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).