Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students’ failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors’ components such as the experience of field-dependent type students. For this reason, this study was carried out to explore the thinking process of students who fail and investigate the thinking processes of students who succeed in generalizing linear patterns. The results of this study provide an effective learning strategy solution for field-dependent students in generalizing linear patterns. This study employed a qualitative approach with a case study design to junior high school students. The results indicated that students in the field-dependent cognitive style looked at pattern questions represented in the form of geometric images globally without looking at the structure of the image. Two strategies for generalizing linear patterns used by field-dependent students were examined, namely recursive and different strategies.
<span lang="EN-GB">A body of literature has suggested the benefits of flipped classrooms in mathematics learning at university. However, there is still a lack of evidence regarding the benefits in the context of mathematics teacher education programme. This study aimed to examine the effectiveness of a flipped classroom application in a mathematics teacher education programme at a private university in Indonesia. A total of thirty-one pre-service teachers participated in the study. Multiple data collection methods were employed including observation, written journals and tests. The data were then analysed both quantitatively and qualitatively. The findings showed that flipped classroom promotes independent learning, with the type of classroom encouraging students to work together with other peers and improved learning awareness. However, some challenges were highlighted in flipped classroom application such as technical issues, editing recording skills, and it was time consuming. Recommendations are offered in reference with the findings. </span>
Background. Student reasoning in learning mathematics contributes significantly to the achievement of student mathematics learning outcomes. The main objective of this study is to investigate the process of reversible reasoning in students for inverse problems, in the case of Adjie (Ad). The research method used to reveal the reversible reasoning in Adjie's case using descriptive qualitative research methods. Sampling was carried out using purposive sampling technique where the research sample was selected based on reversible reasoning criteria. Retrieval research data uses the results of students' mathematical work, think aloud, interviews, and the components that cause reversible reasoning. The results of our study found that the process begins with an obstacle that causes Ad to be unable to continue the resolution process, resulting in a metacognition process by analyzing the problem again analytically and developing other heuristic strategies. Ad shows a change in perspective where he initially interpreted inverse as the act of swapping independent and dependent variables and switched to interpreting inverse as the opposite of a function process involving analogy and image representation. The contribution of this research provides knowledge that reversible reasoning can occur in understanding and solving mathematical problems in inverse material.
This research aimed to describe the levels of feeling of rightness (FOR) of students. This research used a qualitative method with an explorative type. The subjects of this research were 3 students of 5th grade selected from 77 other students in Indonesia. In uncovering FOR subject of this research, instruments were used in the form of problems about the open-ended polygon perimeter and interview guidelines. The data of this research were the subjects' answers to the problems of polygon perimeter and the results of interviews with subjects related to these answers. The data were analyzed using the FOR subject level indicator rubric. There were three levels of FOR which were the findings in this research, namely low, medium, and high. Low FOR level was indicated by the answers crossed out and the objectives or goal changed. Medium FOR level was indicated by crossed out answers, objectives or goals changed, problems text read repeatedly, indecisive statements about the truth of the answers that have been generated, and doubts in determining the steps to be taken. High FOR level was indicated by answers that were not crossed and goals that were not changed.
This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels of validity and reliability. After learning abilities and levels van Hiele algebra, students were asked to answer two questions descriptions to determine the ability of students in answering the question of algebraic geometry punctuated by interviews. From this study illustrated that students who have achieved level 3 van Hiele able to properly solve problems of algebraic geometry in the content by utilizing the deduction reasoning thinking skills to build the structure geometry in an axiomatic system in solving the problems faced. Teachers play an important role in pushing the speed students through a higher level of thinking through the right exercises. Suggestions for further research can develop on different topics but still within the context of algebraic geometry.
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