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Open AccessArticle

Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus

by Farzad Radmehr 1,2,* and Michael Drake 3
1
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran
2
Department of Mathematical Sciences, Faculty of Engineering and Science, University of Agder, 4630 Kristiansand, Norway
3
School of Education, Victoria University of Wellington, Wellington 6140, New Zealand
*
Author to whom correspondence should be addressed.
Educ. Sci. 2020, 10(3), 55; https://doi.org/10.3390/educsci10030055
Received: 26 January 2020 / Revised: 24 February 2020 / Accepted: 26 February 2020 / Published: 3 March 2020
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. View Full-Text
Keywords: fundamental theorem of calculus; integral calculus; integral-area relationship; metacognitive knowledge; monitoring strategies fundamental theorem of calculus; integral calculus; integral-area relationship; metacognitive knowledge; monitoring strategies
MDPI and ACS Style

Radmehr, F.; Drake, M. Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus. Educ. Sci. 2020, 10, 55.

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