Algebra is mandatory learning in junior high school. That is a continuation of arithmetic with the bridge being variable. Students often have difficulty in understanding it, especially quadratic equations. The purpose of this study is how students’ cognitive processes in understanding the principles of quadratic equations. It was an exploratory study conducted on research subjects. The subjects were junior high school students selected based on their ability to understand concepts and principles about quadratic equations. That’s done through tests about understanding quadratic equations. There were 16 selected research subjects. They were interviewed in-depth by researchers using interview guides. Interview data were analyzed qualitatively based on genetic decomposition. The results of this study are that students can use square, rectangular and unit square cards to determine the principle of factorization of quadratic equations. Students can generalize until completing a perfect quadratic equation. The conclusion is that the cognitive process of students who learn to use learning media based on square and rectangular able to reach a high level (trans-level).

Derivatives are one of the objects of calculus that is difficult for students to learn. The purpose of this study was to describe the cognitive processes of students in understanding the application of derivatives. This is a qualitative research involving one subject with the initials L. The main instrument of this research is the researcher who is guided by an assignment sheet and an interview guide. Data collection was carried out through task-based interviews. To get complete and accurate data recorded through audiovisual. Data were analyzed descriptively through genetic decomposition based on APOS (action-process-object-schema) theory. The results of this study are that L can coordinate the process-object of all the properties of a given function, with adjacent or overlapping intervals in all h domains so that a mature scheme of function graph sketches is formed. So that an accurate function graph sketch is obtained. The conclusion is that L's cognitive process of applying derivatives is at a high level. It's a trance level.