PrepTest 126, Section 1, Question 6
Mathematics teacher: Teaching students calculus before they attend(51 more words not shown)
Which one of the following(9 more words not shown)
- AOnly those who,(18 more words not shown)
- BOnly those parts(14 more words not shown)
- CCognitive tasks that(13 more words not shown)
- DTeachers who teach(26 more words not shown)
- EThe level of(19 more words not shown)
Reading the argument
Calculus could help a student prepare for later study. It also could make an unprepared student think, “I'm terrible at math. I quit.” I can see why the teacher wants to avoid introducing it too soon.
But is leaving mathematics necessarily something we must prevent? Someone might discover that their talents lie elsewhere and happily pursue another subject. Not everyone needs to become a mathematician. The teacher treats the risk of students abandoning math as a reason to restrict who gets introduced to calculus, and that recommendation needs a judgment about which risks we should avoid.
What we’re looking for
We're asked for a principle that helps justify the recommendation. I'd expect something saying we should protect students' interest in math or minimize the risk of driving them away. Keep the recommendation clear: check that students are ready for the abstraction before introducing calculus. The teacher isn't telling us never to teach it.
Working the answers
- ACorrect
This gives a broader rule than the one I predicted: introduce new intellectual work only to people who can handle its mental challenges without losing motivation. Calculus is the new work, its abstraction is the mental challenge, and abandoning math is the loss of interest the teacher worries about. The principle supports checking readiness before teaching it. We don't need the answer to repeat the words of our prediction.
- B
This restricts everyone to the most concrete material. The teacher doesn't say that abstract material is off limits to all pre-university students. Students who are ready could be taught calculus. B replaces the readiness distinction with a different rule about which topics to teach.
- C
Exceptional effort isn't the same thing as a level of abstraction a student cannot yet handle. More fundamentally, C describes a possible effect on motivation without giving a principle about what teachers should do. We need support for the recommendation about whom to introduce to the work.
- D
Showing how math applies to a concrete problem—for example, using it in a physics problem—is a teaching method. It doesn't establish the teacher's proposed requirement that students already be able to handle the abstraction before being introduced to calculus. How to teach material and who is ready for it are different questions.
- E
This goes against the recommendation. The teacher says we must consider whether students can handle the abstraction. E says abstraction shouldn't be considered when judging whether the topic is appropriate. That doesn't help justify the teacher's rule.
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