The Process of System of Linear Equations in Three Variables Solving Procedure’s Construction Using Analogy: Individual VS Paired

The process of knowledge construction can provide meaningful learning experiences for students. This is because students build new knowledge themselves by connecting one knowledge to another. The purpose of this qualitative research is to describe the process of new procedure’s construction using analogy. The subjects of the research consisted of three students of grade X high school (one student took the test individually, two students took the test in pair). Data analysis based on the APOS theory’s stage (Action, Process, Object, and Schema). At the action stage, both individual and paired students determine what is known and asked about the system of linear equations (SLE) in three variables problem based on analogy with the known things and asked about the SLE in two variables problem. They correctly determine the solution set of SLE in three variables. They also checked the correctness of the solution set of SLE in three variables correctly. At the process stage, they outline the steps of defining the solution set of SLE in three variables clearly. At the object stage, individual student cannot explain other methods of solving SLE in three variables, while paired students explain four other methods of solving SLE in three variables, that is the method of elimination, substitution, graphing, and matrix. At the schema stage, individual student cannot generalize some methods of solving SLE in three variables, whereas paired student generalize some methods of solving SLE in three variables. They also concluded the most effective method of solving SLE in three variables, that is the combined method. Individual student also explains that there is a SLE in three variables that has no solution, whereas paired students cannot explain it. They can construct new procedure well, despite errors in their process. In the process of new knowledge construction, the student's prior knowledge determines the quality of its construction process.