Senior high school students thinking levels in permutation and combination using solo taxonomy - Article

Oct 15, 2026

Uploaded by Mabel

The Ghanaian mathematics curriculum emphasizes critical thinking, yet senior high school learners often show weaknesses in higher-order reasoning. This mixed-method study used the SOLO (Structure of the Observed Learning Outcome) taxonomy to assess thinking levels in permutation and combination among 256 males and 104 females randomly selected from three Ghanaian SHS. Tests and interviews provided data, analyzed descriptively and inferentially using Kruskal-Wallis tests. Results indicated predominantly low thinking levels and significant differences across study programmes.

LanguageEnglish

CategoryExam

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Pages13

Reading Time33 min

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Abstract

Article History

Keywords

Introduction

Background on mathematical thinking

Critical thinking in the Ghanaian curriculum

Asian Journal of Contemporary Education ISSN(e): 2617-1252 DOI: 10. 55493/5052 . v9i2 .5511 Vol. 9, No. 2, 143-155. © 2025 AESS Publications. All Rights Reserved. Senior high school students thinking levels in permutation and combination using solo taxonomy Stephen Junior Appiah 1 Emmanuel Kojo Amoah2+ Emmanuel Antwi Adjei3 Peter Akayuure4 1Department of Mathematics, Okomfo Anokye Senior High School, Wiamoase, Ashanti, Ghana. [1](1 Email: appiahstephen812@gmail.com)[ Email:](1 Email: appiahstephen812@gmail.com)[ ](1 Email: appiahstephen812@gmail.com)[appiahstephen812@gmail.com](1 Email: appiahstephen812@gmail.com) 2,4Department of Mathematics Education, University of Education, Winneba, Winneba, Ghana. 2 Email: [ekamoah@uew.edu.gh](ekamoah@uew.edu.gh)[ ](ekamoah@uew.edu.gh)[4](4Email: pakayuure@uew.edu.gh)[Email:](4Email: pakayuure@uew.edu.gh)[ ](4Email: pakayuure@uew.edu.gh)[pakayuure@uew.edu.gh](4Email: pakayuure@uew.edu.gh) 3Department of Mathematics, Abuakwa State College, Kyebi, PMB, Kyebi, Ghana. 3 Email: [eaadjei8@gmail.com](eaadjei8@gmail.com) (+ Corresponding author) ABSTRACT Article History Received: 19 June 2025 Revised: 21 July 2025 Accepted: 25 July 2025 Published: 1 August 2025 Keywords Common core programme Critical thinking Permutation and combination Senior high school SOLO taxonomy. Although the Ghanaian mathematics curriculum emphasizes critical thinking as a core competence, students still appear to lack this skill. In this mixed-method study, the Structure of the Observed Learning Outcome (SOLO) taxonomy was used to assess senior high school students’ thinking levels in permutation and combination. A sample of 256 males and 104 females was randomly selected from three senior high schools for the study. The data were collected using tests and interviews, and analyzed descriptively and inferentially using Kruskal-Wallis tests. The results showed that while only one-fifth of the students reached the higher relational and extended abstract thinking levels, the majority (73.9%) remained at the lower levels of pre-structural, unistructural, and multi-structural thinking. These students struggled to apply basic counting and multiplication principles in solving higher-order thinking problems. The Kruskal-Wallis H test further revealed statistically significant differences in thinking levels across the study programmes. General Science students demonstrated the highest thinking levels, followed by General Agriculture and Business students. The study concluded that students’ thinking levels in permutation and combination were low. It is recommended that teachers, textbook authors, and curriculum developers adopt representations and activity-based teaching strategies to help students develop a conceptual understanding of the topic. Contribution/ Originality: This current study analyzes the thinking levels of Ghanaian SHS students based on the SOLO taxonomy to identify the very low levels at which they understand basic concepts and also highlights significant differences in levels of understanding across various programs of study, suggesting possible pedagogical interventions. 1. INTRODUCTION Every day, people engage in mental actions often referred to as thinking. Almost every problem in human life necessitates the use of thinking to solve it. Remembering, considering, giving reasons, reflecting, and deciding on something to solve a problem are mental actions in the human mind (Celik & Ozdemir, 2020) . In the face of 21stcentury challenges, every individual should possess the thinking skills necessary to solve every problem. When an individual thinks about solving a mathematical problem, it means that the person is engaging in mathematical thinking. Schoenfeld and Sloane (2016) state that mathematical thinking is the ability to think and make judgments independently. The process of mathematical thinking involves translating incoming external information i

FAQs

What framework was used to assess students’ thinking levels?

The study assessed thinking levels using the SOLO (Structure of the Observed Learning Outcome) taxonomy.

How many students participated in the study?

A total of 360 students participated, including 256 males and 104 females.

What did the results show about students’ thinking levels in permutation and combination?

Most students remained at lower SOLO levels, with only about one-fifth reaching higher relational and extended abstract levels.

Oct 15, 2026

Uploaded by Mabel