The state Education Department will overhaul its standardized testing program by the spring of 2007, acting Education Commissioner Lucille E. Davy announced Wednesday. The tests are to be redesigned in time for students in third through eighth grades and high school to take the revised version in the spring of 2007. Davy said students will likely take them later in the school year than March, when they now take them. That would give schools more time to teach students what they are expected to learn at each grade level. Also, the results will be more detailed for each student, with information on exactly which questions each pupil got right and wrong. That information could help teachers identify and try to fix each student’s weaknesses. Starting this year, the federal government is requiring all students in third through eighth grades to take standardized tests each year. New Jersey, which does not have tests for students in grades five through seven, plans to use a commercial test that is not customized for New Jersey for those students this year only.