Provided with formal training in a variety of proven pedagogical methods, English can be taught to a class full of people who each speak unrelated languages by an instructor whose only language is English.
A. Provided with formal training in a variety of proven pedagogical methods, English can be taught to a class full of people who each speak unrelated languages by an instructor whose only language is English.
Wrong - because provided should modify instructor no english.
B. By an instructor whose only language is English, it can be taught to a class full of people who each speak unrelated languages, provided with formal training in a variety of proven pedagogical methods.
Wrong - because provided should modify instructor, not the class.
C. Teaching it to a class full of people who each speak unrelated languages, an instructor whose only language is English can be provided with formal training in a variety of proven methods.
Wrong - because Teaching is modifying the instructor. And the rest is nonsensical.
D. To a class full of people who each speak unrelated languages, an instructor whose only language is English can teach it, provided with formal training in a variety of proven pedagogical methods.
Wrong - Modifier issue
E. Provided with formal training in a variety of proven pedagogical methods, an instructor whose only language is English can teach it to a class full of people who each speak a variety of unrelated languages.
Correct - Since provided correctly modifies the instructor.