TR63 vol 18 no 1 of the Mathematics Teaching-Research Journal
Editorial of the Early Spring Issue 63 volume18no1
Wenjuan Li
College of Staten Island of the City University of New York, USA
The current issue features articles addressing four main themes: student learning obstacles, realistic mathematics education, technology-enriched learning, and teacher training and development. By bringing research from Croatia, Hungary, Indonesia, Malaysia, Morocco, South Africa, Türkiye, the United States, and Vietnam, the articles offer diverse perspectives that transcend one-size-fits-all solutions and enrich the global discourse in mathematics education. Specifically, they present strategies for leveraging students’ thinking to inform instructional design, designing effective technology learning environments, and promoting high-quality teaching practices. Together, this issue provides valuable insights across the educational ecosystem that directly inform the work of teachers, researchers, and policymakers. We hope these papers serve as a catalyst for future research and classroom innovation, ultimately fostering a more vibrant mathematics education landscape internationally.
The editorial team extends its gratitude to all authors for their valuable contributions to the Mathematics Teaching–Research Journal. Their work is essential in cultivating meaningful dialogue between mathematics education research and classroom practice.
Learning Obstacles and Trajectories
Learning trajectories provide a roadmap for designing instruction that builds on students’ mathematical strengths. Anticipating learning obstacles and predicting learning paths allows teachers to tailor instruction to students’ evolving mathematical thinking. The first three studies explore students’ learning obstacles from a phenomenology perspective and offer instructional strategies for addressing common learning obstacles of fractions, variables, and inequalities. Andriatna, Sujadi, Kurniawati, Wulandari, and Nursanti examine Indonesian junior high school students’ learning obstacles of fractions and share a lesson design based on the 5Es model to address the identified ontogenic and epistemological obstacles. Fitria, Susiswo, and Susanto identify cognitive disconnect as a key obstacle in middle school students’ understanding of variables and emphasize that instruction should deliberately link arithmetic and algebra through gradual representations and systematic scaffolding to bridge cognitive disconnection. Siagian’s analysis of students’ concept images in learning inequalities highlights the need to bridge procedural proficiency and conceptual understanding. Next, two studies integrated the RME approach to articulate hypothetical learning trajectories of learning division and developing trigonometric ratios concepts. Duyen and Loc’s study presents a hypothetical learning trajectory of division and a four-lesson intervention to develop first-grade students’ robust understanding of partitive and quotitive division. Andiani, Darhim, and Nurlaelah’s study demonstrates that contextualized activities informed by a hypothetical learning trajectory enhance high school students’ understanding of trigonometric ratios and facilitate their transfer to real-world contexts.
Learning Obstacle in Fraction Concept: A Hermeneutic Phenomenology Study
Riki Andriatna, Imam Sujadi, Ira Kurniawati, Arum Nur Wulandari, Yuli Bangun Nursanti (Indonesia)………………………………………………………………………..pages 6-30
Analisa Fitria, Subanji Susiswo, Hery Susanto (Indonesia)………………pages 31-59
Exploring the Concept of Inequality Through the Lens of Concept Image Students
Muhammad Daut Siagian, Izwita Dewi (Indonesia)…………………….…pages 60-96
Nguyen Thi Hong Duyen, Nguyen Phu Loc (Vietnam)…………….…pages 97-123
Learning Trajectory of Trigonometric Ratios Applying Realistic Mathematics Education
Dini Andiani, Darhim, Elah Nurlaelah (Indonesia)…………………………pages 124-151
Technology-enriched Learning
These technology-focused studies demonstrate that when integrated effectively, digital tools and instructional innovations have a transformative impact on mathematics learning by developing deeper conceptual understanding, fostering student engagement, and providing personalized learning experiences. Sugiman, Maulyda, and Rahmawati document the process of designing an augmented reality-based and learning tool based on the Didactical Technology Design framework and highlight its potential in creating interactive learning environments to improve primary students’ numeracy skills. Nugroho, Arliani, and Sugiman demonstrate that integrating Realistic Mathematics Education into instructional websites (RME-Web) can enhance junior high students’ computational thinking skills more effectively compared to traditional RME or direct-learning approaches. Uyun, Mailizar, and Elizar report that the flipped classroom model enhances Grade 11 students’ mathematics learning outcomes and overall engagement, though behavioral engagement showed no significant difference. The two studies on GeoGebra by Matić and Bošnjak and Torma, Kiss, and Waldhauser highlight how the tool can enhance students’ understanding through accessible visualization representations and sustained engagement. Last but not least, Kartika and Clark examine the argumentation structures created by generative AI and by undergraduate students using the Claim-Evidence-Reasoning (CER) framework. The findings indicate that generative AI tends to rely on pattern recognition and naïve empiricism rather than rigorous logical reasoning. Accordingly, they advocate for positioning AI as a pedagogical supporting tool in the classrooms.
Sugiman, Mohammad Archi Maulyda, Rina Dyah Rahmawati (Indonesia)……pages 152-177
Hery Nugroho, Elly Arliani, Sugiman Sugiman (Indonesia)……….pages 178-233
Ma Ul Uyun, Mailizar Mailizar, Elizar Elizar (Indonesia) ………….…..pages 224-245
Improving Understanding of Trigonometric Functions Using GeoGebra
Ljerka Jukić Matić, Snježana Bošnjak (Croatia)……………..….pages 246-265
Using GeoGebra in Teaching Advanced Geometry: A Case Study
Bence Torma, Bernadett Kiss, Tamás Waldhauser (Hungary)……………….…….pages 266-280
Hendra Kartika (Indonesia), Lauren Jeneva Clark (Indonesia, United States)……. pages 281-299
Teacher Training and Development
These four studies shed light on advancing the preparation of pre-service teachers and in-service mathematics teachers’ teaching practice. Demirci, Akkoç, and Çeziktürk develop a Techno-pedagogical integration matrix to examine how pre-service teachers use the 5E model to plan technology-enhanced lessons. The study offers a unique case of integrating the SMAR model and the 5E model to guide effective use of technology in mathematics teaching. Acar and Bozkurt investigate pre-service teachers’ awareness of Sustainable Development Goals and emphasize the importance of equipping future educators with knowledge and strategies to foster sustainability consciousness in students. Gholami reports a lesson study grounded in a collaborative, constructivist-based approach to teacher professional development. The findings highlight the value of reflective, community-based approaches in fostering effective mathematics teaching and learning. Drawing on Casa et. al’s four types of mathematical writing, Ngoako and Machaba analyze a teacher’s writing practices in a 10th-grade classroom and reveal the need to integrate various writing strategies and opportunities to enhance students’ mathematics learning.
Tuğba Hangül Demirci, Hatice Akkoç, Özlem Çeziktürk (Türkiye)……………….pages 300-319
Gaye Acar, Fatma Bozkurt (Türkiye)……………………………….pages 320-355
Hosseinali Gholami (Malaysia)…………………………………………………….pages 321-344
Rosina Ngoako, France Machaba (South Africa)…………….……..pages 345-365
This issue concludes with two articles that focus on students’ reasoning and emotions in mathematics learning. Nhiry, Hanini, and Abouhanifa present a student work analysis of inductive reasoning. They developed a set of criteria to assess Moroccan secondary school students’ inductive reasoning skills and suggest that instruction should include exploratory tasks, conjecture-making opportunities, and pattern-focused discussions to support high-level inductive reasoning. Suparman, Juandi, Turmudi, Martadiputra, and Diana show that students’ achievement emotions in doing some mathematics-related activities vary by gender, major, school type, or age. The study reveals the need for providing differentiated interventions to support stable emotional achievement in mathematics learning.
Meryem Nhiry, Mohamed Hanini, Said Abouhanifa (Morocco)…………….……..pages 366-398
Suparman, Dadang Juandi, Turmudi, Bambang Avip Priatna Martadiputra, Nana Diana (Indonesia) ………………………………………………………………………..pages 399-436
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