Q11 - Secondary school students

[GeneW]

Can someone please explain why A is correct and E wrong?

Thank you in advance.

[ohthatpatrick]

Question type: Sufficient Assumption

Task: pick an answer choice that, when added to the premise(s), proves the conclusion with 100% airtight validity.

Because our task is mathematical in nature, you can almost always SOLVE for the correct answer on Sufficient Assumption before you look at the answers. Also, because our task is to prove something with 100% airtight validity, the correct answer normally needs to be of conditional strength (the phrase "do not always" in choice E is too wishy-washy to prove something MUST BE TRUE).

First focus on what words/ideas you need to prove in the CONCLUSION:

CONC:
Broad mastery not achieved "”> not being taught w/ approp. methods to their learning styles

Now our job is to see whether anything in the premises mentions the idea on the left or the idea on the right.

PREM:
Taught w/ approp. methods AND devote signif. effort "”> broad mastery achieved

Weird. The premise mentions both ideas in the conclusion (albeit in their negated forms). We should write the contrapositive of the premise since that will look more like the conclusion we’re trying to prove.

CONTRA of PREM:
Broad mastery not achieved "”> not being taught w/ approp method OR not devoting signify. effort

This is an unusual Sufficient Assumption set-up. Normally we’re looking to connect some idea mentioned only in the premise to some idea mentioned only in the Conclusion.

Here, our premise looks a LOT like our conclusion. They’re almost saying the same thing.

Let me give you an analogy and see if you can figure out what we’re missing:

I want to prove this claim:
If Sheila goes to prom, she’ll go with Bob.

And here is the one fact I can give you:
If Sheila goes to prom, she’ll go with Bob or Ernie.

What new fact do you need to add to the fact I gave you so that we can prove the original claim?




We need to add that Sheila is not going to go prom with Ernie. We need to somehow take Ernie out of the running.

Let’s say I’m sitting on the fence about whether to go to law school, but I am certain that
IF I go to law school, I will go to Harvard or Yale.

Yale just rejected me.

Okay, well, then my new truth is that
IF I go to law school, I will go to Harvard.

So in order for us to go from our premise of:
~Broad Mastery "”> ~Approp. methods or ~devote signif. effort
to our conclusion of
~Broad Mastery "”> ~Approp. methods
we need to remove the concern about "not devoting enough effort".

We need to be sure that when we fail to achieve broad mastery, it is ALWAYS the result of failing to use appropriate methods, and NEVER the result of having appropriate methods but insufficient effort.

That's what (A) gives us.
It lets us know that when approp. methods are used, students ALWAYS devote significant effort.

So if broad mastery is ever not achieved, we know we can blame our methods, not the students' effort.

That's what the conclusion wants to prove.

More formally,
(A) gives us a rule that says
Approp. methods "”> devote signif. effort
the contrapositive of that is
~Devote Signif Effort --> ~Approp. methods

So if we go back to the conditional from the Prem:
~Broad Mast --> ~Approp. methods OR ~Devote Signif Effort

Well, since ~Devote Signif Effort --> ~Approp. methods
then no matter which half of the OR consequence we go with, we still get ~Approp. methods.

Let's adapt the law school analogy from before. Say I'm given this fact:
If I can borrow money from my Dad and I can get into Harvard, then I'm going to law school.

Contrapositive:
~Law school -> ~borrow money or ~get into Harvard.

Now we want to prove this claim:
If I don't go to law school, then you can be sure I didn't get into Harvard.

Well, Person X could come along and make this objection:
"If you don't go to law school, I'm not SURE you didn't get into Harvard. Maybe you DID get into Harvard but just couldn't borrow money from your Dad."

The way to eliminate this objection is to say, similar to (A), "If I got into Harvard, my Dad would definitely let me borrow money."

It wipes that borrowing-money concern away and shows that going to law school would only fail to happen if I didn't get into Harvard.

(B) says
~Devote Signif Effort --> ~Broad Mastery (the 'even if' means that approp. methods are irrelevant to this connection)

It should be a red flag that this reads backwards from the conditional in the premise.

Conversationally, this tells us that if you can't borrow money from your Dad, you won't go to law school. This idea seems to just strengthen Person X's objection to our conclusion. We need to wipe away the concern that lack of borrowing money will be a dealbreaker (or in the original argument, we need to wipe away the concern that lack of significant effort could be a dealbreaker).

(C) and (D) are completely useless because they don't bring up "devoting significant effort" so we should spend NO time thinking about them.

(E) makes a wishy-washy claim that won't help with our black-and-white task.

In our analogy, this would be saying "people who do borrow money from their Dad do not always go to law school".

Does that help shoot down Person X's objection? Not at all.

Hope this helps.

[pewals13]

One way to see this:

If you have A+B----->C

And want to conclude:

-C----> -A

Just add A---->B

Anytime you have -C you know you have to have -A because if you have A you would also need B and having both A and B violates the contrapositive of the original rule (-C---->-A or -B)

[eve.lederman]

Embarrassingly enough I just spent an hour on this question and I finally understood it.

Premise:
Methods + effort -> mastery
~Mastery -> ~methods or ~effort
Conclusion:
~Mastery -> ~methods

To guarantee that ~mastery -> ~methods, we need to also show that ~effort -> ~methods, since it is also a possibility that ~mastery -> ~effort.

(A) says that methods -> effort AKA ~effort -> ~methods


D and E are implied by the stimulus since we know that Method/effort is sufficient only if they are accompanied by effort/method
C didn't really do anything and it's the reversal of the conclusion.
B is reversed and also gets part of the evidence wrong. the evidence says that methods and effort are sufficient for mastery. B says that it's necessary.

Please let me know if any of this is wrong!

Thanks!

[ohthatpatrick]

You crushed it! An hour well spent?

[einuoa]

As a followup question, for answer choice E,

if it reads
"Secondary school students who devote significant effort to their studies NEVER achieve broad mastery of the curriculum,"

would that make answer choice E also correct?

S.E -> ~B.M.
and since the conclusion reads -B.M. -> Methods appropriate;

answer choice E would render the significant effort portion irrelevant because the necessary condition is already fulfilled.

Any clarification is appreciated, thanks!

[ohthatpatrick]

I see where you're going with that, but that version of (E) would contradict the first sentence of the argument.

Appropriate methods AND Signif. Effort --> Broad Mastery

and you're saying (E) could say
Signif. Effort --> ~Broad Mastery

Those two conditionals would contradict each other.

If I taught someone with appropriate methods, I have a chance of helping them achieve broad mastery.

Now it comes down to whether they devote significant effort.

But, wait a sec, one of my conditionals says if they devote significant effort, they DO achieve mastery; the other says if they devote significant effort, they DON'T achieve mastery.

Ahhhhhh!

[EricaL584]

I understand why A is correct.

If I change C to "Secondary school students do not achieve broad mastery of curriculum ONLY IF they are not taught with methods appropriate to their learning styles", will it make C the correct, too?