C & I 330
Oct. 9, 2001
Where Have All the “Isms” Gone?
“Isms” abound in educational literature, and yet seldom are they clearly defined.
Although defining them can be problematic, it is important that readers gain some notion
of their basic tenets. For this reason, I have attempted to categorize them for the general
purpose of clarification, remaining fully aware that this method is reductionistic and
encourages dualistic modes of thinking. It must be noted, however, that in reality, few
philosophies remain stringently subdivided and categorized.
Perennialism – This is an educational philosophy whose followers believe in a fixed truth
that centers on a belief in God. It considers truth to be found through reasoning and
revelation, and that goodness is the product of rational thinking.
Idealism – This is an educational philosophy whose followers believe in the idea of
refined wisdom. It is based on the view that reality is found within an individual’s mind,
and that truth is the consistency of ideas.
Realism – This is an educational philosophy whose followers hold the view that reality is
what we observe. Its proponents believe that truth is what is sensed and observed by the
Experimentalism – This is an educational philosophy whose followers hold the belief that
things are always changing. It is based on the view that individuals experience reality
through what they experience. Its proponents believe that truth is what works right now.
Existentialism – This is an educational philosophy whose proponents believe that the
individual personally interprets the world, whereby, defining truth, reality, and goodness.
Logicism – This is a mathematical philosophy that centers on the need for logical
theorems. It states that mathematical theorems of math must be developed as theorems of
logic. (Gottfried Wilhelm Leibnez 1666).
Intuitionism – This is a mathematical philosophy that was built on the intuition of natural
numbers and insists on constructive methods. (L.E.J. Brouwer 1908).
Formalism – This is a mathematical philosophy that in concerned with formal symbolic
systems devoid of concrete content. (David Hilbert 1899).
Divisions of Mathematical Motivation
Pure Mathematicians – These are specialists who have become interested in math for its
Applied Mathematicians – These are specialists who have become interested in math for
its practical uses.
Philosophical World Views
Platonic View – A belief that that we find knowledge that is already present in an
immutable eternal reality.
Rationalism – An offshoot of the Platonic view that believes that it is possible to
gain impressions of reality through the intellect.
Empericism – An offshoot of the Platonic view that believes that it is possible to
gain impressions of reality through the senses.
Aristitilian View – A belief that we create knowledge through deductive logic and action.
Absolutism – This is a philosophy that states that knowledge is right or wrong, certain,
and exact. It holds that knowledge is gained through the use of facts and fixed methods.
Relativism – This is a philosophy that states that knowledge is related to the mind and
that knowledge can change depending on circumstances and conditions.
Fallibilism – This is a philosophy that states that knowledge is fallible and eternally open
to revision. (Lakatos)
Positivism – This is a philosophy that states that knowledge is scientific. This belief
excluded the possibility for metaphysical and theological influences.
Behaviorism – This theory holds to the idea that learning occurs as a result of responses
Cognitivism – This theory views learning as involving the acquisition or reorganization of
the cognitive structures through which humans process and store information.
Constructivism – This theory states that learning occurs when knowledge is connected to
a learners prior experiences, mental structures, and beliefs.
Symbolism – The action of representing information through the use of symbols. –
Diophantus of Alexandrea was probably the first to use abbreviations. Until his time all
mathematical problems and solutions were written in pure prose.
Reductionism – The action of reducing the whole to its component parts, whereby,
ignoring the relationship between the two.
Although I realize that this is a very simplistic structure to an exceptionally
complex area of study, this process has help me to construct my own understanding of
key ideas and build a framework by which to attach future ideas and concepts. Knowing
each individually will more effectively allow me to grasp the complexity of the overlaps
that naturally occur.