Pre-service teacher’s mathematical knowledge for teaching in problem-based learning

Mathematical Knowledge for Teaching (MKT), comprising Mathematics Content Knowledge (MCK) and Mathematics Pedagogy Content Knowledge (MPCK), is essential for pre-service teachers. However, numerous studies have shown that pre-service teachers are weak in content and difficult to plan to teach. Therefore, a shifting effort dealing with the learning activities within the teacher training program from a teacher-centered to student-centered approach should be made. One learning model succeeding in the student-centered approach is Problem-Based Learning (PBL). Studies on PBL as an effort to improve the MCK and MPCK of pre-service teachers have never been done before. There were two models of PBL applied in this experimental study: PBL with authentic problems (PBL1) and PBL with authentic problems and teaching practices (PBL2). The aspects of MCK studied are knowing, applying, and reasoning. While the aspects of MPCK are creating representation for the explanation, understanding mathematical structures, and anticipating students' thinking. The results of the study showed that there were significant differences between MCK and MPCK achievements in PBL1, PBL2, and conventional learning classes conventional. PBL1 and PBL2 classes were considered superiors since the pre-service teachers predominantly control the learning activities and were active in finding solutions. Hence, there were differences in the effect of the learning models on the aspects of MCK and MPCK.