This research aim is to know the students' understanding in adding number up to 20 using traditional game of dakocan and to acquire learning trajectory of adding number up to 20 using traditional game of dakocan for the first grade of primary school. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 33 first grade students of Sekolah Dasar Negeri (SDN) 98 Palembang as one of partners' school of Pendidikan Matematika Realistik Indonesia (PMRI). The result of this research shows that the students' understanding in adding number up to 20 can be stimulated by using traditional game of dakocan as a context. All of strategies and model that is used by students and also their result discussion shows how construction and contribution of students can help them to understand concept of adding number up to 20. All the activities that are done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students has an important role in understanding the concept from informal to the formal level. Learning trajectory using dakocan that is produced consist of playing dakocan, put the model of dakocan to the frame ten dakomatika to understand the relation of part and whole of ten combination in adding number, and solving contextual problem in adding number up to 20.

Kreano 6 (1) (2015): 33-38 Kreano Ju r n a l M a t e m a t i k a K r e a t i f -I n o v a t i f http://journal.unnes.ac.id/nju/index.php/kreano Media Pembelajaran Geometri Menggunakan PendekatanPendidikan Matematika Realistik Berbasis GeoGebra AbstrakTujuan dari penelitian ini adalah untuk mengembangkan media geometri menggunakan pendekatan Pendidikan Matematika Realistik Indonesia (PMRI) berbasis GeoGebra. Metode yang digunakan adalah Research and Development (R&D) dengan model 4D Thiagarajan yang terdiri dari tahap pendefinisian, perancangan, pengembangan, dan diseminasi. Hasil penelitian ini menunjukkan bahwa hasil validasi media dari validator 1 mendapat skor 46 atau dalam nilai sangat baik, dan dari validator 2 mendapat skor 45 atau dalam nilai baik. Sedangkan hasil validasi materi dari kedua validator manyatakan bahwa media yang dikembangkan ini sangat baik dengan skor masing-masing 51 dan 50. Media ini dapat menciptakan proses pembelajaran yang berpusat pada siswa, mengeksplorasi khasanah kearifan lokal yang digunakan sebagai konteks pembelajaran yang memenuhi semua karakteristik PMRI dan berbasis GeoGebra. AbstractThe aim of this research is to develop geometry media using PMRI approach based on GeoGebra. This research used methodology of research and development (R&D)

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Students of Mathematics education often struggle with integration problem, but yet the root of the problem related to critical thinking is rarely investigated. This article reports research where the first-year students of Mathematics Education of PGRI University Semarang were given an integral problem, then individually they were interviewed related to the answer they have made. The findings of students' difficulties in working on integration problem were confirmed through several questions in the interview which aimed to uncover their critical thinking process related to concepts, procedures, and problem solving. This study shows that student difficulties in Integration by disc method such as failure in identifying radius of a rotary object, specify partition, and integration bounds are closely related to their failure to think critically related to concept, skills, and problem solving aspects of critical thinking.

This research aims to produce a Learning Trajectory Based Instruction (LTBI) that can help the ninth grade students understand the concept of congruence of the two-dimensional shape by examining Lawang Sewu as one of Central Java historical buildings. LTBI is defined as a teaching and learning trajectory that uses Hypothetical Learning Trajectory (HLT) for instructional decisions. The present research uses the design research developed by Gravemeijer and Cobb that consists of three phases; the preliminary design, design of the experiment (pilot experiment and teaching experiment), and  retrospective analysis. In this study, a series of learning activities is designed and developed based on the Realistic Mathematics Education (PMRI) approach. This research produced LTBI that consists of a series of learning processes embodied in three activities of (1) identifying and finding the properties which shapes are congruent shapes by watching Lawang Sewu video, (2) proofing two shapes are congruent through transformation (translation and rotation), and (3) solving problem related to the congruence of two-dimensional shape. The activity can help to improve the students’ understanding of the concept of congruence. Nevertheless, the present study is limited to the first stage of Gravemeijer and Cobb’s design research, namely preliminary design.