Algebraic thinking is the ability to generalize about numbers and calculations, find concepts from patterns and functions and form ideas using symbols. It is important to know the student's algebraic thinking process, by knowing the student's thinking process one can find out the location of student difficulties and the causes of these difficulties. This study aims to analyze students' algebraic thinking processes in constructing new knowledge of high-ability students based on the Cognitive System of Marzano's Taxonomy. The subjects in this study were twenty one mathematics teacher candidates who took linear programming courses. The algebraic thought process of prospective instructors in solving linear equation problems is described using a qualitative descriptive technique in this study. The data collection technique starts with giving algebraic thinking questions and interviews/observations. Data reduction, data display, and deriving conclusions are the data analysis techniques employed. The results of the research show that algebraic thinking processes with types "Generasional Representasi Sequential Concrete" students are able to extract conclusions and organize better. Algebraic thought processes with types "Generational Representation of Concrete Random" students are able to build models and form generalizations but their representation is not good enough that they cannot be communicated properly.