This paper is the result of the 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 uses in all of the class of PJHS, the students engagement in learning activity is very low, and most of the students do not attain minimal mastery achievement. (2) Based on essay test found that performance of the students in mathematical understanding and representation test is categories small.

Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out secondary school students are so poor in MRA. Considering the problem, this research developed instruction materials based on Joyful Problem-based learning (JPBL) to endorse eighth graders of public secondary school students grasp their MRA. The study took place in the Province of North Sumatera, Indonesia. A number of 88 students engaged as subjects. The study administered MRA test before and after implementing the instruction materials. Data is analyzed descriptively and by t-test. The result showed that the learning materials developed is effective in improving the students' MRA. It increased significantly, though categorized mediocre. The study contributed to the existing instruction materials in pursuing MRA.

Human must have the ability to understand, because understanding can prevent people from misunderstandings and conflicts. Similarly, public junior high school (PJHS) students need to have mathematical understanding ability (MUA) for a reason, that is, MUA is an important part in problem solving. In fact, MUA of PJHS students was still low. This research was conducted to contribute in improving students' MUA. There were 158 students engaged in the experiment classroom as well as in the conventional one taken from PJHS 1, 2, and 4 from district of Deli Serdang, PJHS 17 and 22 from Medan City, Indonesia. Joyful problem based learning (JPBL) approach was applied to attain the purpose of the research. The study used essay-test to measure students' MUA. The score obtained was then analyzed by t-independent test, while student performance in solving MUA problems was described descriptively. Results of the research: (1) Students MUA' score was higher in the experiment classroom than in the conventional one. (2) The improvement of students MUA in the experiment classroom belongs to medium category. (3) The students' performance in MUA was better in the JPBL classroom than it was in the conventional one. Some students faced difficulties both in explaining the solution and in giving example of a mathematical concept. Overall, the students' performance was best at the aspect of presenting problem in mathematics equation. Based on the findings, the study suggests teachers to give reinforcement in both aspect where students lacked of by, for example, encouraging them to solve a variety of problems which eliciting the aspect of explaining and giving examples.

To make students actively involved in learning to grasp mathematical higherorder thinking skills (MHOTS) is not easy. Meanwhile, the ability is so important for students to master for it takes place when students continue their studies to a higher level as well as work within a variety of professions, especially in the era of the industrial revolution such nowadays. Many factors affect students' thinking abilities, including learning factors. This study, which implemented constructivism-based learning, aims to investigate the role and contribution of constructivism-based learning approaches as well as mathematical prior knowledge (MPK) to the achievement of MHOTS of middle secondary school students. The data tested through Multivariate Analysis at the 0.05 significance level. In general, this study found that: (1) In the experimental class, the learning approach plays an important role in the way it increased students' MHOTS significantly.(2) The average contribution of constructivism-based learning to MHOTS was at the range of 18% to 57%. (3) Student activity in learning increased significantly. (4) In some cases, there is an effect of interaction between learning factors and MPK towards the achievement of MHOTS. The study recommended the teachers to have courageous in implementing constructivism-based teaching and learning to improve students" MHOTS.

Life skills such as social skill and emotional quotient recognized as soft-skills. Indonesian students softskills such as generous and helpful tends to decrease time to time which considered to threat nation character. Meanwhile, many researchers reported soft-skills is a dominant factor to determine one successfulness in life. Moreover, many hypothesize that it contributes much on mathematical higher-order thinking skills (MHOTS). Therefore, this research took place to help students keep and enhance their aspects of soft-skills. This quasi-experiment research applied constructivism-based learning at a public junior high school. Instruments used to collect data on soft-skills were questionnaire, interview, and observation. An essay test was administered to get data on students MHOTS. The data then analyzed using t-test and variance analysis. The findings showed that: (1) Learning approach contribute significantly toward student mathematical high order thinking skills as much as 57.4%. Constructivism learning approach gives more influence to the students student mathematical high order thinking skills than direct instruction, (2) Student soft-skills contributed only 29.9 % (categorize low) toward mathematical high order thinking skills. However, student soft-skills in the guided discovery classroom is better than its counterpart in the direct instruction classroom, (3) Learning approach and soft-skills simultaneously influence significantly toward student mathematical high order thinking skills. Therefore, it is recommended that teachers not only focus on the cognitive development of students but must care about the development of affective aspects as well.