Abstract
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.
Highlights
Metacognitive knowledge is “knowledge of cognition in general as well as awareness and knowledge of one’s own cognition” [1] (p. 46)
The findings highlight that some aspects of Year 13 students’ metacognitive knowledge are less developed compared to first-year university students, mainly in relation to the importance of knowing the justification behind the formulas and monitoring strategies that can be used in integral problems
The number of studies focusing on metacognition in relation to the teaching and learning of mathematics at upper secondary and tertiary levels is limited
Summary
Metacognitive knowledge is “knowledge of cognition in general as well as awareness and knowledge of one’s own cognition” [1] (p. 46). Integral calculus is one of the topics involved in mathematical courses at these levels, one that has several applications in different disciplines (see, [5]) and is a key subject in transitioning from secondary to tertiary education [6]. It is part of gateway mathematics courses at universities for many majors and is important for the development of the sciences [7]. No study was found that explored metacognitive knowledge in relation to students’ learning of integral calculus.
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