Constructive Habituation as an Educational Approach to Process-Object Reification in Mathematics

• Main Author: Peterson, Alonzo F.
• Other Authors: James Wandersee
• Format: Others
• Language: en
• Published: LSU 2004
• Subjects: Curriculum & Instruction
• Online Access: http://etd.lsu.edu/docs/available/etd-11102004-120902/

Sfard and Thompson (1994) state that what matters most is that educators develop ways of thinking, teaching, and learning mathematics. This study introduced constructive habituation, a new strategy developed to aid both students and teachers in the thinking, teaching, and learning of mathematics. Constructive habituation attempts to unite constructivist teaching methods aimed at supporting students conceptual understanding of content and habituationist teaching method aimed at establishing routine responses to routine tasks. This study is exploratory in nature, designed to investigate if constructive habituation is a more effective means than a traditional teaching method in helping students reach process-object reification as evidenced by higher levels of student achievement. The study primarily addressed introductory function concepts and symmetry and transformations of functions. The subjects were university students enrolled in a precalculus I course. The results indicated that constructive habituation was not a more effective means in helping students reach process-object reification than a traditional teaching method. No significant differences were found for any of the variables examined. However, some promising practical results were revealed. The students taught using the experimental method averaged more than nine points higher than the students taught using a more traditional teaching method on an examination that evaluated their understandings of the relationship between changes made to the graph of a function and changes made to its formula. Explanations on why constructive habituation may not have reached its intended goal are given. A discussion is presented of the developmental stage at which constructive habituation may become an effective pedagogical method. Study also includes a brief history of the major pedagogical movements over the last half century and the psychological perspectives that influenced each.