This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research subjects were 25 students from the

The aims of this research is to explore students’ literation abilities descriptively and teacher’s response in Math instruction of lesson study for learning community based realistic mathematics education. Literation ability is the ability of the individual to form, use, and interpret mathematics in various contexts. Realistic mathematics education aims to present the real world context to students. The research subjects were 29 seventh grade students of MTs Ma’arif Ambulu. The descriptive approach of qualitative method becomes a choice to understand literation ability and teachers’ response. Data collection was done by observation, PISA test questions, student and teacher interviews, and documentation. Data analysis was using the theory of induction and reduction. The results of the research showed that the students were positively responding to this approach. The ratios of mathematical literacy ability based on the total students respectively were 44.83% on level 4 and 31.03% on level 5, and 24.14% on level 3. The teacher’s response showed that this approach could change the atmosphere to be more active between the teacher and the students as well as the students with their fellow. The teacher could optimize his role; recognize his weakness through reflection with the team so that he had the opportunity to prepare the next strategy to improve quality.

This research aimed to analyze the students’ metacognition through jumping task based on lesson study for the learning community. This research is qualitative descriptive research. Data collection was done by observation, tests, interviews, think aloud and documentation. The test was given to students when an open class in class VIII of MTs Miftahul Hidayah. From the test results, students were grouped into three based on their level of ability. Two students were selected from each group to be interviewed and deepened through thinking aloud technique. Two students were selected from each group to be interviewed and deepened through thinking aloud technique. Data analysis is in the form of data induction and reduction theory. The results showed that students who had good metacognitive knowledge skills became effective and efficient when they were applying metacognitive control skills. Hence, the students who had poor metacognitive knowledge skills, they experienced difficulties when they were applying metacognitive control skills. The contribution of jumping tasks based on lesson study for learning community is very helpful in enhancing students’ metacognition abilities and skills to individually, in groups and classically.

This research aims to analyze students' metacognition in learning mathematical problem solving based on Lesson Study for Learning Community (LSLC) if reviewed from reflective and impulsive cognitive styles. The research method employed in this research is descriptive qualitative. The data collection is done by observation, tests, interviews, think aloud and documentation. The test is given to 30 students when an open class in class VII of MTs Miftahul Hidayah. Based on the test results, students are grouped into two in reviewed from reflective and impulsive cognitive styles. Three students were selected from each group to be interviewed and deepened through a think-aloud technique. The form of data analysis is classified into induction and reduction theory. The results of this research indicates that 18 students (60%) have reflective cognitive styles and 12 students (40%) have impulsive cognitive styles. Reflective cognitive style students, the scores obtained are better by using a relatively long time and can do aspects of metacognition well. While the scores obtained by impulsive cognitive style students are lower with the use of the time that is relatively faster and unable to perform aspects of metacognition well.

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