Eksperimen Pembelajaran Dengan Model Problem Based Learning (PBL) Dan Discovery Learning (DL) Terhadap Hasil Belajar Matematika Ditinjau Dari Kemampuan Penalaran Matematis Peserta Didik SMP Muhammadiyah 2 Surakarta Tahun Ajaran 2018/2019

ABSTRACT This study aims to analyze the influence of (1) the influence of Discovery Learning learning model on mathematical learning outcomes, (2) the influence of Problem Based Learning model on mathematical learning outcomes, (3) the influence of Discovery Learning and Problem Based Learning models on mathematical reasoning skills. This research uses quantitative methode with quasi experiment design. This research at the SMP Muhammadiyah 2 Surakarta 2018/2019. The subject of this research are savent grade of SMP Muhammadiyah 2 Surakarta 2018/2019 with sample of two classes. Experimental classes with Problem Based Learning learning models and Control classes with Discovery Learning models. The Class determination using cluster random sampling technique. The methods of data collection are questionnaire, observation, and documentation methods. The analyis of data techniques used two-way variance analysis techniques with unequal cells. The results of this study using a signification rate of 5% obtained three results. First, there are differences in the effect of PBL and DL methods on mathematics learning outcomes. Where the DL methods has a better influence on mathematics learning outcomes. Second, there are differences in the effect of mathematical reasoning abilities on mathematics learning outcomes. Students who have reasoning abilities in the high category have better mathematic learning outcomes than those in the medium and low categories. Third, there is no interaction between learning methods and reasoning abilities on mathematics learning outcomes