The qualitative effect of problem-based learning model toward students' mathematical imitative and creative reasoning

Reasoning is one of the abilities needed in solving mathematical problems. Based on Lithner perspective, reasoning divided into imitative reasoning and creative reasoning. There are three indicators for each reasoning, that are plausibility, mathematical foundation, novelty for creative reasoning aspect and imitation for imitative reasoning aspect. The aim of this research is to analyze the qualitative effect of problem-based learning model toward students' mathematical imitative and creative reasoning. In order to do so, we used descriptive qualitative methods by taking eighth-grade students (around thirteen to fourteen years old) in one of the Junior High School in Tasikmalaya. We used the data from a written test, observation and interviews. The results revealed that problem-based learning model suitable for students who have dominantly mathematical creative reasoning abilities. The characteristics of students who have dominantly mathematical imitative reasoning abilities prefer to be told rather than finding out. Based on the results, we conclude that each student has a different learning style according to his abilities.