<![CDATA[Abductive reasoning is a problem-solving method that allows for the creation of hypotheses based on incomplete information. In this article, we explore the potential of using abductive reasoning to help solve algebraic problems. We begin by providing an overview of abductive reasoning and its key features. We then present a case study in which we apply abductive reasoning to a specific algebraic problem. Our results demonstrate the effectiveness of using abductive reasoning to generate new hypotheses and ultimately solve the problem. Finally, we discuss the implications of our findings for the teaching and learning of algebra, as well as potential future research directions in this area. Based on several observations, some students experienced difficulties in problem-solving activities. Their inability may be caused by the complexity of making conclusions from the facts provided in problem-solving. Student failure in problem-solving shows that the importance of problem-solving needs to be better taught in learning mathematics. One prominent factor that can support problem-solving in practice is reasoning. Therefore, increasing reasoning and proof is a fundamental aspect of learning mathematics. Theoretically, and developing Abductive Reasoning as teaching material for Linear Algebra courses to find solutions to algebraic problems in mathematics learning activities.]]>
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