Learning in the industrial revolution 4.0 requires the optimal use of technology in the learning, one of which is by learning to use mathematical e-modules that can be operated on smartphones using an android operating system. This study aimed to create valid, practical, and effective android-based e-modules. This research was research and development (R&D) with the Plomp development model, which consists of the preliminary research phase, the development or prototyping phase, and the assessment phase. The subjects of this study were students of grade X in SMA N 5 Pekanbaru. The results of this study were the android-based e-module was valid, practical, and effective. The validity of e-modules was classified based on the results of the experts' evaluation. The practicality of the e-module was classified based on the questionnaire responses of teachers and students, who can use the e-module well, can help students in understanding the material, and interested in using it. The effectiveness of e-modules was classified by the percentage of student's completeness learning after using e-modules more than 70%.

This study came from the low of problem solving mathematics ability and the low of student activities. The Low of problem solving ability because most of the learners are not able to solve mathematical problems related to the real world. The Low of problem solving ability because most of the learners are not able to solve mathematical problems related to the real world. The purpose of this study is to reveal the development process and to produce the RPP and LKPD with CTL approaches which are valid, practical and effective in improving problem-solving ability and student's activities on grade XI Senior High School. This development research is conducted using Plomp development model. Plomp development model consisted of three phases; they are preliminary research, prototypee phase and assessment phase. Based on the development has been conducted, acquired Lesson Plan and Mathematics Students' Worksheet with CTL approach for grade XI SMA which are valid, practical and effective.

This study is a quasi-experimental nonrandomized pretest-posttest control group design. The experiment group is treated by APOS theory instruction (APOS), that implements four characteristics of APOS theory, (1) mathematical knowledge was constructed through mental construction: actions, processes, objects, and organizing these in schemas, (2) using computer, (3) using cooperative learning groups, and (4) using ACE teaching cycle (activities, class discussion, and exercise). The control group is treated by conventional/traditional mathematics instruction (TRAD). The main purpose of this study is to analyze about achievement in proof. 180 students from two different universities (two classes at the Department of Mathematics UNAND and two classes at the Department of Mathematics Education UNP PADANG) were engaged as the research subjects. Based on the result of data analysis, the main result of this study is that the proof ability of students' in the APOS group is significantly better than student in TRAD group, so it is strongly suggested to apply APOS theory in Abstract Algebra course.

This study aimed to improve students’ achievement in elementary linear algebra through APOS theory approach. This study is pre-experimental one-shot case study design. The sample were 32 students who participating in the lecture of chemistry mathematics II academic year 2018/2019 at Andalas University. Instrument used in this study was problem solving test in elementary linear algebra which consisted of four item test that measures the ability to solve daily life problem with system of linear equation, determine determinant of the matrix, determine invers of matrix, and determine eigen value and eigen vector of matrix. Descriptive statistics and t-test with α = 0.05 level of significance were used for data analysis. The results show that: (1) APOS theory approach can improve students’ achievement in elementary linear algebra significantly and (2) there was no a significant gender gap in students’ achievement in elementary linear algebra.

The purpose of study was to develop a Mathematics learning tool based on a realistic, valid and effective mathematical approach to improve the ability of fraction concepts. This is part of the research & development which has three stages, and they are: (1) Preliminary research, (2) Prototyping, including (a) designing, (b) formative evaluation, and (c) prototype revision, and (3) Assessment. The instruments were test of the fraction concept ability, and questionnaire of motivation. The analysis of data was the inferential and descriptive statistics. The results is that realistic mathematical learning tools were feasible to apply and were easy to use, easy to understand and very helpful for the learning process. The learning tool could strengthen students' motivation. The conclusion was that as for the ability of understanding fraction concepts, students who use realistic mathematical learning tools is higher than students who learn conventionally. Thus, a real-time mathematics-learning tool can replace conventional learning.