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Have they taken things out or have they just shifted them around?

Ms. Gerson said the Common Core is also intended to end the “math wars,” in which educators and parents battled over whether the emphasis should be on mastering basic math skills or conveying deeper concepts. With fewer topics to cover, “It is not an either/or situation anymore,” she said. “It’s a real return and attention to memorization and recall, drilling around math facts.”

But then students are supposed to be able to figure out how to use their math knowledge to solve problems that go beyond traditional word problems.

New York, like many other states, has been making a transition to the new standards. This fall will be the first school year they are fully put in place in New York.

Ms. Baldi, who taught second grade for the previous four years at P.S. 169 and will teach kindergarten this year, said she had changed how she taught math. In the past, she said she used to present a math topic first before giving exercises for her students to solve. Taking heed of the Common Core’s instruction that “mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution,” Ms. Baldi began to give a new problem “cold turkey,” without introduction or explanation, and let groups of students try to figure it out.

“I’m more of a facilitator, and I’m taking more of a step back,” she said.

Only after the students brainstormed their own solutions would she discuss the different ways of solving it. “I thought that they got a better understanding, because they got to tackle the problem on their own and got to hear from the other students,” she said.