Updating mastery of mathematics scholarly knowledge is vital for mathematics teachers' professional development in Indonesia. External transposition refers to the transposition of mathematics scholarly knowledge to the school curriculum. During the COVID-19 pandemic, online learning becomes the primary strategy for strengthening the external transposition knowledge of mathematics teachers in Indonesia. This study aims to describe the process of providing online learning situations in lifting the in-service mathematics teachers' external transposition knowledge during the COVID-19 pandemic. The online learning involved 57 in-service high school mathematics teachers in Indonesia as participants. The scholarly knowledge to be delivered was the visualization of matrix multiplication. This qualitative study is a didactical design research that includes a prospective learning situation analysis, a meta-technopedadidactic analysis, and a retrospective analysis. In the prospective learning situation, the solutions for re-situating face-to-face learning to online learning were disclosed. Moodle was used as the Learning Management System, and GeoGebra Classroom was used as the Task Response System. A meta-technopedadidactic is an educator's ability to comprehensively analyze pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in using technology in a learning situation. The finding in the meta-technopedadidactic analysis showed the role of technology as a visualization tool in online learning, evidence of participants' external didactic transposition, constraints, and collaboration in learning. Finally, the retrospective analysis suggested some future improvements for better online learning situations. This study contributes to the comprehensive organization of e-learning courses in Indonesia for mathematics teachers' professional development based on pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in the use of technology. Despite some of the study's limitations, the findings have the potential to be an advantage for the long-term sustainability of e-learning as a new norm for teachers' professional development programs, rather than just a foreshadowing of the pandemic.

Model desain pembelajaran (MDP) dalam pembelajaran matematika adalah rancangan pembelajaran matematika yang disesuaikan dengan kebutuhan peserta didik demi tercapainya tujuan pembelajaran. Rancangan tersebut meliputi rancangan tujuan pembelajaran, strategi pembelajaran, bahan ajar yang digunakan dalam pembelajaran, dan penilaian pembelajaran. MDP terdiri atas beberapa komponen, yaitu peserta didik, tujuan pembelajaran, analisis pembelajaran, strategi pembelajaran, bahan ajar, dan penilaian belajar. MDP, khususnya dalam pembelajaran matematika memiliki beberapa fungsi, yaitu menjadikan peserta didik sebagai fokus dalam  pembelajaran matematika; menciptakan pembelajaran matematika yang efektif, efisien, dan menarik; mendukung koordinasi antara desainer dan mereka yang menginstruksikan; memfasilitasi diseminasi;  dan memfasilitasi kesesuaian antara tujuan, aktivitas, dan penilaian dalam pembelajaran matematika. Adapun jenis MDP matematika meliputi: MDP berorientasi kelas (Model ASSURE), MDP berorientasi sistem (Model ADDIE), MDP berorientasi produk (Model Hannafin & Peck), MDP prosedural (Model Dick & Carey), dan MDP melingkar (Model Kemp).

Sekolah Penggerak is one of the best episodes of the many Merdeka Belajar episodes. A separate curriculum known as Kurikulum Merdeka was prepared to support the program. The change in the principal’s competency model then became one of the unique phenomena in the curriculum change. The facts reveal that school principals cannot adapt quickly to this phenomenon, so this study aims to help school principals adapt more quickly to changes in competency models with coaching techniques. This study uses a phenomenological design because it wants to know the experiences that principals experience regarding the use of coaching techniques in responding to the phenomenon of changing competency models. The participants were three principals (51-55 years old) with 2-5 years of experience as principals. The instruments used are coaching questions developed in Sekolah Penggerak. Data is collected online through Google Meet and analyzed using qualitative data analysis techniques. The study results then revealed that coaching techniques could  to assist school principals in developing a model of school leadership competence, especially self-development and other people’s development, as well as learning leadership. This study also hopes that the principal will actively involve parents or guardians of students as mentors and learning resources.

[English]: Understanding various meanings of fractions is a foundation to learn related fractions topics. However, students are struggling with this essential topic. This hermeneutic phenomenological study aims to further investigate the meaning of fractions developed by secondary school students, the process of constructing the meaning using models, and factors that hinder the development of the meaning. It involved twenty-two students given fractions tasks, and some students of the different categories of mathematics ability were selected to be interviewed. A thematic analysis using NVivo-12 found that some students interpret fractions as a tool and integers. Most of the students in all categories tend to espouse fractions as ratio and quotient. However, they cannot use the models to represent the meanings. This study reveals that the students’ developed meanings of fractions are limited and different from what primary students have. In addition, there is an inconsistency between the espoused meanings and the use of models. The limitation and inconsistency are considered to be affected by teachers’ lack of content knowledge on the topic and less attention to using models in teaching fractions. This study implies that (mathematics) teachers education should pay more attention to the meaning of fractions and their related models in learning. [Bahasa]: Memahami makna pecahan merupakan dasar untuk mempelajari topik-topik terkait pecahan. Namun, siswa masih mengalami kesulitan dalam topik penting ini. Penelitian fenomenologi hermeneutika ini bertujuan untuk mengkaji lebih lanjut makna pecahan yang dibangun oleh siswa sekolah menengah, proses mengkonstruksi makna menggunakan berbagai model, dan faktor-faktor yang menghambat pengembangan makna pecahan. Penelitian ini melibatkan dua puluh dua siswa yang diberikan tugas matematika dan beberapa siswa dari berbagai kategori kemampuan matematika dipilih untuk diwawancarai. Analisis tematik menggunakan NVivo-12 menemukan bahwa beberapa siswa memaknai pecahan sebagai alat bantu dan bilangan bulat. Sebagian besar siswa pada semua kategori kemampuan matematika cenderung memaknai pecahan sebagai rasio dan hasil bagi. Namun, mereka tidak bisa menggunakan model untuk merepresentasikan makna pecahan tersebut. Penelitian ini menunjukkan bahwa makna pecahan yang dimiliki oleh siswa terbatas dan berbeda dari makna pecahan yang dimiliki siswa sekolah dasar. Selain itu, terdapat inkonsistensi antara makna pecahan yang diungkap siswa dengan penggunaan model. Keterbatasan dan inkonsistensi tersebut dianggap dipengaruhi oleh kurangnya pengetahuan konten guru tentang materi dan kurangnya penggunaan model dalam mengajar pecahan. Dalam hal ini, pendidikan guru (matematika) harus lebih memperhatikan makna pecahan dan penggunaan model pecahan dalam pembelajaran.

Pembelajaran matematika dalam implementasinya mengalami masalah dalam hal learning obstacle yang dialami siswa cenderung lebih tinggi. Berkaitan dengan hal tersebut, ada salah satu strategi pembelajaran yang diharapkan mampu mengurangi learning obstacle yang dialami siswa, yaitu strategi pembelajaran ‘Black Tea’. Strategi ini didasarkan pada filosofi interpretive and critical pedagogy. Adapun beberapa langkah pembelajaran dalam strategi pembelajaran tersebut adalah: (1) guru melakukan analisis pendahuluan mengenai learning obstacle apa saja yang dialami siswa dalam pembelajaran matematika; (2) guru sengaja melakukan kesalahan pada saat proses pembelajaran; (3) guru memastikan siswa menyadari bahwa guru melakukan kesalahan; (4) guru meminta siswa untuk mengkonfirmasi perbaikan yang diberikan; dan (5) guru bersama-sama dengan siswa membuat kesimpulan perbaikan atas kesalahan yang dilakukan guru.