Abstract
This paper is the result of first phase of the research about the development of students’ mathematical understanding and representation ability through Joyful Problem-based Learning (JPBL) at Public Junior High School in North Sumatera, Indonesia. The population is all of the students of public junior high school (PJHS) in North Sumatera. Samples choose based on stratified random sampling. The samples are the students of PJHS 27 Medan, PJHS 1 Percut Sei Tuan, PJHS 1 Tebing Tinggi, and PJHS 2 Pematangsiantar. The techniques used for collecting data is observation, interview, and essay test. The research findings: (1) Based on interview and observation found that conventional approach still use in all of the class of PJHS; The students engagement in learning activity is very low as well as students self-regulated learning; Most of the students do not attain minimal mastery achievement, (2) Based on essay test found that achievement of the students in mathematical understanding and representation test is categories low. Keywords: mathematical understanding, mathematical representation, joyful problem-based learning  DOI : http://dx.doi.org/10.22342/jme.7.1.2816.43-56
Highlights
Abstrak Makalah ini merupakan hasil penelitian tahap pertama tentang perkembangan kemampuan pemahaman dan representasi matematis siswa melalui Joyful Problem-based Learning (JPBL) pada SMP Negeri di Sumatera Utara, Indonesia
Mathematical understanding as well as mathematical representation is an integral part of mathematical problem solving, while problem solving is the hearth of doing mathematics
It means that the goal of learning various mathematical concepts is in order to perform problem solving, while through problem solving the students developed other kind of mathematical ability such as mathematical comprehension and representation
Summary
Abstrak Makalah ini merupakan hasil penelitian tahap pertama tentang perkembangan kemampuan pemahaman dan representasi matematis siswa melalui Joyful Problem-based Learning (JPBL) pada SMP Negeri di Sumatera Utara, Indonesia. According to Hiebert & Carpenter (1992), mathematical ideas, procedures or facts are understood if they are parts of an internal network, exist in cognitive structure of the student It seems that there is a connection between mathematical understanding and mathematical representation. Teacher should teach the student such that the student has the opportunity in solving mathematical problems as well as mathematical understanding and representation Another fact, the writer suspects that student low achievement in such kind of mathematical skills is because of learning approach teacher used, learning material, and rarely engagement of the student in solving mathematical problems. The teacher usually use conventional approach, while Ronis (2008) stated that conventional teaching learning is not bad but not enough to develop high order thinking skill such as problem solving skill. The student rarely included in problem solving ability and the teacher give less attention in making learning material
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