Students’ Mathematical Creative Thinking Obstacle and Scaffolding in Solving Derivative Problems

Abstract

The difficulties experienced by students in studying derivative material are difficulties understanding the definition of derivatives and representations of these derivatives. Derivatives are a material that is quite difficult to develop mathematical creative abilities because they have many functions and symbols. This difficulty indicates a barrier to thinking in students. This research is descriptive qualitative research with five research subjects of Tadris Mathematics at the Curup State Islamic Institute. Each student can think creatively mathematically on the indicators of flexibility, fluency, and originality, but the levels are different. The level of mathematical creative thinking ability can depend on the questions or problems and the material being studied. However, one of the indicators of the ability to think creatively mathematically, which is very weak for students, is originality because students seem rigid with what they have obtained from lecturers and books. Students find it difficult to come up with ideas in solving problems. Barriers to thinking creatively mathematically can occur due to several factors, including 1) due to a lack of prior knowledge of students in understanding problems and determining ideas in planning solutions; 2) a lack of strong concepts possessed by students. One way for lecturers to overcome these obstacles is to provide scaffolding. The provision of scaffolding is carried out using Treffinger learning with several stages, namely basic tools, practice with process, and working with real problems. In practice with process stage, students solve problems by using analogical reasoning to develop their mathematical creative thinking abilities. The stages of analogical reasoning used to consist of the stages of recognition, representation, structuring, mapping, applying, and verifying. This study's findings are that two new stages are added to the early stages of analogical reasoning, namely the stages of recognition and representation.