Capturing students’ mathematical representation in Ill-well-structured problem solving

Multiple mathematical representations are one aspect that determines the success of solving mathematical problems. However, not all students can use multiple representations appropriately. This research aims to capture what types of mathematical representations are raised by students in solving two types of problems: well-structured and ill-structured. One hundred thirty-two high school students in Kediri participated in this exploratory study using a qualitative methodology. Based on the completeness of the steps for solving difficulties and being communicative, two subjects were chosen from among the participants. In-depth interviews were also done to investigate mathematical representations when answering social arithmetic issues in the form of ill-structured and well-structured problems. The triangulation approach was used to analysed the data. Based on data analysis, the researcher discovered that subjects prefer to solve well-structured problems with verbal-verbal representations and used visual-verbal representation to solve ill-structured problems. Students count, detect, correct, and verify their answers using verbal representations, but they use visual representations to discover and remedy errors. When students solve ill-structured problems, the researcher observed a translation from one type of representation to two kinds of representation. This shows a non-constant translation, which might be investigated further in future research.