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All Journal Plusminus: Jurnal Pendidikan Matematika Jurnal Didactical Mathematics Journal of Mathematics Instruction, Social Research and Opinion
Mulia Putra
Universitas Singaperbangsa Karawang
Humanities Education Languange, Linguistic, Communication & Media Mathematics Social Sciences Other

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From Design to Practice: Understanding by Design as a Framework for Developing Didactic Competence in Pre-Service Teachers Rita Novita; Mulia Putra; Safrina Junita; Regina Rahmi
Plusminus: Jurnal Pendidikan Matematika Vol. 5 No. 3 (2025): November
Publisher : Department of Mathematics Education Program IPI Garut

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31980/plusminus.v5i3.3252

Abstract

Mahasiswa calon guru sering mengalami kesulitan dalam menyelaraskan tujuan pembelajaran, penilaian, dan kegiatan pembelajaran sehingga rancangan pembelajaran yang disusun cenderung tidak koheren. Penelitian kualitatif ini bertujuan untuk mengkaji peran kerangka Understanding by Design (UbD) dalam mendukung pengembangan kompetensi didaktik mahasiswa calon guru. Penelitian melibatkan 26 mahasiswa calon guru (14 Pendidikan Bahasa Inggris dan 12 Pendidikan Matematika) yang mengikuti Program Pendidikan Profesi Guru (PPG) tahun 2025 di Banda Aceh. Data dikumpulkan melalui analisis rancangan pembelajaran, jurnal reflektif, dan wawancara, kemudian dianalisis menggunakan reflexive thematic analysis. Hasil penelitian menunjukkan bahwa sebelum penerapan UbD, sebanyak 84,6% partisipan belum mampu mengaitkan tujuan pembelajaran, penilaian, dan kegiatan pembelajaran secara selaras, terutama karena penilaian masih dipahami sebatas jenis asesmen. Setelah penerapan UbD, rancangan pembelajaran menjadi lebih terarah dan selaras antara tujuan dan penilaian. Namun demikian, sebagian penilaian masih berada pada tingkat kognitif rendah dan belum mendukung keterampilan berpikir tingkat tinggi. Temuan ini menunjukkan bahwa UbD efektif sebagai scaffold untuk membangun kompetensi didaktik dasar, tetapi perlu didukung penguatan literasi asesmen dalam pendidikan profesi guru. Pre-service teachers often struggle to align learning objectives, assessment, and instructional activities, resulting in fragmented lesson design. This qualitative study examines how the Understanding by Design (UbD) framework supports the development of didactic competence among 26 pre-service teachers (14 English and 12 Mathematics) enrolled in a 2025 professional teacher education (PPG) program in Banda Aceh, Indonesia. Data were collected through lesson plan analysis, reflective journals, and interviews, and analyzed using reflexive thematic analysis. Findings show that prior to UbD instruction, 84.6% of participants failed to coherently connect objectives, assessment, and learning activities, particularly conceptualizing assessment only in terms of types rather than evidence of learning. After applying UbD, lesson designs became more aligned, with clearer connections between goals and assessment. However, assessment tasks frequently remained at low cognitive levels, limiting opportunities for higher-order thinking. The study demonstrates that UbD effectively scaffolds foundational didactic competence by promoting alignment and reflective instructional reasoning, but does not automatically lead to higher-order assessment design. These findings highlight the importance of integrating UbD with explicit assessment literacy support in professional teacher education.
From Multiplicative Growth to Institutionalized Exponential Knowledge: A Praxeological Analysis of Exponential Learning in a Secondary Mathematics Textbook Laila Cantika; Septiani Yugni Maudy; Mulia Putra
Jurnal Didactical Mathematics Vol. 8 No. 2 (2026): Oktober 2026
Publisher : Program Studi Pendidikan Matematika, Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/dm.v8i2.18499

Abstract

This study investigates the praxeological organization of exponent learning in a Grade 10 mathematics textbook through the lens of the Anthropological Theory of the Didactic (ATD). The study aims to examine how exponent knowledge is introduced, developed, and institutionalized through the relationships among tasks, techniques, technologies, and theories. A qualitative document analysis was conducted using the exponent chapter of the 2021 Indonesian Mathematics Electronic School Book. The analysis focused on Exploration 1.1, Exploration 1.2, and Exercise 1.1, which cover the initial development of concepts of exponents. Mathematical tasks were identified and reconstructed into local praxeologies, which were subsequently synthesized into a global praxeological organization. The findings reveal a coherent learning trajectory consisting of three successive phases. Exploration 1.1 constructs exponentiation through multiplicative growth situations, enabling students to develop meaning from repeated multiplication. Exploration 1.2 extends this understanding by identifying and generalizing the properties of exponents. Exercise 1.1 institutionalizes exponent knowledge by transforming exponent properties into tools for justification, equation solving, and symbolic simplification. The reconstructed global organization demonstrates a progression from meaning construction to formal mathematical practice. The analysis further shows that the visibility of the praxis block increases throughout the chapter, whereas technological explanations become less explicit during the institutionalization phase. These findings contribute to textbook research by illustrating how the sequencing of praxeological components shapes students' opportunities to construct, generalize, and apply mathematical knowledge. The study also highlights the value of ATD as a framework for examining the epistemological organization of mathematical content in school textbooks
Learning Obstacles in Understanding Pyramid Volume: An Epistemological and Didactical Analysis within the Didactical Design Research Framework Vallieskha Nurmanita Dhaffah; Septiani Yugni Maudy; Mulia Putra
Jurnal Didactical Mathematics Vol. 8 No. 2 (2026): Oktober 2026
Publisher : Program Studi Pendidikan Matematika, Universitas Majalengka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31949/dm.v8i2.18713

Abstract

Understanding the concept of pyramid volume remains challenging for many students, even after prior study. These difficulties indicate learning obstacles that need to be identified before designing effective instructional interventions. This study aimed to identify students’ learning obstacles related to the concept of pyramid volume within the prospective analysis phase of Didactical Design Research (DDR). A qualitative approach was employed involving 35 ninth-grade students from SMP Negeri 13 Tambun Selatan who completed a diagnostic test consisting of six validated items. Based on variations in students’ response patterns, six students were purposively selected for in-depth interviews. To strengthen the credibility of the findings, interviews with a mathematics teacher were also conducted. Data were analyzed using the Miles and Huberman interactive model, including data reduction, data display, and conclusion drawing. The findings revealed seven learning obstacles, comprising four epistemological and three didactical. The epistemological obstacles included difficulties in understanding relationships among pyramid elements, distinguishing points and planes in identifying pyramid bases, recognizing two-dimensional properties as prerequisites for determining pyramid bases, and understanding the meaning of one-third in the pyramid volume formula. The didactical obstacles were associated with procedurally oriented instruction, insufficient reinforcement of prerequisite concepts, and limited opportunities for independent learning. These findings demonstrate that students’ conceptual difficulties are closely related to instructional practices experienced during learning. Therefore, the identified obstacles provide an important foundation for designing learning trajectories and didactical situations that support meaningful understanding of pyramid volume concepts.
From Students’ Ways of Thinking to Meaning Construction: Hermeneutics Perspective of the ε-δ Definition Aditya Prihandhika; Mulia Putra
Journal of Mathematics Instruction, Social Research and Opinion Vol. 5 No. 3 (2026): September
Publisher : MASI Mandiri Edukasi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58421/misro.v5i3.1537

Abstract

The  definition is widely recognized as one of the most conceptually demanding topics in differential calculus and introductory real analysis, as students often rely on intuitive notions of closeness without fully grasping its formal logical structure. Building on prior findings on students’ ways of thinking, this study investigates how such ways of thinking contribute to the construction of mathematical meaning related to the  definition. This study employed a qualitative hermeneutic design involving written responses, task-based interviews, and reflective memos from 28 undergraduate students enrolled in calculus and introductory real analysis courses. Data were analyzed through a hermeneutic cycle consisting of naïve reading, selective highlighting, thematic interpretation, and the integration of students’ interpretations with the formal mathematical meaning of the  definition. The findings reveal three dominant interpretive themes: distance meaning, where  and  are understood as measures of closeness; responsive dependency, where δ is interpreted as a response to a chosen ; and control meaning, where  functions as a mechanism for regulating input proximity. Persistent challenges include equality, dependency and confusion in quantifier sequencing. This study contributes by extending students’ ways of thinking into a hermeneutic account of meaning construction, providing an epistemic basis for future didactic transposition studies. The findings also suggest instructional approaches that explicitly address distance, dependency, and logical sequencing in teaching the  definition.
Co-Authors Aditya Prihandhika Laila Cantika Regina Rahmi Rita Novita Safrina Junita Septiani Yugni Maudy Vallieskha Nurmanita Dhaffah