*Benchmarks for Science Literacy: Chapter *15* ***THE RESEARCH BASE**

**2 THE NATURE OF MATHEMATICS**

** 2C) MATHEMATICAL INQUIRY**

Typical student beliefs about mathematical inquiry include the following: There is only
one correct way to solve any mathematics problem; mathematics problems have only one
correct answer; mathematics is done by individuals in isolation; mathematical problems can
be solved quickly or not at all; mathematical problems and their solutions do not have to
make sense; and that formal proof is irrelevant to processes of discovery and invention
(Schoenfeld, 1985, 1989a, 1989b). These beliefs limit
students' mathematical behavior (Schoenfeld, 1985). Further research is needed to assess when and how students
can understand that mathematical inquiry is a cycle in which ideas are represented
abstractly, the abstractions are manipulated, and the results are tested against the
original ideas. We must also learn at what age students can begin to represent something
by a symbol or expression, and what standards students use to judge when solutions to
mathematical problems are useful or adequate.