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The goal of this research is to determine the influence of the realistics mathematics education (RME) approach by oriented higher order thinking skills (HOTS) on the results of students’ mathematics learning on the subject of the calculus in SMAN 10 and SMAN 12 Padang. The method used is the experimental research with pre and post-test design randomized control group. The data analysis technique used is the test for normality and homogeneity test followed by using a t-test. The results revealed that there were an increase in student mathematic learning outcomes approach realistic mathematics education oriented higher order thinking skills in class XI MIPA SMAN 10 and SMAN 12 Padang. There is impact-oriented approach to realistics mathematics education approach by oriented higher order thinking skills to understanding student learning in class XI SMAN 10 and 12 MIPA Padang.

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Critical thinking is one of the higher order thinking ability that needs to be developed in the 21st century. In fact, that the students’ critical thinking ability are still low. In learning geometry students are still dependent on the teacher in receiving information, the media are inadequate in learning geometry so that students have not been trained to solve geometry problems with critical thinking. Thus a geometrical learning devices was made based on the van hiele theory. Before using the geometry learning devices, it is validated first with the experts, asking the teacher’s response, and student responses through questionnaires and interviews. The subjects of this study were class VIII students of SMP 13 Padang. The results showed that the response of teachers and students showed the geometry learning devices is practical criteria.

Based on the preliminary research stage conducted in Public Junior High School (SMPN) 3 Muara Bungo, it is obtained that students’ reasoning ability is low and has yet achieved optimum result. This is due to inappropriate learning device available in which it is yet facilitating the students in improving their mathematics reasoning. Therefore, it is of vital importance to develop learning devices in the form of lesson plan (RPP) and student worksheet (LKPD) based on Realistic Mathematics Education (RME). RME provides more opportunities for the students to be more active in comprehending mathematics concept, think logically, and are able to draw a problem fine conclusion. The purpose of this research is to obtain valid, practical, and effective learning device based on RME for class VII of Junior High School. Research data were collected through observation, interview, document, questionnaire, and mathematical reasoning ability. The research participants are students of class VII SMPN 3 Muaro Bungo. This is a model development research. Plomp model was employed as the development model in this research. There are 3 phases on this model, namely, preliminary research phase, development or prototyping phase, and assessment phase. However, this research focuses only on preliminary research phase. It is including things required to design the expected learning device. The result of preliminary research is 1) students’ mathematical reasoning ability has optimum yet; 2) class VII students are in their transition from elementary school to junior high school level; hence mathematics learning requires concrete learning object or mathematics learning should be linked with their daily life; 3) RPP used provides less support to improve students ability in mathematical reasoning and it provides less opportunities for the students to be more active; 4) students expected that LKPD has to be detail, attractive, fun, and easy to comprehend.