PrepTest 35, Section 3, Question 1
The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. Illustrating algebraic concepts graphically would be equally effective pedagogically, even though the deepest mathematical understanding is abstract, not imagistic.
The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. Illustrating algebraic concepts graphically would be equally effective pedagogically, even though the deepest mathematical understanding is abstract, not imagistic.
The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. Illustrating algebraic concepts graphically would be equally effective pedagogically, even though the deepest mathematical understanding is abstract, not imagistic.
The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. Illustrating algebraic concepts graphically would be equally effective pedagogically, even though the deepest mathematical understanding is abstract, not imagistic.
The statements above provide some support for each of the following EXCEPT:
Pictorial understanding is not the final stage of mathematical understanding.
People who are very good at manipulating symbols do not necessarily have any mathematical understanding.
Illustrating geometric concepts graphically is an effective teaching method.
Acquiring the ability to manipulate symbols is part of the process of learning geometry.
There are strategies that can be effectively employed in the teaching both of algebra and of geometry.
Explanations
Cool beans. Apparently graphic illustrations help us learn geometry and some parts of algebra, even though the "deepest mathematical understanding" is abstract instead of image-based. Got it.
We're asked to identify which answer choice does not have support in the passage. It should be pretty clear which of these answer choices comes out of left field.
Let's dive in.
This answer's wrong. We totally have evidence for this: "...the deepest mathematical understanding is abstract, not imagistic."
Bingo. This is the right answer. Where do we have proof of this in the passage? Spoiler: we don't. If you're wanting to push back, pay close attention to the passage's first sentence. Just because it's easier to understand geometry with images and symbols tells us nothing about people who are good at manipulating symbols.
This one's wrong. It's supported in the first sentence: "graphical illustrations...enable students to learn geometry more easily." That provides support for the idea that using such illustrations is effective.
This is wrong, too. We have evidence for this at the end of the first sentence: "...which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation."
This is also wrong. We have support for the geometry bit in the first sentence, and then the second sentence opens with, "Illustrating algebraic concepts graphically would be equally effective pedagogically." Pedagogically just means "as it relates to teaching." So, yeah, we have strategies we can effectively employ for both geometry and algebra—namely, graphical illustrations.
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