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    Review of “Guidelines for Quantitative Reasoning”

    W. D. Phillips

    February 2005



    Quantitative Reasoning Outcomes


    Quantitative Reasoning and Mathematics


    Quantitative Reasoning Outside of Mathematics


    The Level of Mathematics


    The Use of Technology


    Creating a Quantitative Reasoning Course


    Justifying Quantitative Reasoning




    n.b.: ‘effect’ should be changed to ‘affect’ throughout



    I have talked about skills characteristic of an educated person. Permit me to list a few aspects of the quantitative knowledge I think everyone should have:

    ·        Understand and calculate simple probabilities and odds

    ·        Understand that a joint probability cannot be greater than the probability of either event alone [the conjunction fallacy]

    ·        Have an understanding of the importance of base rates when evaluating event likelihoods

    ·        Understand that random events tend to exhibit short-run patterns that are often mistaken for trends; these “trends” disappear in the long run

    ·        Understand why large samples are more trustworthy than small ones, other things equal

    ·        Be able to use matrices (tables) to organize information pertinent to a decision

    ·        Have a sense of the costs associated with an incorrect decision, and the costs associated with collecting information (data) to reduce the probability of an incorrect decision

    ·        Be able to create and to interpret graphical displays of quantitative information, and be able to avoid being misled by improperly constructed graphical displays

    ·        Understand the difference between point and interval estimates, and know why it is important to know the precision and likely error range of a quantitative statement

    ·        Know what various trend patterns (linear, negatively accelerated, positively accelerated, etc) imply about extrapolation and extension of the trends

    ·        Understand that trend patterns can and do change

    ·        Understand that operational definitions of quantities have a profound bearing on what can be concluded about the underlying constructs

    ·        Understand the difference between causal and correlation relationships

    My training is in applied statistics and cognitive psychology, so the skills that come to my mind tend to be drawn from these areas. Many other important aspects of quantitative knowledge and reasoning could be included as well. Still, because of the nature of quantitative information to which we are exposed every day, solid understanding of probability and statistical concepts (not necessarily methods) is necessary for everyone.

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