Volume, 11 Nomor 2 July 2023 pagr. 90- 104 p-ISSN:2541-4232 dan e-ISSN: 2354-7146
Ethnomathematics Exploration on Typical Angkola Woven Patterns, Sipirok, South Tapanuli, North Sumatera
Hakim Fahrezi1*, Siti Salamah Br Ginting2
1 Pendidikan Matematika/ Fakultas Ilmu Tarbiyah dan Keguruan/Universitas Islam Negeri Sumatera Utara Medan
Email: [email protected]
2 Pendidikan Matematika/Fakultas Ilmu Tarbiyah dan Keguruan/Universitas Islam Negeri Sumatera Utara Medan
Email: [email protected]
©2023 –Daya matematis: Jurnal inovasi pendidikan matematika. This article open acces licenci by CC BY-NC-4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
Abstract
This research explores the application of mathematical elements found in certain cultures. The object that is the focus of this research is the woven fabric typical of the Angkola ethnic group, which is part of the cultural heritage of the Angkola tribe in South Tapanuli district, North Sumatra province. Descriptive qualitative is the research model used in this study and ethnography is the research approach used, focusing on ethnomathematics in the motifs of Angkola's typical woven fabrics. The summary result of the research is that there is an application of mathematical concepts in this cultural heritage object, namely the basic concept of flat geometric shapes
,
the applied concept of geometric transformation, and the concept of sets. With this research it is hoped that it can contribute to new ethnomathematics research references and can be used as a reference for new mathematical category learning approaches, especially for the province of North Sumatra.Keywords : Fabric motifs ; Sipirok's typical Angkola weaving ; South Tapanuli Keywords: Fabric motifs ; Sipirok's typical Angkola weaving ; South Tapanuli
INTRODUCTION
Mathematics is a branch of science that can be called a science that is certain (Priyatna & Wiguna, 2021) . Mathematics is basically very closely related to arithmetic activities that require accuracy and thoroughness in its application. Mathematics learning has long been applied in the world of formal education and non-formal education. One example of the world of formal education is school. Seeing the current situation, there are also a number of mathematical problems that can be found in the field, especially in learning activities. At this time the problem that is often found in the world of education, especially regarding the application of mathematics in a classroom learning environment is the incompatibility of the application of the approach applied to the abilities of students in a class, for example, research conducted by previous researchers, namely essence based on research problems.
mathematics faced by the class (Sari, 2019) . In the self-study approach, there are various styles or approaches used in carrying out learning activities in a class. An example of an approach that may be familiar in the world of education is trying an approach from an ethnomathematics perspective.
Basically, the ethnomathematics approach is a slice of mathematics on culture in the local area to solve problems in everyday life or in a cultural group (HA Hasibuan & Hasanah, 2022) . So the key to ethnomatematics is ensuring the application of mathematical concepts to a culture. Culture is a heritage that has been passed down by our ancestors from the past until now, in other words, culture is all activities that have been produced by previous humans (Ananda & Mentayani, 2022) . Every culture certainly has heritage values that must be preserved (Fahril & Kurniati, 2018) . Preserving the existing culture is a form of defending the country and caring for the basic environment. One example
(Received: 13-03-2023; Reviewed: 21-04-2023; Revised: 23-06-2023; Accepted: 25-06-2023; Published: 29-07-2023)
of an ethnic group that has quite a lot of evidence of cultural heritage in the province of North Sumatra is the Angkola ethnicity.
Angkola is an indigenous ethnic group originating from the province of North Sumatra, which geographically originates from the South Tapanuli area (Siregar, 2021) . The Angkola ethnic group has a lot of cultural heritage as evidenced by the preservation of their traditions and culture to this day.
One of the various cultural heritages of the Angkola ethnic group that is iconic as souvenirs for the area is the Sipirok ethnic woven cloth. The typical Sipirok woven fabric of the Angkola ethnicity is a woven fabric typical of the Sipirok area, South Tapanuli district, North Sumatra (Habibah & Efi, 2019) . This form of woven work can usually be seen in its use in traditional ceremonies, traditional performances, and various traditional events within the Angkola ethnic group. However, with the development of the times, the use of woven fabrics typical of the Sipirok ethnic Angkola is commonly used in everyday life and is often even displayed in fashion shows. Based on the description of the research to be carried out, it can be found applied aspects of mathematics in the basic concepts of
2- dimensional geometric shapes
, the concept of Geometry Transformation, and the concept of Sets.Then from some of the explanations that have been described in this study, the purpose of this research was to explore the mathematical concepts that exist in the typical Sipirok woven fabric of the Angkola ethnicity by looking at it from an ethnomathematics perspective. This ethnomathematics research on the Sipirok woven cloth object typical of the Angkola ethnicity from South Tapanuli can still be said to be new because no one has raised the title in the field of ethnomathematics research. This is what underlies the researchers want to examine this research, especially for the province of North Sumatra..
METHOD
The research method used in this research is a descriptive qualitative method. Descriptive qualitative method is a qualitative research method presented in the form of descriptive data, which describes a more in-depth oral and written description that can be researched from an individual, group, organization, or certain community in a more complete viewpoint study situation (Azmi & Asbari , 2022). The research approach used by researchers is an ethnographic approach from an ethnomathematical perspective. Ethnomathematics is a manifestation of mathematics that is based on culture (Nurhasanah & Puspitasari, 2022). In accordance with existing research. The purpose of this research is to find and study mathematical concept ideas that can be found in the cultural elements studied (AR. R. Hasibuan & Br Ginting, 2021).
The object of research in this study is the motif on the typical Sipirok woven cloth of the Angkola ethnic group, North Sumatra. The location of the research was U.D Sipirok, South Tapanuli district, North Sumatra province. The data collection techniques used in research are data collection techniques such as interviews, observation and documentation (Sugiyono, 2013). The interview was conducted with an informant named H. M. Alinafiah Sitompul. Observations are carried out directly at the location of the research object and indirect observations are carried out through literature review to study references related to the research object. As well as carrying out documentation activities on objects with typical Sipirok woven cloth motifs from the Angkola ethnic group. The instrument sheets (interviews, observations and documentation) used have passed validation tests with research lecturers.
The reference for the data analysis technique used in this research is using an existing ethnomathematics research guide (Sawita & Br Ginting, 2022), namely using the Spradley model data analysis technique, namely by applying steps such as analysis of related cultural domains, analysis of related cultural taxonomies. researched, analyzing cultural components, and analyzing the cultural themes studied.
RESULT AND DISCUSSION
A. The basic concept of a 2-dimensional flat geometric shape
The concept of introducing the basic shapes of flat geometric shapes was first taught at the elementary/MI level in the 2013 curriculum in class I. Two-dimensional geometry means the relationship between two lines, namely width and length, which is better known as a flat shape (Citra Syaputri, 2022) . In the objects of the typical Sipirok angkola woven cloth motifs, there are 6 applications of the basic concepts of 2-dimensional flat geometric shapes that can be identified, namely isosceles triangle, parallelogram, rhombus, square, rectangle and circle. The following is an explanation of the basic concept of flat geometric shapes in the typical sipirok angkola woven fabric motif:
1.
Isosceles triangle
It can be identified in the picture that one of the parts in the motif on the Angkola woven fabric above is the basic flat geometric object, namely an isosceles triangle.
There are characteristics of an isosceles triangle found in the motif above, namely having two sides that are the same length, have the same magnitude with respect to 2 angles, and have one fold symmetry.
2. Parallelogram
It can be identified that the object in one of the motifs on the angkola woven fabric
is a parallelogram. There are characteristics of a parallelogram found in the motif
above, namely that it has the same length on parallel sides, has dividing diagonals,
has diagonals that intersect each other, has dividing diagonals, has opposite angles
of the same size, has no axis of symmetry. , and there are angles equal to.
3. Rhombus
It can be identified in the picture that one of the parts in the motif on the Angkola woven fabric above is the basic flat geometry object, namely a rhombus. There are characteristics of a rhombus found in the motif above, namely there are 4 sides that have the same length, there is a diagonal that divides with right angles, there are 2 adjacent angles equal to , and it has as many as 2 axes of symmetry, fold and rotate.
4. Square
It can be identified in the picture that one of the parts in the motif on the Angkola woven fabric above is the basic flat geometry object, namely a square. There are characteristics of the square found in the motif above, namely it has 4 sides that are the same length and magnitude, has 4 fold and rotate symmetries, has 4 axes of symmetry, has 4 angles that are the same size, namely and there are 2 diagonals that are the same length.
5. Rectangle
It can be identified in the picture that one of the parts in the motif on the angkola
woven cloth above is a basic flat geometric object, namely a rectangle. There are
characteristics of a rectangle found in the motif above, namely that it has two sides of the same length and width, has the same angles of , has 2 fold and rotational symmetries, and has 2 diagonals of the same size.
6. Circle
It can be identified in the picture that one of the parts in the motif on the angkola woven cloth above is a basic flat geometric object, namely a circle. There are characteristics of a circle found in the motif section above, namely that it has a total angle, has a radius that connects a center point with an arc point on the circle, and has a diameter that divides the circle into 2 equal sides.
Based on the findings above, an example question and answer can be created that relates to the material in the basic concepts of geometric shapes of 2-dimensional flat shapes for class I SD/MI, such as;
Task
Observe the image below! Then answer the following questions:
After you have made your observations, answer the following questions
- Is the image of the angkola magic cloth motif part of the basic shape of a flat shape in 2- dimensional geometry? If yes, what basic flat shape is applied to the motif part of the image!
- Try to explain the characteristics of the flat shapes that are attached to the picture part of the motif!
- Make an example problem for the formula for calculating the area of a circle of objects from applying flat shapes to the image part of the motif!
Answer
- Yes, based on observations that the image is the basic shape of a 2-dimensional flat shape, namely a circle.
- As for the shape of the characteristics that can be found in these motifs, there are characteristics of the circle found in the motif above, namely having a number of angles,
having a radius that connects a center point with an arc point on the circle, and there is a diameter that divides circle into 2 equal sides.
- For example, the radius of the circle is 14 cm and . So to find the area, use the formula multiplied by the radius squared (cm).
B. 2D geometric transformation
The concept of introducing the basics of geometric transformations is taught in Mathematics at the SMP/MTs level in the 2013 curriculum in class IX. Geometric transformation is the concept of changing the location and size of a point, line, curve or plane which can be described in image or matrix form (Sebastian et al., 2021). In the objects of the typical Sipirok angkola woven cloth motifs, there are 4 applications of geometric transformation concepts that can be identified, namely rotation, translation, reflection and dilation. Rotation is part of the concept of geometric transformation, namely the activity of shifting all points in the geometric plane along a circular arc with the point being the center of the circle (Bustan et al., 2022). Translation is part of the concept of geometric transformation, namely the activity of moving each point on a shape/plane that follows the length of a straight line with the condition that the distance and direction are the same (Edi, 2021). Reflection is part of the concept of geometric transformation, namely the activity of moving a plane/shape with the condition that the displacement distance on the plane/shape must have the same value between the starting point and the mirror as between the displacement points in the mirror (Hada et al., 2021). Dilation is part of geometric transformation, namely the activity of changing the scale or size (enlarging or reducing) in a plane but does not change the characteristic shape of that plane, so it can be said that the initial geometric plane is always congruent with the geometric image (Noviani et al., 2021). The following is an explanation of the geometric transformation concept that can be identified in the typical sipirok angkola woven fabric motif:
1. Rose flower motif
a. Parallelogram rose flower motif
The rose flower motif (parallelogram) has a philosophy about girls or in the words of the angkola is boru. This means that a boru must be a person who smells like roses, it means that a boru must be a good role model for fellow boru. From the results of research that has been carried out on the rose flower motif on typical sipirok woven fabric, it can be identified that there is a flat-sided geometric shape, namely a parallelogram, and there is an application of geometric transformation, namely the concept of rotation, translation and reflection.
In the picture above, it is known that the rose flower motif has as many rotations applied to the motif object and has a total of 4 rotations.
Then in the picture above it is known that the rose flower motif realizes a translation in geometric transformation by having the characteristics of moving the rose flower motif in different positions, with the same spacing pattern, the same size, and having the same direction and distance..
Finally, in the image above it is known that the rose motif realizes the concept of reflection in geometric transformation by finding the characteristics of reflection at each point in the plane of the rose motif objects between each other.
b. Circle rose flower motif
The rose flower motif which is shaped (circle) is more specifically placed on all genders and is very different from the parallelogram rose flower motif. And has almost the same philosophy, namely that an individual (more generally) haruslah being a person can complete life and the fragrance in flowers is marked as one's life journey. From the results of research that has been done on the rose flower motif on sipirok's typical woven fabric, it can be identified that there is a geometric shape, namely a circle and there is an application of geometric transformation, namely the concepts of rotation, translation, and reflection.
In the picture above, it is known that the circular rose flower motif has applied rotation to the motif object and has a total of 8 rotations.
Then in the picture above it is known that the circular rose flower motif realizes a translation in geometric transformation by having the characteristics of moving the flower motif in different positions, with the same spacing pattern, the same size, and having the same direction and distance.
Finally, in the picture above it is known that the circular rose motif realizes reflection on geometric transformations by having the characteristics of a reflection at each plane point on the rose flower motif object to each other.
c. Singap Motive
Singap motive is a symbol of the tip of the roof on a house. This motif has the philosophy that a person must be able to behave like a roof that is able to withstand the trials of burdens and obstacles in life which are philosophized in forms such as heat and rain. From the results of research that has been carried out on the singap motif on typical sipirok woven cloth, it can be identified that there is the application of geometric transformations such as the concepts of translation and reflection.
In the picture above it is known that the Singap motif realizes translation into geometric transformations by having the characteristics of a transfer between the Singap motif patterns in different locations, with the same pattern spacing, the same size, and having the same direction and distance.
Finally, in the picture above it is known that the singap motif realizes reflection on geometric transformations by having the characteristics of a reflection at each plane point on the object of the singap motif such as the base of the motif shape and a reflection of the singap motif between each other.
d. Hiok-hiok Motive
The shark motif has a philosophical meaning that a group of small birds that fly have a sound like a shark. This motif means that the shark motif always cares for each other's flock. This means that we as humans must live side by side and not prioritize selfishness. self. From the results of research that has been carried out on the hiok- hiok motif on typical sipirok woven fabric, it can be identified that there is the application of geometric transformations such as the concept of reflection.
In the picture above, it is known that the shark motif realizes reflection in geometric transformations by having the characteristics of a reflection at each point of the plane of the shark motif object between each other.
e. Pusuk Robung Motif
The pusuk robung motif is a philosophical part of the bamboo plant, namely the pusuk robung. This motif has the meaning that a person must have a purpose in life and provide many benefits for life and grow to be like a pusuk robung which means a person must have dreams for a brighter future. From the results of research that has been done on the pusuk robung motif on sipirok's typical woven fabric, it can be identified that there is an application of geometric transformations such as the concept of reflection.
In the picture above, it is known that the Pusuk Robung motif realizes reflection in geometric transformations by having the characteristics of a reflection at each plane point in the Pusuk Robung motif reflecting each other.
f. Room Motif
The space motif is a visualization of the shape of the motif on the snake's scales.
According to the ancients, when we find a snake on the street, of course, worry will arise reflexively from within, this means that one must be careful in living life. This alert attitude will later be used as a living example in moving forward in life. From the results of research that has been carried out on space motifs on typical sipirok woven fabrics, it can be identified that there is an application of geometric transformations such as the concept of reflection and dilatation.
In the picture above, it is known that the space motif realizes reflection in geometric transformations by having the characteristics of a reflection at each plane point in the space motif object between each other.
Finally, in the picture above it is known that the spatial motif also applies the concept of dilation, which can be seen that there is a modification of the shape of a part of the spatial motif which is placed outside of the spatial motif.
Based on the conceptual findings described above, an example question can be created related to geometric transformation material in class IX SMP/MTs, such as:
Test
Observe the image below! Then answer the following questions:
After you have made your observations, answer the following questions
- Is the picture above part of the type of motif on the typical Sipirok Angkola woven fabric?
If so, what kind of woven motif can be identified in the picture above? Try to explain the meaning of the motive above!
- Does the motif image apply the mathematical concept of geometric transformation? If so, what transformation concepts can be found? Try to explain in detail!
Answer
- Yes, the picture above is part of one type of motif on the typical Sipirok angkola woven cloth called the rose flower motif. The rose flower motif has a philosophy that is about girls or in the words of the angkola it is boru. This means that a boru must be a person who smells like roses, it means that a boru must be a good role model for fellow boru.
- Yes, the motif above applies the mathematical concept of geometric transformation. One example of the application of the concept of geometric transformation that can be illustrated in the image above is the concept of rotation. It is known that the rose flower motif has as many rotations applied to the motif object and has a total of 4 rotations.
C. Classification/Grouping of Class VII Association members
The concept of sets was first taught in Mathematics at the SMP/MTs level in the 2013 curriculum in class VII. A set is an entire collection that can be expressed in the form of an object (Rizqi et al., 2021). The following is a description of the concept of assemblage that can be identified in the typical sipirok angkola woven cloth motif.
Association registration:
1. All commonly used motifs, all sipirok woven motifs which are always used on sipirok woven fabrics can be associated with the concept of a set. The concept of a universal set can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as Q (All sipirok woven motifs) = {beads, sirat, pune, monument, uslus, pusuk robung, cover mumbang, hiok-hiok, sijobang, space, singap, simata, pass, jojak, flower, rose}. Then it can be stated that Q(n) = 16
2. The motifs are of the floral type, the sipirok woven floral motifs which are always used on sipirok woven fabrics can be associated with the concept of a set. The concept of subsets can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as R (sipirok woven floral motifs) = {pusuk robung, cover mumbang, simata, flower, rose flower}. Then it can be stated that R(n) = 5
3. The motifs are of the fauna type, the fauna motifs of sipirok weaving which are always used on sipirok woven fabrics can be associated with the concept of set. The concept of subsets can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as S (sipirok woven fauna motif) = {pune, hiok-hiok, sijobang, ruang, luslus}. Then it can be stated that S(n) = 5
4. Artistic motifs, the artistic motifs of sipirok weaving which are always used on sipirok woven fabrics can be associated with the concept of set. The concept of subsets can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as T (sipirok weaving artistic motif) = {sirat, singap, jojak}. Then it can be stated that T(n) = 3 5. Motifs that are living creatures, the living creature motifs in sipirok weaving which are always
used on sipirok woven fabrics can be linked to the concept of assemblage. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered using group registration steps such as U (sipirok woven living creature motifs) = {pusuk robung, lid mumbang, simata, flower, rose flower, pune, hiok-hiok, sijobang, Ruang, luslus}. Then it can be stated that U(n) = 10
6. Motifs that are non-living creatures, non-living motifs in sipirok weaving which are always used on sipirok woven fabrics can be linked to the concept of assemblage. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered using group registration steps such as V (non-living motifs woven in sipirok) = {sirat, singap, jojak}. Then it can be stated that V(n) = 3
7. Motifs whose constituent elements are geometric triangular shapes, motifs which are geometric triangular flat shapes in sipirok weaving which are always used on sipirok woven fabrics can be linked to the concept of assemblage. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered using set registration steps such as W (Motifs that are geometrical triangular flat shapes) = {pusuk robung, singap}. Then it can be stated that W(n) = 2
8. Motifs whose constituent elements are flat parallelogram geometric shapes, motifs which are flat parallelogram geometric shapes in sipirok weaving which are always used on sipirok woven fabrics can be linked to the concept of assemblage. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered using the set registration steps such as Then it can be stated that X(n) = 1
9. Motives whose constituent elements are circular geometric in nature, motifs that are geometrically flat in sipirok woven circles which are always used in sipirok woven fabrics can be associated with the concept of set. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered by means of set registration steps such as Y (Motive that is a parallelogram geometric shape) = {interest}. Then it can be stated that Y(n) = 1
10. Motifs whose constituent elements are geometric flat rhombuses, motifs which are geometric flat rhombuses in sipirok weaving which are always used in sipirok woven fabrics can be associated with the concept of set. The concept of subsets can be found in sipirok woven fabric. Then, each type is registered by means of set registration steps such as Z (Motive which is geometrically rhombus) = {pune}. Then it can be stated that Z(n) = 1.
Based on the conceptual findings described above, an example question can be created related to set material in class VII SMP/MTs such as:
Test
The following are the most frequently used types of Sipirok typical Angkola woven fabric motifs such as beads, sirat, pune, monument, uslus, pusuk robung, cover mumbang, hiok-hiok, sijobang, ruang, singap, simata, pass, jojak, flower, rose flower. So from this description, try to classify and make examples of subsets into two forms of examples that can be developed!
All motifs that are commonly used, all sipirok woven motifs that are always used on sipirok woven fabrics can be associated with the concept of a set. The concept of a universal set can be found in sipirok woven fabrics.
Then, each type is registered by means of set registration steps such as Q (All sipirok woven motifs) = {beads, sirat, pune, monument, uslus, pusuk robung, cover mumbang, hiok-hiok, sijobang, space, singap, simata, pass, jojak, flower, rose}. Then it can be stated that Q(n) = 16, then the two examples of subsets that can be assumed are like :
a. The floral motifs, sipirok woven floral motifs which are always used on sipirok woven fabrics can be associated with the concept of a set. The concept of subsets can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as R (sipirok woven floral motifs) = {pusuk robung, cover mumbang, simata, flower, rose flower}. Then it can be stated that R(n) = 5
b. Animal-type motifs, the sipirok woven fauna motifs which are always used on sipirok woven fabrics can be associated with the concept of a set. The concept of subsets can be found in sipirok woven fabrics. Then, each type is registered by means of set registration steps such as S (sipirok woven fauna motif) = {pune, hiok-hiok, sijobang, ruang, luslus}.
Then it can be stated that S(n) = 5 CONCLUSIONS AND SUGGESTIONS
The conclusion that can be drawn from the ethnomathematics exploration research on the Sipirok typical Sipirok woven cloth motif, South Tapanuli, North Sumatra which has been carried out is that a form of application of mathematical concepts contained in the typical Sipirok angkola woven cloth, namely the basic concept of 2-dimensional flat geometric shapes, the concept of transformation, has been found. geometry and the concept of sets. Firstly, the hope of this research is that the ethnomathematical concept in the typical sipirok angkola woven cloth can be used as a unique inspiration for a new learning style in mathematics subjects that seems more exciting for target areas, especially the province of North Sumatra. Second, the hope of this research is that it can inspire mathematics researchers to make, choose, and focus on ethnomathematics as their research.
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