Profil Konstruksi Pemahaman Mahasiswa pada Konsep Fungsi Distribusi Probabilitas Berdasarkan Teori APOS

Rahma Ramadhani; Iesyah Rodliyah; Nihayatus Sa’adah; Nanndo Yannuansa; Tafsillatul Mufida Asriningsih

doi:10.31932/j-pimat.v8i2.7613

Profil Konstruksi Pemahaman Mahasiswa pada Konsep Fungsi Distribusi Probabilitas Berdasarkan Teori APOS

Rahma Ramadhani, Iesyah Rodliyah, Nihayatus Sa’adah, Nanndo Yannuansa, Tafsillatul Mufida Asriningsih

Abstract

Understanding probability distribution functions requires procedural skills and connections among random variables, probability mass functions (PMFs), probability density functions (PDFs), and cumulative distribution functions (CDFs). This descriptive qualitative study examined students’ understanding of these concepts using APOS theory (Action, Process, Object, and Schema). Diagnostic test responses and semi-structured interviews from three purposively selected students were analyzed using APOS indicators. The results showed that the students had procedural skills but differed in conceptual consistency. M1 calculated interval probabilities using CDF differences and PDF integration but initially showed inconsistent understanding of CDF properties. M2 connected PMFs/PDFs, CDFs, and probability calculations relatively consistently, although the evidence was insufficient to confirm an integrated and stable Schema. M3 incorrectly applied the complement rule and inconsistently explained jumps in discrete CDFs. The novelty of this study lies in analyzing the connections among PMFs/PDFs, CDFs, and probability determination using the APOS framework. The findings suggest that instruction should encourage students to explain CDF properties, compare probability calculations using CDF differences and PDF integration, and justify the use of the complement rule. The findings are limited to the three selected students and the diagnostic tasks analyzed.

Keywords: APOS, probability distribution function, students, conceptual understanding, probability.

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DOI: https://doi.org/10.31932/j-pimat.v8i2.7613