System of Linear Equations: A Comparative Study Between Cramer’s Rule and Paravartya’s Rule
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Abstract
Background and Aims: Solving systems of linear equations is essential in mathematics education, influencing real-world problem-solving and advanced applications. This study compares the effectiveness of Cramer’s rule and Paravartya’s rule in enhancing Grade 8 students' achievement in linear equations, aiming to address challenges in teaching methods.
Methodology: A mixed-methods approach was used, combining a quasi-experimental pretest-posttest design with a sequential exploratory design for qualitative data. Quantitative data were obtained through assessments, and qualitative data were collected from student feedback and analyzed thematically.
Results: Findings revealed statistically significant improvements in students’ mathematics achievement from pretest to posttest using both methods (p < 0.05). Pretest scores were relatively low , but posttest scores showed notable improvements. Despite the absence of statistically significant differences in posttest outcomes between the two methods (p = 0.613), both approaches proved effective in enhancing problem-solving abilities. Key challenges identified included difficulties with signed numbers, large computations, equation transformation, and procedural steps. Students employed coping strategies such as memorization, chunking, consistent practice, and peer support. A Learning Activity Sheet (LAS) was developed to reinforce learning, promote active engagement, and accommodate diverse learning styles.
Conclusion: The study concludes that both Cramer’s rule and Paravartya’s rule effectively enhance students' performance in solving systems of linear equations. Challenges related to procedural complexity were mitigated through structured interventions, peer collaboration, and practice. The findings highlight the need for targeted instructional strategies and the development of supportive resources, like LAS, to promote mathematical cognition and active learning.
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