Answer by taking a quote from the following article:

Lyndon Baines Johnson (; August 27, 1908 - January 22, 1973), often referred to by his initials LBJ, was an American politician who served as the 36th President of the United States from 1963 to 1969, assuming the office after having served as the 37th Vice President of the United States from 1961 to 1963. A Democrat from Texas, he also served as a United States Representative and as the Majority Leader in the United States Senate. Johnson is one of only four people who have served in all four federal elected positions.

Johnson, whose own ticket out of poverty was a public education in Texas, fervently believed that education was a cure for ignorance and poverty, and was an essential component of the American dream, especially for minorities who endured poor facilities and tight-fisted budgets from local taxes. He made education the top priority of the Great Society agenda, with an emphasis on helping poor children. After the 1964 landslide brought in many new liberal Congressmen, LBJ launched a legislative effort which took the name of the Elementary and Secondary Education Act (ESEA) of 1965. The bill sought to double federal spending on education from $4 billion to $8 billion.; with considerable facilitating by the White House, it passed the House by a vote of 263 to 153 on March 26 and then it remarkably passed without change in the Senate, by 73 to 8, without going through the usual conference committee. This was an historic accomplishment by the president, with the billion dollar bill passing as introduced just 87 days before.  For the first time, large amounts of federal money went to public schools. In practice ESEA meant helping all public school districts, with more money going to districts that had large proportions of students from poor families (which included all the big cities). For the first time private schools (most of them Catholic schools in the inner cities) received services, such as library funding, comprising about 12 percent of the ESEA budget. Though federal funds were involved, they were administered by local officials, and by 1977 it was reported that less than half of the funds were actually applied toward the education of children under the poverty line. Dallek further reports that researchers cited by Hugh Davis Graham soon found that poverty had more to do with family background and neighborhood conditions than the quantity of education a child received. Early studies suggested initial improvements for poor children helped by ESEA reading and math programs, but later assessments indicated that benefits faded quickly and left pupils little better off than those not in the schemes. Johnson's second major education program was the Higher Education Act of 1965, which focused on funding for lower income students, including grants, work-study money, and government loans.  Although ESEA solidified Johnson's support among K-12 teachers' unions, neither the Higher Education Act nor the new endowments mollified the college professors and students growing increasingly uneasy with the war in Vietnam. In 1967, Johnson signed the Public Broadcasting Act to create educational television programs to supplement the broadcast networks.  In 1965, Johnson also set up the National Endowment for the Humanities and the National Endowment for the Arts, to support academic subjects such as literature, history, and law, and arts such as music, painting, and sculpture (as the WPA once did).

Would this also benefit children in poor communities?
Higher Education Act of 1965, which focused on funding for lower income students, including grants, work-study money, and government loans.