Secondary school students achieve broad mastery of the curriculum if they are taught with methods appropriate to thei...

shunhe on August 10, 2020

Hi @rwhittle@colgate.edu,

Thanks for the question! So this is one that can be helped out a lot with diagramming, so let’s diagram it out. First sentence is a pretty classic if-then statement, so we can just diagram that

Taught with appropriate methods (TAM) & Devote significant effort to studies (DSES) —> Achieve broad mastery of curriculum (ABMC)

And the second sentence is also an if-then, which we can diagram

~ABMC —> ~TAM

And this is going to be the conclusion. So we have

Premise: TAM & DSES —> ABMC
Conclusion: ~ABMC —> ~TAM

Now, taking the contrapositive of the premise, we get

~ABMC —> ~TAM v ~DSES

And so now we need to somehow get from this statement to

~ABMC —> ~TAM

so one easy way of doing so would be, for example, an answer choice that stipulates DSES. Of course, it’s not that simple, but it’s not too much harder either. Take a look at (A), which tells us “as long as secondary school students are taught with methods appropriate to their learning styles, they will devote significant effort to their studies.” In other words, “if they are taught with appropriate methods, they’ll devote significant efforts,” or

TAM —> DSES

Now this tells us that whenever we have TAM, we’re going to get DSES too. So let’s say we have ~ABMC. Can we have TAM? Well, if we have TAM, we have SES. But if we have ~ABMC, we have to not have one of those two! Which means if we have ~ABMC, we have to have ~TAM. In other words ??~ABMC —> ~TAM

And so assuming (A) will get us to our conclusion.

(E), on the other hand, is wrong because it just tells us that if you devote significant effort to your studies, you don’t always achieve broad mastery of the curriculum. So this just tells us

DSES <—some—> ~ABMC

And that doesn’t help us get to the conclusion we want.

Hope this helps! Feel free to ask any other questions that you might have.