Students' cognitive processes in understanding the application of derivatives

Wahyu Widada (Department of Mathematics Education, Universitas Bengkulu. Jl. WR Supratman, Bengkulu, Indonesia)
Dewi Herawaty (Department of Mathematics Education, Universitas Bengkulu. Jl. WR Supratman, Bengkulu, Indonesia)
Wayan Gede (Education Office in the Seluma District, Pasar Tais, Jl Merdeka, No. 03, Talang Saling, Seluma, Bengkulu 38878, Indonesia)
Khathibul Umam Zaid Nugroho (Educational Doctoral Program, Universitas Bengkulu. Jl. WR Supratman, Bengkulu, Indonesia)
Abdurrobbil Falaq Dwi Anggoro (Senior High School 5 Kota Bengkulu. Jl. Cen anda, Bengkulu, Indonesia)
Shadaqnas Dewarif Tri Anggoro (Senior High School 5 Kota Bengkulu. Jl. Cen anda, Bengkulu, Indonesia)

Annals of Mathematical Modeling
Vol. 2 No. 1 (2022)

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.