Investigating the Role of Algebra in Solving Equations

This case study examines the use of algebra in solving equations by Senior High School Students at Winneba Secondary School. More specifically, it looks at the effects of students’ grasp of algebraic concepts on their capabilities to solve both linear and quadratic equations and seeks to establish which algebraic skills most strongly correlate with achievement in solving multi-step equations. In this instance, we conducted an experiment with an experimental research design. Data were collected using a stratified random sample of 100 students through uniquely designed tests measuring algebraic understanding and proficiency in solving equations. 68.5% and 64.2% were the mean scores recorded for algebraic concepts and solving equations respectively. These results illustrate that the average score obtained on the Algebraic Concepts Test (M = 68.5, SD = 12.3) was greater than the average with regard to Linear and Quadratic Equations Test (M = 64.2, SD = 14.1). The mean difference between the two tests was 4.30, a difference which was significant, t (99) = 3.24, p < .001. In the context of solving multi-step equations, simplification (β = 0.42, p < 0.001) and factorization (β = 0.31, p < 0.001) emerged as the strongest predictors, accounting for 65% of the variance in the performance model (R² = 0.65). The results from this study underscore the need to cultivate both conceptual understanding and procedural fluency in algebra to enhance students’ overall problem-solving capabilities. Suggested actions advocate for conceptual-focused teaching frameworks, stronger reinforcement of intermediate algebraic concepts, improved teacher preparation programs aimed at blending theory with practice, and more effective teaching strategies. This research contributes significantly to the enhancement of mathematics instruction not only at Winneba Secondary School but also in comparable educational environments.