Students' mathematical performance, metacognitive experiences and metacognitive skills in relation to integral-area relationships

Previous studies have explored students' understanding of the relationship between definite integrals and areas under curves, but not their metacognitive experiences and skills while solving such problems. This paper explores students' mathematical performance, metacognitive experiences and metacognitive skills when solving integral-area tasks by interviewing nine university and eight Year 13 students using a think-aloud protocol. The findings show that the students could have benefitted from their teachers and lecturers placing greater emphasis on both their conceptual understanding of integral-area relationships and their metacognitive experiences and skills.