Mathematics Education

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https://hdl.handle.net/20.500.14540/64

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Effect of manipulative materials in teaching geometry
(2016) Basnet, Nir Kumar; Eka Ratna Acharya
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Ethnomathematical Studies on the Heritage of the Tharus
(Faculty of Education, 2009) Adhikari, Indra Prasad
The present study is entitled ‘ETHNOMATHEMATICAL STUDIES ON THE HERITAGE OF THE THARU’. It is a fresh attempt made at searching Tharus' mathematical knowledge, ideas and concepts with respect to their practical work basis. This study is carried on cultural, historical, pedagogical and mathematical perspective. It emphasizes the kind of mathematical process that are involved, in basketry, clay work, dancing and house painting. It also links those processes with mathematics curriculum. The researcher adopted the qualitative research methods to unveil local ideas of mathematics to interpret Tharus’ mathematical concepts. Seven informants were selected purposively in which three are women and four are men. For data colletion, the reshercher used in-depth interviews; participants' observation and photos of Tharus' goods used and made which are linked up with their society. All the possible information was recorded with the help of field notes and photos. The major findings of this study on basketry, clay, dancing, and house painting works are: i) while making baskets Tharus construct geometrical shape such as spherical, globular, height globular, truncated globular, cylindrical, cubical, and combined of these shapes. They also make triangular, hexagonal, check, wrap, square, parallel and coil patterns. For this they use estimation, counting, fingers measuring, and making equal size of weft, the rapping equal number of weft, and taking equal amount of coil material. ii) For clay work, they make rectangular, cubical, truncated cubical, half globular, elliptical, basin and parallelepiped shapes. In this work, they used estimation, making same size of coil material, counting coil numbers, measuring inner diameter, diagonal, sides and moulding. iii) With regard to dancing they use the concept of arrangement of row, column, and circle, center of circle, motion, and repetition of action, rotation, reflection, reduction and enlargement. The estimation, counting, walking step counting, seeing others’ actions guessing are used while dancing iv) For house painting they use rectangle, square, parallel line, triangular pattern, ratio and proportion, position, location, gap between figure, flower, zoomorphic, and anthropomorphic figures. For this they use counting, measuring, estimating, guessing, and trial and error. The dissertation is divided into six chapters. The Chapter 1 includes socio-cultural, economical and educational background of Tharus in Dang, statement of the problem, rationale of the study and research question. The Chapter 2 is the literature review of ethnomathematical ideas, history, philosophy, pedagogy and technology. The Chapter 3 includes methodology, its design and strategies. The Chapter 4 deals with the mathematical process and ideas that are analyzed with respect to practical activities. The Chapter 5 comprises mathematizing Thars' mathematics. The Chapter 6 discusses educational implication, finding, and suggestions for further research, glossary, reference and appendixes.
Indigenous Mathematical Concepts of Gopali Community from their Cultural Perspective
(Faculty of Education, 2007) Dahal, Ramchandra
This study is focused on the perception of mathematical knowledge among illiterate Gopali people of Chitlang village of Makwanpur district. The Gopalis taken for the study are recognized as gwala/ sapu in the social community of Nepal. They have the identity of first ruler of ancient Nepal. So, the study concerned with ethno-mathematics this community is the appropriate one. The traditional practices followed by them were the main area of the study. Especially the ethno-mathematical practices, existing in Gopali people were the sources of the study. The study is focused on their measurement system, numerical system, and geometrical practices among them. Illiterate children, women and men were considered for in-depth study and common practices were achieved from the religious as well as cultural activities in the group participation. The participant observation and interview were two tools adopted for the collection of information. The study was guided by ethno-methodology as well as grounded theory. The study concluded that the ethno-mathematical practices has supported in preserving their cultural identity. Naturally, the ethno-mathematics and culture are interlinked. The perception of mathematics preserved by Gopalis differs from the school mathematics. There is discontinuity between traditional and modern measurement system but similar practices are found still among the illiterate group. Natural units are still practiced in present context. In the case of domestic purpose, mathematical concepts adopted by them are sufficient. The study is also concluded that the origin of ethno-mathematics is preserved by them. We can not claim that the formal mathematics is adopted in their traditional practices. Whatever mathematical concepts they have seem practical. The study demands the cultural preservation and academic application at their primary level education from which cultural identity as well as importance of indigenous knowledge is preserved. For these a serious planning is required while designing curriculum and in teaching-learning process as well. The study tried to relate their ethno-mathematical practices in the educational implication. The transformation of learning from old generation to new generation can be exited in the similar context but in different situation it cannot be applicable and has great chance to disappear. The new generation of Gopalis are involved in different occupations and some of them have been migrated which may led to the non existence of indigenous knowledge. So, the documentation and implementation of practices of ethno-groups should give priority for the preservation of cultural identity. The conclusion drawn from the study is the identification of ethno-mathematics existing in their cultural and religious practices which should be preserved and at the same time, it has to chanalyzed in the formal education of the community. It is being the study of ethno-mathematics, the events, and practices of the Gopalis were observed in the mathematical sense or their knowledge related to mathematics is tried to cover by the study. Whatever information was mentioned here is based on the Gopalis situated in Makawanpur area. The interpretation of collected information carefully given priority for the cultural preservation, but it is not good to modify the cultural practices. Ramchandra Dahal
Pedagogical discourse in mathematics classroom
(Faculty of Education, 2023) Budhathoki, Boj Bahadur
The study of pedagogical discourse in mathematics classrooms was aimed to explore the current situation of existing mathematics classroom discourse, oversee the challenges, unearth the engagement of students and teachers in pedagogical activities in culturally diverse classrooms, and uncover the methods for promoting student- friendly mathematics classroom discourse. A qualitative ethnographic method was applied within the constructivism paradigm linking with, existing relevant theories, and various scholarly works of literature to accomplish the study. The existing multifaceted realities were explored by analyzing the sequential process of transcribing, coding, categorizing, and thematizing the datasets obtained from the methods of classroom observations, in-depth interviews, and focus group discussions. This study has applied Bourdieu's cultural capital theory, Vygotsky's sociocultural theory, Gardner's multiple intelligence theory, and Freire’s critical pedagogy theory while preparing the theoretical and conceptual framework and used thematic analysis methods during the data analysis part. The results showed that mathematics teachers used the writing of the mathematical formulae on the whiteboard, problem-solving, questioning the students, and answering the questions as a regular classroom activity, and beyond that, they also applied interactive pedagogical approach that engaged students in discussion, debate, interaction, and logical reasoning with ample examples in the classroom. Instructional discourse in mathematics education was worthwhile and collaborative in small groups, writing-centered, systematically planned, and organized in generating and transferring knowledge between students and teachers. In systematic, creative, and inspired communication, mathematics teachers have shown to be competent, diligent, experienced, and skilled in the areas of knowledge creation and transfer related to cultural contexts in culturally diverse classrooms. Although the mathematics teachers realized that the mathematics curriculum and textbooks were not integrated into line with the local and native cultures of real life, the teachers spared no effort to enliven the classroom discourse by orchestrating plentiful examples of incorporating existing cultures into relevant topics. Mathematics teachers integrated some of the existing cultural practices into mathematics as much as possible by involving students in lessons, drawing diagrams, collaborating with classmates, constructing teaching-learning materials, answering questions, reasoning, and dealing with fieldwork and laboratory work. The classroom discourse was innovative through these ideas: motivational and creative teaching methods, a fearless environment, student-friendly pedagogical approaches, and impeccable ICT- integrated teaching methods. However, teachers and students faced many challenges in the mathematics classroom in a multicultural environment. Although the community schools implemented an English-medium teaching method, teachers and students were not prepared to teach and learn in the English medium. This language mismatch further complicated the organization of classroom discourse. Classroom discourse was only a bilingual practice of Nepali and English although class members functioned as a miniature multilingual society, where marginalized student groups felt threatened and dominated by the culture and language of the larger groups. In such a situation, even though the teachers tried their best to make the classroom discourse meaningful; cultural and linguistic contradictions unexpectedly existed. Learning difficulties were encountered as a result of frequent student absences. The presence of large numbers of students in some classrooms made it inappropriate to correct classroom tasks and engage students equally in mathematics classroom discourse. The integration of ICT enhanced the pedagogical discourse to understand the basic concepts of mathematics although some old-aged teachers faced challenges in integrating ICT into mathematics teaching because they were given little in-service training to use the latest ICT tools which were not enough to cope with the modern tools in education. There was no adequate system for training teachers to teach mathematics in multicultural classrooms. The findings of this research can be employed in policy-level implications, program implications, pedagogical implications, motivational implications, theoretical implications, and training implications.
The Upshots of Mathematical Knowledge and Skills Achieved in Friendship Groups through Cooperative Learning Paradigm
(Faculty of Education, 2009) Kshetree, Mukunda Prakash
The cooperative learning paradigm has been figure out as an umbrella method of all other methods. It has itself many methods but each and every one has been found to be dedicated to make the learning creative, joyful, socialized, team working and meaningful based on the potentiality of prior knowledge of the students as their cultural capital. As the method runs through social activity and teamwork, it seeks the true and direct participation of the learners with their own head and soul. It has mainly been spinning on the three theories; psychology of building knowledge through mental exercise/action of Piaget, Lave and Vygotsky’s anthropological perspective of learning through scaffolding and Dewey’s philosophy of truth is subjective. In this closure, the study was undertaken with the purpose of digging out the effectiveness of cooperative learning approach through the ‘friendship group’ formation in terms of immediate learning, withholding and ultimately the net gain in learning. In the mean time, it was tried to find out the problems being faced by the teachers while adopting cooperative learning system, self-regulation of the students and relevancy of this approach in Nepalese classroom situation. To ease my study, I had further formulated the principal research questions into other components as well. The basic framework of the theoretical closure was made to lay on the foundation of epistemology, ontology and axiology of the cooperative learning paradigm. In this study, the review of literature has covered the general overview of different types of related literatures to frame up the study with specific ingredients and some theoretical closures that to link the issues raised herewith. As I was basically concerned with the perception, participation and output of the learning of the students based on their cultural and social property, I adopted the qualitative research method along with the quantitative one. The research method used was non-equivalent control group of quasi-experimental design. The study was done by taking sample of size 74 students comprised of control and experimental groups from two schools of Kathmandu valley. The major tools of qualitative method were observation of classrooms with checklist and interview of students, subject teachers, general teachers, head teachers, subject experts, supervisors and curriculum experts with interview guidelines. Similarly, the pretest, posttest and retention test were administered to collect the data for quantitative analysis. The quantitative data were analyzed with the help of 13.0 version of SPSS package whereas the qualitative data were properly arranged and triangulated with the theoretical closures and previous findings and then gave the final meaning to my findings. The major findings were the significant achievements of the students of experimental group, who were taught according to the cooperative learning phenomena with the help of cooperative teaching incidents through friendship groups. The achievements were taken into account of immediate learning, last longer memory, net gain and three cognitive domains. Similarly, the study has shown the self-esteemness of the students and relevancy of cooperative learning method with some modifications in Nepalese classroom set-ups. In this study, I also realized that the importance of learning environment which includes classroom set up, friendship groups, cultural and social capital, valuing and relating the pre-existed knowledge of students to achieve the mathematical knowledge and skills.

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