Implementation of Real Analysis Learning

        One of the required subjects for students of mathematics study programs is real analysis. Real analysis courses require extensive understanding, logical reasoning, generalization reasoning, abstraction and proof of theorems which are very numerous and difficult. Proof plays a very important role in mathematics because proof is an absolute and fundamental part of mathematics and an inseparable part of mathematics. Because it is an essential part of doing doing, communicating, and recording mathematics. Based on the facts on the ground, it was found that most students find real analysis difficult and have difficulty in working on or learning real analysis.

Based on the experience of attending a real analysis course, it was found that many students had difficulty in several ways, namely assessing the truth of a statement, understanding information, finding ideas and writing ideas. Yuslenita Muda (2017), a lecturer at the Suska State Islamic University of Pekanbaru who is studying real analysis said it is difficult for students because it is too abstract, even though his name is real. These difficulties make students have a low interest in real analysis courses, which causes student learning outcomes and activities in the lecture process is also very low.

To be able to develop and communicate a mathematical proof well, students are required to have creativity, intuition and experience. As for how students can understand analytical subjects, namely students more actively studying groups with friends, the active role of tutors in group learning, requires habituation to be able to solve problems related to real analysis and consult with lecturers. By doing the things above, students will be able to learn analysis properly and correctly so that they assume that real analysis is easy.

The actions taken by real analytical instructors to develop the quality of learning so that students easily learn real analysis is by applying the lesson study method. Through the lesson study model lecturers collaborate with other lecturers in the planning, implementation, and reflection learning stages. Bill Cerbin and Bryan Kopp (Sudrajat, 2008) suggest that lesson study has 4 main objectives, namely to: (1) gain a better understanding of how students learn and teachers teach; (2) obtain certain results that can be utilized by other teachers, outside the lesson study participants; (3) systematic learning enhancement through collaborative inquiry; and (4) building a pedagogical knowledge, where a teacher can draw knowledge from other teachers. So hopefully the learning process in the real analysis course can run well and the achievement of learning objectives by implementing lesson study.

Based on how to learn real analysis, it can be concluded that to understand real analysis, namely, (1) students are expected to get used to working on various problems related to real analysis and consultation with lecturers, and (2) lecturers are expected to apply the lesson study method by the order of implementation is the preparation phase, the implementation phase, and the reflection phase. So that learning real analysis will be easy for lecturers and students.