To find the assumption of the parent's argument, an answer choice with the truthful information must be selected in order for the passage argument to be accurate. To do this, the thrust of the passage needs to be determined.

Option A - Correct
For any teacher to be a qualified teacher, he/she must have been certified by the department of education, otherwise, he/she is considered unqualified.

Option B - Incorrect
This is not true. We cannot be so sure if the department of education is the only entity that determines the qualification of a teacher. Also, we don't know anything about other measures, and entities that teachers must pass through before they are eligible to get certified by the department of education.

Option C - Incorrect
This is off-topic! The comparison of effectiveness between qualified and unqualified teachers are not relevant to the argument.

Option D - Incorrect
This claim cannot be verified from the passage as there are no statistics given on the number of unqualified teachers from other schools.

Option E - Incorrect
This is too absolute. However, we cannot be so sure from the passage whether unqualified teachers are in the process of becoming certified or not.