EKSPLORASI KEMAMPUAN MATEMATIKA DAN SELF-EFFICACY TERHADAP KEMAMPUAN PEMODELAN MATEMATIKA SISWA SMP DALAM PENYELESAIAN MASALAH MATEMATIKA
Exploration of Mathematical Competence and Self-Efficacy on Junior High School Students' Mathematical Modeling Ability in Solving Mathematical Problems.
Jeliana Intan Permata. 2025. Eksplorasi Kemampuan Matematika dan Self-Efficacy Terhadap Kemampuan Pemodelan Matematika Siswa SMP dalam Penyelesaian Masalah Matematika. Disertasi, Program Studi Pendidikan Matematika Pascasarjana Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Surabaya. Promotor Prof. Dr. Mega Teguh Budiarto, M.Pd., dan Kopromotor Dr. Yusuf Fuad, M.App.Sc.
Kata kunci: Pemodelan matematika, kemampuan matematika, self-efficacy, dan regresi berganda.
Penelitian ini bertujuan untuk mengeksplorasi ada atau tidaknya pengaruh kemampuan matematika dan self-efficacy siswa terhadap kemampuan pemodelan matematika siswa kelas VIII SMP dalam penyelesaikan masalah matematika, dengan menggunakan penelitian eksploratif yang merupakan kombinasi pendekatan kuantitatif dan pendekatan kualitatif. Desain penelitian yang digunakan adalah explanatory sequential. Populasi penelitian adalah seluruh siswa kelas VIII SMP/MTs di Kabupaten Landak, Provinsi Kalimantan Barat, yang terakreditasi terdiri dari . Sampel ujicoba dipilih secara acak adalah SMP Swasta Maniamas Ngabang. Sedangkan sampel penelitian juga dipilih secara acak adalah SMP Negeri 1 Ngabang, SMP Negeri 1 Sengah Temila, dan SMP St. Benediktus Pahauman.
Instrumen penelitian meliputi Tes Kemampuan Matematika (TKM), Tes Pemodelan Matematika (TKPM), dan Angket Self-Efficacy (ASE) yang diadaptasi dari Koyuncu et al. (2017). Validitas ketiga instrumen dinyatakan tinggi berdasarkan Aiken’s V , dengan penilaian oleh tiga doktor Pendidikan Matematika dan satu guru. Uji keterbacaan oleh satu guru dan tiga siswa kelas VIII SMP Swasta Maniamas Ngabang menunjukkan instrumen mudah dipahami dan layak digunakan. Hasil uji coba menyatakan TKM, TKPM, dan ASE valid dan reliabel; TKM dan TKPM memiliki tingkat kesukaran sedang dan daya pembeda baik. Instrumen tambahan berupa Panduan Wawancara telah disetujui dosen pembimbing dan dinyatakan layak secara konteks, konten, dan bahasa.
Pengumpulan data dilakukan selama tiga hari berturut-turut terhadap siswa sampel, yang wajib menyelesaikan TKM, TKPM, dan ASE di bawah pengawasan peneliti dan satu guru matematika. Hari pertama siswa mengerjakan TKM (90 menit), hari kedua TKPM (90 menit), dan hari ketiga ASE (45 menit). Jawaban dikoreksi, diberi skor, dan dikategorikan kemampuan tinggi , sedang , dan rendah . Hasil TKM: tinggi, sedang, rendah; TKPM: tinggi, sedang, rendah; ASE (skor dikonversi dari ordinal ke interval): tinggi, sedang, rendah.
Dengan bantuan SPSS v.26 dan berdasarkan skor TKM, skor TKPM, skor ASE, serta regresi berganda, dilakukan uji hipotesis: “Ada pengaruh signifikan dari kemampuan matematika siswa dan self-efficacy siswa terhadap kemampuan pemodelan matematika siswa pada siswa kelas VIII dalam penyelesaian masalah matematika”. Semua asumsi dan persyaratan sudah terpenuhi, seperti uji normalitas, uji linieritas, uji multikolinieritas, uji heteroskedastisitas dan uji autokorelasi, maka uji regresi linier berganda menyatakan bahwa nilai Dengan demikian terdapat pengaruh yang signifikan dari variabel penelitian dan terhadap variabel terikat dengan persamaan regresi . Analisis regresi menunjukkan bahwa peningkatan satu satuan kemampuan matematika meningkatkan kemampuan pemodelan matematika sebesar , dengan asumsi bahwa skor self-efficacy konstan, sedangkan peningkatan satu satuan self-efficacy meningkatkan sebesar , dengan asumsi bahwa skor kemampuan matematika konstan. Kedua variabel berkontribusi positif, dengan pengaruh dominan dari kemampuan matematika. Secara keseluruhan, variasi kemampuan pemodelan matematika dapat dijelaskan oleh kemampuan matematika dan self-efficacy siswa.
Pemahaman mendalam tentang proses dan pola pemecahan masalah siswa dalam pemodelan matematika ditunjukkan melalui pemilihan purposive siswa SMP St. Benediktus Pahauman. Analisis jawaban menunjukkan bahwa siswa umumnya mampu menyelesaikan tahap awal seperti understanding dan simplifying, namun mengalami penurunan signifikan pada tahap working within mathematics, interpreting, dan validating, terutama pada soal kompleks. Kesalahan paling sedikit terjadi pada tahap understanding, meningkat pada mathematizing, dan tertinggi pada working within mathematics. Ilustrasi jawaban tertulis dan wawancara semi-terstruktur dilakukan pada enam subjek yang dipilih berdasarkan: (i) karakteristik jawaban, (ii) jenis kesalahan, (iii) konsistensi skor TKM, TKPM, dan ASE, serta (iv) kesediaan mengikuti wawancara.
Siswa dengan kemampuan matematika dan self-efficacy tinggi menunjukkan performa unggul dalam pemodelan matematika: cepat memahami dan menyederhanakan masalah, membangun model yang tepat, serta menginterpretasikan solusi secara akurat. Mereka juga menunjukkan kemampuan reflektif dan kritis dalam verifikasi, evaluasi solusi, dan pertimbangan alternatif. Siswa dengan kemampuan dan self-efficacy sedang memiliki potensi dasar, namun terbatas dalam eksplorasi dan penyempurnaan model, terutama pada soal kompleks. Siswa mampu memulai pemodelan, tetapi kesulitan dalam representasi, strategi, dan perhitungan, serta ragu dalam mengembangkan dan memvalidasi model. Sementara itu, siswa dengan kemampuan dan self-efficacy rendah mengalami hambatan sejak awal, kurang memahami konsep dasar, tidak mandiri, dan hanya mampu menyelesaikan soal-soal sederhana.
Penelitian ini menyimpulkan bahwa kemampuan matematika dan self-efficacy berpengaruh signifikan terhadap kemampuan pemodelan matematika siswa kelas VIII, dengan kontribusi terbesar dari kemampuan matematika. Hasil regresi berganda yang didukung analisis isi dan wawancara menunjukkan perbedaan karakteristik pemodelan antar kategori kemampuan siswa. Temuan ini menegaskan pentingnya integrasi kemampuan matematika dan self-efficacy dalam pembelajaran. Siswa dengan kemampuan rendah dan sedang mengalami kesulitan memahami soal karena rendahnya literasi membaca dan kesalahan prosedural, sehingga pembelajaran perlu menekankan literasi matematis, pemahaman konsep, dan soal kontekstual berbasis budaya lokal untuk meningkatkan representasi dan pemahaman yang bermakna.
Jeliana Intan Permata. 2025. Exploration of Mathematical Competence and Self-Efficacy on Junior High School Students' Mathematical Modeling Ability in Solving Mathematical Problems. Dissertation, Postgraduate Mathematics Education Study Program, Faculty of Mathematics and Natural Sciences, State University of Surabaya. Promotor Prof. Dr. Mega Teguh Budiarto, M.Pd., and Copromotor Dr. Yusuf Fuad, M.App.Sc.
Keywords: Mathematical modeling, mathematical competence, and self-efficacy, and multiple regression.
This study aims to explore whether or not there is an influence of students' mathematical ability and self-efficacy on the mathematical modeling ability of eighth-grade junior high school students in solving mathematical problems, using exploratory research which is a combination of quantitative and qualitative approaches. The research design used is explanatory sequential. The study population was all eighth-grade junior high school/Islamic junior high school students in Landak Regency, West Kalimantan Province, which were accredited A consisting of 12 public junior high schools and 6 private junior high schools. The trial sample was randomly selected from SMP Maniamas Ngabang. While the research samples were also randomly selected from SMP Negeri 1 Ngabang, SMP Negeri 1 Sengah Temila, and SMP St. Benediktus Pahauman.
Instruments are used the Mathematics Competence Test (MCT), the Mathematical Modeling Test (MMT), and the Self-Efficacy Questionnaire (SEQ) adapted from Koyuncu et al. (2017). Using the Aiken's V method, with assessments by three Mathematics Education doctors and one teacher stated that three instruments were valid with Aiken score . Readability tests by one teacher and three eighth-grade students of SMP Maniamas Ngabang, showed that the instruments were easy to understand and appropriate for use. The trial results stated that the MCT, MMT, and SEQ were valid and reliable; the MCT and MMT had a moderate level of difficulty and good discriminatory power. An additional instrument in the form of an Interview Guide was approved by the supervisor and was declared appropriate in terms of context, content, and language.
Data collection was conducted over three consecutive days on sample students, who were required to complete the MCT, MMT, and SEQ under the supervision of the researcher and one mathematics teacher. On the first day, students worked on the MCT ( minutes), on the second day on the MMT ( minutes), and on the third day on the SEQ (45 minutes). Answers were corrected, scored, and categorized as high ability , medium , and low ability . The results of the MCT: high, medium, low; MMT: high, medium, low; SEQ (scores converted from ordinal to interval): high, medium, low.
Used SPSS and based on the MCT score, MMT score, SEQ score, and multiple regression, a hypothesis test was conducted: "There is a significant influence of students' mathematical ability and students' self-efficacy on students' mathematical modeling ability in class VIII students in solving mathematical problems". All assumptions and requirements have been met, such as normality test, linearity test, multicollinearity test, heteroscedasticity test and autocorrelation test, then the multiple linear regression test states that the value. Thus, there is a significant influence of the research variables and on the dependent variable with the regression equation . The regression analysis shows that an increase of one unit of mathematical ability increases the mathematical modeling ability by 0.933, assuming that the self-efficacy socre remains constant. While an increase of one unit of self-efficacy increases by 0.087, assuming that the mathematical ability socre remains constant. Both variables contributed positively, with mathematical ability being the dominant influence. Overall, 67.4% of the variation in mathematical modeling ability can be explained by students' mathematical ability and self-efficacy.
To deep understanding of students' problem-solving processes and patterns in mathematical modeling is demonstrated through a purposive selection of students from SMP St. Benediktus Pahauman. Analysis of the answers shows that students are generally able to complete the initial stages such as understanding and simplifying, but experience a significant decline in the working within mathematics, interpreting, and validating processes, especially on complex problems. The fewest errors occur in the understanding stage, increase in mathematizing, and the highest in working within mathematics. Illustrations of written answers and semi-structured interviews were conducted on six subjects selected based on: (i) answer characteristics, (ii) types of errors, (iii) consistency of MCT, MMT, and SEQ scores, and (iv) willingness to participate in interviews.
Students with high mathematical ability and self-efficacy demonstrate superior performance in mathematical modeling: quickly understanding and simplifying problems, constructing appropriate models, and accurately interpreting solutions. They also demonstrate reflective and critical skills in verification, solution evaluation, and consideration of alternatives. Students with moderate ability and self-efficacy possess basic potential but are limited in exploring and refining models, especially on complex problems. They are able to initiate modeling but struggle with representation, strategies, and calculations, and are hesitant to develop and validate models. Meanwhile, students with low ability and self-efficacy experience obstacles from the start, lacking a grasp of basic concepts, lacking independence, and only being able to solve simple problems.
This study concludes that mathematical ability and self-efficacy significantly influence the mathematical modeling ability of eighth-grade students, with the largest contribution coming from mathematical ability. Multiple regression results, supported by content analysis and interviews, show differences in modeling characteristics across student ability categories. These findings emphasize the importance of integrating mathematical ability and self-efficacy in learning. Students with low and medium abilities experience difficulties understanding problems due to low reading literacy and procedural errors. Therefore, learning needs to emphasize mathematical literacy, conceptual understanding, and contextual problems based on local culture to improve meaningful representation and understanding.