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This paper reports a two-year research project studying Indonesian primary and secondary teachers' mathematics-related beliefs (MrB) and mathematical problem-solving knowledge for teaching (MPSKT). In the first year, a quantitative study involving 80 primary teachers, 70 lower secondary school, and 55 upper secondary schools from four districts in East Java province, Indonesia was carried out to examine whether there is a difference between the MrB and the MPSKT among them. In the second year, a multiple case study involving ten primary teachers and 13 lower secondary teachers was conducted to understand their MrB and MPSKT through some particular issues related to three domains of MrB: nature of mathematics, mathematics teaching, mathematics learning. Results indicate that there is no significant difference of MrB between primary and secondary teachers, while there is a significant difference between the MPSKT of primary teachers and secondary teacher. Findings also suggest that inconsistencies not only occur between the three domains of MrB but also occurs between particular issues discussed within one domain. Also, this study highlights that teacher beliefs about nature of mathematics were mainly influenced by teachers' experience when learning mathematics during their schooling experience while teacher beliefs about teaching and learning were mainly influenced by the demand of current reform of mathematics curriculum.

Combinatorial thinking is a way of thinking in solving combinatory problems. Combinatory problems are one of the difficult problems for students to solve. This study aims to analyses students’ combinatorial thinking processes in solving problems. Given two combinatory problems that consist of problems with multiplication rule and combination. The Problems were given to two 11th grade senior-high school students. The results obtained were that there was a tendency for male Participants to do the two different ways which are direct counting and using diagram. The female participants did the work with one way which is direct counting. On more complex issues, namely about combination, students' thinking models go through stages of set of outcomes. From this research, it is expected that combinatory material learning is emphasized on the discovery of formulas by students themselves inductively, especially deductively. So that in this case the students interpret the combinatory formula more.

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