When voters in 2014 approved a $58 million property-tax levy to pay for city-subsidized preschool, elected officials largely sold the idea as a way to help erase the gaps in achievement among ethnic groups that show up even before children enter school. And now, more than halfway through the program’s four-year trial period, a new study of its results to date suggests it is preparing more children for kindergarten, with the greatest gains among students of color and those from low-income households or families that don’t speak English. “The results are very encouraging,” said Seattle Mayor Tim Burgess, who as a city council member campaigned heavily for the 2014 measure. In particular, Burgess highlighted the study’s comparison of the quality of Seattle’s preschool pilot to similar programs in Boston, New Jersey and San Antonio, all of which have been around longer.