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

**2 THE NATURE OF MATHEMATICS**

Research related to students' beliefs about the nature of mathematics has started to
receive increasing attention. For literature reviews of the available research see McLeod
(1992) and Schoenfeld (1992). Studies of the
National Assessment of Educational Progress have recently included items related to
student beliefs about mathematics as a discipline (Brown et al., 1988; Carpenter et al., 1983; Dossey et al., 1988). In addition, research
on mathematical problem solving has recently included investigations of the beliefs
students hold about the nature of mathematics (Schoenfeld, 1985, 1989a, 1989b, 1992). These studies have
examined students' perceptions of mathematics as rule-oriented versus process-oriented or
as a static versus a dynamic discipline, students' beliefs about the nature of
mathematical problem solving, and students' perceptions about the role of memorization in
learning mathematics. Little emphasis has been given to students' understanding of
mathematics as the study of patterns and relationships, or to the relationships between
mathematics, science, and technology, or to the nature of mathematical inquiry as a
modeling process.

** 2A) PATTERNS AND RELATIONSHIPS**

Preliminary research hints that students have difficulty making connections between
mathematical expressions, sentences, and sequences that share common structural patterns.
They focus instead upon incidental similarities or differences (Ericksen, 1991).