{
  "abstract": "Research on mathematical reflective thinking skills has generally focused on improving learning outcomes through various instructional models. However, limited attention has been given to examining the role of learning independence as a moderating variable that may influence the effectiveness of the Discovery Learning model, particularly in the topic of Systems of Linear Equations in Two Variables (SPLDV). Therefore, this study aims to evaluate the effectiveness of the Discovery Learning model in enhancing the mathematical reflective thinking skills of senior high school students by considering learning independence as a moderating variable. This study employed a quantitative approach using a non-equivalent control group design, involving an experimental group taught through the Discovery Learning model and a control group taught using the expository learning model. Data were collected using a mathematical reflective thinking test and a learning independence questionnaire, both of which were validated and demonstrated satisfactory reliability. Data analysis included descriptive statistics, normality and homogeneity tests, and hypothesis testing using an independent-samples t-test, N-gain analysis, and two-way ANOVA. The results showed that the two groups had comparable initial abilities. However, after the intervention, a statistically significant difference was found, with the experimental group achieving higher post-test scores and greater N-gain improvement than the control group. Furthermore, students' mathematical reflective thinking skills differed significantly according to their level of learning independence, with students demonstrating high levels of learning independence achieving better performance. The interaction between the learning model and the level of learning independence was also found to have a significant effect on students' mathematical reflective thinking skills. These findings indicate that the Discovery Learning model is an effective instructional strategy for enhancing students' mathematical reflective thinking skills, particularly when supported by high levels of learning independence. Therefore, future research is recommended to investigate other moderating variables and to examine the effectiveness of this model across different mathematical topics and educational levels.\n\nAbstrak\n\nPenelitian mengenai kemampuan berpikir reflektif matematis umumnya berfokus pada peningkatan hasil belajar melalui berbagai model pembelajaran, namun masih terbatas dalam mengkaji peran kemandirian belajar sebagai variabel moderasi yang dapat mempengaruhi efektivitas model discovery learning, khususnya pada materi Sistem Persamaan Linear Dua Variabel (SPLDV). Oleh karena itu, penelitian ini bertujuan untuk menilai seberapa efektif model Discovery Learning dalam meningkatkan kemampuan berpikir reflektif matematika siswa SMA dengan mempertimbangkan kemandirian belajar sebagai variabel moderasi. Penelitian ini menggunakan pendekatan kuantitatif dengan desain kelompok kontrol non-ekuivalen, yang melibatkan kelompok eksperimen yang diajar melalui Discovery Learning dan kelompok kontrol yang diajar melalui model ekspositori. Data dikumpulkan menggunakan tes berpikir reflektif matematika dan kuesioner kemandirian belajar, yang keduanya telah divalidasi dan terbukti reliabel. Analisis data meliputi statistik deskriptif, uji normalitas dan homogenitas, serta pengujian hipotesis menggunakan uji t sampel independen, analisis N-gain, dan ANOVA dua arah. Hasil penelitian menunjukkan bahwa kedua kelas memiliki kesamaan dalam kemampuan awal, setelah diberi perlakuan, terdapat perbedaan signifikan dengan kelas eksperimen memperoleh skor post-test dan peningkatan N-Gain yang lebih tinggi daripada kelas kontrol. Selain itu, kemampuan berpikir reflektif matematika bervariasi secara signifikan berdasarkan tingkat kemandirian belajar, dengan siswa dengan kemandirian tinggi memperoleh hasil yang lebih unggul. Hubungan antara model pembelajaran dan tingkat kemandirian belajar pada keterampilan berpikir reflektif matematika juga terbukti signifikan. Penelitian ini menunjukkan bahwa model Discovery Learning efektif digunakan sebagai strategi pembelajaran untuk meningkatkan kemampuan berpikir reflektif matematis siswa. Oleh karena itu, penelitian selanjutnya disarankan untuk mengkaji variabel moderasi lainnya serta menguji penerapan model ini pada materi dan jenjang pendidikan yang berbeda.",
  "abstract_shown": true,
  "affiliations": [
    "Universitas Sultan Ageng Tirtayasa"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ipat"
    },
    {
      "affs": [
        0
      ],
      "name": "Hepsi Nindiasari"
    },
    {
      "affs": [
        0
      ],
      "name": "Syamsuri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/522ph1nyfkwqs.bib",
  "cited_by": 0,
  "doi": "10.15294/kreano.v17i1.57528",
  "fulltext_url": "https://journal.unnes.ac.id/journals/kreano/article/view/57528",
  "id": "522ph1nyfkwqs",
  "issns": [
    "2086-2334",
    "2442-4218"
  ],
  "landing_url": "https://doi.org/10.15294/kreano.v17i1.57528",
  "language": "en",
  "licence": "CC-BY-SA",
  "licence_label": "CC BY-SA",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "L"
    ],
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2604|Mathematics Education and Pedagogy"
    ]
  ],
  "openalex": "W7166879148",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-01",
  "publisher": "Universitas Negeri Semarang",
  "ris": "https://research.draconitic.com/paper/522ph1nyfkwqs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:46:19Z",
      "native_id": "24eec8d1182847179b33c586279f6c49",
      "source": "doaj",
      "url": "https://doi.org/10.15294/kreano.v17i1.57528"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematics Education and Pedagogy",
      "subfield": "general"
    }
  ],
  "title": "The Effectiveness of Discovery Learning on Mathematical Reflective Thinking Skills Based on the Level of Learning Independence of High School Students",
  "title_text": "The Effectiveness of Discovery Learning on Mathematical Reflective Thinking Skills Based on the Level of Learning Independence of High School Students",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:46:19Z",
  "url": "https://research.draconitic.com/paper/522ph1nyfkwqs",
  "venue": "Kreano: Jurnal Matematika Kreatif-Inovatif",
  "versions": []
}