For years, prescriptive, teacher-oriented, objectivist classrooms have endured as a mainstay of the American educational enterprise. Research in the past two decades has created a climatic change in education. Piagetian Constructism, the construction of disseminated knowledge into a learner, has overtaken our laboratories and schools. To this degree, the role of the learner and the function of the teacher have been researched to further explain the differences between the traditional versus the constructivist approaches in mathematics instruction.
             Tradition maintained that knowledge should be transferred to inert, passive students from shaping, assessing teachers. Thus, knowledge was formed by the teacher in the manner of the teacher within the students' minds. From point A to point B to point C, a student could chart a discourse based on information given. Constructivist theories support the theory that knowledge moves from teacher to learner. From there, constructivism differs from previous methods of learning, such as the traditional objectivism. Knowledge, per constructivism, flows along non-linear lines. Thus, learners shall not go from one point to another, picking up exacting bits of data to be regurgitated with ease and practice later down the line. Research has proven that learners, locks, do not all utilize the same keys. Instead, "knowledge and reality. . . [has] many keys." (Bodner, Klobuchar, & Geelan, 1) The higher order thinking skills, the problem solving behaviors, which students so desperately need cannot be memorized, as traditionalists have taught. Rather these behaviors, i.e. performances, can only be measured by outcomes from problem-solving contexts and situations. The particulars based, bottom-up approach to learning that is constructivism teach inductive reasoning, based on Gladys Giebler's findings. Students, who might have difficulty absorbing and applying concepts in ...