Aflich Yusnita Fitrianna, - and Rizky Rosjanuardi, - and Sufyani Prabawanto, - and Al Jupri, - (2025) PENALARAN SECARA ALJABAR DAN RESILIENSI MATEMATIS SISWA PADA IMPLEMENTASI DESAIN DIDAKTIS MATERI FUNGSI KOMPOSISI DAN INVERS BERDASARKAN TAHAP KOGNITIF. S3 thesis, Universitas Pendidikan Indonesia.
Abstract
Penerapan Kurikulum Merdeka menekankan pentingnya pengembangan penalaran aljabar dalam pembelajaran matematika, termasuk pada materi fungsi komposisi dan invers. Namun, siswa masih mengalami kesulitan dalam memahami konsep ini, terutama dalam aspek generalisasi, representasi, dan penggunaan notasi yang tepat, yang berkaitan dengan tahap perkembangan kognitif siswa. Selain itu, rendahnya resiliensi matematis siswa turut mempengaruhi kemampuan mereka dalam menyelesaikan tugas-tugas penalaran aljabar. Oleh karena itu, diperlukan desain didaktis yang mempertimbangkan hambatan belajar dan tahap kognitif siswa. Tujuan penelitian ini mendeskripsikan secara komprehensif penalaran aljabar dan resiliensi matematis siswa melalui implementasi desain didaktis materi fungsi komposisi dan invers berdasarkan tahap kognitif. Penelitian ini menggunakan pendekatan kualitatif dengan desain Didactical Design Research (DDR). DDR diterapkan melalui tiga tahapan yaitu analisis prospektif, metapedidaktik, dan retrospektif. Penelitian ini dilakukan pada siswa kelas XI di salah satu SMA Negeri di Kabupaten Bandung Barat dengan partisipan penelitian sebanyak 27 siswa pada tahap analisis prospektif serta 35 siswa pada tahap analisis metapedidaktik dan retrospektif, serta 2 orang guru. Pengumpulan data dilakukan melalui Test of Logical Thinking (TOLT), tes penalaran aljabar, angket resiliensi matematis, wawancara, studi dokumentasi, dan observasi. Keabsahan data dijamin melalui credibility, transferbility, dependability, dan confirmability. Analisis data mengikuti model Miles dan Huberman yang mencakup reduksi data, penyajian data, serta penarikan kesimpulan dan verifikasi. Hasil penelitian mengungkap enam temuan yaitu: (1) Profil tahap kognitif siswa menunjukkan bahwa siswa terbagi dalam tahap konkret, transisi, dan formal, dengan karakteristik Siswa tahap konkret hanya menguasai dua indikator TOLT, yaitu penalaran proporsional dan kombinatorial secara terbatas. Siswa tahap transisi mampu memenuhi empat indikator, sementara siswa tahap formal memenuhi lima indikator, termasuk penalaran korelasional dan pengontrolan variabel. (2) Hambatan belajar siswa dalam memahami fungsi komposisi dan invers meliputi hambatan ontogenik konseptual, ontogenik instrumental, epistemologis, dan didaktis, pada aspek representasi, generalisasi, dan justifikasi. (3) Resiliensi matematis siswa pada tahap konkret menunjukkan mudah menyerah dan kurang percaya diri dalam menyelesaikan masalah, siswa tahap transisi memiliki motivasi tetapi masih mengalami ketidakstabilan dalam mengatasi kesulitan, siswa tahap formal menunjukkan daya juang, mampu menggunakan pengalaman kegagalan untuk memperbaiki strategi penyelesaian masalah, serta lebih percaya diri dalam diskusi kelompok. (4) Desain didaktis yang dikembangkan berdasarkan teori Brousseau yang meliputi tahapan pembelajaran situasi aksi, formulasi, validasi dan institusionalisasi dengan mengintegrasikan aspek penalaran aljabar dan resiliensi matematis. (5) Setelah implementasi desain didaktis, kemampuan penalaran aljabar pada siswa tahap konkret lebih mampu menggunakan representasi yang tepat, siswa tahap transisi dapat memahami konsep fungsi komposisi tetapi masih kurang tepat dalam penyederhanaan dan justifikasi. Siswa tahap formal menunjukkan perbaikan dalam generalisasi konsep dan dapat mengembangkan justifikasi yang lebih sistematis. (6) Setelah implementasi desain didaktis, resiliensi matematis siswa mengalami perkembangan, yaitu siswa tahap konkret mulai menunjukkan motivasi dalam menyelesaikan tugas, meskipun masih memerlukan bimbingan dalam menghadapi kesulitan. Siswa tahap transisi lebih aktif dalam berdiskusi dan menunjukkan sikap pantang menyerah dalam menyelesaikan soal yang lebih kompleks. Siswa tahap formal lebih percaya diri, dapat berkolaborasi secara efektif, serta mampu menggunakan pengalaman kesalahan sebagai bagian dari proses pembelajaran. (7) Desain didaktis empiris berbasis tahap kognitif disusun untuk mengoptimalkan pembelajaran fungsi komposisi dan invers dengan pendekatan yang sesuai bagi setiap tahap kognitif siswa. Implementation of the Kurikulum Merdeka emphasises the importance of developing algebraic reasoning in mathematics learning, including composition and inverse function material. However, students still have difficulties understanding this concept, especially in the generalization, representation, and proper use of notation, which are related to the stage of cognitive development of students. In addition, students' low mathematical resilience also affects their ability to complete algebraic reasoning tasks. Therefore, a didactical design that takes into account the learning obstacles and students' cognitive stage. The purpose of this study is to comprehensively describe students' algebraic reasoning and mathematical resilience through the implementation of didactical design of composition and inverse function material based on the cognitive stage. This research used a qualitative approach with Didactical Design Research (DDR) design. DDR is implemented through three stages, namely prospective, metapedidactic, and retrospective analysis. This research was conducted on grade XI students in one of the public high schools in West Bandung Regency with research participants of as many as 27 students at the prospective analysis stage and 35 students at the metapedidactic and retrospective analysis stages, as well as 2 teachers. Data were collected through the Test of Logical Thinking (TOLT), algebraic reasoning test, mathematical resilience questionnaire, interviews, documentation studies, and observations. Data validity was guaranteed through credibility, transferability, dependability, and confirmability. Data analysis followed the Miles and Huberman model which included data reduction, data presentation, and conclusion drawing and verification. The results of the study include (1) The profile of students' cognitive stages shows that students are divided into concrete, transitional, and formal stages, with characteristics Concrete stage students only master two TOLT indicators, namely proportional and combinatorial reasoning in a limited manner. Transitional-stage students are able to fulfil four indicators, while formal-stage students fulfil five indicators, including correlational reasoning and controlling variables. (2) Students' learning obstacles in understanding composition and inverse functions include conceptual ontogenic, instrumental ontogenic, epistemological, and didactic obstacles in representation, generalization, and justification. (3) Mathematical resilience of students at the concrete stage shows easy giving up and lack of confidence in solving problems, transition stage students have motivation but still experience instability in overcoming difficulties, formal stage students show fighting power, are able to use the experience of failure to improve problem-solving strategies, and are more confident in group discussions. (4) The didactical design developed is based on Brousseau's theory which includes the stages of action situation learning, formulation, validation and institutionalization by integrating aspects of algebraic reasoning and mathematical resilience. (5) After the implementation of the didactical design, the algebraic reasoning ability of concrete stage students is more capable of using appropriate representations, transitional stage students can understand the concept of composition functions but are still less precise in simplification and justification. Formal-stage students show improvement in concept generalization and can develop more systematic justifications. (6) After the implementation of the didactical design, students' mathematical resilience developed, namely concrete stage students began to show motivation in completing the task, although they still need guidance in facing difficulties. Transition stage students are more active in discussions and show an unyielding attitude in solving more complex problems. Formal-stage students are more confident, can collaborate effectively, and are able to use error experiences as part of the learning process. (7) Empirical didactical design based on cognitive stage is arranged to optimize the learning of composition and inverse functions with an approach that is appropriate for each cognitive stage of students.
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| Item Type: | Thesis (S3) |
|---|---|
| Additional Information: | https://scholar.google.com/citations?user=X1xnQ-IAAAAJ&hl=en&oi=ao ID SINTA Dosen Pembimbing: Rizky Rosjanuardi: 5978531 Sufyani Prabawanto: 5995121 Al Jupri: 5974523 |
| Uncontrolled Keywords: | Tahap kognitif, Materi Fungsi Komposisi dan Invers, Kemampuan Penalaran Aljabar, Resiliensi Matematis, Desain Didaktis Cognitive Stage, Composition and Inverse Function Topics, Algebraic Reasoning Ability, Mathematical Resilience, Didactical Design |
| Subjects: | L Education > L Education (General) L Education > LB Theory and practice of education Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Pendidikan Matematika - S3 |
| Depositing User: | Aflich Yusnita Fitrianna |
| Date Deposited: | 30 Apr 2025 04:11 |
| Last Modified: | 30 Apr 2025 04:11 |
| URI: | http://repository.upi.edu/id/eprint/132591 |
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