Mathematics and Educational Administration

Publication Date01 February 1972
Mathematics and Educational Administration
This paper is devoted to the topic of
mathematics might be more
efficiently used in educational administration. The position taken here
is that mathematics is a branch of philosophy whose subject matter
is a set of abstract entities and identified operational rules. It is a
vocabulary of symbols that can be used to label objects and, more
importantly, a set of grammatical rules for using the vocabulary. The
paper begins with a review of some recent developments reported in
the social science literature on the uses of mathematics in political
science, sociology and economics, and ends with some illustrations of
how these developments could lead to similar applications in both
the practice and theory domains of educational administration.
Educational administration is an applied science. As a field of
study, it has its traditional roots in the social sciences. While the
utility of mathematical thinking is neither new nor a topic of
diminishing interest to theorists and empirical researchers within
the social sciences, discussions of its utility or application in the
practice and theory domains of educational administration are
seldom explored.
Evidence of the utility of mathematics in the social sciences can
be found in the early metaphysics of Aristotle and Plato,1 or it can
be seen in the recent (1971) descriptions of major advances in the
social sciences since 1900.2 In this latter case social scientists have
observed that quantitative problems or findings (or both) charac-
terize two-thirds of all advances, and five-sixths of those were made
after 1930.
My purpose here will be review some of the more recent develop-
ments reported in the social science literature that are based on
exploring the utility of mathematics and then to specify how some
DR. JAMES F. McNAMARA is a Research Associate at the Center for the
Advanced Study of Educational Administration and an Associate Professor
of Public Affairs and Administration in the Lila Acheson Wallace School of
Community Science and Public Affairs at the University of
The author
acknowledges the assistance given by Dr. Sanford Tempkin in the preparation
of this paper.
Mathematics and Administration 165
of these developments might be utilized in the study of educational
administration. No single essay can hope to provide an adequate
discussion of all aspects suggested here. At most, one can only
pick out a few major themes and cite particularly interesting pieces
of evidence.
Before we turn to some of these developments, it seems essential
that some time be allocated to clearing away parts of the underbrush
or misconceptions that have grown up around the term mathematics.
A common misperception is that mathematics always requires the
use of numbers. It is also often heard that mathematics is appro-
priate as a tool only when we have data which is precisely measured.3
Some see mathematics as a scientific discipline dealing with topics
such as algebra, topology, symbolic logic, calculus, or statistics and
probability theory. Others view mathematics as a language.
The position taken here is that mathematics is a branch of
philosophy whose subject matter is a set of abstract entities such as
sets of element, numbers, and identified operational rules. Given this
orientation, mathematics is a vocabulary of symbols that can be used
to label objectives and, more importantly, a set of grammatical
rules for using the vocabulary. Both mathematics and social
science deal with sets of abstract entities. For example, there is the
anthropologist's set of cultural systems, the political scientist's
concept of democratic equality, or the economist's perfectly com-
petitive market. It is precisely the abstract nature of these domains
that makes mathematics potentially a powerful tool in social analysis.
Accordingly, educational administration also deals with sets of
abstract entities, and here also one might examine the utility of
mathematics as a tool. To pursue this line of inquiry, it seems helpful
to begin with some recent evidence on how mathematics has been
utilized within the social sciences, a domain familiar to most
students of educational administration.
To begin a discussion along the lines suggested in the subtitle
above, one needs first to select an appropriate point of entry.
Alternative choices for such a point are several. One could begin by
an examination of the literature on the history of mathematics or,
by still maintaining a historical perspective, constrain his subject to
a particular social science, i.e., the influences of mathematics in
political science or economics. If the focus is to be on measurements
as a means to move toward inductive generalizations, an initial
entry point might be an investigation of the econometrics, psycho-
metrics or sociometrics literature.
An interest in mathematics as a tool in theory construction might
lead one to first consider studies in areas such as learning theory and

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