Derivative Applications in Motorcycle Mechanics: An Exploration of Vocational Students’ Contextual Understanding

Muhammad Syafey Siregar; Dewi Aminah Hasibuan; Rama Nida Siregar

doi:10.22460/jiml.v8i4.30689

Authors

Muhammad Syafey Siregar UIN Syahada Padangsidimpuan, Padangsidimpuan, Indonesia
Dewi Aminah Hasibuan UIN Syahada Padangsidimpuan, Padangsidimpuan, Indonesia
Rama Nida Siregar UIN Syahada Padangsidimpuan, Padangsidimpuan, Indonesia https://orcid.org/0000-0002-8285-7096

DOI:

https://doi.org/10.22460/jiml.v8i4.30689

Keywords:

Contextual Understanding , Derivative Applications , Motorcycle Mechanics , Vocational High School

Abstract

Derivatives play a crucial role in vocational mathematics learning, particularly in understanding dynamic processes in automotive engineering contexts. However, students often experience difficulties connecting abstract derivative concepts with real mechanical phenomena encountered in workshop activities. This study aims to explore the contextual understanding of derivative applications in motorcycle mechanics among Grade XI Motorcycle Engineering (TBSM) students. This research employed a descriptive qualitative approach involving 27 Grade XI TBSM students at a vocational high school. Data were collected through classroom observations during integrated mathematics–vocational learning activities, in-depth semi-structured interviews, and analysis of students’ learning documents and worksheets. The observations focused on students’ engagement and interpretation of derivative concepts in authentic motorcycle mechanics contexts. Interviews were conducted to explore students’ reasoning related to first and second derivatives, while document analysis was used to examine students’ written representations and problem-solving strategies. Data triangulation was applied to ensure credibility and consistency of findings. The results show that students demonstrate strong contextual understanding of first derivatives, particularly in interpreting rates of change related to motorcycle speed variations. However, their understanding of second derivatives, especially in analyzing acceleration patterns and torque characteristics, remains limited. Students exhibit moderate ability in interpreting RPM graphs, with some difficulty in identifying slope changes and engine performance behavior. Practical workshop experiences, real engine performance data, and the use of diagnostic tools significantly support students’ contextual mathematical reasoning. In conclusion, aligning mathematics instruction with authentic vocational practices enhances students’ conceptual understanding of derivatives.

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