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The research aims to analyze the gap between teachers' and students' understanding of language literacy and mathematical symbols. The study was designed with a concurrent triangulation strategy. The research respondents consisted of 20 teachers and 120 class VII students. Data collection through questionnaires, interviews, and cognitive tests. Qualitative data was analyzed descriptively, and quantitative data was analyzed inferentially. The results of the analysis of quantitative data show that there is a linear (significant) relationship between understanding language and mathematical symbols and mathematical literacy skills. The results of the qualitative data analysis describe that the teacher's understanding of language and mathematical symbols (high criterion) does not necessarily support the students' understanding of language and mathematical symbols. We confirm the suspicion that there is a gap in the ability of teachers and students to understand language and mathematical symbols. Students need to improve their understanding of mathematical language and symbols. The pattern of errors is based on the teacher's conception of learning in the previous class, so the process of transitioning the teacher's knowledge to students' understanding of mathematics experiences obstacles. The implication is that the process of transitioning meaning from mathematical symbols to written and spoken language must be carried out when the teacher introduces or teaches new topics to students, and the context in which mathematical symbols are used must be followed by clarification.

The purpose of this study was to investigate the critical role of equilibration in organizing and building students' cognitive structure in the practice of learning mathematics. This qualitative research was designed using a phenomenological study approach. Participants in this study were 30 high school students of XI level. The main research instrument was the interview guide format and the document of cognitive test questions with the circle equation material. Research data obtained were tested for the validity of the data by triangulation. Method triangulation was done by comparing student work data and interview data. Theory triangulation is done by comparing the descriptions of the data obtained with the relevant theoretical sources. The results showed that in the context of knowledge construction (cognitive structure), there is a strong relationship between the process of assimilation and accommodation with equilibration. The role of balance in forming cognitive structures is to guide students to organize previous knowledge (schemas) and new knowledge and create thinking structures to become more complex by considering the socio-cultural dimension (environment) in mathematics learning. Further studies suggest that when selecting topics for equilibration-based activities, teachers should provide an effective learning environment to support the formation of cognitive structures to become more prosperous and complex.

This study aims to determine the distribution of the percentage of proportional reasoning tasks in the comparison chapter in task series book MANDIRI (Mengasah Kemampuan Diri) Mathematics Grade VII Curriculum 2013, Revised Edition, 2016 Publisher Erlangga, written by Kurniawan. This research is a qualitative research using a descriptive approach. The task data from the book are documented and then analyzed based on indicators from each level of proportional reasoning. The tasks in the comparison chapter consist of two types of tasks, namely multiple choice tasks and essay tasks. There are 225 tasks in the comparison chapter. Based on the results of the study, it was found that the distribution of tasks based on the level of proportional reasoning found that tasks with level 1 (qualitative) were 31 (13.78%), tasks with level 2 (additive) were 22 items (9.78%), tasks with level 3 (pre-multiplicative) were 116 tasks (51.56%), tasks with level 4 (implicit multiplicative) were 24 items (10.67%) and tasks with level 5 (multiplicative) were32 items (14.22%).

Penelitian ini bertujuan untuk mendeskripsikan kemampuan literasi matematika siswa berdasarkan kompetensi reproduksi dan koneksi ditinjau dari gaya belajar siswa SMP Negeri 1 Rowosari Kabupaten Kendal. Jenis penelitian adalah deskriptif kualitatif. Objek yang digunakan merupakan siswa kelas VII A siswa SMP Negeri 1 Rowosari Kabupaten Kendal dan subjek dalam penelitian ini adalah enam orang yang mewakili gaya belajar siswa. Metode yang digunakan adalah penelitian eksploratif. Hasil penelitian menunjukan Gaya belajar siswa kelas VII A SMP Negeri 1 Rowosari Kabupaten Kendal dominan memiliki gaya belajar visual, auditorial dan kinestetik, namun terdapat 1 siswa dengan gaya belajar visual-auditorial dan 1 siswa dengan gaya belajar visual-kinestetik. Gaya belajar Visual mendominasi level 2 dengan kompetensi Reproduksi dan 1 orang mencapai level tertinggi dengan kompetensi Refleksi. Siswa dengan gaya belajar Auditorial lebih banyak berada pada level 2 dengan kompetensi Reproduksi tetapi ada 4 orang berada pada level Koneksi. Siswa dengan gaya belajar Kinestetik dengan kompetensi Reproduksi sebanyak 1 orang siswa dan kompetensi Koneksi sebanyak 6 orang siswa.

This study aimed to (1) analyze the role of scaffolding in deconstructing pseudo-thinking structure, and (2) analyze the development of students' thinking structures after receiving scaffolding. The study was framed with a qualitative methodology by involving case study design. This research was conducted at State Junior High School 31 in Semarang City, Indonesia. Data was collected through tests, observation, and interview methods. Result of the study indicated that (1) scaffolding has changed the pseudo thinking process into a real thought process, and (2) scaffolding could develop students’ thinking structure into a more complex (abstract) level. Their thinking structure was initially on the stage of comparative thinking structure before receiving scaffolding assistance and after receiving scaffolding, to developed into the stage of logical reasoning thinking structure. In other words, scaffolding could become a useful strategy to help students go through different Zone of Proximal Development (ZPD).

Penelitian ini bertujuan untuk mengetahui tingkat kelayakan media Islamic Math Comics materi perbandingan SMP. Penelitian ini berbentuk penelitian pengembangan R&D (research & development) menggunakan metode ADDIE (analyze, design, develop, implement, and evaluate). Dalam penelitian ini hanya dibatasi sampai tahap design saja. Media ini dikembangkan dengan mendesain gambar manual, scan, dan adobe photoshop. Islamic Math Comics merupakan komik matematika materi perbandingan bernuansa islami mengandung bimbingan karakter dan meningkatkan pemahaman matematis siswa. Setelah dihasilkan produk awal akan dilakukan validasi dari ahli materi, ahli media, dan guru matematika. Analisis data menggunakan deskriptif kualitatif. Hasil penelitian ini dari aspek materi diperoleh skor 3,19 “Sangat Layak”, aspek bahasa diperoleh skor 3,33 “Sangat Layak”, dan aspek penyajian diperoleh skor 3,30 “Sangat Layak”. Jadi media ini berada dalam kategori “Sangat Layak” digunakan dan tidak terlepas dari saran atau masukan validator seperti mengembangkan isinya agar lebih sinkron, menambahkan soal tantangan, dan mencantumkan KD/KI secara tertulis. This study aims to determine the level of feasibility of Islamic Math Comics media for comparison SMP material. This research is in the form of R&D development research (research & development) using the ADDIE method (analyze, design, develop, implement, and evaluate). In this study only limited to the design stage. This media was developed by designing manual images, scans, and Adobe Photoshop. Islamic Math Comics is an Islamic comic comparison material containing Islamic character guidance and improving students' mathematical understanding. After the initial product is produced, validation will be carried out from the material experts, media experts, and mathematics teachers. Data analysis using descriptive qualitative. The results of this study from the material aspects obtained a score of 3.19 "Very Feasible", the aspect of language obtained a score of 3.33 "Very Feasible", and the aspect of presentation obtained a score of 3.30 "Very Feasible". So this media is in the category of "Very Eligible" to be used and is inseparable from validator suggestions or input such as developing its contents to be more synchronous, adding challenge questions, and including KD / KI in writing.

Tujuan penelitian ini adalah untuk menguji adanya pencapaian KKM dari kemampuan komunikasi matematis siswa kelas VIII, dan menganalisis tingkat perkembangan kognitif dari kemampuan komunikasi matematis siswa kelas VIII ditinjau dari Taksonomi SOLO. Penelitian ini campuran kuantitatif dan kualitatifdengan desain concurrent embeddeddengan penelitian kualititatifsebagai metode primer (porsinya lebih besar). Populasipenelitian ini sebanyak 182 siswa kelas VIII di SMP Negeri 10 Semarang. Melalui teknik random sampling diperolehkelas VIII-E (sebanyak 30 siswa) sebagai kelas eksperimen. Instrumen penelitian meliputi soal tes tertulis, lembar pengamatan dan pertanyaan wawancara. Melalui teknik purpose sampling diperoleh perwakilan siswa tiap kelompok untuk diwawancari. Hasil penelitian menyimpulkan rata-rata kemampuan komunikasi matematis siswa kelas VIII mencapai KKM yang ditentukan, dan tingkatan perkembangan kognitif dari kemampuan komunikasi matematis siswa kelas VIII ditinjau dari Taksonomi SOLO belum sepenuhnya mencapai perkembangan kognitif berpikir abstrak atau tingkat permikirankualitatifsebagaimana diamanatkan dalam kurikulum 2013. Kata kunci: analisis, komunikasi matematis, taksonomi SOLO. ABSTRACT This study aims to find out the attainment of the minimum mastery criteria of the mathematical communication skills of Grade VIII students, and analyze the level of cognitive development of the Mathematical communication skills of Grade VIII students in terms of SOLO Taxonomy. This research is a mixture of quantitative and qualitative concurrent embedded design. Where qualitative research as a primary method (the portion is bigger). The population of the study was 182 students of class VIII at SMP Negeri 10 Semarang. Through cluster random sampling techniques obtained class VIII-E (as many as 30 students) as an experimental class. Research instruments include written test questions, observation sheets and interview questions. Through the purpose sampling technique obtained by representatives of students from each group to be interviewed. The results of the study concluded the average mathematical communication skills of Grade VIII students reached the KKM, and the level of cognitive development of Grade VIII mathematical communication skills in terms of SOLO Taxonomy has not yet fully reached the cognitive development of abstract thinking or the level of qualitative thinking as recommended in the 2013 curriculum. Keywords:Analysis, mathematical communication, SOLO taxonomy

Elementary school teachers in Indonesia are required to master many subjects to be taught to their students. It is undeniable that the teachers’ mastery of knowledge (material) in some subjects inadequate. Therefore, it is worth to argue that there was a misconception in mathematics teaching in elementary schools. This research was designed using a qualitative approach. The participants of this study were 30 elementary school teachers in Semarang city area, Central Java province, Indonesia. The research data were obtained through questionnaires, and interviews. The purpose of the study was to discuss the types and causes of the misconception of mathematics teaching in elementary schools. Alternative solutions were also presented to problem-solving so that misconceptions do not occur anymore in mathematics teaching. The findings show that, teachers evenly experience types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; and (6) process-object error in teaching mathematics in elementary schools. Some misconceptions have taken root and are difficult to remove, called "ontological misconceptions" because of teachers' years of belief that the knowledge they received was true when in fact it was not quite right.

Pembelajaran yang lebih ditekankan pada prosedur dan hasil dalam penyelesaian masalah tidak akan mengaktifkan strukur kognitif (berpikir) siswa dan tidak meningkatkan kemampuan berpikir matematis. Siswa hanya akan meniru prosedur yang dilakukan guru. Penelitian ini merupakan studi kasus pembelajaran matematika di kelas IV sekolah dasar pada materi pembagian bilangan bulat. Tujuan penelitian adalah mendeskripsikan struktur kognitif siswa dalam menyelesaikan masalah. Penelitian menggunakan metode kombinasi (kualitatif-kuantitatif) dengan desain concurrent embedded. Teknik pengumpulan data dilakukan secara trianggulasi yaitu observasi partisipan, wawancara yang mendalam, serta studi dokumentasi. Hasil penelitian menunjukkan bahwa struktur kognitif Siswa A memiliki struktur kognitif komparatif dan siswa B memiliki struktur kognitif penalaran logis. Siswa menggunakan struktur kognitif untuk memproses informasi dan menciptakan makna dengan cara (1) membuat koneksi, (2) menemukan pola, (3) mengidentifikasi aturan, dan (4) mengabstraksikan prinsip-prinsip. Kata kunci: struktur kognitif, berpikir matematis, bilangan bulat. ABSTRACT Learning that is more emphasized on procedures and results in solving problems will not activate the cognitive structure (thinking) of students and does not improve the ability to mathematical thinking. Students will only imitate the procedures performed by the teacher. This research is a case study of mathematics learning in the fourth grade of elementary school in integer division material. The research objective is to describe the cognitive structure of students in solving problems. The study uses a combination method (qualitative - quantitative) with concurrent embedded design. The data collection technique is done in triangulation, namely participant observation, in-depth interviews, and documentation studies. The results showed that the cognitive structure of class IV students reached the level of comparative cognitive structure (group A) and cognitive structure of logical reasoning (group B). Students use cognitive structures to process information and create meaning by (1) making connections, (2) finding patterns, (3) identifying rules, and (4) abstracting principles Keywords: cognitive structure, mathematical thinking, integers.

Penerapan model pembelajaran Logan Avenue Problem Solving Heuristik yang dikombinasikan dengan nuansa islami dapat membantu siswa lebih baik lagi dalam memahami materi trigonometri sebagaimana tujuan dari penelitian ini. Penelitian ini merupakan penelitian campuran dengan metode primernya menggunakan metode kualitatif dan sekundernya menggunakan metode kuantitatif. Teknik pengumpulan data menggunakan teknik tes, dan wawancara. Data hasil penelitian dianalisis dengan uji normalitas, homogenitas, ketuntasan, dan uji perbedaan rata-rata. Hasil penelitian menunjukkan bahwa: (1) Deskripsi kemampuan komunikasi matematis siswa kelas X MA Miftahul Ulum Ngemplak antara lain: a) Subjek penelitian tinggi dapat memenuhi indikator kemampuan komunikasi matematis dengan benar dan lengkap, b) Subjek penelitian sedang dapat memenuhi indikator namun masih terdapat kesalahan, c) Subjek penelitian rendah mampu memenuhi indikator tetapi masih banyak melakukan kesalahan. (2) Kemampuan komunikasi matematis siswa kelas eksperimen mencapai KKM 70 dengan hasil rata-rata kemampuan komunikasi matematis siswa sebesar 80,76. (3) Rata-rata hasil kemampuan komunikasi matematis siswa yang menerima pembelajaran LAPS Heuristik Bernuansa Islami lebih tinggi yaitu sebesar 80,76 daripada rata-rata siswa yang menerima pembelajaran direct learning yaitu sebesar 68,26.

This research was a descriptive research. Description of research result was presented quantitatively and qualitatively. Subjects of the research were 30 (thirty) 8th graders of SMPN 10 (State Junior High School) in Semarang, Indonesia. Data were collected through tests, documentation, observations, and interview. Student answers documents were observed and analyzed with SOLO Taxonomy guidance. The objective of the study was to analyze and provide an interpretation of students abstract reasoning level in cognitive development based on intended learning outcomes. The result of findings from students’ answers basically showed that students' abstract reasoning on the lower, middle and upper level, was alike to stages of structure complexity improvement. There were two main changes from concrete thinking to abstract thinking: quantitative stage (uni-structural and multi-structural) occurred first, as the number of details in student responses increased and then changed qualitatively (relational and extended abstract) because the detail was integrated into a structural pattern.