This study aims to analyze students’ creative thinking skills in answering the problem-solving questions. This study employs qualitative design, involving 110 fifth graders in Malang Municipality and Regency as the subjects. The obtained data were analyzed using the descriptive-explorative approach. The findings reveal that the high-achievers in Mathematics showed good skills in the aspects of fluency and flexibility, but were still struggling in the novelty aspect.  The average-achievers showed good skills in flexibility aspects but were lacking in the fluency and novelty aspects. They showed an understanding of Mathematics problems but found it difficult to decide the solving strategies, and thus their answers were lacking in structure and less systematic. When solving a problem, the calculation made seemed rushing, was less careful, and frequented with trial and error strategy. The low-achievers showed difficulties in understanding the problems. Their answers were not systematic, not well-structured, and not detailed. This indicates that the low-achievers had not shown creative thinking skills in fluency, flexibility, and novelty aspects.

This research aimed at analyzing the influence of ‘Process Oriented Guided Inquiry Learning’ model assisted by realia media, in which it was to improve the scientific literacy and critical thinking skill of primary school students, especially for the material of energy. This quasi-experiment research used single factor independent groups design. The research sample of this research were fourth grade students of SD Inpres Oeba 2 Kupang City, East Nusa Tenggara Province, of which students were in the academic year of 2019/2020. The technique of sample collection was carried out purposive sampling for 2 classes. The IVA class was used as the experimental class (POGIL model assisted by the realia media), in which it consisted of 30 students and the IVB class was used as the control class (expository learning) that consisted of 28 students. The learning was carried out in four meetings. The data of scientific literacy and the results test of critical thinking were collected by means of objective test on the energy material. Multivariate Analysis of Variance (MANOVA) was used to analyze the data using significance level of 0.05. The results indicate that (1) There is a significant difference between the students’ scientific literacy who gain the POGIL learning assisted by the realia media and the students’ scientific literacy who get the expository learning; and (2) There is a significant difference between the critical thinking of students who get POGIL learning assisted by realia media and the students who get the expository learning. It can be concluded that there is a significant difference between the scientific literacy and the students’ critical thinking taught by the POGIL learning that assisted by realia media to the students who use expository learning. Since there is a significant difference, it means that the POGIL learning assisted by realia media has an influence on the students' scientific literacy and critical thinking.

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 Department of Mathematics Education, Ibrahimy University. The test was given to collect data related to mathematical thinking processes expected by prospective teachers to students. Collected data including observations, tests, and interviews were tested in the aspect of their validity by triangulation. The qualitative descriptive was used to analyze the data. The results indicated that: (1) The average GPA (Grade Point Average) of the high, medium, and low group prospective teachers' were 93.25; 89.89; and 83.63 with a standard deviation of 1.754 each; 1.054; and 5.370, respectively (2) The prospective teachers expected that the students' mathematical thinking processes were able to carry out all of four mathematical thinking processes based on Mason Theory; (3) The prospective teachers expected that students were able to use Mason Theory on every stage of the Polya model problem solving; and (4) The expectation of prospective teachers were specializing (89%), generalizing (75%), conjecturing (62%), and convincing (59%). The results suggest for following up in a teachers or lecturer’s meeting in order to find out the expectations of their students' mathematical thinking processes, both in mathematics or other disciplines.

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.