Self-study
Mathematics teacher: Teaching students calculus before they attend university may significantly benefit them. ███ ██ ████████ ███ ██████ ████████ ██████ ████ ███ █████ ███ ███ █████ ██ ███████████ █████████ ████ ███ ███████ ███ █████ ██ ███████████ ███████████ ██ ██ ██ ███ █████ ██ █████ ██████████████ ████████ █████████ ██ ████ ████ ████ ████ ███ ██████ ███ █████ ██ ███████████ █████████
Summary
The math teacher claims that we must ensure that pre-university students can handle the level of abstraction in calculus, if we want to try teaching them calculus at all. This is because teaching calculus to students who can’t handle the level of abstraction might lead them to stop learning math altogether.
Notable Assumptions
The math teacher assumes that it’s important to maintain students’ interest in studying math. That’s the link between the premise that teaching calculus too early could lead students to abandon math and the conclusion that we must ensure students are ready for calculus.
So, the principle we’re looking for will tell us that if students may abandon math when taught calculus before they’re ready, then we should ensure their readiness before teaching them calculus.
6.
Which one of the following ██████████ ████ █████ ██ ███████ ███ ███████████ █████████ █████████
a
Only those who, ███████ ██████ ███████████ ███ ████ ███ █████████ ██████████ ████ ███ ████████████ ████ ████████ ██████ ██ ██████████ ██ ███
So, if a cognitive challenge—such as the abstraction in calculus—will destroy someone’s motivation, then we should avoid that challenge. This matches the assumption that we shouldn’t teach calculus when it would make students abandon math (or in other words, lose motivation).
b
Only those parts ██ ████████████████ ███████████ ████ ███ ███ ████ ████████ ██████ ██ ██████ ██ ██████████████ █████████
The math teacher never raises the idea of teaching only certain parts of calculus, so this principle doesn’t apply.
c
Cognitive tasks that ███████ ███████████ ██████ ████ ██ █████████ ███ ██████████ ██ █████ ███ ███████ █████
The math teacher doesn’t claim that calculus involves exceptional effort, so this principle isn’t triggered.
d
Teachers who teach ████████████████ ███████████ ██ ██████████████ ████████ ██████ ██ █████ ████ ████████ ███ ██████ ██ █████ ███████████ ████ ████ ███ ███████████ ██ ███████████ ██ ████████ ████████ ██ ██████
The math teacher isn’t discussing what teaching strategies are more or less effective, but rather the question of whether to teach calculus at all—making this irrelevant.
e
The level of ███████████ ████████ ██ █ █████ ██████ ███ ██ ██████████ ██ ███████████ ███████ ████ █████ ██ ███████████ ███ ██████████████ █████████
This straight-up contradicts the argument; the level of abstraction involved in calculus is clearly one of the math teacher’s primary considerations.