Reasoning in mastering the foundations of mathematics and mathematical competence is one that should be owned by students. While a model of discovery learning is one of the models of learning that must be applied at school in accordance with the curriculum learning goals of 2013, the purpose of this research was to describe the mathematical reasoning abilities of students through a model of discovery learning. The research method used was a qualitative exploratory type approach. The data has been obtained through mathematical reasoning tests and interviews. The result of this study is: 1) High ability students only mastered the indicator to propose allegations. The ability to file allegations limited to the ability to estimate answers with the reasons but the evidence provided was not appropriate; 2) Medium-capacity students only mastered the indicator to propose allegations. Ability to file allegations limited to the ability to estimate answers with the reasons but the evidence provided was not appropriate; 3) Low ability students could not master the six indicators of mathematical reasoning ability. In the indicator of filing suspicion, students estimated answers together with the reasons through trial and error, and students did not know the supporting concepts used in showing evidence. Student’s inability in mathematical reasoning was caused by the inability to master the concept correctly as well as not able to understand the problem and to provide evidence in solving the problem. Therefore, the application of discovery learning should be carried out continuously and consistently so that students can develop reasoning abilities well.Keywords: mathematical reasoning, discovery learning.
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