Algebraic and Visual Representation in Solving Mathematics Problems Based on Empirical Thinking - Rif’at, Mohamad; Sudiansyah, Sudiansyah; Peterianus, Septian (Al-Jabar: Jurnal Pendidikan Matematika, 2021)
The researcher investigated and explored a solution of non-directed or no hint of mathematics problems presented visually or algebraic, and to embed the empirical verification thinking. The tip is a way to solve, so the students can answer the questions based on their state of mind by observing their trajectories of thinking from the steps of the solution. That is conducted at the Mathematics Education Department of Tanjungpura University at West Borneo of Indonesia for two semesters. The problems are from Researcher Repertoire, test item of Teacher Profession Education of National Indonesia, and Flanders Mathematics Olympiad. Before the issues given to the students, the construct validity has calculated from intake participants using Cramer’ Test with C coefficient is equal to 0.83. We analyze the students’ empirical verification thinking of their solutions. The analysis is about the trend of the thinking, model of representation, and completeness of the logical steps. The results are: the pattern of thinking tends to linear model or of meta-pattern, the description tends to be non-linear or varies of the solution, and the logical steps tend to be a non-recognizable form of thinking. In general, the more visual representations, the less thinking models of the representations; the answers based on algebraic thinking; the visual illustrations are limited, where the algebraic without any manipulation and not need any hint; and the visual images used are part of it in solving the problems and no manipulation.