How did Progressives want to reform education during the Progressive Era? By establishing universities in major cities by changing the subjects studied by requiring children to attend school by increasing teachers' education requirements

The correct answer is "by requiring children to attend school"

The Progressive Era lasted from 1880 and 1920s and was an era with social activism and political reform, focused on minorities.

During that time, people weren't required to go to school, nor finish education. Because of that during that era, Progressives expanded the number of high schools and required children to attend school by passing compulsory schooling laws.