Commentary on Theories of Mathematics Education

204 B. Dahl
Unified Theory and Truth
Can we reach the truth about learning mathematics? Eisner stated: “Insofar as our
understanding of the world is our own making, what we consider true is . . . the
product of our own making” (1993, p. 54). This is, in my view, a circle argument
since “the social items that are claimed to generate social facts must themselves be
understood to be generated by other social items, and so on ‘ad infinitum”’ (Collin
1997, p. 78). Furthermore it is inconsistent to reject ‘truth’ while replacing it with a
new ‘truth’, namely that the ‘truth’ does not exist. Nozick argues (2001) that he feels
uncomfortable with this kind of quick refutation of relativism; i.e.: that all truth is
relative, in itself is a nonrelative statement. Nozick (2001, p. 16) then defines the
‘relaxed relativism’ as “the relativist granting that some statement is nonrelative,
namely, the statement of the relativist position itself (along with its consequences)”.
He continues: “This makes it look as though relativism about truth is a coherent
position. . . . To say that relativism about truth is a coherent position is not to say
that it is the correct position” (Nozick 2001, pp. 16–17). Nozick also argues that
the ‘weak absolutist’ can hold that some truth are relative (Nozick 2001, pp. 20
& 65). Thus relativism does not undercut itself if we take into consideration its
domain of application. Nozick then introduces the concept of ‘alterability’: “the
relativity of a truth is not the same as its alterability. Even if it is a nonrelative
truth that my pen is on my desk, that is a fact easily changed. Whereas if it is
merely a relative truth that New York City is adjacent to the Atlantic Ocean or
that capitalism outproduces socialism, these are not facts that are changed easily”
(Nozick 2001, p. 23). Following this line of reasoning, I would argue that even if
relativism about truth is a true position, it does not change the fact that there are
ways of working with mathematics that are “unhelpful” (or more helpful) if the
desired “output” of the activities is that the pupils should have learnt certain things.
These facts are not easily changed. Thus, even talking Nozick’s argumentation into
consideration, the truth about how to learn mathematics might still exist. I would
also follow Phillips who argues that truth exists independently of us but we can
never reach it. Objectivity and truth are not synonyms, but through criticism we
can approach truth and the, at any time, most rational theory is therefore the most
objective (1993, p. 61). We can never reach the final truth, but this does not mean
that any theory is as good as any other.
But is the truth then a unified theory or do we have to live with a situation as the
one of the Formalist mathematicians? Hawking writes that “we might be near finding
a complete theory that would describe the universe and everything in it” (1994,
p. 29). This is one view, but it fits with the modern ideal that there is “a ‘grand
narrative’ . . . namely, the ‘enlightenment’ view that reason, in the light of systematically
researched evidence, will provide the solution to the various problems we
are confronted with” (Pring 2000, p. 110). It also relates to Naturalism that has the
assumption “that there is only space-time Reality and that this reality is sufficiently
understandable in terms of scientific methods” (Arbib and Hesse 1986,p.3).
Johnson states that it is disputed if a unified theory can be achieved (1995,p.55).
Furthermore a theory of everything is self-referential since science assumes that human
beings (scientists) are rational beings who through accurate observation and