Analysis of Grade 11 Students’ Conceptual Understanding in Probability Concepts: A Perspective of Skemp Understanding Theory

Emmanuel Appoh Andam; Francis Kwadwo Awuah; William Obeng-Denteh

doi:10.37284/eajes.8.2.2987

Emmanuel Appoh Andam Kwame Nkrumah University of Science and Technology
Francis Kwadwo Awuah Kwame Nkrumah University of Science and Technology
William Obeng-Denteh Kwame Nkrumah University of Science and Technology

DOI: https://doi.org/10.37284/eajes.8.2.2987

Keywords: Skemp’s Theory of Understanding, Probability Concepts, Cognitive Ability Test, Mathematics Education, Relational and Instrumental Understanding

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Abstract

This study investigates Grade 11 high school students' conceptual understanding of probability concepts through the framework of Skemp's understanding theory. Recognising the critical role of mathematics in everyday life and its application across various fields, this study emphasises the need for deep comprehension rather than mere memorisation. Utilising a qualitative descriptive methodology, the research analyses the scripts of eight (8) students in response to a cognitive ability test focused on probability, revealing distinct patterns of understanding categorised as relational and instrumental. The findings indicate that while some students exhibit relational understanding, demonstrating the ability to explain concepts and apply knowledge flexibly, many struggle with instrumental understanding, relying on rote memorisation and showing difficulty in problem-solving. The study identifies specific misconceptions and gaps in understanding, such as equiprobability bias, representativeness bias, belief bias and proportional reasoning. These misconceptions hinder the students' engagement with probability concepts. Ultimately, this research highlights the necessity for improved instructional strategies that promote relational understanding, fostering meaningful connections between mathematical concepts. The insights gained from this analysis aim to inform educators and curriculum developers, providing a foundation for targeted interventions that enhance students' mathematical comprehension and application in real-world scenarios

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