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Design research from a learning design perspective
... The experimental design phase was structured into two interconnected cycles, in accordance with the iterative methodology outlined by Gravemeijer and Cobb (2006). The first cycle functioned as a preliminary trial to identify instructional shortcomings and student responses to the initial HLT design, while the second cycle focused on refining and reevaluating the revised instructional framework. ...
... These categorizations reinforce the idea that conceptual understanding is a critical objective in mathematics instruction and can be systematically assessed using Bloom's taxonomy. Consequently, the study illustrates how the structured alignment between instructional activities and Bloom's cognitive levels supports the progressive modeling process from contextual to formal mathematical understanding, as described by Gravemeijer and Cobb (2006). Thus, this study reaffirms that instructional designs based on Bloom's taxonomy can effectively foster students' conceptual development in mathematics. ...
Students’ persistent difficulties in understanding three-dimensional geometric figures, particularly cylinders, due to limited spatial visualization and difficulty identifying relationships among their elements, such as cylinder nets. These difficulties are often rooted in traditional instructional practices that emphasize procedural tasks over conceptual development. Despite various interventions, there remains a lack of structured instructional models based on cognitive development frameworks to support students’ conceptual growth in geometry. Addressing this gap, the present study aims to develop and evaluate a Hypothetical Learning Trajectory (HLT) grounded in Bloom’s taxonomy to enhance students' understanding of cylinders. This study employed a design research methodology consisting of three phases: preliminary design, design experiments, and retrospective analysis. Two experimental cycles were conducted with 28 fifth-grade students, categorized into low, moderate, and high levels of understanding. Data were collected through classroom observations, student worksheets, tests, and interviews, and analyzed qualitatively. The HLT consisted of four key learning activities: modeling a cylinder, identifying its elements, constructing the net, and solving application problems, mapped to Bloom’s cognitive levels of remembering, understanding, and applying. Findings revealed that students showed significant improvement in the first three activities, with increased spatial reasoning and conceptual clarity. However, difficulties persisted in the final activity involving reasoning and problem-solving. The results indicate that the proposed Bloom’s taxonomy-based HLT offers a systematic framework for guiding geometry instruction. This study contributes a practical and theoretically grounded instructional model that can support teachers in designing adaptive learning experiences. Further research is recommended to explore its application across diverse topics and student groups.
... Penelitian ini menggunakan metode penelitian design research, yaitu metode penelitian yang fokus utamanya adalah pada pengembangan teori dan aktivitas pembelajaran yang dilakukan melalui 3 tahap yaitu preparing for the experiment/preliminary design (persiapan untuk penelitian/ desain pendahuluan), the design experiment (desain percobaan), dan retrospective analysis (analisis retrospektif) (Gravemeijer & Cobb, 2006). Penelitian ini bertujun untuk merancang dan mengembangkan lintasan belajar siswa dalam memahami materi Potensi Sumber Daya Alam (SDA) melalui Lembar Kerja Peserta Didik (SDA) berbasis literasi. ...
Penelitian ini bertujuan untuk merancang lintasan belajar kontekstual berbasis literasi melalui Lembar Kerja Peserta Didik (LKPD) pada materi Potensi Sumber Daya Alam untuk siswa kelas VII. Latar belakang penelitian ini didasarkan pada rendahnya literasi siswa dalam pembelajaran IPS serta minimnya penggunaan pendekatan berbasis konteks lokal. Metode yang digunakan adalah design research dengan tiga tahapan: preliminary design, design experiment, dan retrospective analysis. Proses pengembangan LKPD dilakukan melalui analisis kebutuhan, serta uji coba one to one dan small group. LKPD dirancang secara multimodal, mengintegrasikan infografis, teks bacaan, dan video edukatif. Hasil penelitian menunjukkan bahwa penggunaan LKPD berbasis literasi mampu meningkatkan keterlibatan siswa, pemahaman konsep, serta kemampuan literasi seperti membaca, menafsirkan informasi visual, dan berpikir kritis. Pembelajaran menjadi lebih bermakna dan kontekstual, serta mendorong kolaborasi antar siswa. Penelitian ini merekomendasikan penggunaan LKPD berbasis literasi sebagai strategi efektif dalam pembelajaran IPS di tingkat sekolah menengah.
... Learning trajectories describe the conceptual and pedagogical progression that students follow when learning a topic, providing a structured approach to instruction (Gravemeijer & Cobb, 2006;Afriansyah & Arwadi, 2021). In the context of statistical literacy (Gal, 2019), a well-defined learning trajectory can help educators design more effective instructional strategies, ensuring that students develop statistical reasoning progressively(van Dijke-Droogers et al., 2022). ...
Literasi statistik merupakan keterampilan penting, terutama bagi calon guru yang akan mengajarkan konsep-konsep statistik kepada siswa. Namun, banyak calon guru yang kesulitan dalam memahami dan menerapkan konsep statistik secara efektif. Penelitian ini bertujuan mengkaji secara sistematis temuan-temuan terdahulu mengenai penggunaan Learning Trajectory (LT) dalam pembelajaran literasi statistik bagi calon guru, guna merancang kerangka pembelajaran yang lebih terstruktur dan aplikatif. Metode yang digunakan adalah Systematic Literature Review (SLR) berdasarkan model Xiao & Watson, yang mencakup tiga tahap: perencanaan, pelaksanaan, dan pelaporan tinjauan. Artikel diperoleh dari database Education Resource Information Centre (ERIC), melalui proses seleksi bertahap yang terdiri dari penyaringan kualitas, penyaringan kelayakan, dan penyaringan relevansi, hingga diperoleh 7 artikel akhir dari 31 artikel awal. Teknik analisis yang digunakan adalah thematic coding untuk mengidentifikasi pola dan kesenjangan dalam penelitian sebelumnya. Hasil menunjukkan bahwa learning trajectory berpotensi besar dalam meningkatkan pemahaman statistik calon guru dengan menyelaraskan pembelajaran secara progresif, meskipun integrasi konteks lokal dan fokus eksplisit pada calon guru masih jarang ditemukan. Kesimpulannya, learning trajectory yang dirancang secara kontekstual dapat menjadi jembatan antara teori dan praktik dalam pembelajaran literasi statistik untuk calon guru. Statistical literacy is an essential skill, particularly for prospective teachers who will be responsible for teaching statistical concepts to students. However, many prospective teachers struggle to understand and effectively apply these concepts. This study aims to systematically examine previous findings on the use of Learning Trajectories (LT) in statistical literacy instruction for prospective teachers, to design a more structured and applicable instructional framework. The method employed is a Systematic Literature Review (SLR) based on the Xiao & Watson model, which consists of three stages: planning, conducting, and reporting the review. Articles were sourced from the Education Resource Information Centre (ERIC) database through a multi-step selection process involving quality screening, eligibility screening, and relevancy screening, resulting in a final sample of 7 articles out of an initial 31. Thematic coding was used to identify patterns and gaps in prior research. The results indicate that learning trajectories hold significant potential to enhance prospective teachers’ statistical understanding by supporting progressive learning; however, the integration of local contexts and a specific focus on prospective teachers remain limited. In conclusion, contextually designed learning trajectories can serve as a bridge between theory and practice in statistical literacy instruction for prospective teachers.
... The intended mathematical activity is to rediscover mathematical concepts and ideas by looking at the real world with the help of teachers. Mention that Gravemeijer (Gravemeijer & Cobb, 2006) formulated three principles of RME: (1) guided reinvention and progressive, (2) didactical phenomenology, and (3) self-developed models. ...
As the low mathematical connection problem shows, students are unable to make mathematical connections on their own. Thus the ability to make mathematical connections is very necessary for training students. This study aims to describe students' mathematical numeracy literacy skills using AKM questions with adapted PISA standards and the difficulties faced by students in solving the given questions. The subjects of this study were grade XI students of SMA Wachid Hasyim 2 Taman Sidoarjo who were selected in one class with a total of 28 students. The type of research used in this study is Mixed Methods Research. The techniques used in this study are test techniques to determine students' ability to solve math numeracy literacy problems, questionnaire techniques to find out students' difficulties, and interviews for in-depth examinations. From the results of the study, it was found that level 1 and 2 category questions were very good, students were able to provide explanations in the form of mathematics and use simple procedures to solve problems. In level 3 and 4 category questions are sufficient, students are still able even though they are not optimal in understanding concepts, representing, and designing solving strategies. On the level 5 question, the category is less. This is because students are less able to represent, reflect, and communicate questions properly and correctly. Level 6 category questions are lacking because students have not been able to apply and master technical mathematical operations, develop new strategies and approaches to deal with new situations, and communicate well. The biggest difficulty faced by students is in analyzing problems, representing, designing solving strategies, accuracy of calculations, and communicating them with argumentation.
... This method aims to develop and validate theories related to learning processes, strategies or materials in order to overcome educational problems and improve the quality of learning. This approach is carried out through collaboration between teachers and researchers (Akker & Gravemeijer, 2020;Bustang et al., 2013;Gravemeijer & Cobb, 2006). ...
Banyak siswa kesulitan memahami konsep laju karena pembelajaran masih bersifat teoritis dan kurang relevan dengan pengalaman mereka. Sehingga penelitian ini ditujukan untuk menghasilkan learning trajectory materi laju menggunakan konteks membajak sawah. Penelitian ini melibatkan siswa kelas VII di salah satu SMP negeri di Belitang. Pengumpulan data melalui lembar aktivitas siswa dan lembar observasi. Penelitian menggunakan design research tipe validation studies yang terdiri dari tiga tahap penelitian yakni preparation experiment, design experiment dan retrospective analysis. Penelitian memberikan hasil bahwa learning trajectory materi laju terdiri dari tiga tahapan yakni mengeksplorasi kegiatan membajak sawah dengan mencari perbandingan antara luas sawah dengan waktu membajak sawah; menentukan satuan dari luas sawah dengan waktu membajak sawah, dan mendiskusikan definisi laju serta melakukan penyelesaian masalah tentang laju. Konteks membajak sawah memudahkan siswa untuk memahami konsep laju secara lebih konkret dan aplikatif. Melalui hasil penelitian ini memberikan masukan bahwa dalam mengajarkan materi laju, perlu mengintegrasikan dengan konteks realistic yang berada disekitar siswa. Many students have difficulty understanding the concept of rate because learning is still theoretical and less relevant to their experience. So, this research is aimed at producing a learning trajectory for rate material using the context of plowing rice fields. This research involved class VII students at one of the state junior high schools in Belitang. Data collection through student activity sheets and observation sheets. The research uses validation studies type design research which consists of three research stages, namely preparation experiment, design experiment and retrospective analysis. The research shows that the learning path for rate material consists of three stages, namely exploring the activity of plowing rice fields by finding a comparison between the area of the rice field and the time for plowing the field, determining the unit of area of the rice field with the time for plowing the field, and discussing the definition of rate and solving problems regarding rate. The context of plowing rice fields makes it easier for students to understand the concept of rate in a more concrete and applicable way. The results of this research provide input that in teaching rate material, it is necessary to integrate it with realistic contexts that surround students.
... Design research typically unfolds in three distinct phases: preparation for the experiment, which involves identifying problems and establishing a theoretical framework; designing the experiment, where the instructional materials and strategies are implemented and tested; and retrospective analysis, which involves analyzing and refining the results to enhance understanding and improve future practices (Gravemeijer & Cobb, 2006). This structured methodology ensures both practical relevance and theoretical rigor in addressing educational challenges. ...
Statistics is a critical subject for developing students' academic and career competencies, yet it remains challenging for many students due to its abstract nature. To address this issue, a study was conducted to design a learning trajectory for teaching statistical concepts by integrating technology, ethnomathematics, and realistic mathematics education (TE-RME) within the culturally relevant context of pranata mangsa, a traditional Javanese calendar system. Employing a design research methodology, the study involved 32 eighth-grade students from a junior high school in Semarang, Indonesia. It was conducted in three phases: preparation for the experiment, designing learning activities, and retrospective analysis. The resulting learning trajectory consisted of three structured activities: observing pranata mangsa videos to collect and present data, deriving formulas for measures of central tendency, and exploring methods for calculating data dispersion. Findings indicated that the integration of pranata mangsa in the TE-RME framework significantly enhanced students' understanding of statistical concepts by connecting abstract ideas to culturally meaningful contexts. This approach facilitated quicker and more meaningful learning, demonstrating the effectiveness of incorporating local wisdom into mathematics education. The study also highlights the potential for future research to explore other culturally relevant contexts to teach mathematical concepts, further advancing the field of culturally responsive education.
... The selected participants demonstrated varied levels of mathematical proficiency categorized as high, moderate, and low. Following the design research framework outlined by Gravemeijer and Cobb (2006) and Akker et al. (2009), the study was implemented in three key phases: preliminary design, design experiment, and retrospective analysis. ...
Mastery of the concepts of ratio and proportion is essential in mathematics education, as it underpins students’ ability to develop logical reasoning and proportional thinking skills critical for advanced mathematical understanding. Despite its importance, students often struggle with these concepts due to the lack of learning activities that meaningfully connect mathematics to real-life contexts and cultural relevance. This disconnect highlights a gap in instructional approaches that fail to bridge abstract mathematical content with students’ lived experiences. Addressing this issue, the present study introduces a novel integration of the Pendidikan Matematika Realistik Indonesia (PMRI) approach with local cultural context, specifically the traditional Sumatran dish, namely lemang, to enhance students' conceptual grasp of ratio and proportion. The study aims to design and implement a PMRI-based learning sequence centered on the lemang context to facilitate meaningful learning experiences among junior high school students. Employing a design research methodology, the study involved seventh-grade students at SMP IT An-Nida Lubuklinggau, with data collected through student activity sheets (SAS), classroom observations, interviews, and documentation. Findings indicate that the integration of PMRI with the lemang context significantly supports students' progressive understanding of ratio and proportion, fostering both cognitive engagement and cultural appreciation. This research contributes to the enrichment of mathematics education by demonstrating how culturally contextualized PMRI designs can promote deeper learning and affirm the relevance of mathematical knowledge in students' everyday lives.
... The method used in this research is the design research method which consists of three stages (Gravemeijer & Cobb, 2006): (1) experimental preparation, (2) experimental design, and (3) retrospective analysis. Data collection techniques in this research: (1) Interviews with teachers and students, (2) Observation, and (3) Documentation to analyze and clarify hypotheticals. ...
Geometry is an essential topic things to needs to be mastered by participants, one of the topics on geometry is quadrilateral. However, in conditions in the field students Still have difficulty understanding quadrilateral topics. Research This aims to design Hypothetical Learning Trajectory (HLT) Quadrilateral Topics for Grade VII Junior High School Students according to with needs of students and appropriate with the process of thinking student with analyze the effectiveness of HLT applied. The method used in the study This is method design research consisting of three stages : (1) preparation experiment to design HLT (2) design experiment that implements HLT which has been designed, and (3) analysis retrospective that analyzes effectiveness HLT applied in learning. Deep data collection techniques study this : (1) Interviews with teachers and students, (2) Observation and observation, and (3) Documentation For analysis and clarifying HLT. Subject study This consists of 20 students of SMPN 2 Cimahi Class VII with characteristics of heterogeneous students with high, medium, and low ability. This article serves results at stage preparation experiment, design experiments, and analysis retrospective as well as analyze HLT material effectiveness quadrilateral. Track design Study includes, objectives learning material quadrilateral, activities and tasks designed learning For material quadrilateral, and hypothesis channel think a student in understanding draft material quadrilateral. The study This produced HLT which consists of a series of activity learning material rectangle on indicator understand properties quadrilateral, and find around quadrilateral. Analysis results show that HLT is designed in study This Still needs development For activities on the topic properties square, but gives change positive to student class VII in understanding draft around quadrilateral. Analysis results effectiveness reviewed from completeness Study produced by 85% of studes Already achieve KKM on the material quadrilateral, thing This show that the HLT was designed Already effective applied in learning.
Penelitian ini bertujuan untuk menilai kebutuhan dalam pembelajaran matematika di tingkat sekolah dasar melalui pemanfaatan media AI Canva pada materi perkalian. Penelitian ini menggunakan metode kualitatif dengan pendekatan studi kasus yang dilakukan di beberapa sekolah dasar di Jakarta. Data diperoleh melalui wawancara dengan guru matematika, observasi di kelas, serta kajian terhadap dokumen pembelajaran yang ada. Temuan penelitian mengindikasikan bahwa penggunaan media AI Canva dapat membantu siswa dalam memahami konsep perkalian secara lebih efektif, dengan menyajikan materi secara visual yang menarik dan interaktif. Respon dari guru dan siswa terhadap media ini cenderung positif, karena dapat meningkatkan keterlibatan siswa dalam pembelajaran. Penelitian ini menyarankan agar pengembangan media pembelajaran berbasis AI terus diperluas, khususnya dalam konteks pembelajaran matematika di sekolah dasar.
In this article, a general model is proposed for design research in education that grows out of the author’s research and work in related design fields. The model emphasizes the stage sensitivity of (a) research questions, (b) data and methods, and (c) the need for researchers to design artifacts, processes, and analyses at earlier stages in their research that can then be profitably used (perhaps by different researchers) in later stages.
In this article, the authors first indicate the range of purposes and the variety of settings in which design experiments have been conducted and then delineate five crosscutting features that collectively differentiate design experiments from other methodologies. Design experiments have both a pragmatic bent—“engineering” particular forms of learning—and a theoretical orientation—developing domain-specific theories by systematically studying those forms of learning and the means of supporting them. The authors clarify what is involved in preparing for and carrying out a design experiment, and in conducting a retrospective analysis of the extensive, longitudinal data sets generated during an experiment. Logistical issues, issues of measure, the importance of working through the data systematically, and the need to be explicit about the criteria for making inferences are discussed.
Educational research is not very influential, useful, or well funded. This article explores why and suggests ways that the situation could be improved. Our focus is on the processes that link the development of good ideas and insights, the development of tools and structures for implementation, and the enabling of robust implementation in realistic practice. We suggest that educational research and development should be restructured so as to be more useful to practitioners and to policymakers, allowing the latter to make better-informed, less-speculative decisions that will improve practice more reliably.
The article highlights and problematizes some challenges that are faced in carrying out design-based research. It states that the emerging field of learning sciences is one that is interdisciplinary, drawing on multiple theoretical perspectives and research paradigms so as to build understandings of the nature and conditions of learning, cognition and development. A fundamental assumption of many learning scientists is that cognition is not a thing located within the individual thinker but is a process that is distributed across the knower, the environment in which knowing occurs and the activity in which the learner participates. In other words, learning, cognition, knowing and context are irreducibly co-constituted and cannot be treated as isolated entities or processes.
In this article, we report on a design experiment conducted in an 8th grade classroom that focused on students' analyhsis of bivariate data. Our immediate goal is to document both the actual learning trajectory of the classroom community and the diversity in the students' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. On a broader level, we also focus on the learning of the research team by documenting the conjectures about the stuydents' statistical learning and the means of supporting it that the research team generated, tested, and revised on-line while the experiment was in progress. In the final part of the article, we synthesize the results of this learning by proposing a revised learning trajectory that can inform design and instruction in other classrooms. In doing so, we make a contribution to the cumulative development of a domain-specific instructional theory for statistical data analysis.
In this study, we seek to describe how the meaning of a tool was co-constructed by the students and their teacher and how the students used the tool to construct mathematical meaning out of particular tasks. We report the results of a qualitative, classroom-based study that examined (1) the role, knowledge and beliefs of a pre-calculus teacher, (2)how students used graphing calculators in support of their learning of mathematics, (3) the relationship and interactions between the teacher's role, knowledge and beliefs and the students' use of the graphing calculator in learning mathematics, and (4) some constraints of the graphing calculator technology that emerged within the classroom practice. We found five patterns and modes of graphing calculator tool use emerged in this practice: computational tool, transformational tool, data collection and analysis tool, visualizing tool, and checking tool. The results of this study suggest that nature of the mathematical tasks and the role, knowledge and beliefs of the teacher influenced the emergence of such rich usage of the graphing calculator. We also found that the use of the calculator as a personal device can inhibit communication in a small group setting, while its use as a shared device supported mathematical learning in the whole class setting.
If design-based research is the answer, what is the question? Journal of the Learning Sciences Ontological innovation and the role of theory in design experiments
- C Dede
Dede, C. (2004). If design-based research is the answer, what is the question? Journal of the Learning Sciences, 13(1), 105-114. diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. Journal of the Learning Sciences, 13(1), 77-103