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The purpose of this study was to determine the thoroughness of VII grade students who taught by the Selective Problem Solving (SPS) model and to know the description of students' mathematical problem solving ability based on Polya's stages on SPS learning model. Data collection method used the method of participant observation, tests, interviews, and documentation.The method used in this study is a mixed methods with sequential explanatory design where the first stage of research used quantitative methods, and the second stage used qualitative methods. The subjects of this research are six students from VII D grade of SMPN 41 Semarang consist of: two students from top group, two students from middle group, and two students from lacking group in mathematical problem solving ability test. The results showed that: (1) mathematics learning in VII grade with SPS models can achieve learning completeness; (2) the students from top group were able to solve the problem through Polya's stages except looking back stage; (3) the students of middle group were able to understand the problem well, but have not been able to carry out thoroughly stage of planning, implementing problemsolving, and looking back; (4) the students from less group have not been able to solve the problem through the Polya's stage which includes understanding the problem, devising a plan, carrying out the plan, and looking back.
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