Abstract:

State and National standards require that we “apply and adapt a variety of appropriate strategies” when engaging in mathematical problem solving (NCTM, 2000). According to Guilford (1967), divergent thinking is the mental process by which we draw from many ideas while searching for different solutions to the same problem or set of situations. The researchers examine in-service teachers’ divergent thinking as they attempt to solve problems in a hybrid geometry course. The course is designed to encourage “out-of-the-box” thinking during small group and individual problem solving. Students explore problems and seek solutions from multiple perspectives. The participants are grade 6 - 12 mathematics teachers enrolled in a graduate level, hybrid geometry course as a part of a Masters program. Data collection includes online discussion board entries, observations of in-class student discussions with the teacher/classmates, analysis of written solutions to given problems, students’ reflections on the given problems, and end of course interviews. Preliminary results indicate different levels of divergent thinking when teachers are prompted to do so by course instructions. The use of technologies such as MS Excel, dynamic geometry software, and graphing calculators serve as key elements in sparking divergent thinking.

Keywords:

Hybrid Courses, Problem Solving, Teacher Education-Inservice/Professional Development, Geometry, Technology.