Enhancing creative reasoning through mathematical task: the quest for an ideal design

This study aimed to: i) identify the types of completion and ways of completing mathematical tasks carried out by students based on the type of their educational institution (junior high school/SMP and junior Islamic high school/MTs); and ii) explore the tendency of the type of reasoning students use in completing the tasks. This study involved 93 students at grade 8 of prominent SMP and MTs in Sidoarjo Regency, East Java, Indonesia. Variety of ways and solutions to mathematical tasks and the tendency to type students' reasoning were explored through creative reasoning tests. Interview techniques by telephone were implemented to further explore the types of student reasoning: local creative reasoning (LCR) or global creative reasoning (GCR). The results showed that in comparison to MTs students, SMP students have more varied answers and ways to solve mathematical tasks. However, in certain cases MTs students show some unique answers. The type of creative reasoning that students tend to use is of the LCR. These findings indicate the importance for mathematics teachers to design mathematics tasks that develop GCR-type creative reasoning. Examples and exercises in mathematics textbooks should also be directed at developing this type of creative reasoning.