The school board has determined that it is necessary to

The school board has determined to reduce the staff and decided to remove the least efficient ones first.
Out of the given options, only A is strong. Obviously if the school does not have a method to determine the effectiveness, they cannot implement this plan.

Hence the assumption has to be that "there is a way of determining the effectiveness of teachers"

Correct Option: A

No matter the difficulty of the question, let us solve this methodologically and make sure we carry this process forward when solving harder questions.

Understand the argument:

Conclusion (Plan): It is necessary to reduce the number of teachers.
How the board plans to accomplish this plan: We will use effectiveness as a measure to determine the least effective teachers and eliminate them. We will not consider the seniority of teachers as a measure.

Now let us think about what can cause the plan to fail. I believe this should be our task/strategy when questions ask to find the assumption made in someone's plan.

The primary assumption here is that the board assumes the outcome. They assume its plan will work. In assuming this, it also has to assume that there exists a way to determine the effectiveness of the teachers.

Let us move on to answer choice analysis:

Choice A: Correct. Negate this and your plan will fail.
Choice B: If anything, this choice breaks the conclusion without even us negating it. This is a weakener. This choice implies one may not measure the effectiveness accurately.
Choice C: Interesting choice if one overthinks like me. At best, this choice implies that the teachers with the most experience (more experience = senior teachers) are the best teachers.

First of all, what is best? best is very subjective. Just for the sake of understanding, let us assume best = most effective.
This choice would then mean: senior teachers are most effective.
But still, one question remains, even if senior teachers are most effective, how can one make sure the board can effectively judge the effectiveness of the teachers. This choice is out of scope.

One can try negating choice C and can see the conclusion will not break as this choice does not impact it.

Choice D: Out of scope.
Choice E: Irrelevant but could also be weakened at best. if anything, this choice breaks the conclusion without even us negating it. This choice implies using effectiveness is not a good measure. It does not harms the conclusion as much as option B does, but still raises doubts to the plan proposed.