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INTERNALIZATION PROCESS OF REASONING AND PROOF STANDARDS FOR ELEMENTARY SCHOOL TEACHERS IN MATHEMATICS LEARNING

Reasoning and Proof ability are one of the five standards in NCTM. Its implementation in learning can be transformed into problem-based learning (PBL). The purpose of this study is to provide a description related to the internalization of Reasoning and Proof standards in the mathematics learning process in elementary schools. The type of research used is qualitative with descriptive analysis. The research subjects were 24 elementary school teachers in Cluster IV Mataram City. The data collection process was carried out by a survey method that was conducted online using the Google form platform. To strengthen the results of the questionnaire, interviews were also conducted via WhatsApp phone to each research subject. The results of the research showed that 45.8% (11 subjects) had never heard of the terms reasoning and proof, while 54.2% (13 subjects) had never heard of the terms reasoning and proof. The deepening of the results of this study found that the feasibility of Reasoning and Proof standards in learning was still not optimal. In addition, several interesting facts were found related to the method of proof that teachers often use, namely giving examples that are close to students (relate).

An Evaluation of the Primary Fourth-Grade Mathematics Textbook in Jordan in the Light of NCTM Standards: تقويم كتاب الرّياضيّات للصف الرّابع الأساسيّ في الأردن في ضوء معايير (NCTM)

This study aimed at evaluating the content of the Jordanian mathematics textbook for the elementary fourth-grade in order to find out the extent that the fourth-grade mathematics textbook includes the standards of the American national for Council mathematics teachers (NCTM-2000), which concerned with mathematical operations (problem-solving, reasoning and proof, mathematical communication, Connections mathematical, mathematical representation) from the point of view of mathematical Connections teachers in Ma'an Governorate, thus, to find out the reasons for the low achievement of students in mathematics international tests. In order to fulfill these objectives, the descriptive analytical approach was used, that is a list of (NCTM) standards was prepared and changed into a questionnaire which was applied on a sample consisted of (119) male and female mathematics teachers for the primary fourth grade representing the study community. The results of the study showed that the extent to which the basic (NCTM) standards are included in the mathematics book for the fourth grade was at a moderate percentage on average about (2.76), the mathematical connection standard had the highest availability at (3.10), followed by the mathematical communication standard (3.08), the representation of mathematical operation at (2.99) respectively, and the problem solving standard at (2.51), whereas the reasoning and proof standard had the least representation. The findings also indicated there were statistically significant differences with regard to the experience variable and for the favor of (11-and more) category. Regarding the social gender, it did not have an effect. The study sets out several recommendations such as, developing the mathematics curriculum in the light of national standards, increasing the percentage of (NCTM) standards in the fourth-grade mathematics textbook, and the necessity to focus on issues connected with proof and reasoning, and problem solving.

Development of the language personality of a junior school student in russian lessons

The article deals with the problems of developing the language personality of a Junior school student in Russian lessons. The communicative goal of teaching Russian in primary school is aimed at forming a system of knowledge about the language and on its basis developing students ‘ communication skills. The priority communicative goal allows you to change the traditional approach to the selection of learning content, to guide the school course of Russian language is not only learning about the language, but also on the development of skills to use them in different situations. According to the authors, an effective means of developing a language personality should be work aimed at understanding the role of words and text in speech communication. At the same time, the word should be understood as a unit that can convey a message, question, and Express a feeling; and the text - as thematically related sentences for solving speech problems - description, story, reasoning, and proof.

Muatan penalaran dan pembuktian matematis pada buku teks matematika SMA kelas X Kurikulum 2013

Penelitian ini bertujuan untuk mendeskripsikan muatan penalaran dan pembuktian matematis pada buku teks matematika SMA kelas X Kurikulum 2013. Penelitian ini menggunakan pendekatan kualitatif deskriptif jenis analisis isi. Sumber data penelitian adalah buku teks Matematika kelas X Kurikulum 2013 edisi revisi 2016 yang diterbitkan oleh Pusat Kurikulum dan Perbukuan Balitbang Kementerian Pendidikan dan Kebudayaan Republik Indonesia. Teknik pengumpulan data dalam penelitian ini adalah pembacaan dan pencatatan dengan menggunakan instrumen yang telah divalidasi berupa pedoman analisis dokumen. Data penelitian dianalisis menggunakan skema Kripendorff yang meliputi pengumpulan data, penentuan sampel, perekaman/pencatatan, reduksi, penarikan kesimpulan dan narasi. Hasil penelitian menunjukkan bahwa pada bagian materi, siswa memiliki kesempatan yang besar untuk menalar dan membuktikan melalui membaca justifikasi namun memiliki kesempatan yang kecil melalui pengembangan justifikasi. Pada soal evaluasi, siswa belum memiliki kesempatan untuk menalar dan membuktikan melalui pengerjaan soal dengan indikator mengevaluasi argumen. Artinya, buku teks belum sepenuhnya memberikan kesempatan bagi siswa untuk belajar menalar dan membuktikan. AbstractThis study aimed to describe the content of mathematical reasoning and proof in the high school mathematics textbooks 10th grade Curriculum 2013. This research used descriptive qualitative approach type of content analysis. The source of research data was the high school mathematics textbook of 10th grade Curriculum 2013 edition of revision 2016 published by Ministry of Education and Culture of the Republic of Indonesia. Data collection techniques in this study was the reading and recording using instruments that had been validated in the form of document analysis guidelines. Research data was analyzed using Kripendorff scheme which included unitizing, sampling, recording/coding, reducing, inferring and narrating. The results showed that in the learning material section students had big opportunities to learn reasoning and proof through justification reading, but they had small opportunities in justification developing. In evaluation section, students had not opportunities to learn reasoning and proof through argument evaluation problem solving. Therefore, the textbook had not fully provided opportunities for students to learn reasoning and proof.

PROFIL KEMAMPUAN PENALARAN MATEMATIS DALAM PEMECAHAN MASALAH PADA MAHASISWA CALON GURU MATEMATIKA

NCTM (2000) menetapkan 5 keterampilan proses yang perlu dimiliki siswa dalam pembelajaran matematika yaitu: (1) pemecahan masalah (problem solving); (2) Penalaran dan pembuktian (reasoning and proof); (3) Komunikasi (communication); (4) Koneksi (connection); dan (5) Representasi (representation). Berdasarkan 5 keterampilan proses di atas, penalaran merupakan salah satu keterampilan yang memegang peranan penting. Tujuan penelitian ini adalah untuk mendeskripsikan profil profil kemampuan penalaran matematis dalam pemecahan masalah pada mahasiswa calon guru matematika. Jenis penelitian ini adalah penelitian kualitatif deskriptif karena mendeskripsikan bagaimana profil kemampuan penalaran dalam pemecahan masalah pada mahasiswa calon guru matematika melalui jawaban yang diberikan siswa terhadap tes tertulis serta wawancara. Subjek yang akan dijadikan penelitian ini adalah mahasiswa calon guru matematika Program Studi Pendidikan Matematika Universtias PGRI Semarang. Pemilihan subjek pada penelitian ini menggunakan teknik purposive sampling. Pengumpulan data dilakukan dengan teknik tes tertulis dan wawancara. Analisis data dilakukan berdasarkan data hasil tes tertulis dan data hasil wawancara. Kemudian dilakukan triangulasi metode untuk menghasilkan data dari subjek penelitian yang valid. Hasil dari penelitian ini adalah Subjek dengan gender laki-laki memiliki kemampuan penalaran matematis sebagai berikut: menyajikan pernyataan secara lisan, tertulis, tanpa menggunakan gambar, mampu membuat dugaan bahwa untuk mengetahui waktu yang diperlukan kedua mobil berpapasan adalah dengan menjumlahkan kecepatan kedua mobil, mampu menjelaskan dengan menggunakan model, tetapi subyek tidak melakukan koreksi terhadap jawabannya. Subjek dengan gender perempuan memiliki kemampuan penalaran matematis sebagai berikut: mengidentifikasi fakta dan masalah yang diketahui dalam soal tersebut dengan jelas dan logis, subjek juga mengilustrasikan permasalahan menggunakan gambar, subyek mampu memilih konsep dan aturan yang akan digunakan dalam penyelesaian masalah secara tepat, Subjek melaksanakan rencana yaitu dengan mengalikan kecepatan mobil A dengan waktu (t) tertentu dijumlahkan dengan kecepatan mobil B dengan waktu (t) tertentu., dan subyek tidak melakukan koreksi terhadap jawabannya, karena telah yakin dengan jawaban tersebut.