<![CDATA[The way students who want to become teachers represent their mathematical reasoning when they solve mathematical problems—using case studies and qualitative techniques. Data were gathered from the vignette results of student work. They are using snowball sampling for subject selection. Three third-semester mathematics education program participants served as the study's research subjects—ways for gathering data, such as interviewing and recording. Three steps of the analysis were completed: presentation of data, elaboration of conclusions and verification. As a consequence of meeting all markers of mathematical thinking representation, the S1 and S2 subjects with high and moderate academic talents had good mathematical thinking representation abilities. Because S3 students with limited intellectual skills cannot still represent mathematical ideas.]]>
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