Actual and partial vandalism: Metacognitive impairment in mathematics problem-solving

Abstract

Problem-solving is an important aspect in mathematics education, and this cannot occurs optimally when students only have one knowledge and facts about mathematics. Therefore, students need to have the ability to monitor and organize their knowledge using their metacognition problem-solving skills, which plays an important role in determining the real problem and understanding how to achieve a goal or solution. The purpose of this study is to understand students' metacognitive failure in calculus courses. This qualitative research was carried out in May 2021 at the Islamic University of Malang by giving mathematical problems on the Fundamental Theorem of Calculus (FTC). Presently, no research has explored the metacognitive knowledge on the teaching and learning of mathematics at the university level. Data were collected by interviewing students on cases encountered during calculus learning. The data were analyzed using a shortened version of the grounded theory due to time or resource constraints. The convenience sampling method was used to select students due to the lecturers' inability to determine their background and calculus abilities in the first year by using the principle of grounded theory, such as open, axial, and selective coding processes, as well as comparative analysis w. All students enrolled in the calculus course are invited by email, of which three stated that they participated voluntarily. Two questions about the FTC were used to explore their factual, conceptual, and procedural knowledge. The results showed that there were two types of vandalism, namely actual and partial.