Logical Reasoning

PT140 · S3 · Q11 Secondary school students

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Secondary school students achieve broad mastery of the curriculum if they are taught with methods appropriate to their learning styles and they devote significant effort to their studies.

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Conclusion

If broad mastery isn't achieved by students in a certain secondary school, then we know they weren't taught with method appropriate to their learning styles.

Evidence

If secondary school students are taught with methods appropriate to their learning styles and devote significant effort to their studies, then they will achieve broad mastery.

Evaluate

The premise is a conditional with an AND in the trigger.

Taught with approp meth and → Broad mastery Devote signif effort

The contrapositive: ~Taught w/ appropr meths ~Broad Mastery -> or ~Devote signif effort

Our author's conclusion resembles this contrapositive, only it is saying

~Broad Mastery -> ~Taught w/ appropr meths

That's cheating! Given a rule like, A → B or C I can't just go around concluding that A → B

It would be like saying this:

Our one possible objection to this argument is, "Hey, author, if broad mastery isn't achieved, it might be that they weren't taught with appropriate methods or it might be that they didn't devote significant effort (or both).

How can you so confidently conclude that if they don't have broad mastery, they definitely didn't have appropriate methods?

Goal

We need an answer to eliminate the other idea in the Or outcome.

The author established that if broad mastery isn't achieved, it's either because of inappropriate methods or lack of sufficient effort. To prove her conclusion that it always shows a lack of appropriate methods, we need to rule out the possibility that it's because of a lack of sufficient effort.

If we know these secondary students DID devote significant effort and they still didn't achieve broad mastery, then we would have to blame inappropriate methods, as the author's conclusion is doing.

11.

The conclusion can be properly drawn if which one of the following is assumed?

Correct
As long as secondary school
Why this is right
"As long as" = "Provided that" = sufficient trigger, so this answer would be diagrammed like this: Approp Methods → Devote Signif Effort Contrapositive would be ~Devote Signif Effort → ~Approp Methods To formally show how this answer proves the conclusion, we have to think through an "Either Way You Slice It" binary lens. The students either did or didn't devote significant effort (that's a binary). If they didn't devote significant effort, then there weren't appropriate methods used, which agrees with the author's conclusion. If they did devote significant efforts, then the failure to achieve broad mastery can only be blamed on inappropriate methods, so again we're agreeing with the author's conclusion. Either route you take leads you to the author's conclusion, that there were inappropriate methods. To put it another way, our only room for objection with the author was that maybe the students were taught with appropriate methods but didn't devote enough effort. This answer choice rules out the possibility of making such an objection, because it's saying that appropriate methods guarantee that students will devote enough effort. A lack of effort couldn't be the sole cause, because there's no such thing as a student who's taught with appropriate methods but doesn't devote significant effort. This answer allows for three types of students: 1. devoted enough effort, appropriate teaching methods 2. devoted enough effort, inappropriate teaching methods 3. not enough effort, inappropriate teaching methods It will not allow this type of student to exist: 4. not enough effort, appropriate teaching methods Student #1 would achieve broad mastery. So if a student is not achieving broad mastery, they have to be type 2 or type 3, both of which involve inappropriate teaching methods.
Skill tested: Sufficient Assumption · how this choice captures the argument's function is the move to repeat next time.
50% picked this
Even if secondary school students
Reversal / Out of Scope
We're trying to prove that "these hypothetical students were not taught with appropriate methods". An answer that begins "even if they were taught with appropriate methods" is automatically irrelevant to our goal. This answer is weirdly taking the rule we were given in the premise and making a Necessary vs. Sufficient error in interpreting it. It ends up saying ~Devote Signif Effort → ~Broad mastery The original rule is more like this ~Broad Mastery → ~Devote Signif Effort It's not wrong because it's a reversal, it's just wrong because reversing the logic does nothing to help us prove the conclusion. The author presented this argument: A and B → C Thus, ~C → ~A And this answer is saying ~B → ~C Joining this answer with the premise does nothing to help us derive ~C → ~A.
16% picked this
Secondary school students do not
Reversal of Conclusion
This, like (B), gives us a reversed version of something we heard. It says, ~Approp Meth → ~Broad Mastery but the conclusion said ~Broad Mastery → ~Approp Meth It's not wrong because it's a reversal, but reversed logic doesn't help us prove the conclusion (that's why it's wrong). The author presented this argument: A and B → C Thus, ~C → ~A And this answer is saying ~A → ~C Joining this answer with the premise does nothing to help us derive ~C → ~A.
21% picked this
Teaching secondary school students with
Too Weak / Nothing New
"does not always" will almost never work to 100% prove something, so it's almost always going to be wrong on Sufficient Assumption. We already knew what this answer choice is telling us. Teaching with appropriate methods doesn't guarantee broad mastery; it's the combo of Appropriate Methods + Devoting Lots of Effort that guarantees broad mastery.
2% picked this
Secondary school students who devote
Too Weak / Nothing New
"does not always" will almost never work to 100% prove something, so it's almost always going to be wrong on Sufficient Assumption. We already knew what this answer choice is telling us. Devoting significant effort doesn't guarantee broad mastery; it's the combo of Appropriate Methods + Devoting Lots of Effort that guarantees broad mastery.
10% picked this

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