PrepTest 111, Section 4, Question 1
The graphical illustrations mathematics teachers use enable students(50 more words not shown)
The statements above provide some(7 more words not shown)
- APictorial understanding is(7 more words not shown)
- BPeople who are(12 more words not shown)
- CIllustrating geometric concepts(6 more words not shown)
- DAcquiring the ability(11 more words not shown)
- EThere are strategies(14 more words not shown)
Reading the argument
Imagine learning about triangles without ever seeing one. A picture could make the lesson much easier to follow. When a teacher labels a side x, the student can see what that symbol stands for instead of treating it as a mark with no connection to anything.
That helps me understand the first sentence: pictures give students an intuitive grasp of geometry, which helps them learn to calculate with symbols. I can also imagine a graph helping with algebra. But would pictures help just as much there? That comparison is something I'd want evidence for if we were evaluating the argument.
The question gives us a different job. Four answers have some support in the passage, and we need the exception. So let's keep the author's claims as our basis rather than choose an objection to the comparison.
What we’re looking for
One distinction worth tracking is between a useful teaching aid and the deepest understanding. Pictures can help students learn even though the deepest mathematical understanding is abstract. A visual starting point doesn't have to be the final stage. Now let's see which answer goes beyond what the passage supports.
Working the answers
- A
This fits the final qualification. The deepest understanding is abstract rather than pictorial, so understanding through pictures isn't the final stage described. Pictures can still be useful along the way. Because A has support, it isn't our answer.
- BCorrect
We aren't told that someone can be very good at manipulating symbols while having no mathematical understanding at all. The passage says intuitive understanding helps students acquire the ability to work with symbols. It doesn't examine people who already have that ability and establish that some could entirely lack understanding.
B might sound plausible as a comment about memorizing procedures, but plausibility isn't support from this passage. We would have to add a claim about how symbol manipulation and understanding can come apart. That's why B is the exception.
- C
This is directly supported by the opening sentence. Graphical illustrations help students learn geometry more easily. An answer doesn't need to combine every statement in the passage to have support; repeating a claim the passage explicitly makes is enough.
- D
The passage describes learning to manipulate symbols for calculation as something the intuitive understanding of geometry makes easier. That places the skill within the process of learning geometry. We don't need to know that it is the entire process, or the deepest stage, to support D.
- E
Graphical illustration is the shared strategy. The author says it helps in geometry and would be equally effective in algebra. E makes the more modest point that a strategy can work in both subjects. Our question while reading about whether the benefit is really equal doesn't make E unsupported by what the author says.
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