Learning mathematics until today still left a lot of records that had to be improved, including passive learning, low ability of learners in problem-solving activities, the rarity of authentic assessment, emphasizing only on cognition, and others. This was a study of the literatures concerning the teaching of metacognition in mathematical problem solving. The PME learning model was a modified theory of Darling-Hammond (2003), which was a theoretical-conceptual product that offered the strategies to improve the ability of metacognition in problem solving. This metacognition strategies implemented through metacognitive activities, ie : planning, monitoring, and evaluating (PME). On PME learning model: (1) the activity planning, monitoring, evaluating explicitly raised in the core activities of learning and mathematical problem-solving activities; (2) the learning process recommended using social constructivist teaching in small groups; (3) placing the role and duties of teachers as counselors, classroom manager, motivator, facilitator, and evaluator; (4) The support system for the effectiveness of PME learning model were: Lesson Plan (LP) and Worksheet for students (WS); and (5) the direct effect was expected increasing of the metacognition ability, and the nurturant effect was expected to increase in problem solving performance.

Abstrak. Rencana Pelaksanaan Pembelajaran (RPP) merupakan deskripsi tertulis tentang rencana kegiatan pembelajaran yang seharusnya dapat diimplementasikan dalam praktik pembelajaran. Penelitian ini bertujuan menganalisis kualitas RPP dan implementasinya dalam pembelajaran matematika SMA. Penelitian dilakukan secara kualititatif. Subjek penelitian meliputi 32 orang guru matematika SMA. Analisis data digunakan metode triangulasi (membandingkan data observasi, kuesioner, dan wawancara terbatas). Hasil menunjukkan bahwa kualitas RPP berada pada kategori cukup di semua indikator, sedangkan implementasinya berada pada kategori cukup hanya pada indikator perumusan materi ajar dan kegiatan pembelajaran, pada indikator yang lain berada pada kategori kurang. Dalam hal ini guru matematika SMA disarankan dapat mengembangkan RPP yang lebih berkualitas dan implementatif, yang mampu membiasakan siswa pada kegiatan pemecahan masalah, pengembangan HOTs dan kinerja metakognitif, serta melakukan kegiatan evaluasi yang komprehensif.

This study aims to develop a self-evaluation instrument used to measure the achievement of metacognitive performance, especially in the implementation of PME learning model. The development design used is R & D design model from Thiagarajan but modified to "3-D" (Define, Design, and Develop). The approach used is a mix-methods approach. A qualitative approach is carried out through literature review, then tested through expert validation. While the quantitative approach is carried out through experimental studies, to analyze the validity and reliability of the measurement model can be done with LISREL. The research subjects consisted of 128 students from four high schools in Brebes Regency. From the results of this study were obtained: (1) the instrument developed was stated to be good with little revision; (2) the results of the validity test show that only the 21st indicator has a standardized loading factor = 0.46 < 0.5 or invalid, which means all indicators are valid except the 21st indicator; and (3) the reliability test results obtained by CR ≥ 0.70 and VE ≥ 0.50, which means the instrument has a good level of reliability. So this self-evaluation instrument is feasible to use to evaluate metacognitive performance on PME learning model.

Abstract. The PME learning model is a model designed to optimize metacognitive learning through planning, monitoring, and evaluating activities (Amin & Mariani, 2017). This study aims to analyze the effect of applying the PME model Lesson Plan (LP) in the development of metacognitive performance to improve the collaborative problem-solving (CPS) abilities in mathematics learning. The subjects are 37 of twelfth graders of Senior High School, Kersana-Brebes. The data are collected with student questionnaire and problem solving test, and then they are analyzed with paired sample t-test. The analysis includes (1) Accomplishment level of PME model LP – a Control Tally Sheet (CTS-PME) is available to control it; (2) Students’ metacognitive performance – students fill Effectiveness Questionnaire (EQ-PME) are adopted from Darling-Hammond's metacognitive strategy; (3) ability of collaborative problem solving – students work on student’s worksheet (SW). The results are: (1) sig. = 0.000 <0.05 and t-cal = -4.820, - which means that LP shows significant increase in planning, monitoring and evaluating in learning activities; (2) sig. = 0.000 <0.05 and t-cal = -7.854. It shows that the LP implemented can increase the students’ metacognitive performance; and (3) sig. = 0.001<0.05 and t-cal = -4.671. these numbers tell us that the LP can increase significantly the students’ ability of collaborative problem solving.