Algebraic Reasoning in Controversial Problem-Solving: Multiple Representations

Muniri Muniri; Musrikah Musrikah

doi:10.25217/numerical.v8i2.5631

Authors

Muniri Muniri 1Universitas Islam Negeri Sayyid Ali Rahmatullah Tulungagung, Indonesia
Musrikah Musrikah Universitas Islam Negeri Sayyid Ali Rahmatullah Tulungagung, Indonesia

DOI:

https://doi.org/10.25217/numerical.v8i2.5631

Keywords:

Controversy, Multiple Representations, Adaptive Reasoning

Abstract

Controversial issues have the potential to stimulate differences or cognitive conflicts in problem-solving, both in terms of approach, argumentation, and the solutions produced. Resolving cognitive conflict can be done not only through conventional logical thinking but also by understanding objects that encompass facts, concepts, principles, and skills, as well as considering external aspects surrounding the problem. This study aims to explore the controversy reasoning problems of university students in solving multiple representation problems. This research is a case study with a qualitative approach. The selected subjects were students who experienced controversy in solving multiple representation problems. The instruments used were tests and interviews. Data analysis was carried out through data reduction, data presentation, and conclusion drawing. There are three levels of controversial reasoning: clarification level, exploration level, and initial level. Among 99 students solving multiple representation problems, the results showed that 19 students (19.19%) were at the initial level, 45 students (45.45%) at the exploration level, and 35 students (35.35%) at the clarification level. Qualitatively, controversial reasoning at the clarification level is the best compared to the exploration and initial levels. The advantage of subjects at the clarification level is that, besides understanding the problem, their algorithmic skills are highly structured. These subjects are also able to provide concise, logical arguments and find the correct solution.

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