Integral is one of major topics in Calculus course. Many university students fail in calculus course because their understanding on the concept of Integral especially in understanding definition of integral is low. This situation encourages us to design a calculus lesson to build students understanding on Integral especially integral definition by using Realistic Mathematics Education as an approach. For that, we try to design a series of instructional activities starting from introducing sigma to definition of Integral in order to know students difficulties in understanding this topic. Some first-year university students in Universitas Negeri Padang are chosen to test our Hypothetical Learning Trajectory (HLT) in our preliminary research. The result is students had difficulties in connecting the sigma, area and definition of integral. This happens because the students did not see that the activities that have been designed as a whole that cannot be separated. Therefore, it is recommended to design a series of instructional activities which is focus on connecting sigma, area and definition of integral.
Industrial revolution 4.0 in which digital technology being more integrated in all aspects of human life will demand the new reform of education world. Not only can it affect the curriculum being taught, but it will also lead to the changes of the methods and approaches in conducting the lesson. One of the changes is the use of digital learning. Universitas Negeri Padang has regulation of conducting lesson through e-learning platform proportionally for all courses, including the course of Ordinary Differential Equation. Ordinary Differential Equation is a mandatory course that should be taken by mathematics department’s students. In order to support students to develop their under standing about the concept and its application while using digital learning method, the researchers develop some tutorial video as supplementary media. Therefore, this study aimed to describe the practicality of the tutorial video. This is a descriptive research where the data were collected using closed questionnaire. The respondents were 39 mathematics students of Universitas Negeri Padang who joined Ordinary Differential Equation Course in the semester of January-June 2020. The result indicates that the video tutorials used in the course are in the category of very practice with the score percentage 86,6%.
The low learning outcomes and student’s difficulties in understanding calculus courses, espe-cially integral topic, encourage us as researcher to design a calculus lesson for first year students by using realistic mathematical approach (Realistic Mathematics Education). For that we try to design a series of instructional activities starting from understanding integral as an anti derivative. The in-structional activity is designed and developed based on the learning process that occurs in the class-room by involving 30 first year students in FMIPA UNP. The classroom learning compared with our Hypothetical Learning Trajectory (HLT). The results of teaching experiment show that students' un-derstanding of derivative plays important role in understanding the integrals, in general students have difficulty in communicating their ideas in determining the anti-derivative of a function. Through class-room discussions students can get ideas and discuss it in determining the anti-derivative of a function. Based on these results it is recommended to conduct classroom discussions to build students' under-standing in studying calculus especially integral as an anti derived.
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