Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was conducted on students majoring in mathematics from three different universities in East Java as research subjects. The data was collected through a mathematical proof test instrument and interviews which is then qualitatively analyzed. The results of the study show that there were students who completed the test through the assimilation scheme only, and there were students who completed the test using both assimilation and accommodation schemes. Students construct their thinking processes through 5 stages, namely: identifying, determining rules to be used, proving with symbol manipulation, reviewing, and justifying. Students use the five stages of thinking to construct knowledge. However, students who use assimilation schemes made some errors in proving the mathematics problem due to their carelessness in doing the proving with symbol manipulation and reviewing stages.