Abstract:

In order to support the development of reasoning skills, it is very necessary and important for students to meet mathematical proof from an early age and to carry out actions in this process, and this is why "can young students make proof?" brings to mind the question. In line with this question, the purpose of this study is to examine the reasoning of middle school students in the process of proving the given problems and propositions. For this purpose, in the 2019-2020 academic year, seventh-grade students studying at a state middle school were selected as participants. In this study, in which qualitative research approach was adopted, the data were collected through open-ended tasks. The study findings revealed that students who did not understand the tasks left the task unanswered, rewrote it, used the data in task incompletely, incorrectly or went outside the data and sometimes did not understand the premise of the proposition in the task. When the reasoning of the students who understood the tasks was examined, it was determined that they generally made empirical verification in number tasks that require direct proof. In geometry tasks that require direct proof, it was determined that they mostly made incorrect justification by giving an example as opposed to another quadrilateral covered by a quadrilateral, justification with symbols on the prototype drawing, or justification based on incorrect drawing, and some students make deductive reasoning. In tasks in which they need to give counterexamples, was observed that some students made non-logical justifications caused by a lack of prior knowledge in the tasks, while many students made deductive reasoning. In this study, it can be said that students in general have difficulty making arguments in the proving process, often tend to generalize using special situations and use their previous learnings without transformation.

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