Creative Problem Solving with Tangrams

With the world changing so rapidly, students need to by educated differently than in the past. Among the changes indicated by numerous research studies and national commissions is the realization that students need to increase their problem solving skills in mathematics. At the root of the current challenges in mathematics education are the issues of how children learn. Cognitive theories suggest that children learn best by building upon their initial experiences and becoming actively involved in constructing their own knowledge. One way to accommodate students\u27 natural tendencies to learn through experience is to provide learning activities to enhance problem solving skills in geometry. Geometry is a field of mathematics that helps students relate mathematics in a meaningful way to the real world. There are many geometric manipulative materials, among them tangrams, an ancient Chinese puzzle, which lends itself to exploration of spatial reasoning, spatial relationships, and geometric problem solving. For the purposed of this thesis, tangrams were employed in three third grade classrooms. Activities were designed to involve students in a gradual learning process where exploration, cooperative group work, journal writing, homework assignments, and problem solving all served to build significant experiences for the students and teachers alike. Critical and creative thinking skills were taught as students solved and created puzzles of increasing difficulty and related them to various aspects of mathematical thinking including geometrical interpretations of arithmetical computations, fractional relationships, symmetry and other properties of shapes. Chapters I and II of this thesis present the rationale for this project based on current theories and findings in mathematics education and critical and creative thinking. Chapter III describes the activities in detail, provides teaching commentary on the lessons, and suggests improvements on all aspects of the implementation for teachers who may wish to embark on a similar project. Chapter IV presents and analyzes comments taken from the students\u27 journals and the feed-back questionnaire given to the two other teachers. The consensus was that tangrams enabled these third graders to become more active and confident thinkers, creators, solution finders, and problem solvers