Transformation of Semiotic Representations and Students' Thinking Processes in Mathematical Problem Solving: A Cognitive Analysis Study of Students in High School

The skill of transforming semiotic representations is so important that the students who do not have this skill are considered weak in utilizing mathematical ideas and relationships studied. Likewise, having good ways of thinking (WoT) is a condition for being a good mathematical problem solver too. Therefore, the aim of this research is to describe students' semiotic representation skills and WoT in solving mathematical problems. To achieve this goal, researchers conducted qualitative research with a case study design through the following three steps: First, after conducting a literature review regarding semiotic representation theory and WoT, the researcher designed questions (problems) that involved aspects of semiotic representation skills of algebraic material and their application. Second, give two test items to 31 class XI students (aged 16–17 years), followed by interviews. Third, the test results are analyzed using a mathematical semiotic representation perspective. The results of the analysis show that in problem 1, students' semiotic representation skills involving simple (less complex) content were stated to be good, and they also had good algebraic invariant WoT. On the contrary, it is stated as less. In problem 2, students' semiotic representation skills are stated to be lacking and have non-referential symbolic WoT. These results conclude that students who have good semiotic representation skills also have good WoT, and vice versa. This indicates that semiotic representation skills and WoT are the keys to success in solving mathematical problems.