Chicago's public schools are the worst in the nation and parents there should consider private education for their children, Education Secretary William J. Bennett said. The remarks provoked an angry exchange between Bennett and Mayor Harold Washington, who blamed the school woes on federal spending cuts and called Bennett "caretaker of the dismantling of education all over the country." Bennett, in Chicago for a forum on school reform, denied the charge. He cited American College Test scores for high school students, in which half of Chicago's public high schools ranked in the bottom 1% of U.S. schools in average scores for the multiple-choice college entrance exam in English, mathematics, social science and natural science. Bennett urged the use of government vouchers for private-school tuition, a Reagan Administration proposal.