Logical reasoning PrepTest 126 · Section 1 · Question 6

Correct. Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Strengthen (Principle)

Stimulus Summary:
If students aren't ready for the abstraction of calculus, they may hate math, so we should make sure they're ready for that abstraction before teaching it.

Answer Anticipation:
Strengthen (Principle) questions task us with finding an answer that justifies the judgment in the conclusion based on the details in the premise. It's generally the case that a few details are presented, but only one or two are directly related to the judgment being made, so we should start with that judgment and figure out what the author is relying on to justify it.

Here, the conclusion is that it should be ensured that students are ready for calculus's level of abstraction before teaching it. Why? Because if they're not, then they'll lose interest in math altogether.

So the principle will connect that detail to the conclusion:
If introducing a subject too early would result in people losing interest in it, then it shouldn't be introduced until the people are ready.

Answer Explanation:
This answer is in the ballpark of our anticipation, so we should think through it. It sets up "meet[ing] the cognitive challenges" without giving up on a subject as a necessary condition to being introduced to a subject. The stimulus relies on people being ready for the abstraction of calculus as being a precondition for them being introduced to it. Dealing with mathematical abstraction absolutely counts as meeting a cognitive challenge, so this answer justifies the conclusion. If being able to meet a cognitive challenge without losing interest is necessary before one should be introduced to a subject, then making sure students can understand the mathematical abstraction must happen before they should be introduced to calculus.

Key Takeaway:
Strengthen (Principle) questions task us with finding a principle that justifies the judgment in the conclusion based on details from the premises. However, there are generally several details mentioned. Starting with the conclusion and working backwards should help you identify which ones are relevant to the judgment, and which are background or even run counter to that conclusion.

Incorrect. The Math Teacher is fine with teaching abstract math to students who are ready for it before university, so this answer doesn't justify her conclusion about teaching calculus to pre-university students. Additionally, there's no indication that calculus is a university-level mathematics.

Incorrect. While your mileage may vary, there's no indication in the stimulus that the abstraction needed for calculus, or calculus itself, presents cognitive tasks that require exceptional effort. While it appears that the abstraction is difficult to understand, it could require little effort once it is understood. This answer is, therefore, out of scope.

Incorrect. There's no indication that calculus is a university-level mathematics (that term never shows up in the stimulus). Additionally, the Teacher is concerned with ensuring students are able to handle the abstractions of calculus, so it's suggested that making it concrete isn't necessary to teach it.

Incorrect. The Math Teacher is very much concerned with the level of abstraction involved and whether students are ready to handle it, so this answer runs counter to her argument.