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Students show deficient understanding on fraction division and supporting that understanding remains a challenge for mathematics educators. This article aims to describe primary students’ understanding of partitive fraction division (PFD) and explore ways to support their understanding through the use of sequenced fractions and context-related graphical representations. In a design-research study, forty-four primary students were involved in three cycles of teaching experiments. Students’ works, transcript of recorded classroom discussion, and field notes were retrospectively analyzed to examine the hypothetical learning trajectories. There are three main findings drawn from the teaching experiments. Firstly, context of the tasks, the context-related graphical representations, and the sequence of fractions used do support students’ understanding of PFD. Secondly, the understanding of non-unit rate problems did not support the students’ understanding of unit rate problems. Lastly, the students were incapable of determining symbolic representations from unit rate problems and linking the problems to fraction division problems. The last two results imply to rethink unit rate as part of a partitive division with fractions. Drawing upon the findings, four alternative ways are offered to support students’ understanding of PFD, i.e., the lesson could be starting from partitive whole number division to develop the notion of fair-sharing, strengthening the concept of unit in fraction and partitioning, choosing specific contexts with more relation to the graphical representations, and sequencing the fractions used, from a simple to advanced form.

[English]: This article aims to critically review researches on characters and values in mathematics teaching and learning. Data for the review was the research articles authored by Indonesian mathematics education researchers and published in the online peer-review journals. The articles were searched in national scientific databases, DOAJ, and Google Scholar. The searches resulted in forty articles which aim to develop students' character and values through mathematics lesson. Five steps, i.e., text interpretation, coding, analysis, discussion, and reconsideration, are employed to analyze the articles qualitatively. The review reveals the articles lack of theoretical basis in the conceptualization of character/values, the development of character/values, and their measurement. Twenty-six articles on character did not define the notion clearly; meanwhile, the other articles only cite some definitions, but no operational definition was made. Character is a multifaceted construct which requires an operational definition to measure its development. In developing character and values, various strategies were utilized, but the most authors have not addressed theoretical analysis and rationale on their feasibility and relations the conceptualization of the notions. All articles did not provide any explanation on whether the instruments used were developed with respect to the nature of character or values development and fulfill psychometric properties. In this case, we argue that the researches were unfocused and not extensive. In this article, related theories and prior works are thoroughly discussed to shed light on the researching topics. Further research which relates to character education program in Indonesia is also elaborated. Keywords: Review, Character, Values, Mathematic teaching [Bahasa]: Artikel ini bertujuan mengulas secara kritis penelitian terkait karakter dan nilai dalam pembelajaran matematika. Data untuk ulasan merupakan artikel hasil penelitian yang ditulis oleh peneliti pendidikan matematika Indonesia dan diterbitkan di jurnal daring yang sudah melalui ulasan sejawat. Artikel dicari melalui basis data ilmiah nasional, DOAJ, dan Google Scholar. Pencarian menghasilkan 40 artikel yang bertujuan membangun karakter dan nilai siswa dalam pembelajaran matematika. Artikel dianalisis secara kualitatif melalui lima langkah yaitu interpretasi teks, penyusunan kode, analisis, diskusi, dan pertimbangan kembali. Ulasan menunjukkan bahwa artikel tersebut memiliki kekurangan dasar teoritis dalam konseptualisasi karakter/nilai, pengembangan karakter/nilai, dan aspek pengukuran. Dua puluh enam artikel yang membahas karakter tidak mendefinisikan istilah tersebut dengan jelas, sedangkan artikel yang lain hanya mengutip beberapa definisi tetapi tidak membuat definisi operasional. Karakter memiliki makna yang bervariasi sehingga membutuhkan definisi operasional untuk mengukur perkembangan pada diri siswa. Dalam mengembangkan karakter dan nilai, beragam strategi digunakan tetapi kebanyakan penulis tidak menjelaskan analisis teoritis and rasionalisasi kenapa strategi tersebut dapat digunakan dan berkaitan dengan konseptualisasi karakter/nilai. Semua artikel tidak memberikan penjelasan apakah instrumen yang dikembangkan sesuai dengan karakteristik perkembangan karakter atau nilai dan memenuhi kriteria psikometri. Dalam hal ini, penelitian terkait karakter/nilai tersebut belum fokus dan berskala kecil. Dalam artikel ini, beberapa teori yang relevan dan hasil penelitian sebelumnya dijelaskan secara mendalam untuk memberikan arah penelitian topik tersebut. Penelitian lebih lanjut yang berkaitan dengan program pendidikan karakter di Indonesia juga dibahas. Kata kunci: Analisis, Karakter, Nilai, Pembelajaran Matematika

This article aims to explore a possible criterion of digital technology mathematics teachers’ professional development[1]. The criterion was canvassed through qualitative exploratory study which involve a hybrid model of DigiTech TPD, online published articles of related TPD, and theoretical perspective which relate to digital technology in mathematics education. Related frameworks (Drijverset al, 2010; Trocki Hollebrands, 2018) and content analysis were utilized to analyze the first two data. Theoretical perspectives of digital technology in mathematics education were accounted to reflect prior data and explore the criterion. We found that the current TPD[2]has not developed the knowledge of task design and supported teachers' roles in orchestrating technology-rich mathematics teaching as seen in the low level of tasks and teachers' orchestration in the classroom. Related articles on TPD in Indonesia show that the programs have not touched decisive factors of successfully implementing digital technology. An alternative criterion for DigiTech TPD is explored which includes three aspects namely theoretical approach, model and content. It could be alternative point of departure for designing and conducting DigiTech TPD in Indonesia.

[English]: The research aimed to analyze how novice teachers use digital technology and transform their practices from without-technology to with-technology mathematics teachings. Two upper secondary mathematics teachers were involved in this research. They were novice teachers in the use of digital technology in mathematics teachings. Classroom video recording and transcripts were the primary sources of data, meanwhile interview with the teachers and field notes are the supporting data. The teachings videos were categorized into some episodes, transcribed and analyzed following the phases of analyzing classroom video recordings and transcript by Cobb and Whitenack (1996). To capture the whole picture of the teachers’ practices, data analysis was referred to instrumental orchestration (Drijvers et al., 2010) and didactics tetrahedron unfolded (Hollebrands & Okumuş, 2018). In this research, we found that the observed teachers’ orchestrations are mostly non-technology orchestrations. The teachers have a different focus; one focuses only on mathematics and another focus on mathematics through the use of technology. The research concludes that old-fashioned classroom practices can be the pitfall for using digital technology in the mathematics classroom. Keywords: GeoGebra, Mathematics task, Digital technology, Pitfall, Teachers’ practices [Bahasa]: Penelitian ini bertujuan menganalisis bagaimana guru pemula menggunakan teknologi digital dalam kelas dan perubahan praktik pembelajaran setelah menggunakan teknologi. Dua guru matematika SMA menjadi subjek dalam penelitian. Subjek merupakan guru pemula terkait penggunaan teknologi digital dalam pembelajaran matematika. Data utama penelitian diperoleh melalui rekaman video pembelajaran. Hasil wawancara dengan guru dan catatan lapangan digunakan sebagai data pendukung. Video pembelajaran dikelompokkan menjadi beberapa episode, dibuat transkrip dan dianalisis berdasarkan langkah-langkah analisis rekaman video dan transkrip pembelajaran oleh Cobb and Whitenack (1996). Untuk memperoleh gambaran menyeluruh praktik guru, analisis data merujuk pada kerangka orkestra instrumental (Drijvers et al, 2010) dan segiempat didaktik terbuka (Hollebrands & Okumuş, 2018). Penelitian ini menemukan bahwa sebagian besar orkestra guru dalam pembelajaran masih bercirikan pembelajaran tanpa teknologi. Dua guru dalam penelitian ini memiliki fokus yang berbeda dalam pembelajaran yaitu fokus hanya pada matematika dan fokus pada matematika melalui penggunaan teknologi. Hasil penelitian tersebut menunjukan bahwa praktik rutin guru tanpa teknologi bisa menjadi hambatan dalam pembelajaran berbasis teknologi. Kata kunci: GeoGebra, Tugas matematika, Teknologi digital, Hambatan, Praktik guru

Abstrak: Penelitian kualitatif ini bertujuan untuk mengungkap strategi yang digunakan mahasiswa dalam melakukan pembuktian soal Geometri. Subjek dalam penelitian ini adalah mahasiswa yang telah menempuh mata kuliah Geometri. Pengumpulan data dilakukan dengan menggunakan metode tes dan wawancara. Hasil penelitian menunjukkan bahwa strategi pembuktian pada soal Geometri dengan tipe pembuktian sintaksis (syntactic proof production) antara lain adalah dengan mengidentifikasi dan memanipulasi pernyataan atau informasi dalam soal, menterjemahkan informasi dalam soal, memilih teorema atau dalil yang relevan, menggunakan simbol atau notasi matematika yang formal dalam melakukan tahapan pembuktian, menggunakan bantuan sketsa, dan menarik kesimpulan dari setiap pernyataan yang telah didapatkan. Sementara strategi pembuktian pada soal Geometri dengan tipe pembuktian semantik (semantic proof production) antara lain adalah dengan menggunakan intuisinya untuk membuat asumsi, dugaan atau perkiraan yang dianggap benar dan melakukan penalaran atas asumsi yang dibuat dan menggunakan sketsa untuk membantu memudahkan pembuktian. Abstract: This qualitative research aims to reveal the strategies that used by students in doing the proof of Geometry. The subjects in this study are students who have taken courses of Geometry. Data is collected through test and interview. The research shows that the strategy of proof of geometry with syntactic proof production type are identifying and manipulating the statement or information in the question, translating the information in the question, choosing the relevant theorem, using formal mathematical symbol or notation in conducting the proof stage, using a sketch, and making a conclusions from every statement that has been obtained. The strategy of proof of geometry with semantic proof production are using his intuition to make assumptions, guesses or estimates that are considered correct and reasoning and using sketches to help facilitate proof.

[Bahasa]: Sejarah merupakan sumber pengetahuan. Sejarah memberikan informasi berharga terkait perkembangan di masa lampau yang mendukung kemajuan di masa sekarang. Dalam hal ini, sejarah matematika juga memberikan pengetahuan bagaimana konsep matematika berkembang. Sejarah matematika menjelaskan, sebagai contoh, bagaimana al-Khwarizmi mengembangkan metode kuadrat sempurna dalam menyelesaikan persamaan kuadrat. Melalui sejarah matematika, kerja keras para matematikawan dalam menemukan dan mengembangkan suatu konsep atau penyelesaian suatu permasalahan bisa menjadi kisah inspiratif. Pengetahuan yang diperoleh melalui sejarah matematika sangat bermanfaat untuk digunakan dalam pembelajaran. Tulisan ini mencoba menjawab kenapa dan bagaimana penerapan sejarah matematika dalam pembelajaran melalui kajian pustaka (library research). Referensi terkait berupa ebook, artikel jurnal online dan proceedings konferensi dianalisis dengan memfokuskan pada dua hal, yaitu: manfaat sejarah matematika dalam membangun sikap positif siswa terhadap matematika; dan cara menerapkan sejarah matematika dalam pembelajaran matematika di Indonesia. [English]: History is a source of insight. History gives valuable information regarding the development in the past which contributes to the advance nowadays. In this case, the history of mathematics (HoM) also provides knowledge on how mathematics concept developed. The history of mathematics explains, for example, how al-Khwarizmi developed one of the methods in solving a quadratic equation. In the history of mathematics, how mathematicians worked hard in inventing and developing a concept or a solution upon a mathematics problem can be inspired story. Insight from the history of mathematics can be very useful for learning mathematics. This paper tries to answer why and how the use of history of mathematics in mathematics learning through library research. References consist of e-books, online journal articles and conference proceedings are thoroughly analyzed focusing on two cases, i.e. how the history of mathematics builds positive attitude of students toward mathematics; and how it can be implemented in Indonesia mathematics classroom.