Efforts to improve the mathematical representation, learning must begin from the real objects in daily life, which are culturally oriented related to horizontal mathematics in the form of ethnomathematics. The objective of this study was to determine the comparison of the ability of mathematical representation between students taught by realistic mathematical approach and conventional learning; determine the comparative ability of mathematical representation between students who are ethnomathematical and non-ethnomathematical oriented; determine the existence of interaction influence of learning approach and the orientation of mathematics material to the ability of mathematical representation. This research was a quasi-experimental study, which uses the pretest-posttest design of non-equivalent group design. The research instrument used was the test of mathematical representation ability. Data were analyzed using multivariate test of covariate analysis. The results showed that there were differences in the ability of mathematical representation between students who were taught by realistic mathematical approach and conventional learning after controlling students’ early ability; there is a difference in the ability of mathematical representation between students who are ethnomathematical and non-ethnomathematical oriented after controlling students’ early abilities; there is an interaction effect of the learning approach and the orientation of mathematical material on the ability of mathematical representation after controlling the student’s early ability.

The easiness of learning can be experienced if learning contents and contexts are related to students' daily activities. One of them is a learning approach that has realistic characters based on ethnomathematics. The purpose of the study was to determine the influence of ethnomathematics and realistic mathematical approach on the ability to understanding concepts. The research was a quasi-experimental study to implementation of the realistic mathematics learning based on ethnomathematics. We were using the 2×2 factorial experiment design. The samples was 84 students of all students in one of the senior high schools in Rejang Lebong. Samples were selected with intact-group techniques. Data collection is done using instruments of understanding the ability of mathematical concepts. Data were analyzed by using covariate analysis. The results were the ability to understanding mathematical concepts from students taught with realistic mathematical learning approaches is higher than those taught with direct instruction, when two groups of students given ethnomathematics-oriented material.

Mathematics becomes an important subject in elementary school. Numbers are one part of school mathematics. Learning that links between concepts and what is close to students' minds makes it easy for students in the process of reaching concepts. This is CM based on local culture. This research used a 2x2 factorial design. The population is all elementary school students from the "Integrated Islamic Foundation" in Bengkulu City. Samples were taken by using an intact group technique. The total sample is 60 students. With the local culture-based CM learning for experimental class and conventional learning for control class, the research instrument is a test of the ability to understand the concept of numbers. It is a valid and reliable instrument. The data was analyzed using the ANCOVA statistical test. The results of this study are Fo (A) = 9.7289 with, df = (1, 57) and p-value = 0.090 <0.05, which means Ho is rejected. It is showed that there is a linear effect of the covariate (initial ability) to understand the concept between the students who follow the learning by using CM with a local cultural approach. Fo (B) = 4.8096, df (1, 57) and p-value = 0.016 <0.05. In this case, Ho was also rejected. Thus, it can be inferred that there is the influence of CM learning with a local cultural approach on the ability to understand number concepts. It can be concluded that the average score and comprehension of the number concept for students who were taught by using CM learning was higher than the students who were taught with conventional learning models. Finally, the mean score for students' ability to understand the number concepts among the students who were given local culture-based materials was higher than the students who were given the materials which are not based on local culture.

Problem-solving is one of the goals of mathematics learning. Ethnomimetic-based realistic mathematics learning is learning with starting-point contextual problems that are close to students’ minds. This study aims to determine the effect of ethnomathematics-oriented realistic mathematics learning on problem-solving abilities. That is a type of quasi-experimental research. The study design was a non-equivalent control group. The population is SMA N 2 Kota Bengkulu in 2019. The sample of this study was 68 students from Class X MIPA A and X MIPA D. The research instrument was a test of problem-solving skills. Data were collected through tests and analysed by covariate analysis. The results of this study are that realistic mathematics learning oriented to ethnomathematics has a positive effect on the ability to solve. The conclusion is that realistic mathematics learning with ethnomathematics orientation can improve mathematical problem-solving skills for secondary school students. We suggest that mathematics teachers can develop realistic mathematics learning tools with ethnomathematics as a starting point for learning.

The mathematical abilities can be measured through students’ mental and physical activities. One of them is using genetic decomposition analysis of APOS theory. The purpose of this study was to describe the ability to understand the concept of derivative functions for interlevel students during ethnomathematics learning. The research is part of our development research.The subjects were high school students majoring in mathematics and science in Bengkulu. The research was carried out in a participatory manner in the regular learning process by applying the ethnomathematics approach. Subjects were interviewed based on the assignments given. Data were analyzed qualitatively by applying genetic decomposition. To obtain inter-level characteristics, the description of genetic decomposition continued with fixed-comparison methods. The result was able students to encapsulate the process of function properties or intervals in the domain so that the object is formed about the sketch of the function graph h.

A triangle is an abstract object in Lobachevsky’s Geometry. The local content is needed as a starting point for learning geometry. This study aims to describe student’s understanding of triangles in Lobachevsky Geometry through local culture. This is an exploratory study. The focus is on analyzing the needs of student’s ability to understand the properties of Lobachevsky’s geometry. The subjects of this study were mathematics education students in Bengkulu, Indonesia. In-depth interviews are based on assignments about triangular problems. The problem is taken from the culture of Bengkulu society about “glutinous rice cake”. Data were analyzed through a collection of interviews and other physical activity. The results of this study are the subjects can connect the elements together to form a coherent unity based on observations of sticky rice cake. They produced a new product by organizing several elements into different forms or patterns from before, namely triangles with a large number of angles of less than 180. The conclusion of this study is that student’s understanding of triangles in Lobachevsky Geometry has reached the level of creating a new proposition, namely the number of angles in triangles in Lobachevski Geometry is less than 180.

Geometry becomes a difficult subject for students. The abstract object was one of the factors. Therefore, more concrete learning media are needed. One of them was augmented reality assisted by GeoGebra. The purpose of this study was to determine the ability to understand the geometrical concepts of high school students through augmented reality learning assisted by GeoGebra. Treatment was given to students through learning using GeoGebra-assisted augmented reality. This was a quasi-experimental study with a pre-test post-test control group design. This research instrument was a test of the ability to understand the concept of geometry. The test was used to measure students’ initial abilities, and this was referred to as a covariate. Also, to measure the ability to understand concepts after students follow augmented reality learning assisted by GeoGebra. Data were analyzed by covariate analysis (ANCOVA). The results of this study were F = Fo (A) = 9,150 with p-value = 0,000 <0,005. That means, there are differences in the ability to understand the concept of geometry between those taught with augmented reality which is assisted by GeoGebra and conventional learning. Other results show that t = 6.723 with p-value = 0.000 <0.05. This shows that the ability to understand the geometry concepts of students taught with augmented reality assisted by GeoGebra was higher than students who were taught conventionally after controlling for covariates. The conclusion was that the ability to understand the concepts of geometry through GeoGebra-assisted augmented reality learning was better than students taught with ordinary learning.

The cognitive theory views individuals as active information processors, so that individuals were able to represent each information according to the level of knowledge they have. Student representation can be seen as its genetic decomposition. Ethnomathematics was a vehicle for unlimited series learning. The purpose of this study was to describe the genetical decomposition of students about infinite series through the Bengkulu ethnomathematics. This was the initial research from a series of development research. This stage we interviewed in depth 10 high school students in Bengkulu, Indonesia. The research instrument was the researchers themselves who were guided by interview guides about understanding concepts and the principle of infinite series. Interviews were conducted during and after Bengkulu’s ethnomathematics learning. Data were analyzed through fixed comparison techniques. The results of this study were found that students can coordinate two or more actions about convergence of sequences, but not for convergence of infinite series. Conversely, there were students who can describe a particular object about converging an infinite series but not coordinated with the processes that were built for converging sequences. Also, there were students who can coordinate the action-process related objects so that a schema of converging sequence was formed, but for infinite series only in the form of separate actions or processes. The conclusion of this study was the genetic decomposition of students in understanding the infinite series through ethnomathematics learning at the intermediate level (inter level). The student before ethnomathematics learning was at the lower level (intra and pre-intra levels).