Review of “Guidelines for Quantitative Reasoning”

W. D. Phillips

February 2005

 

 

Quantitative Reasoning Outcomes

• Outcomes themselves are reasonably clear
• Degree of understanding and ability to be achieved is not specified
• Could be achieved at a cursory level by a single, specifically designed course
• Could be achieved more deeply by components of several courses

 

Quantitative Reasoning and Mathematics

• What do the phrases “courses in mathematics” and “traditional math fare” mean? These phrases bring forth associations to my mind, but more specificity would put me on firmer ground in what follows.
• A quantitative reasoning course is just that — a course that focuses on making decisions and evaluating claims through quantification (measurement) and manipulation of quantities.

 

Quantitative Reasoning Outside of Mathematics

• This section does not make much sense to me
• Exactly what is the “traditional approach?” Derivations, proofs, and abstract problems?
• What exactly is a “math topic?” Does this refer to approaches or techniques (calculus, linear algebra, geometry, and the like)?
• The last sentence of the second paragraph is right on target

 

The Level of Mathematics

• “Rigor” is a term that has become vague and imbued with surplus meaning
• I doubt whether the level of mathematics per se is of much importance. What matters is the capabilities of the person who has learned the techniques.

 

The Use of Technology

• I agree with the message, but not the tone, of this section

 

Creating a Quantitative Reasoning Course

• Why is it that “a quantitative reasoning course requires breadth?”
• Does “breadth” mean many examples and applications within a topic area?
• Does “breadth” mean a survey course? (I doubt it; survey courses are currently out of favor.)
• The last paragraph of the document suggests to me that by “breadth” the authors may mean “amount,” but this is a guess
• The examples are reasonably clear and appropriately capture aspects of what should be emphasized. Every course—quantitative or otherwise—should strive to instill understanding, not merely teach rote application of rules, methods, algorithms, or checklists.
• What is meant by “modes of mathematics?” Should this be “models of mathematics?”
• The last paragraph of this section is very important. Almost every variety of human inquiry benefits from measurement and manipulation of quantities. Students can and should acquire numerical skill and understanding in all of their academic endeavors. Acquiring proficiencies that are the hallmark of educated people — effective thinking, writing, speaking, evaluating, deciding, and creating — as an integral part of the process of learning discipline-specific facts and theories, is how education ought to proceed.

 

Justifying Quantitative Reasoning

• The suggestion of including typical examples of assignments involving quantitative manipulation is a good one.
• Unfortunately, course titles frequently are not very informative, and sometimes they are downright misleading. I doubt whether titling will shed any light on the degree of quantitative focus of a course.

 

 

 

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

Addendum

 

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.