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.