Özet:

This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview techniques were carried out in order to find out more about the ability of connections and generate knowledge about the transposition in making mathematical problem solving designs. The test is given to 3 students who have high ability, medium ability and low ability. Analysis of the data in this study is through the provision of problem solving tests and interviews using time triangulation, which provides tests and interviews for each student with a different time. The results in this study indicate that highly capable subjects have excellent mathematical connections and didactic knowledge is well utilized and able to provide alternative answers that differ from researchers so that a didactic transposition is formed, that is knowledge to be taught with knowledge, subjects of mathematical ability are able understand the problem well but are not careful enough in solving problem so that previous knowledge is underutilized, the subject of low mathematical ability is not able to understand the problem well and is unable to solve problems in the form of algebra so that the initial knowledge possessed is not well connected.

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