At some schools, Pennsylvania Secretary of Education Ronald Tomalis said, the drops are “noticeable” – 25 percent or more.

In some school systems, investigators have found evidence of outright doctoring of previous years’ tests – and systemic fraud that took place across multiple grades and subjects.

In Philadelphia and elsewhere, some educators have already confessed to cheating, and investigators have found violations ranging from “overcoaching” to pausing a test to reteach material covered in the exam, according to people familiar with the investigations.