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#11 - Secondary school students achieve broad mastery

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Complete Question Explanation

Justify the Conclusion—SN. The correct answer choice is (A)

This is a difficult question involving a sophisticated conditional reasoning inference. Many people found this question to be difficult, and it provides a good example of how diagramming complicated conditional relationships can help you identify inferences.

The stimulus begins with a conditional rule that includes a compound sufficient condition. The order of presentation of this rule, with the necessary condition coming first in the sentence, makes the rule that much more difficult to understand quickly. Reordered, the rule states that if students are taught with methods appropriate to their learning style, then if they also devote significant effort to their studies, they will achieve broad mastery of the curriculum.

TMA = students taught methods appropriate to their learning styles
DSE = students devote significant effort to their studies
ABM = students achieve broad mastery of the curriculum

..... ..... ..... Sufficient ..... ..... Necessary

..... ..... ..... TMA

..... ..... ..... + ..... ..... :arrow: ..... ABM

..... ..... ..... DSE

Next, the stimulus concludes that if the students in a particular school do not achieve broad mastery of the curriculum (ABM), then it must be the case that those students are not taught with methods appropriate to their learning styles (TMA):

..... ..... ..... ABM ..... :arrow: ..... TMA

This conclusion partially describes the contrapositive of the conditional premise presented above. However, the actual contrapositive of that relationship is:


..... ..... ..... ..... ..... ..... ..... TMA

..... ..... ..... ABM ..... :arrow: ..... or

..... ..... ..... ..... ..... ..... ..... DSE

Written out, the contrapositive provides that if the students do not achieve broad mastery in the curriculum (ABM), then: 1) the students are not taught with methods appropriate to their learning styles (TMA); or, 2) the students do not devote significant efforts to their studies; or, 3) the students are neither taught with methods appropriate to their learning styles nor do they devote significant efforts to their studies (TMA and DSE).

By comparing the argument’s conclusion with the contrapositive, we can see that the author explicitly identifies one of the three necessary condition options, i.e., TMA, without providing any evidence to support this choice. What makes this question particularly tricky, however, is that the author’s explicit statement that the students are not being taught with methods appropriate to their learning styles (TMA), does not rule out the possibility that they also fail to devote significant effort to their studies (DSE). Because the options are not mutually exclusive, explicitly identifying one option does not inherently preclude the other option from being the case.

The question stem tells us that this is a Justify the Conclusion question, meaning the correct answer choice will contain information proving the conclusion is valid. To have such a strong effect in this conditional argument, the correct answer will provide a conditional relationship requiring that, no matter what, if the students do not achieve a broad mastery of the curriculum, then they are not being taught with methods appropriate to their learning style. In other words, regardless of which necessary condition option is selected, the term TMA must ultimately be in the diagram as a necessary condition. Here is how we can diagram that conditional relationship, with this expanded representation of the contrapositive in bold:

..... ..... ..... ..... ..... ..... ..... TMA

..... ..... ..... ABM ..... :arrow: ..... or

..... ..... ..... ..... ..... ..... ..... DSE ..... :arrow: ..... TMA

So, the prephrase for this Justify the Conclusion question is that if a student does not devote significant effort to their studies, then it must be the case that they are not being taught with methods appropriate to their learning styles.

Answer choice (A): This is the correct answer choice, because it contains the contrapositive of our prephrased relationship. Again, the prephrased relationship would be diagrammed as:

..... ..... ..... DSE ..... :arrow: ..... TMA

The contrapositive to this relationship is:

..... ..... ..... TMA ..... :arrow: ..... DSE

In other words, if the students are taught with methods appropriate to their learning styles, then they will devote significant effort to their studies—a restatement of the relationship described in this answer choice.

Answer choice (B): Do not be confused by the beginning of this answer choice. The “even if” language essentially tells you to set aside for the moment any evidence that secondary school students are taught with methods appropriate to their learning styles, i.e., disregard evidence that TMA. Instead, the choice says, focus on this relationship—if students do not devote significant effort to their studies, then they will not achieve broad mastery of the curriculum. We can diagram this as:

..... ..... ..... DSE ..... :arrow: ..... ABM

This relationship does not fit the relationship identified in our prephrase, and it is one part of a Mistaken Negation of the relationship provided in the premise.

Answer choice (C): As with answer choice (B), this choice also presents a partial Mistaken Negation of the conditional rule provided by the premise in the stimulus. Here, the sufficient condition is the students not being taught with methods appropriate to their learning styles (TMA), which can be diagrammed as:

..... ..... ..... TMA ..... :arrow: ..... ABM

Answer choice (D): This answer choice is incorrect, in part because it deals causal reasoning, which was not used in the stimulus. The language “does not always result in” is saying that teaching secondary school students with methods appropriate to their learning skills (TMA), one of the sufficient conditions from the original rule, does not always cause students to achieve a broad mastery of the curriculum. This choice is attractive to those who fail to recognize the difference between causal and conditional reasoning.

Also, this choice is attractive to those who misunderstood the task. Assuming the language in this answer choice were not causal, it would come close to being a valid Must Be True inference. It would be accurate to say that if only one of the sufficient conditions were met, then the necessary condition may not be met. In the context of this answer choice, it would be a valid Must Be true inference if it were to say that “teaching secondary school students with methods appropriate to their learning styles may not always indicate a broad mastery of the curriculum by those students.”

Answer choice (E): As with answer choice (D), this information invokes one of the two sufficient conditions and could be attractive to someone who misinterpreted this as a Must Be True question.
Rhei1Kel
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I have been sitting here completely confused why the correct answer is A. I am really getting into my head and must be missing something obvious. Here is how I approached this justify quesiton:

Premise: Students achieve broad mastery (ABM) if they are taught methods approrpriate (MA) and they devote significant effort (DSE).

-Diagram for premise: MA and DSE ---> ABM
CP: Not ABM ---> Not MA -OR- Not DSE

Conclusion: If ABM is not achieved those students are not being taught MA.

-Diagram for Conclusion: Not ABM ---> Not MA

This is where I get confused because the conclusion is already the contrapositive of the premise, so Im not sure what kind of an answer it could be. I just figured it would have to have the element of devoting significant effort.

I chose E because it relates to the part of CP of the premise that is not included in the conclusion. It is still possible to not achieve mastery even though they are devoting significant time because they are not being taught methods that are appropriate, which is the conclusion.

How is A correct? I am not even sure what A is saying. The 2 elements are on the same side of the diagram but A is connecting them together conditionally, why is that even relevant?

Any insight on this problem will be very much appreciated! I had a hard time explaining my thoughts because i'm not even sure what they are on this problem so anything will help!

Thank you!
Ron Gore
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Hi Rhei,

This is definitely a confusing question. The good news is that nearly all of your work on it was accurate. To start, your description of the argument in the stimulus is spot on:

Rhei1Kel wrote:-Diagram for premise: MA and DSE ---> ABM
CP: Not ABM ---> Not MA -OR- Not DSE

Conclusion: If ABM is not achieved those students are not being taught MA.

-Diagram for Conclusion: Not ABM ---> Not MA


Where you go awry is when you say that the conclusion is already the contrapositive of the premises. That isn't true because, to use your phrasing, the contrapositive would be:

..... ..... ..... MA
ABM :arrow: ..... or
..... ..... ..... DSE

Without providing any reason to support the necessary condition being MA as opposed to the other two potential scenarios (i.e., 1) DSE; or 2) MA and DSE), the argument just picks MA. We have to justify this apparently arbitrary selection.

In other words, we need an answer choice that proves that, no matter what, if ABM then MA. In order to do this we need to show, absolutely, that any time we're told ABM, we'll wind up with MA. The only way to do prove this is to provide a conditional rule that tells us even if DSE then MA.

In other words, the relationship would be:

..... ..... ..... MA
ABM :arrow: ..... or
..... ..... ..... DSE :arrow: MA

With that addition, no matter whether we're told MA or DSE, we'll know that MA must be the case.

Answer choice (A) is correct because it tells us the contrapositive of this relationship, and would be diagrammed as:

MA :arrow: DSE

the contrapositive of which is

DSE :arrow: MA

which ties onto the original conditional relationship as identified in bold, above.

As I said, this is a VERY difficult question, and a difficult connection to identify. Remember your task in a Justify question, which is to prove that the conclusion is valid. In this case, you had to prove that if ABM then MA, no matter what.

In terms of answer choice (E), you are correct that this states something that is possible. But your job in a Justify question isn't to select the answer choice that tells you what is possible. It's to pick the answer choice that proves, 100%, that the conclusion is valid.

Please let me know if I can be of further help.

Thanks,

Ron
reop6780
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The correct answer is A while I chose B.

The stimuli has conditionals:

premise 1) Methods appropriate and Devote significant effort -> Broad mastery.

conclusion) NOT Brad mastery -> NOT Methods appropriate


Since if I negate the necessary condition of Brad mastery from premise 1, I have NOT Methods appropriate OR NOT Devote significant effort.

Since the necessary condition of the conclusion is NOT Methods appropriate, I was expecting an answer of possible premise 2 stating Devote significant so that Methods appropriate should definitely negated.

I did not find any answer of my expectation.

From my understanding the correct answer A has a conditional: Method appropriate -> Devote significant effort.

I do not know how this works as a premise reach the conclusion at this moment especially I believe the gap to fill should be the presence of Devote significant effort.

Thank you, always for your help!
Lucas Moreau
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Hello, reop,

I can see what the trouble is. It's saying, as you correctly state, Methods Appropriate + Devote Significant Effort :arrow: Broad Mastery. The trick is how contrapositives of conditional relationships with more than one sufficient or necessary condition are performed.

If the multiple conditions have an "and", change it to an "or".
If the multiple conditions have an "or", change it to an "and".

In this case, there is an "and" (MA and DSE :arrow: BM), so the contrapositive must change that "and" to an "or". That gives us:

Not!BM :arrow: Not!MA or Not!DSE

So merely by stating Not!Broad Mastery, we cannot definitively say Not!Methods Appropriate on the basis of the contrapositive alone. Only if answer choice A is correct (which gives us MA :arrow: DSE) can we be sure that Not!Methods Appropriate if Not!Broad Master is true.

The reason for this is, if answer choice A is correct, Not!Broad Mastery could not be true if Methods Appropriate was true, since MA :arrow: DSE and MA + DSE :arrow: BM.

Hope that helps,
Lucas Moreau
jostomel
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I am having issues on this question too, and the explanation didn't really make it clear for me. I got the right diagram for both the original and the contrapositive, and I understand the difference between "and" and "or" for contrapositive. Can you help me understand better how my reasoning is wrong?

I thought that for mastery they had to have both a good method and devotion to study, hence the "and". Isn't answer B saying that if they have good methods, then they can't achieve mastery without devotion too?
David Boyle
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jostomel wrote:I am having issues on this question too, and the explanation didn't really make it clear for me. I got the right diagram for both the original and the contrapositive, and I understand the difference between "and" and "or" for contrapositive. Can you help me understand better how my reasoning is wrong?

I thought that for mastery they had to have both a good method and devotion to study, hence the "and". Isn't answer B saying that if they have good methods, then they can't achieve mastery without devotion too?


Hello jostomel,

Riffing off Lucas' useful exposition above: answer B says, "Even if secondary school students are taught with methods appropriate to their learning styles, they will not achieve broad mastery of the curriculum if they do not devote significant effort to their studies." There's a mistaken reversal here, since the second clause diagrams as "BM :arrow: DSE". Maybe something else could let them have broad mastery, e.g., magic ice cream which increases your IQ by 500 points. (Just to make up an example)
Otherwise put, DSE is a sufficient, not a necessary, but answer B calls it a necessary.

Hope this helps,
David
lsatopocalypse
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Quick question:

this is a justify question, so it must be made airtight. I want to know if my way of answering it is correct.So….

premise:
methods appropriate+devote effort ---> broad mastery

conclusion:
NO!broad mastery---> NO!methods appropriate

So the conclusion leaves out "devote effort". I recognized this and tried to find an answer that would address it, but i couldn't find an answer that was satisfactory so I took the contrapositive of the conclusion:

methods appropriate--->broad mastery

which is basically the premise without devote effort, so I thought that if I can find an answer which reincorporates devote effort, which is precisely what choice (A) does, it should be the correct answer. (A) basically says if methods appropriate exist, then devote does as well, and, of course, broad mastery.

So was my line of thinking correct or was it just a fluke that my method allowed me to arrive at the correct answer?

Thanks in advance.
Jon Denning
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Thanks for the question!

Your reasoning is entirely solid here! Basically it comes down to making sure that "devote effort" is said to occur, since with it we would know that the conclusion ("no broad mastery :arrow: not taught appropriate methods," as a loose abbreviation) is true based on the original premise being proven: if being taught with methods appropriate to their learning styles gives you devote effort, that means that being taught with methods appropriate to their learning styles ALONE tells you they'll develop a broad mastery (both sufficient conditions are satisfied as soon as the "teach" condition is, and then the necessary, "broad mastery," must occur).

And of course if taught appropriate methods :arrow: broad mastery is true, then its contrapositive no broad mastery :arrow: not taught appropriate methods must also be true, and thus the conclusion is proven.

I hope that helps!
Jon Denning
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avengingangel
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Hello! A couple of questions:

When the explanation says:

"By comparing the argument’s conclusion with the contrapositive, we can see that the author explicitly identifies one of the three necessary condition options, i.e., TMA, without providing any evidence to support this choice."

Is this saying that the author's conclusion is really just the (partial) contrapositive of their own premise ?? (Therefore no reasoning/support; a circular argument) Because that's how I read the argument to be and that it seems the explanation is saying here.

"The author’s explicit statement that the students are not being taught with methods appropriate to their learning styles (TMA), does not rule out the possibility that they also fail to devote significant effort to their studies (DSE). Because the options are not mutually exclusive, explicitly identifying one option does not inherently preclude the other option from being the case."

Why does this matter at all ?? I recognize that statement to be true, but don't understand how it's relevant in finding the right answer. As stated, "If the students do not achieve broad mastery in the curriculum (ABM), then the students are not taught with methods appropriate to their learning styles (TMA)" is one of the contrapositive options and that alone should/can suffice. Since that is what this argument's conclusion is dealing with/addressing, I am very confused as to why we should be concerned with the other options of the premise's contrapositive. In fact, when diving into the answer choices, I immediately eliminated any ones that mentioned DSE or DSE, as I thought they were thrown in there as distractors.

And related to that question, I have no idea how we got from here:

"The correct answer will provide a conditional relationship requiring that, no matter what, if the students do not achieve a broad mastery of the curriculum, then they are not being taught with methods appropriate to their learning style. In other words, regardless of which necessary condition option is selected, the term TMA must ultimately be in the diagram as a necessary condition."

to here:

"So, the prephrase for this Justify the Conclusion question is that if a student does not devote significant effort to their studies, then it must be the case that they are not being taught with methods appropriate to their learning styles."

It seems like the whole explanation is focusing on TMA / TMA, and then all of a sudden it's like, "So, yeah, obviously, the correct answer should include DSE!!!" Which just doesn't make sense. Could anyone help me better understand ?? Thanks !!!