year in kindergarten and first and second grades, represents an about-face for a school system that in 2010 accelerated nearly half its fifth-graders into above-grade-level math classes.

The school system’s new approach aims to teach for depth, not speed, while keeping students on grade level.

Like most teaching, differentiating is a mix of art and science.

When it works, “it’s like a jazz rhythm,” said Carol Tomlinson, an education professor at the University of Virginia and an expert on differentiation. Ideally, students come together around ideas and then break apart to go deeper or get extra support.

To be successful, the practice requires a lot of planning, teachers collaboration, monitoring of student progress, assessing, grouping and regrouping students. The goal is to provide material that’s challenging enough, but not too challenging, to keep each child interested.

Varied techniques

Carter started her 90-minute math session one morning this month with a lesson on three-digit subtraction. Then she divided her students, based on their performance on a brief quiz the day before.

The first group to approach her half-moon table sat down with small whiteboards and markers. The five students drew pictures to help them think through the subtraction problem in front of them. Using squares, lines and dots to represent hundreds, tens and ones, they solved the problem by crossing out the symbols that corresponded to the number.

Rather than teaching formulas, the curriculum emphasizes lessons on place value and number sense so students can learn why formulas work. Students often use blocks, number lines and charts to solve problems and talk through the answers.

The second group, a little more advanced, practiced a different strategy. They broke each number into hundreds, tens and ones and solved it in three steps.

The third group moved on to practicing multiplication tables. Carter also squeezed in a short lesson from the third-grade curriculum on how to round numbers up or down.

To rotate the groups, Carter rang her bell. “FREEZE! Eyes on me,” she called out as she directed traffic.

Keeping a roomful of 7-year-olds focused can be daunting.

Away from the teacher’s table, students cycled through activities, including a subtraction game with dice at one table, a sorting activity with laminated frogs bearing subtraction problems at another and flashcards on the carpet. “Tugboat Addition” and “Formula Fusion” were ready at the computer station.

The level of concentration in the room rose and fell in spite of clear instructions and the promise of a Golden Lion’s paw certificate for good behavior.

The dice game turned into a dice-spinning contest for two boys. Some students filled out answer sheets quickly — “This is easy!” one said. Others drew circles or wrote imaginary words on the page. One girl tried to help her classmate with a tough subtraction problem, while another melted into tears after a spat.

From her table, the teacher could hear the familiar cries for attention: “Miss Carter!” “Miss Carter!” “Miss Carter?”

‘You can always do more’

Despite the sometimes hectic pace, Carter said the 15- to 20-minute meetings with small groups help her understand who “gets it” and what students need. She has been teaching math in small groups for several years.

Small-group instruction has long been common in elementary reading classes, largely to address disparities in what children learn at home. It has taken root more slowly in math, which is considered more of a school-taught skill, said Tom Loveless, a senior fellow at the Brookings Institution.

But that’s starting to change, according to a survey of teachers for the National Assessment of Educational Progress. Sixty-one percent of fourth-grade teachers said they grouped students based on ability in their math classes in 2011, up from 40 percent in 2003.

The concentrated approach comes on top of micro-adjustments that teachers routinely make for different learning styles or behavior as they get to know their students.

There are the social animals who are more productive when given leadership tasks, fidgeters who can’t concentrate without a walk around the room and English language learners who need more hand gestures or visual clues. Some students get lots of affirmation and encouragement at home, while others need heavier doses at school.

Galway students are growing more diverse and more poor. In the past decade, the share of students at the Silver Spring school with limited English proficiency grew from less than 5 percent to 25 percent. The portion eligible for government-subsidized lunch grew from 32 percent to 58 percent. The higher poverty rate means the school gets extra resources, including smaller class sizes in the early grades. Last year, the school fell short of testing goals under the federal No Child Left Behind law.

Carter teaches writing with an English as a Second Language teacher. Her second-graders are being evaluated for gifted services this year, and one was recently identified for special education.

Carter also gets help from the other second-grade teachers. They work in teams to study the new curriculum and map out reading and math lessons for the next week.

The team meets to plan or share activities and resources, many of which are included in the digital curriculum. They try to anticipate the challenges students will have and suggest targeted strategies.

Administrators come in for quarterly “data chats” and monthly “kid talks” to review performance reports and brainstorm ideas for struggling students.

Carter said that her students are so different it would be great if she had time to work with all of them one on one.

“The hardest thing about being a teacher: You can always do more,” she said.