Parsons, the engineering and construction firm, will oversee DeKalb County schools’ $466 million construction program for the next six weeks. After that, who knows? Parsons and Jacobs Project Management Co. will be paid $644,150 for their trouble. The firms in June won a contract for “supplemental” management, but Superintendent Crawford Lewis gave Parsons “full responsibility” for the program in an Oct. 22 letter. The company takes the reins from chief operations officer Patricia Pope, whose office is under investigation by DeKalb prosecutors.