ABSTRACT
Educational research must serve a variety of purposes. One of these purposes is to invent, develop, and test novel ways of teaching mathematics. Until quite recently, research frequently was confined to out-of-school laboratory settings (Kilpatrick, 1992). This allowed theories to be tested in a fairly controlled environment. However, results and findings from these types of studies have been criticized for being of limited applicability to classroom instruction (Romberg & T. P. Carpenter, 1986). The basis for this criticism was that the instructional methods used in these experiments were not subjected to the constraints of schooling, and, thus, teachers were skeptical that they would prove sustainable in everyday situations.
