A fairly consistent, predictable way of teaching mathematics prevails in classrooms throughout the United States. Memorization of facts as well as the ability to follow rules, execute procedures, and plug in formulas is lauded, and only those students capable of absorbing, accumulating, and regurgitating received items of information in this manner excel in traditional mathematics classrooms (Battista 1994; Brandy 1999; Hiebert 2003). The teacher's role in traditional classrooms is to "provide clear, step-by-step demonstrations of each procedure, restate steps in response to student questions, provide adequate opportunities for students to practice the procedures, and offer specific corrective support when necessary," and the ultimate mathematical authority is the textbook from whence "the answers to all mathematical problems are known and found" (Smith 1996, 390-91).
In direct opposition to traditional mathematics' behaviorist approach, reform-oriented mathematics focuses on a constructivist perspective. While behaviorism emphasizes students' passive absorption of observable behaviors, constructivism asserts that individuals approach a new task with prior knowledge, assimilate new information, and, subsequently, construct their own meaning (Amit and Fried 2002). As children construct their own understanding based on the relationship between prior knowledge, existing ideas, and new experiences, they must be encouraged "to wrestle with new ideas, to work at fitting them into existing networks, and to challenge their own ideas and those of others" so as to subsequently enlarge the framework from which new ideas may be formulated (Battista 1994; Van De Walle 2007, 23). "Once one accepts that the learner must herself [sic] actively explore mathematical concepts in order to build the necessary structures of understanding, it then follows that teaching mathematics must be reconceived as the provision of meaningful problems designed to encourage and facilitate the constructive process" (Schifter and Fosnot 1993, 9).
The National Council of Teachers of Mathematics, as well as other entities promoting mathematics reform, recognizes that the fate of the reform movement lies within the reality that teachers are key figures in effecting change in the ways mathematics is taught and learned in schools (Battista 1994; NCTM 1991). Altering the way educators teach, however, is difficult, and the more ambitious and drastic the instructional program, the more significant and substantial the change (Battista 1994; Hiebert 2003). Subsequently, if the chasm between the arts and the sciences, which was first addressed and enunciated by Snow in 1959, is to be bridged by reform-oriented approaches such as mathematics literature integration, one must delve the many fissures within the subculture of mathematics; the gulf between educators who actively promote change and those who accept and maintain the status quo within their mathematics classrooms, the gulf between traditional and reformative mathematics, and the gulf between approaches and beliefs relevant to mathematics literature integration. Only after these openings and cracks are recognized and addressed, can we stand on the edge of the bicultural abyss and, without fear of falling in, formulate a means of bridging the chasm between the arts and sciences.
The History of Mathematics Reform
Most reforms begin due to an element of dissatisfaction. Relevant to mathematics reform, the dissatisfaction grew from students leaving school with only minimal mathematical knowledge and skills, a dramatic decrease in the number of individuals desiring to pursue mathematically oriented careers, and, perhaps most relevant in today's high stakes accountability culture, students' poor performances on standardized tests (Amit and Fried 2002). However, these elements do not represent the broad realm of reform, nor do they allow for the representation of mathematics reform as a phenomenon involving "the whole complex of students, teachers, researchers, parents, and politicians" (Amit and Fried 2002, 355). …