
Culturally Relevant Mathematics Teaching
Introduction
I studied in a public school located in the village of Nepal. Later, I began teaching mathematics in various private schools. Also, I have been working as a textbook writer for school mathematics. During this period, I have had many experiences that suggest the obstacles faced around mathematics teaching in Nepal. In the following paragraphs, I share some of the notable obstacles to promoting culturally relevant mathematics teaching in the schools of Nepal. Thereafter, bringing some examples of the ideas/concepts from the school curriculum, I discuss how our tendency to see mathematics as a pure subject and pure body of knowledge has been a key obstacle, among others, and how it has hindered culturally relevant teaching.
Obstacles Faced Around Culturally Relevant Mathematics Teaching in Nepal
In my experience, there are many obstacles faced around culturally relevant mathematics teaching and learning in the schools of Nepal. Some of the notable obstacles include (1) emphasis on paper-and-pencil tests and exam marks (2) established assumptions that textbooks are the only source of teaching and learning, (3) disciplinary and departmentalized subject categories, (4) reluctance of mathematics teachers to come out of their comfort zone of classroom teaching, and (5) celebration of the ‘teaching and informing’ nature of teacher-centered pedagogies. All these factors have hindered mathematics teaching from connecting with community experiences, real-life activities, and cultural artifacts. Among all these, I have experienced that the established assumption of mathematics as a ‘body of pure knowledge’ is the key obstacle to contextualized teaching in the schools of Nepal. Therefore, in the subheading below, I have discussed in detail how this notion has been the key hindrance.
Mathematics as the Body of Pure Knowledge
The key obstacle to promoting culturally relevant mathematics teaching is our understanding of mathematics as a body of pure knowledge. During my childhood days, my teachers made less effort to connect mathematics concepts with everyday social and cultural events and activities. Our school teaching and learning always looked for single and proven approach of doing mathematical calculations. At this stage, I believe that such ways of seeking singularity (Luitel, 2018) of mathematical calculation didn’t allow us to think of multiple possibilities. Also, it didn’t allow us to think in the way that mathematical knowledge is embedded in our culture, day to day-to-day activities, and based on learners’ lived experiences (Luitel and Taylor, 2005).
In many of the centrally prescribed mathematics course contents of the Nepal government, the exercises hardly enable learners to see mathematical knowledge in the local context. Such knowledge ‘waiting to be transmitted to students’ (Lerman, 1990) doesn’t motivate teachers and students to access mathematical knowledge from multiple sources (Rogoff, 2003). As mathematics teachers, we maintained the belief that we could not alter mathematical knowledge (D’Ambrosio, 2006). Also, we hold that only ‘pure mathematics’ represents authentic mathematics (Rosa &Orey, 2011). Because of this belief, we neither used local resources as teaching-learning materials nor tried to make it a part of everyday culture. We didn’t bother incorporating knowledge systems arising from both the teachers’ and the students’ lived experiences.
What Literature Suggests?
Despite these, literature suggests many possibilities in the schools of Nepal to make mathematics teaching and learning culturally relevant. Pradhan (2012) made a study of cultural carpentry and suggested that these cultural groups use the concept of geometry in their work. They use cones, cylinders, and concepts of height and base perimeter of cylinders, capacity and volume, the concept of transformation, and the axis of rotation in their wooden works.
Since these are the major course contents of the mathematics curriculum for middle and high schools in Nepal, as a teacher, I can think of connecting classroom learning with those cultural practices. Making these the learning resources and allowing students to make mathematical calculations of these real cultural artifacts would connect lessons with the context.
Teaching and learning mathematics in the schools of Nepal, also I can think in terms of introducing cultural arts of many cultural groups in studying mathematics. CERID (1990) studied the elementary process of learning mathematical concepts and the process of Rasuwa Tamang. This project work has shown that the Tamang have their own systems of measurement, counting, and their own mathematics process, and geometrical concepts are based on the shape and structure patterns of objects existing around them. Similarly, Limbu (2006) studied on Limbus mathematical operation system in their own script, numeral system, and language. In the mathematics class of Nepal, since we can see many students of various cultural groups, it would be an opportunity to bring cultural communities as resources for teaching and learning mathematics.
Connection of Mathematical Shapes (Grade 4) with Cultures: My Experiences
After doing some studies on ethnomathematics, I have begun to think about practicing culturally relevant mathematics in mathematics classrooms. As a textbook writer,
I have also been thinking of including culturally relevant content in school mathematics textbooks in Nepal. At this stage, I believe that mathematics as part of the school curriculum may reinforce and value the cultural knowledge of students. Here are some examples of how I have been connecting mathematical shapes included in grade 4 text contents with culture.
Example 1: Nepali Flag and its Connection with Mathematical Shapes
Source: (u/jnijni, 2021)
Two red triangles overlap to form the triangle-shaped national flag of Nepal. A white crescent moon sits atop the upper triangle, while a white 12-rayed sun sits atop the lower triangle. Other names for the flag include “Nepal Dhwaj” and “Nepal flag.” Angular shapes, pentagonal shapes, triangular shapes, circular sun shapes, semi-circular moon shapes, stripes with parallel widths, cylindrical stands, etc. are the mathematics hidden in the flag of Nepal. It is the only non-quadrilateral national flag in the world. It has 3 acute angles, one right angle, and one obtuse angle on its corner internally.
Example 2: Nepali Money and its Connection with Mathematical Shapes
The Nepalese rupee banknotes are rectangular and vary in size according to their value. The 1 Rupee note is the smallest, while the 1000 Rupee note is the largest. The front of the banknotes features images of historical and cultural landmarks and so many mathematical shapes in them. As we see in the figure above, the coin has many mathematical shapes inside it, and the border shape is circular.
Example 3: Nepali Religious Activities and its Connection with Mathematical Shapes
Puja sthal | Mandap, Mandir |
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Temple | Mosque |
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Puja Thali | |
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As in the above figure, there are many mathematical shapes found in the religious activities followed by different religious groups in Nepal. Culturally, people have been using triangles, rectangles, parallelograms, rhombuses, trapeziums, kites, circles, cylinders, spheres, hemispheres, etc., in their religious practice. For instance, monks wear mala or beads, which are also shaped in spherical shapes. Similar examples of mathematical shapes include Puja Thali, Diyo, Ghanti, Thanka, and so on.
Example 4: Nepali Cultural Foods and its Connection with Mathematical Shapes
Laddu | Peda |
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Spherical | Circular & Cylindrical |
Kasahar | Barfi |
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Spherical | Cuboid-shaped |
Similarly, the bowl of curd (hemisphere), Yomari (conical), Puja Thali (rectangular and circular), Thakali serve with a bowl (hemisphere), etc. can also be connected to our teaching-learning activities related to mathematical shapes.
Additional Possibilities
In my observation, there are many other cultural spaces for us to connect culture and ways of life and make school teaching culturally relevant.
- Mathematical shapes can also be associated with Nepali cultural sports. Some of the examples are KuttiKhel (Rectangular), Bagchal (many shapes), Buddhichal (many shapes), Dandibiyo (cylinder and cone), and volleyball (spherical).
Bagchal | Buddhichal |
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Many plane shapes | Square Patterns |
DandiBiyo | Volleyball |
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Frustum of Cone and Cylinder | Spherical |
- We can connect Nepali cultural dance with mathematical shapes. Its examples include dance (circular), Ghintangghisi (parallel lines and cylindrical sticks), Tharu stick dance (circular and cylindrical sticks), etc.
Deuda dance |
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Circle |
Dhan Nach |
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Circle |
Ghintangghisi |
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Parallel & Cylindrical |
- Nepali cultural dress, like Dhaka clothes (shapes & patterns), ladies Tharu dress (geometrical patterns patchwork), sadi (parallel borders), Sherpa dress Pangden (parallel shapes and patterns), hand-knitted bags (traditional), Radipakhi (shapes and patterns), etc. are other examples.
Dhaka clothes | Sadi |
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Shapes & patterns | Sadi (lines and shapes) |
Ladies Tharudress | Sherpa dressPangden |
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Geometrical patterns | Parallel and patterns |
- We can also connect Nepali household items with mathematical shapes. Its examples include Nanglo, dadu, Panyu, Gundri, Mandro, Bhakari, Chakati, Sukul, Ghum, Doko, Dalo, Dhiki, Jato
Nanglo | Gundri |
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Circle and Patterns | Rectangle & Patterns |
Mandro | Dhiki |
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Rectangles, Patterns and Cylindrical | Cylinder & Cuboid |
- Next are the Nepali buildings like Jhyal, Dhoka, Pali, Chhano, Dhuri, Aangan, and Pidhi.
Nepali ghar | AnkhiJhyal |
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Many Shapes | Geometric Patterns |
Temple | Gologhar |
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Many Shapes | Cylinder & Cone |
- Nepali local measuring items like Mana and Pathi, Tulo and Taraju, Dalo, Thumse, etc. can be connected with mathematical shapes.
Mana & Pathi | Dalo |
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Many Shapes | Cone Frustum & Pattern |
Tulo | Taraju |
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Circle & nets | Many Shapes |
- Mathematical shapes can also be associated with Nepali musical instruments. The examples include Madal, Damaha, Tamka, Jhyali, Khaichadi, Sanai, and Harmonium.
Dhime | Damaha |
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Cylinder & Circle | Hemisphere |
Madal | Harmonium |
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Cylinder & Frustrum | Many Shapes |
Conclusion
This shows that there are many options and possibilities for us to connect Mathematical concepts included in the textbooks of Nepal with cultural artifacts and make our teaching and learning culturally relevant. As a textbook writer for school-level mathematics, the few examples mentioned above are the ones that I have been making some efforts to include the concept of ethnomathematics in the grade four mathematics textbooks as well. I have been including it in the textbooks of other classes as well.
Despite these efforts and suggestions, as discussed above, our ways of taking mathematics as the field of pure knowledge, free of subjectivity and free of cultural connections, have been a major obstacle to bringing such practices into mainstream education. Next, Nepali societies have established mathematics as a high-scoring subject. Because of this, we always encourage students to take mathematics as a subject for exam results. We ask them to follow the prescribed and universally accepted ways of doing mathematics. Thinking in other ways would bring mistakes which would minimize the scores. To avoid this risk, I have experienced that many teachers in the schools of Nepal encourage students to follow the prescribed path rather than connecting the concepts with cultural life.
References
Brandt, A., & Chernoff, E. J. (2015). The importance of ethnomathematics in the math class.
CERID (1990). Elementary process of learning mathematical concepts in Nepal. Kathmandu, Nepal: Author.
Craft House Nepal. (n.d.). Palpali Dhaka topi: Basic handmade Nepali traditional hat. Craft House Nepal. https://crafthousenepal.com/product/palpali-dhaka-topi-basic-handmade-nepali-traditional-hat/
D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. ZDM,40(6), 1033-1034.
Limbu, A. (2006). Mathematical operation and measurement system of Limbu community. Unpublsihed Thesis (M. Ed.), Central Department of Education,Tribhuvan University, Kirtipur, Kathmandu.
Luitel, B. C., & Taylor, P. C. (2005, Apr). Overcoming culturally dislocated curricula in a transitional society: An autoethnographic journey towards pragmatic wisdom. Paper presented at the annual meeting of the American Educational Research Association (AERA).
Luitel, B. C., & Taylor, P. C. (2007). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education. Cultural Studies of Science Education, 2(3), 621-655. https://doi.org/10.1007/s11422-007-9068-7
Pradhan, J. B. (2010). Uncovering frozen knowledge of Chundara: an ethnomathematicalperspective. (Unpublished M. Phil. Thesis), Faculty of Education, TribhuvanUniversity, Kathmandu, Nepal.
Rogoff, B. (2003). The cultural nature of human development. New York, NY: OxfordUniversity Press.
Rosa, M. &Orey, D. C. (2011). Ethnomathematics: the cultural aspects of mathematics. RevistaLatinoamericana de Etnomatemática, 4(2). 32-54
Rosa, M., D’Ambrosio, U., Orey, D. C., Shirley, L., Alangui, W. V., Palhares, P., &Gavarrete, M. E. (2016). Current and future perspectives of ethnomathematics as a program (p. 45). Springer Nature.
u/jnijni. (2021, September 22). I simplified the flag of Nepal while keeping all its details [Online forum post]. Reddit. https://www.reddit.com/r/vexillology/comments/psuw62/i_simplified_the_flag_of_nepal_while_keeping_all/?rdt=35254