Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus

摘要

Previous studies of integral calculus have mainly explored students’ conceptual and procedural knowledge; only a few have focused on students’ metacognition in relation to integral calculus. The study reported here explored students’ metacognitive knowledge of integral calculus by interviewing nine first-year university and eight Year 13 students. The design of the interview questions was based on the structure of metacognitive knowledge in Revised Bloom’s Taxonomy. The findings suggest there are differences between students’ metacognitive knowledge at Year 13 and the first year of university. In particular, the importance of knowing the rationale behind the theorems and formulas was not obvious for Year 13 students. Moreover, students’ metacognitive knowledge could be developed further at both levels, particularly in terms of developing strategies to identify how integral calculus questions could be solved and to check the outcome of problem-solving.