Basic Computational Skills and Calculation Strategies among High-Achieving Secondary School Students in South Africa: An Investigation of Their Effects on Student Performance

Abstract

Purpose: This study aims to comprehensively assess the basic computational skills and calculation strategies of high-achieving Grade 10 students in South Africa and to examine how these skills influence their performance in operations involving decimals and fractions. In particular, it explores whether persistent reliance on counting-based procedures limits students’ conceptual understanding of place value and constrains their ability to flexibly apply more advanced numerical strategies. By focusing on high-achieving students, the study seeks to clarify whether foundational weaknesses remain even among those considered academically successful.

Methodology: A paper-based computational assessment was administered to 30 high-achieving Grade 10 students in a public secondary school in Mpumalanga Province. The test covered the four operations with integers, as well as operations involving decimals and fractions. Calculators were not permitted to ensure that students’ mental and written strategies could be observed. Descriptive statistics were calculated to determine overall performance patterns, and detailed error analyses were conducted to identify strategy use, recurring mistakes, and underlying misconceptions related to place value, equivalence, and multiplicative reasoning.

Findings: The overall mean correct response rate was 58.4%. Students performed relatively well in addition, subtraction, and basic single-digit multiplication, but achievement declined substantially in multi-digit multiplication and division. Even lower performance was observed in decimal operations and particularly in fraction tasks. Across integer items, students relied predominantly on counting strategies, while more efficient approaches such as retrieval, decomposition, or structured algorithms were rarely used. Frequent errors included counting inaccuracies, weak place-value coordination, incorrect alignment in written algorithms, and misunderstandings of decimal shifts. In fraction tasks, both conceptual and procedural errors were evident, indicating fragile understanding of fundamental fraction concepts.

Unique Contribution to Theory, Practice and Policy: The study contributes to theory by demonstrating how sustained dependence on counting may inhibit the development of place-value understanding and higher-order numerical reasoning. For practice, it highlights the importance of explicitly promoting efficient calculation strategies alongside conceptual instruction in the base-ten system. At the policy level, the findings suggest the need to strengthen early mathematics curricula and instructional support systems to prevent the persistence of foundational computational weaknesses into secondary education.