The Department of Education is backing down on proposals to place small secondary schools inside two elementary school buildings for next year amid community protests.

The department had been considering placing a Columbia University-affiliated math and science school in a building in Manhattan that houses P.S. 36, which serves pre-kindergarten through secondgrade students, and putting the Peace and Diversity Academy in a building with P.S. 93 in the Bronx. Department of Education officials said yesterday that the decision to retract the proposals shows their openness to public feedback following a series of community meetings at which parents at the elementary schools said — and often shouted — that they didn’t want older students mixing with their younger children.

“They heard our cries,” the president of the parent-teacher association at P.S. 36, Kim Wynn, said. “We’re glad that they’re not coming into our schools.”

The Bloomberg administration’s efforts over the past several years to open hundreds of new small schools and charter schools around the city have become a frequent cause of strife as the department has sought locations for the new schools in a system already starved for space. The department has also faced criticism for allowing new small schools to exclude special education students and English-as-a-second-language students for the first two years after they open.

Yesterday, the schools chancellor, Joel Klein, responded to that criticism by announcing a $1 million grant for small schools that enroll either 18 special education students or 18 English-language learners in their first two years — which would put them above the citywide average in terms of percentage, a spokeswoman for the Department of Education, Melody Meyer, said. Next year, 20 participating small schools will receive $45,000 a year each to hire specialized teachers.

“It doesn’t nearly go far enough,” a lawyer at New York Lawyers for the Public Interest, which has studied the small schools, Kim Sweet, said. “It’s only 10 schools in a sea of schools that don’t offer these services,” she added, referring to special education services.

The department said it also has revised its school location process after past conflicts.

“We have worked very, very hard in the past six months to incorporate many lessons learned,” the chief operating officer of the Office of New Schools, Jemina Bernard, said.

Ms. Bernard said the department now factors in more time to talk to communities before making a final decision about a school site. She said the process now takes between nine and 12 months, starting from when the department receives revised enrollment data in the fall. After locating schools with extra space on paper, she said, the new schools office then consults with superintendents to narrow down the list of possible locations. The next step, she said, is bringing proposals to communities for feedback.

With P.S. 36 and P.S. 93, Ms. Bernard said parents were mistaken in thinking the announcement that their schools were being considered to share space was final.

“We got criticized. … What folks never really understood is that it was actually early in the process,” she said. “This was a perfect example of having all of those conversations and understanding about the community concerns: We were able to decide, ‘You know what, let’s go back to the drawing board.'”

The department has yet to announce locations for 11 of the 40 new schools it plans to open next year, including the Columbia Secondary School.