<![CDATA[The research purpose is to investigate and explore a solution of non-directed of mathematics problems presented visually or algebraic, and to embed the empirical verification thinking. The problems are from Researcher Repertoire, test item of Teacher Profession Education of National Indonesia, and Flanders Mathematics Olympiad. We analyze the students’ empirical verification thinking of their solutions, i.e. 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. Our recommendations are that the more visual representations need multiple representations, the algebraic thinking needs more the visual illustrations, and the visual images needed in solving mathematics problems.]]>
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