نقش وظایف راه حل های متعدد در توسعه دانش و خلاقیت در هندسه

This paper describes changes in students’ geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that employed MSTs while the rest learned without any special intervention in the course of one school year. This longitudinal study compares the development of knowledge and creativity between the experimental and control groups as reflected in students’ written tests. Geometry knowledge was measured by the correctness and connectedness of the solutions presented. The criteria for creativity were: fluency, flexibility, and originality. The findings show that students’ connectedness as well as their fluency and flexibility benefited from implementation of MSTs. The study supports the idea that originality is a more internal characteristic than fluency and flexibility, and therefore more related with creativity and less dynamic. Nevertheless, the MSTs approach provides greater opportunity for potentially creative students to present their creative products than conventional learning environment. Cluster analysis of the experimental group identified three clusters that correspond to three levels of student performance, according to the five measured criteria in pre- and post-tests, and showed that, with the exception of originality, performance in all three clusters generally improved on the various criteria.

Nir is a 10th grade student, a high achiever in mathematics, who volunteered to be interviewed at the beginning of the study. He loves mathematics and enjoys solving problems. According to his teacher, “he is smart and curious.” During the interview Nir was asked to solve two geometry problems, each in as many ways as he can. This requirement was new to him because usually he is asked to solve problems for which one solution is sufficient.