The strategies used in solving problems can be influenced by cognitive style. This research is a qualitative descriptive study. The purpose of this study was to describe the mathematical critical thinking skills of junior high school students based on the cognitive style of Dependent Field and cognitive style Field Independent in solving SPLDV problems. The subject of this study consisted of 1 student who had the field-dependent cognitive style and 1 student who had the field-independent cognitive style chosen by purposive sampling. Data collection techniques were carried out by administering the cognitive style test of the Embedded Figure Test Group, mathematical problem-solving tests, interview guidelines, and documentation. Data were analyzed based on FRISCO critical thinking category indicators (Focus, Reason, Inference, Situation, Clarity, and Overview) in each step of problem-solving, namely understanding problems, arranging plans, implementing plans, and checking again. Data analysis is done by reducing data, presenting data, and drawing conclusions. The results showed that students who had the cognitive style of field-dependent and students who had the cognitive style FI had good critical thinking skills in each step of problem-solving according to Polya.
This study aims to explore the decision-making process of novice and experienced teachers in designing mathematics problems. Data collection of decision-making process is done by interview based on the results of observations of problems designed by the teacher and the framework that includes the stage of generating ideas, clarifying ideas and assessing the reasonableness of ideas in creating mathematics problems. The findings show that in generating ideas, novice teachers are still less creative than experienced teachers. In clarifying ideas, experienced teachers always associate problem with real contexts close to students, while novice teachers create problems based on contexts that are still less associated to students’ real life. When assessing the reasonableness of ideas, novice and experienced teachers alike have the confidence that the problems are designed according to students’ abilities in which experienced teachers claimed that the problems also supported by students experiences.
Research on cognitive obstacles related to fraction sense in preservice mathematics teachers is significant, because their success depends on their skills. The acquisition of fraction sense is a complicated problem requiring a strategy to solve it. This study presents cognitive obstacles with fraction sense tests in preservice who will teach in secondary schools. It focuses on the following categories of cognitive obstacles: epistemological (language representation, tendency to generalise and rely on intuition) and didactic (less meaningful learning, and strategy). This paper takes a qualitative descriptive approach to examine 20 preservice mathematics teachers. The preservice teachers who encountered cognitive obstacles related to fraction sense testing were then grouped based on the similarity of their answers, and seven of them were selected to be interviewed. The research findings showed that five preservice teachers had overlapping obstacles: language representation and tendency to generalise; tendency to generalise and less meaningful learning; language representation, tendency to rely on intuition and trial and error strategy in; language representation and trial and error; and language representation and tendency to rely on intuition.
High order thinking skills are important for prospective mathematics teachers. This study aims to describe whether High Order Thinking Skills (HOTS) can appear when prospective teachers solve controversial math problems. This research has been conducted using descriptive qualitative research. The instruments that have been used are controversial math test questions and interviews. The research subjects used were 150 prospective mathematics teachers, and three people who experienced controversy were taken to find out their HOTS. The results showed that from the three subjects, information was obtained that analysis and evaluation had emerged when solving controversial problems, but only one subject appeared for creating. Suggestions for the next researcher is to combine critical thinking and HOTS to bring up aspects of creating.
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