Student Testing Improvement and Accountability Act This bill amends the Elementary and Secondary Education Act of 1965 to reduce the required frequency of student achievement tests in mathematics and reading or language arts. Currently, students must be tested in those areas against state academic content and achievement standards in each of grades three through eight. This bill instead requires that those tests be administered at least once during: (1) grades 3 through 5, (2) grades 6 through 9, and (3) grades 10 through 12.