Logical Reasoning

PT111 · S4 · Q1 The graphical illustrations mathematics teachers

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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.

Facts

Causal Chain – graphical illustrations provide an intuitive understanding of geometric concepts → makes it easier to manipulate symbols for calculation → students learn geometry more easily.

Similarity – graphical illustrations of algebra would similarly help students learn that.

Contrast – The deepest math understanding is abstract, not pictorial / graphical / illustrative.

Evaluate / Goal

We need to eliminate four supportable inferences. The correct answer will either have no support or opposite support. Since there are going to be four inferences in the answers, I wouldn't bother trying to guess where this is going.

1.

The statements above provide some support for each of the following EXCEPT:

  1. Pictorial understanding is not the

    Supportable

    We know the deepest stage of math understanding is abstract, and in the context of learning, deepest = last stage. So pictorial/imagistic understanding can't be the final stage, because we know the final stage is abstract.

    11% picked this

  2. Correct

    People who are very good

    Why this is right

    Do we talk about people who are “very good” at manipulating symbols? No, we say an intuitive understanding makes it easier to manipulate symbols, but nothing about people who are very good at it. Do we talk about anyone who has no mathematical understanding? No. So we have no support for the idea that “some people who are very good at manipulating symbols do not have any mathematical understanding.

    Skill tested: Most Supported · how this choice captures the argument's function is the move to repeat next time.

    74% picked this

  3. Illustrating geometric concepts graphically is

    Supportable

    We're told that illustrating geometry “enables students to learn geometry more easily”, so that counts as an effective teaching method.

    3% picked this

  4. Acquiring the ability to manipulate

    Supportable

    This reinforces what we know from our Causal Chain. Intuit Und. ? easier to manip symbols ? easier to learn geometry If manipulating symbols were not part of the process of learning geometry, then the first sentence wouldn't make sense. Illustrations make learning geometry easier by providing an intuitive understanding and making it easier to manipulate symbols. It'd be like if we said “Quoting Shakespeare during my job interview made me more likely to be hired, because it showed I was well-read, which made it seem like I was smart.” That implies that “seeming smart” is one of the things the job interviewer would consider a positive.

    8% picked this

  5. There are strategies that can

    Supportable

    “There are strategies” sounds plural like “Some strategies are effective”, but they both mean “there is at least one”. We know that there is at least one effective strategy that would work in both algebra and geometry (from the last sentence): illustrating concepts.

    4% picked this

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