#6 - Mathematics teacher: Teaching students calculus before

[jgabalski]

Hi, can someone please explain why answer A is the best answer here? I was torn between answer A and C. I haven't gotten to the justify question material yet in the LR book, and am assuming this attributed to my misunderstanding. Thank you for the help.

[Charlie Melman]

Hi J,

The speaker in the stimulus says that teaching pre-university students calculus can benefit them, but that if they can't handle the abstraction involved, they might stop studying math. She concludes that we need to be sure students can handle the abstraction before teaching them calculus.

This is actually a Strengthen question (the "most" before Justify takes this down from a Justify question to a plain old Strengthen question). This argument contains a sneaky assumption: that we shouldn't risk turning students off to math! Lots of Strengthen questions contain this format: they tell you a set of facts, and then tell you that something should be done based on those facts. But they don't tell you why you should do the thing they want you to.

The right answer will tell you why. We can assume all principles in these Strengthen questions to be valid.

Answer choice (A): If this is true, then we shouldn't teach students a new topic unless we know that they will not lose motivation due to the new challenge. Since some students will lose their motivation to study math due to the new challenges that calculus poses, this answer choice directly supports the argument. We ought to be careful about teaching pre-university student calculus; we shouldn't just teach it to everyone.

Answer choice (B): What does "concrete" mean? We don't know. This does nothing to connect 'would lose motivation' with 'shouldn't teach them.'

Answer choice (C): This is very, very tempting. But the stimulus never mentions "exceptional effort." If the stimulus said that dealing with the level of abstraction in calculus requires exceptional effort, then this answer choice would be correct. But it doesn't, and we cannot assume that that is true.

Answer choice (D): Completely out of scope. We don't care about teaching techniques.

Answer choice (E): This directly contradicts the stimulus.

Hope this helps!

[Brett]

Hi,

This explanation makes sense, and thank you for doing so, but I was under the impression that this was a Strengthen Question as the question stem includes, "most helps to justify."

Though, at first I did think this was a Justify the Conclusion Question, but when I checked my answers for the results of this test using the grader, I saw that the question was classified as a Strengthen-PR type.

[Dave Killoran]

Hey Brett,

This is indeed a Strengthen-PR question. I think Charlie got caught up in the original student mentioning justify and then just went with that. I'm going to fix that in a minute so as to avoid future confusion. Thanks for pointing that out!

[avengingangel]

So, I got this question wrong both when I took the test and when I blind reviewed it (I answered C both times). Then finally, after going over it AGAIN & AGAIN, I realize why A is the correct response.

But, I guess I still feel that I haven't really "learned" anything here that will be applicable to other similar types of questions -- I still feel like if I faced this on test day, I would choose C again! That's mainly because my prephrase for this was a principle that was about an action that would not force students to abandon mathematics (that's the "gap" I was attempting to fill), which I felt C addresses.

I even wrote down in the margin when I was reviewing this (before I knew A was the correct response) that "A would be correct if the conclusion were something like 'We should only teach calculus to those who are ready.' " Do you see the disconnect between A & the stimulus that I am seeing here ?? Any guidance on my thought process is appreciated. Thanks.

[avengingangel]

I just read over it again (zillionth time), and am realizing answer choice C is not really a principle, it's a statement. Answer choice A has the word "should" included in it, making it a principle. Is that the/a major difference ?? Now I feel like I can actually take something away from this question!! Thanks for any feedback.

[Francis O'Rourke]

Answer choice (C) is a principle. Principles can be factual or opinionated, so the distinction which you pointed out, between descriptive statements versus statements that make some prescriptive claim, does not disqualify answer choice (C) from being called a principle.

What is important, which you saw in this question, is that we want a principle that connects the facts given in the premises to the opinion given in the conclusion. The speaker made a prescriptive claim (we must or should do something) after giving us only factual premises. The correct answer then will need to contain an ought, or an opinion, and cannot simply tell us more facts as answer choice (C) does.

[bebeg3168]

I read the answer choices and B, C, & D I was able to get rid of...I'm wondering though if I was being too quick (trying to avoid careless mistakes)
B and D never talk about concrete math so I couldn't bring that into the statement to strengthen it.
On C very similar, 'exceptional effort' was never mentioned. I have no idea what that exceptional effort is.
With E I thought is was a principle that contradicted what the stimulus was stating.
A I could only understand the second part of the answer the 'only those' and 'without' I thought was some kind of set up and I wasted a lot of time on this question because of that. Is there an more efficient way to read this type of answer?

[Adam Tyson]

The process of elimination you went through on this is great, Bebe, and can be your best friend on more complex questions with confusing answer choices. To be fast and efficient here you should have first recognized that answer A was confusing you and decided that you must therefore keep it as a contender for the time being. Then, you could have easily eliminated the other four answers for the reasons you did, leaving you nothing but answer A, at which point you stop worrying about it and just pick it! Sometimes the best answer is just the one that you cannot confidently eliminate, perhaps because it is hard to understand.

As I like to say at every opportunity, confusion = contender!