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FORMULATING THE GENETIC DECOMPOSITION FOR PROBABILITY CONSTRUCTION BASED ON STUDENT DESCONSTRUCTED PROBLEM-SOLVING PROCESS Rahayu, Ratri; Amaliyah, Fitriyah; Gunawan, Gunawan; Subekti, Fitrianto Eko
AKSIOMA: Jurnal Program Studi Pendidikan Matematika Vol 14, No 4 (2025)
Publisher : UNIVERSITAS MUHAMMADIYAH METRO

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24127/ajpm.v14i4.14367

Abstract

Probability theory is inherently abstract and structurally complex, often creating substantial cognitive barriers for students when solving problems. This study aims to formulate a genetic decomposition of core probability concepts based on the mental structures constructed by undergraduate learners. Guided by the APOS (Action–Process–Object–Schema) theoretical framework, the research employed a three-phase methodological cycle: (1) epistemological analysis of fundamental probability concepts, (2) design and administration of diagnostic and instructional instruments, and (3) analysis and validation of students’ cognitive structures. The study was conducted at two universities in Central Java, Indonesia, involving four mathematics education undergraduates enrolled in an introductory probability course. Data were collected through content analysis, domain-specific assessment instruments, and semi-structured interviews. The APOS framework was used to trace students’ mental constructions in relation to classical probability, independence, conditional probability, total probability, and Bayes’ theorem. The results reveal that students had not fully internalized the mental objects and schemas required to coordinate these concepts during problem-solving activities. Their reasoning remained largely at the process level, particularly in representing sample spaces, applying counting techniques, and thematizing probability structures. Nonetheless, several elements of their cognitive behavior aligned with the refined genetic decomposition. The findings highlight the necessity of strengthening students’ APOS-based mental constructions to support the development of coherent probabilistic schemas and enhance conceptual as well as procedural fluency.
Problematika Berpikir Kritis Siswa Pada Materi Persamaan Garis Lurus Siswa SMP Muhammadiyah Larangan Saudah, Saudah; Kusno, Kusno; Subekti, Fitrianto Eko
Jurnal Ilmiah Profesi Pendidikan Vol. 11 No. 1 (2026): Februari
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jipp.v11i1.3294

Abstract

Kemampuuan berpikir kritis adalah keterampilan untuk menyelesaikan secara sistematis, logis sehingga dalam mengambil kesimpulan di dasari oleh data yang ada. Keterampilan menganalisis informasi, mengevaluasi argument, dan membuat keputusan berdasarkan fakta yang ada. Penelitian ini bertujuan untuk mendeskripsikan kesulitan kemampuan berpikir kritis siswa. Metode penelitian yang digunakan adalah deskriptif kualitatif dengan Teknik pengumpulan data melalui tes tertulis dan wawancara. Tes tertulis digunakan untuk mengetahui kesulitan siswa dalam menyelesaikan permasalahan sedangkan wawancara digunakan untuk menggali informasi secara mendalam untuk mengetahui informasi berkaitan dengan penyelesaian permasalahan. Subjek penelitian ini adalah siswa kelas VIII SMP Muhammadiyah Larangan. Materi yang digunakan adalah persamaan garis lurus. Analisis data dilakukan dengan triangulasi yaitu membandingkan data dari sumber (tes tertulis dan wawancara). Hasil penelitian menunjukan bahwa: 1) siswa kategori tinggi tidak mengalami kesulitan dalam menyelesaikan permasalahan yaitu menginterpretasi, menganalisis, melakukan pemecahan masalah, dan melakukan evaluasi akan tetapi siswa mengalami kesulitan dalam melakukan inferensi atau menarik kesimpulan; 2) siswa kategori sedang tidak mengalami kesulitan dalam melakukan interpretasi, analisis, pemecahan masalah akan tetapi siswa mengalami kesulitan dalam mengalukan evaluasi dan inferensi. 3) siswa kategori rendah mengalami kesulitan dalam menyelesaikan permasalahan karena siswa mengalami kesulitan dalam menginterpretasi, menganalisis, memecahkan masalah, melakukan evaluasi dan menarik kesimpulan dalam menyelesaikan permasalahan. Berdasarkan hasil penelitian menunjukan bahwa siswa belum terbiasa menyelesaikan soal kontekstual sehingga siswa perlu dibiasakan untuk mengerjakan soal soal kontekstual agar tidak mengalami kesulitan dalam berpikir kritis.
The Teaching strategies for enhancing computational thinking and mathematics: A systematic review Alamanan, Dzakariyo Zaqfan; Subekti, Fitrianto Eko; Nadzeri, Mohamad Basri
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 3 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i3.20146

Abstract

This study aims to systematically examine how different instructional strategies influence students’ computational thinking (CT) and mathematical abilities within mathematics education. Employing a Systematic Literature Review (SLR) guided by the PRISMA framework, this study analyzed 13 peer-reviewed articles published between 2020 and 2025 that met predefined inclusion criteria. The reviewed studies were selected using Publish or Perish software and primarily sourced from Google Scholar and Scopus-indexed journals. The analysis focused on research trends, methodological approaches, educational levels, geographical distribution, subject matter, and the effectiveness of learning strategies in fostering CT and mathematical skills. The results reveal that instructional approaches integrating CT with STEM-oriented models—such as Project-Based Learning (PjBL), the SSCS model, and technology-enhanced learning using augmented reality and digital tools—consistently improve students’ problem-solving, abstraction, and higher-order thinking skills in mathematics. The findings also indicate that learner characteristics, particularly self-efficacy and learning styles, play a significant role in CT development. Most studies were conducted at the junior high school level and were geographically concentrated in Java, highlighting an imbalance in research coverage. In conclusion, this review confirms that innovative, technology-supported, and adaptive learning strategies are effective in strengthening computational thinking within mathematics education. The contribution of this study lies in providing a comprehensive mapping of instructional strategies linked to CT outcomes, offering theoretical insights, methodological guidance, and practical implications for educators and researchers seeking to integrate computational thinking into mathematics curricula more effectively.