Understanding Students' Mathematical Errors and Misconceptions: The Case of Year 11 Repeating Students

摘要

Students' errors are causally determined, and very often systematic. Systematic errors are usually a consequence of student misconceptions. These can include failure to make connections with what they already know. There are beliefs held by students that inhibit learning from errors, such as they cannot learn from the mistakes and that mathematics consists of disconnected rules and procedures. Student errors are unique and they reflect their understanding of a concept, problem or a procedure. This study investigated how much mathematics have been understood and remembered by Year 11 repeating students, how their confidence level affects their responses to test items, and the causes for errors and misconceptions. A total of 74 Year 11 repeating students participated in this study and nine Year 11 mathematics teachers were surveyed. The sets of data were collected from the student test performance, student confidence level scale, and student and teacher questionnaires. The quantitative analyses of the students' results suggested that their test performance was not notably affected by their confidence. However, students' misconceptions seemed to have a significant impact on their progress and achievement in the test. The findings also suggested that students' errors and misconceptions were not only varied but there exist different causes as well.