2013 Conference Proceedings - University of Nevada, Las Vegas

“experiences that are charged with mathematical emotion are not some kind of extraneousdistraction or curious side effect, but they are at the very core of involvement with mathematics”(p. 166). Appropriate emotional conflict can positively affect psychological and learningfunctions; emotions are not always hostile factors to be eradicated from the learning process.Allowing both positive and negative emotions in problem solving is not necessarily demeaningor detrimental (Allen & Carifio, 2007). In fact, Thompson and Thompson (1989) claim thatfrustration is required in developing an appreciation for problem solving. Belavkin (2001) foundthat positive emotions during problem solving were accompanied by increased motivation andconfidence.Despite a common belief that emotion during problem solving can be disruptive, distracting,and diminish performance, emotions experienced during problem solving have been found toenergize, organize, focus, and improve performance (Allen & Carifio, 2007). A challengingproblem coupled with success in finding a solution can inject positive feelings into schemas interms of success, rewards, satisfaction and competence (Allen & Carifio, 1995).MethodologySetting and ParticipantsThe Tower of Hanoi task was purposefully planned for the first week of class and wasintended to set expectations for the course, including collaborative problem solving,communication and justification. Students worked in table groups with manipulatives to modelthe task, recorded the minimum number of moves on a table. They then worked together toidentify the recursive and explicit formulas for n disks.Students (N = 275) were enrolled in the first of three content courses for elementary andmiddle school preservice teachers at a mid-sized university in the southern U.S. The greatestmajority of students were female; approximately half were White and half were Hispanic; 80%were seeking elementary certification.Instruments and AnalysesStudents wrote three-page reflective journals describing their engagement with the Tower ofHanoi task -- how they thought about it, what they tried, methods they used, and what they foundin the end. These qualitative data were collected over nine semesters from 2004-2011. Theresearchers 1) read each journal and identified emotional words or phrases, 2) grouped similarProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 18