ETHNOMATHEMATICS AND BATIK CULTURAL CONVERSATION: A QUALITATIVE-ETHNOGRAPHIC STUDY OF MATHEMATICAL CONCEPTS IN BATIK CEPLOK KASATRIAN

Mathematics as a school subject is designed to solve the everyday problem created by human activities; these problems are domesticated in the different cultures of man all over the world. However, the performance of students keeps dwindling due to the westernize approach of teaching and learning mathematics. In other to solve this precarious situation this paper advocated the use of mother tongue in the teaching of mathematics. Mother tongue approach here refers to first-language education as a medium of instruction. The use of mother tongue in the teaching and learning of mathematics is meant to address the high functional illiteracy of Nigeria where language plays a significant factor. Using mother tongue to teach the basic concepts of numbers, operations and other concepts of mathematics helps build a strong foundation for the understanding and learning of higher mathematics. This approach is effective not only in getting the interest of students in the lesson but as a springboard in teaching new mathematical concepts, principles and in deepening student understanding on how mathematical operations or processes work. The mother tongue concepts of teaching and learning mathematics in this work shall be based on the following sub-topics: Numeration/Counting System, Basic Arithmetic Operations, Rhymes and Geometric Concepts. The paper completely reduced the Eurocentric mathematics beliefs of students and make them discover how best mathematics can be learning from their mother tongue. The paper recommended amongst others that teachers of mathematics should adopt the use of mother tongue in teaching mathematics in order to improve students understanding of the subject.

It has been observed that Asian, in particular Chinese students frequently outperform their Western counterparts in international academic comparisons. However, it is still open to doubt as to whether they actually possess a deeper conceptual understanding than their Western counterparts and as to whether they would perform as well in non-routine mathematical problems (such as open-ended problems). The reason for such queries owes as much to the students' as to teachers' conceptions of mathematics. When mathematics is regarded as an absolute truth or a set of rules governing symbols, students tend to consider doing mathematics as the memorisation of algorithms and learning mathematics as a process of transmission. We posed certain hypothetical situations to students in Hong Kong and China and found that they possess a relatively restricted conception of mathematics. Later, we investigated this phenomenon at greater depth by the use of open-ended problems. We found that students usually approached a mathematical problem by searching for a rule that identifies what is given, what is being asked and the category of topic for the problem. Evidence has also shown that this approach to mathematical problems is largely shaped by the way they experience learning, their response to task demands, and the classroom environment. In other words, such a restricted conception of mathematics which exists both within the students and in the classroom culture has led students to tackle mathematical problems by searching for rules rather than approaching them through a conceptual understanding of the context. It is well known that students' conception of mathematics is closely related to their problem-solving behaviour. This conception is shaped by a number of factors, in particular, by the space of learning in which they 'live'. Of particular significance is the finding that the teachers' conception of mathematics could contribute to the shaping of this 'lived space'. These inter-relationships are the focus of a series of studies which will be reported in the present paper.

A meaningful learning process for students can be done by linking mathematics with real contexts and applied with approaches that are in accordance with the characteristics of students. Ethnomathematics studies include various forms of cultural products related to mathematical concepts and activities in the form of buildings, artefacts, social activities, or in various cultural products. In this study, mathematical concepts will be studied in the form of buildings architecture, namely the Al-Jabbar mosque. This research aims to find mathematical concepts in the Al-Jabbar mosque that can be raised in the learning process in the classroom. The method used is qualitative research. Data analysis techniques with literature study, documentation, field observation, and document analysis. The results of the study are many mathematical concepts contained in the Al-Jabbar mosque and can be raised in classroom learning, namely the concept of area under a parabolic curve, parabolic curve equation, integral, geometry transformation (rotation, dilation, reflection, translation), one-dimensional geometry concepts (point, lines and angles), two-dimensional geometry (various triangles, quadrilaterals, circles), three-dimensional geometry (Hemisphere, prisms, tubes), and number patterns. All concepts found are important materials in learning mathematics in elementary to secondary schools so that they can be integrated in the mathematics learning. Keywords: Ethnomathematics, Al-Jabbar Mosque, Mathematical Concepts, Elementary School, Secondary School.

The lived space of mathematics learning

This research investigates the mathematical concepts embedded within Batik Truntum motifs, including geometry, analysis, arithmetic, and algebra. Employing a qualitative methodology with an ethnographic approach, the study addresses four critical questions: "Where should I begin the search?", "How do I locate the concepts?", "How do I identify significant findings?", and "How do I comprehend these findings?". Through addressing these questions, the researcher successfully analyzed the mathematical concepts inherent in Batik Truntum. Of the four primary mathematical concepts, only geometry was substantiated by experts, encompassing sub-concepts such as geometric transformations, line relationships, and planar geometry. Specifically, transformation geometry includes translation and reflection, while the study of line relationships involves line alignment, and planar geometry covers the topic of circles. This research aims to ensure that the millennial generation remains connected to batik as a vital part of Indonesia's cultural heritage, preventing cultural erosion amidst technological advancements through the intricate and exploratory study of mathematics.

Identifying Taiwanese junior-high school students' mathematics learning profiles and their roles in mathematics learning self-efficacy and academic performance

In this chapter, we put forward the claim that any specific view of internationalisation corresponds to a particular orientation for learning and teaching in mathematics. We use a critical discourse perspective to explore variation in the intentions and outcomes of an ‘internationalised curriculum’ and apply the results to the discipline of mathematics. We support the discussion with reference to several components of our research: in particular, a study on students’ conceptions of mathematics and learning in mathematics, and another study reporting on lecturers’ understanding of the intersections between teaching and sustainability, an important correlate of internationalisation. Our aim is to consider the way in which internationalisation contributes as a ‘value’ orientation for our students’ approaches to their study and indeed to their whole lives. We then apply our model to a practical discussion of the construction of learning environments that support a focus on students’ professional formation and the development of their global perspectives

Ped'oa is a traditional dance performed in mass by the Sabu community in a circle and led by the dance leader or mone pedjoe. This research aims to explore ethnomathematics in the Ped’oa traditional dance of the Sabu Community in the Raijua District. In addition, through ethnomathematics exploration, we can identify various mathematical concepts that exist in the Ped'oa traditional dance of the Sabu community in the Sabu Raijua Regency. This research is qualitative-explorative research with an ethnographic design. The subject of this study consisted of five people who were dancers and leaders of the cultural society. The data in this research is obtained through interviews, observations, and documentation. The data validity test is carried out by triangulation of sources. The data obtained were analyzed using Spradley's model data analysis techniques carried out through domain, taxonomy, componential, and cultural themes analysis. The results of this study showed that there is ethnomathematics in the Ped’oa traditional dance which is indicated by the characteristic of counting, locating, designing, and explaining activities. Based on those activities, mathematical concepts can be identified in the Ped’oa traditional dance, including multiplication, geometry, number patterns, geometric transformations, and mathematical logic. Those various mathematical concepts can be developed by designing mathematics learning tools that can be applied in mathematics learning, both for primary and secondary education levels

Students’ performances in mathematics in Ghana have not been as good as they should be (Ministry of Education Science and Sports, 2007; Ministry of Education Youth and Sports, 2004a). Concepts such as fractions and measurement have often been cited as being problematic to students but these are the very concepts which students have much prior knowledge of, through their engagement in out-of-school/everyday mathematical practices in Ghanaian society. In other contexts researchers have highlighted the role that culture plays in mathematics teaching and learning (Bishop, 1991; Seah, 2004). This study therefore sought to investigate cultural influences on primary school students’ mathematical conceptions and practices in Ghana, as they move between contexts of out-of-school mathematical practices (OOSM) in the home and in-school mathematical practices (ISM) in the school. Three theoretical lenses were drawn to illuminate the problem. These included the cultural nature of mathematical knowledge by Bishop (1988), sociocultural theories on learning by Vygotsky (1978) and students’ transitions between contexts of mathematical practices by Abreu, Bishop and Presmeg (2002). Two main research issues and seven research questions were posed to guide the study. The main research issues were: 1) What are the sociocultural influences on Ghanaian students’ mathematics learning? 2) What are Ghanaian students’ transition experiences between the home and school contexts and how do these affect their learning in school? Questionnaires were administered and responded to by 137 primary school teachers and 24 of their headteachers, from 25 (out of all 74) primary schools, selected through stratified random sampling in the Cape Coast Metropolitan area in Ghana. The selection was followed by interviews with 32 primary school students (four each from grade 4 and grade 6), their teachers and headteachers from four (out the 25) schools. Documentary evidence of how teachers handled culture differences was also collected. The data gathered from the closed ended items in the questionnaire survey were analysed quantitatively through the use of frequency counts and descriptive statistics (means) whilst the open ended items were analysed qualitatively, as were the focus group interviews as well as interviews with teachers and headteachers. The study revealed that exposure to school mathematical culture influences the use of OOSM in ISM in some cases; students’ perceptions about mathematics reflected those of the headteachers and teachers; students identified with school mathematical culture (ISM) despite their recognition of OOSM also as a form of mathematics; evidence of cultural influences was observed especially in students’ conceptions and practices in identification of arithmetic fractions and division (as in sharing) in real life problems; students mistakes appeared to largely depend on out-of-school logic; generally practical activities evoked out-of-school thinking whilst paper and pencil activities evoked in-school thinking; teachers generally ignored cultural differences and rather concentrated on teaching school mathematics. The study recommends the need for teachers to see beyond students’ mistakes, as their mistakes could be based on a different logic system. In order to make mathematics more realistic to students, a three-tier teaching strategy is proposed to gradually expand students’ mathematics schema to include ISM.

Many ethnomathematical studies examine the existence of mathematics concepts in Indonesian cultural products where batik is one of them. However, there is a lacunae from previous studies that examine the existence of mathematical concepts in Batik Sidoluhur. Therefore, the current study aims to explore mathematical concepts in Batik Sidoluhur, such as geometry, algebra, arithmetic, and statistics. The study used ethnography as an approach by answering four principal questions, namely "where do I start looking?", "how do I find it?", "how do I recognize that it has found something significant?" and "how to understand what it is?". By answering the questions, researchers managed to examine the mathematical concept contained in Batik Sidoluhur. From the four mathematical concepts explored, namely geometry, algebra, statistics, and arithmetic, only the concept of geometry is contained in Batik Sidoluhur and has been confirmed by a geometry expert. Sub-concepts of geometry found are (1) sub-concepts of geometry transformations such as translation and reflection, (2) plane geometry such as rhombuses, rectangles, triangles, and circles, and (3) congruence. It is hoped that the results of this study can be used as materials to promote Batik Sidoluhur to the younger generation through contextual and meaningful mathematics learning. In this article also explained how to use the context of Batik Sidoluhur in mathematics learning.

Objective: This study aims to identify ethno mathematics in the Mbaru Niang traditional house of the Wae Rebo community, describe related mathematics concepts, and develop learning tools and learning trajectory for mathematics concepts contained in the culture of the Mbaru Niang traditional house. Theoretical framework: Ethno mathematics is all forms of mathematical activities that are culturally based and varied and can be done every day as needed (Rosa, 2011). Ethno mathematics is a group of ideas about the history of mathematics, the cultural roots of mathematics, the mathematics implicit in everyday rules, and the learning of mathematics (Weldeana, 2016). Ethno mathematics is defined as special ways used by a certain cultural group or society in mathematical activities (Sarwoedi, 2018). Ethno mathematics is mathematics applied by a particular cultural group and studies the relationship between mathematics (mathematics education) and the corresponding social and cultural background, i.e. how mathematics is produced, transferred, disseminated, and specialized in diverse cultural systems (Gerdes, 1994; Zhang & Zhang, 2010). Ethnomathematics is a learning approach that is carried out by teaching mathematics by linking mathematics with the nation's own cultural works and also involving the needs and lives of its people (Zaenuri, et al., 2018). Method: The research method used is descriptive qualitative research with an ethnographic approach. The researcher is the main instrument, and data is collected through observation, interviews, and documentation, data validity using source triangulation techniques. Furthermore, the data were analyzed to describe the research findings. Results and Conclusions: The results showed that there were mathematical activities in the construction of the Mbaru Niang traditional house. These activities include measuring activities with the concept of standard and non-standard units and designing activities related to the concept of geometry. Thus, the mathematical concepts contained in the construction of the Mbaru Niang traditional house can be developed by designing learning tools and learning trajectories that are in accordance with school mathematics. The culture of the Mbaru Niang traditional house is a source of learning mathematics that can be presented according to various contexts in learning mathematics. The study's findings contained several mathematical aspects of the culture of the Mbaru Niang traditional house. These aspects were the concept of geometry (in the form of a conical shape) and the concept of measurement (using non-standard measurements). The measurement concept can be applied to elementary school students, and cone geometry can be applied to junior high school. Thus, identifying and exploring Ethno mathematics in the Mbaru Niang. Implications of the research: Mathematics learning strategies that are oriented towards increasing student success in learning, respecting culture, enhancing cooperation and protecting the natural environment. This is done with the "ethno math" approach through learning in schools. Difficult math concepts can be unraveled with ethno math that is real around students and supported by teacher commitment in implementing learning in the classroom. Originality/value: The novelty of this research is the formation of an ethnomathematics model of mbaru niang that can be integrated in learning mathematics at school in order to provide advice for decision makers in this case teachers and government or education observers to be more pro-active in implementing learning in accordance with the culture around the student.

The purpose of this study is to describe: (1) how the teachers prepared mathematics learning activities in an independent curriculum, (2) how teachers implement an independent curriculum in mathematics learning, (3) the obstacles experienced by teachers in implementing an independent curriculum in mathematics learning. Qualitative research was aapplied in this research. The subject of the research were mathematics teacher of class X SMK in East Jakarta Administrative City. The subjects are selected based on teachers who frequently attended training and independent curriculum webinars and suggestions from the principal. The data collection techniques was done by observation, interviews and documentation. Data validity uses source triangulation. The data analysis technique used Miles and Huberman’s concept that are data collection, data reduction, presentation of data and drawing conclusions. The results of the study can be stated as follows: (1) How to organize independent curriculum implementation activities in mathematics learning is done by: (a) preparing Education Operational Unit Curriculum (KSOP) documents, education calendars, annual programs, semester programs to determine effective weeks, (b) preparing learning outcomes (CP), goals learning (TP), learning objectives flow (ATP), student worksheets (LKPD) and appropriate learning methods, (c) compiling teaching modules and their assessments and preparing Pancasila student profile projects. (2) The process of implementing an independent curriculum in mathematics learning carried out by teachers is in accordance with the lesson plan. Teachers use active learning strategies and learning models to make students active in learning activities and teachers only as facilitators. In learning the teacher also carries out several activities to strengthen the profile of Pancasila students to students in order to achieve learning objectives. (3) The obstacles experienced by teachers in implementing an independent curriculum in mathematics learning include: (a) students still have difficulty adapting to offline learning, (b) students' basic knowledge of mathematics is low and students tend to be passive even though they have been given a stimulus by the teacher.

This study aims to determine the mathematical concepts applied to Javanese gamelan musical instruments. The type of research used in this research is qualitative research with an ethnographic approach, namely describing Javanese gamelan musical instruments as a medium for learning Mathematics. Data obtained through interviews, observation, and documentation. The instrument in this study consisted of the main instrument, namely the researcher himself and auxiliary instruments in the form of interview guidelines, observation sheets, and documentation tools. The data validity technique used is method triangulation and source triangulation. The results of this study indicate that there are mathematical concepts that are applied to Javanese gamelan musical instruments such as one-dimensional geometry, namely the concept of lines, parallel lines and right angles, two-dimensional geometry, namely square, rectangle, circle, trapezoid, and triangle. three in the form of a tube, a sphere, and a truncated cone. With the existence of mathematical concepts in Javanese gamelan musical instruments, it is very possible for mathematics learning media to be designed using Javanese gamelan ethnomathematics so that mathematics contributes to the preservation of the nation's culture.

The Badjaos are known to be shy, ridiculed, discriminated, and cannot interact with other people or races thus affects their behavior in the community and performance in schools. The study aimed at describing the processes and techniques of the individualized learning mechanisms; determining their pre-test and post-test scores; and ascertaining if there was a significant difference in the pre-test and post-test scores of the participants in the individualized learning. We introduced an academic intervention program in Mathematics through tutorials by implementing individualized and personalized interactions. The Mathematical topics and contents included are the results of the needs analysis survey during the focus group discussion (FGD) and key informant interviews (KII). By utilizing the quasi-experimental setup, the pre-test and the post-test results showed some significance regarding mean differences. Qualitative data was also collected. The research activities had developed a harmonious learning environment among stakeholders. The levels of interest of the Badjao children became very promising as manifested by their gestures and behavior in the learning environment. Supporting these results are their performance inside the classroom and the revelation of their teachers. The tutorial program has impacted on the lives of the Badjao children. They appreciated the activity. The Badjao children in the study now can count and comprehend numerical figures without difficulty. They said that it is not difficult to engage these concepts in Mathematics in their everyday living. There is a desire to continue this program to other cultures in Mindanao as well. The research program had developed a sense of cultural understanding and eventually, it was discovered that the learning and tutoring in Mathematics via individualized learning was found to be an efficient tool for learning in Mathematics with the specific cultural background.

Radap Rahayu dance is an original dance from South Kalimantan, Indonesia. This dance is a cultural heritage of Banjar, South Kalimantan. It has ethnomathematics potential that needs to be studied. The study aimed to explore the ethnomathematics aspects of the Radap Rahayu dance. The subjects of this research were Banjarmasin cultural figures and artists, dance lecturers and dance teachers The four focuses of this ethnographic research are, finding the mathematical concepts in the movement, musical instrument accompaniment, clothing, and ethnomathematics implementation of the Radap Rahayu Dance in mathematics learning. Data collection techniques using Focus Group Discussion with observation, interviews, and elaboration of the three research subjects. The data analysis technique refers to Miles and Huberman, with data validity using source triangulation. The research results show four things. First, there is a concept of counting, measurement, reflection, circles, and triangles in the Radap Rahayu dance movements/varieties. Second, there is a concept of symmetry, a circle, and an integral symbol on the musical instrument accompanying the Radap Rahayu Dance. Third, there is a concept of a triangle, symmetry, parallel lines, a circle, and dilatation in the costume of Radap Rahayu Dance. And, the implementation of the ethnomathematics aspects of the Radap Rahayu Dance in Mathematics Learning is found in the student module and Worksheets, which contain project-based activities making mathematics more meaningful and fun. Keywords: Ethnomathematics, Radap Rahayu Dance, Mathematics Learning