Asiedu, Seth (2025) An Analysis of Problem-Solving Skills in Calculus Application Tasks Among Senior High School Students in Ghana. Doctoral thesis, Asia e University.
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Abstract
This study investigated the difficulties that students in Senior High Schools in Ghana face when solving application problems in calculus. For over a decade, mathematics performance in Ghana has been persistently low, with national pass rates for Core Mathematics consistently below 50%. Results in Elective Mathematics are even more concerning, having fallen as low as 26% in 2006. A well-documented and significant part of this struggle involves application problems in calculus, where students are asked to use concepts in practical contexts like physics or economics. The Chief Examiner's reports consistently highlight this weakness. For example, the 2021 report noted that students could not apply integration to find velocity and distance from a given acceleration. This aligns with my own teaching experience, where I have observed that students often struggle to translate word problems to mathematical equations, requiring me to re-teach foundational concepts and straining the available class time. This study involved 960 Grade 11 students from twelve schools, selected from three of Ghana's six school categories in Greater Accra. A sequential explanatory mixed research design was employed, using Polya's problem-solving theory as a framework and the first three levels of Bloom's taxonomy to categorize cognitive skills. A researcher-developed cognitive test was used to assess student skills, and a questionnaire was used to solicit information on teachers' perceptions of problem-solving in calculus. All instruments were checked for reliability and validity. Quantitative data were analyzed using descriptive and inferential statistics. Content analysis of students' responses to the test items was conducted, and the cognitive test results were qualitatively analyzed to identify the errors made by students. Additionally, the responses of teachers to the questionnaire were examined. The results showed that students performed well on topics such as the trapezium rule and finding tangents and normals. However, they faced serious challenges with problems in rate of change, kinematics, optimization (maximization/minimization), and finding areas under a curve. The most common errors committed by students were conceptual, followed by procedural and technical mistakes. Students made more technical errors on questions requiring basic knowledge and comprehension, while conceptual errors dominated at the application level. The study also found a significant impact of school category on achievement, with Category A schools outperforming the other school categories. Teachers perceived rate of change as the most challenging topic to teach and the trapezium rule as the easiest. They reported using strategies like collaborative learning and small group tutoring to help students. The study recommends increased professional development for teachers and that schools in lower categories be equipped with modern facilities to raise them to the standard of top-tier schools.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | Calculus, conceptual, application problems, Bloom’s taxonomy, word problems |
| Subjects: | L Education > LB Theory and practice of education |
| Divisions: | School of Graduate Studies |
| Depositing User: | Nor Aisyah Ghazali |
| Date Deposited: | 07 May 2026 07:15 |
| Last Modified: | 07 May 2026 07:15 |
| URI: | http://ur.aeu.edu.my/id/eprint/1490 |
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