Students' misconceptions in algebraic concepts: A four-tier diagnostic test approach

Misconceptions in algebraic thinking refer to misunderstandings in grasping and manipulating abstract concepts such as variables and mathematical relations. These misconceptions are often consistently applied by students in certain situations even though they deviate from the correct concept. This qualitative study used a case study approach focused on analyzing students' misconceptions in understanding algebra, specifically in the topic system of linear equations in two variables (SLETV). This study utilized a four-tier diagnostic test combined with the Certainty of Response Index (CRI) to identify students' misconceptions. The test consisted of 12 questions covering four aspects of algebraic thinking: problem-solving, mathematical modeling, generalization, and analytical thinking. The subjects were 118 junior high school students in Ponorogo who had studied SLETV materials. The results showed that students experienced misconceptions, such as errors in interpreting mathematical statements, simplifying concepts, and organizing ideas. Although their understanding was incorrect, the students exhibited a high level of confidence in their answers. Teachers should use more explicit approaches to convey abstract concepts and provide appropriate feedback. Diagnostic tools such as the CRI can help teachers identify students' misconceptions and offer more effective remedial teaching, thereby significantly enhancing students' understanding of algebra.