Indigenous artifacts from remote areas, used to design a lesson plan for preservice math teachers regarding sustainable education

Abstract

In the context of sustainable education, remote areas require special treatment. However, teachers are not evenly distributed in terms of quantity and quality. Adaptable, creative, and innovative teachers are needed in remote areas. Therefore, universities must prepare preservice teachers to teach in these places. This study explores indigenous artifacts from local communities related to mathematical content that preservice teachers can adopt to design lesson plans using available resources. Data were collected through the artifacts of indigenous people in a mountainous region on the border of Yogyakarta and Central Java, Indonesia, and the math curriculum content was examined. The relational ideas of the artifacts and the math curriculum content were analyzed. Based on the results, this study shows that artifacts can be incorporated into math learning materials. Elaborating on the artifacts can potentially relate culture and math in the classroom. The artifacts contain mathematical value and are close to students' thoughts. Hence, preservice math teachers can use them to design lesson plans, particularly for math learning. By understanding artifacts in remote areas, preservice teachers will have a particular capability for preparing lesson plans relevant to students’ environment for sustainable education.

Full text

Research article
Indigenous artifacts from remote areas, used to design a lesson plan for
preservice math teachers regarding sustainable education
Niken Wahyu Utami
a
,
*
, Suminto A. Sayuti
b
, Jailani Jailani
b
a
Universitas PGRI Yogyakarta, Yogyakarta, Indonesia
b
Yogyakarta State University, Yogyakarta, Indonesia
ARTICLE INFO
Keywords:
Sustainable education
Indigenous knowledge
Ethnomathematics
Preservice math teacher
Math lesson plan
ABSTRACT
In the context of sustainable education, remote areas require special treatment. However, teachers are not evenly
distributed in terms of quantity and quality. Adaptable, creative, and innovative teachers are needed in remote
areas. Therefore, universities must prepare preservice teachers to teach in these places. This study explores
indigenous artifacts from local communities related to mathematical content that preservice teachers can adopt to
design lesson plans using available resources. Data were collected through the artifacts of indigenous people in a
mountainous region on the border of Yogyakarta and Central Java, Indonesia, and the math curriculum content
was examined. The relational ideas of the artifacts and the math curriculum content were analyzed. Based on the
results, this study shows that artifacts can be incorporated into math learning materials. Elaborating on the ar-
tifacts can potentially relate culture and math in the classroom. The artifacts contain mathematical value and are
close to students' thoughts. Hence, preservice math teachers can use them to design lesson plans, particularly for
math learning. By understanding artifacts in remote areas, preservice teachers will have a particular capability for
preparing lesson plans relevant to students’environment for sustainable education.
1. Introduction
Problems affecting sustainable development include a lack of tech-
nology and limited opportunities for an alternative perspective on
problems. However, education tends to resolve these issues because it
changes an individual's or the community's mindset and behavior mode.
Education is the basis for unlocking human capabilities (WDR, 2018). It
is also a key instrument in transforming or achieving the Sustainable
Development Goals (SDGs) (UNESCO, 2017). Its objectives are to raise
upright and dutiful citizens with the desire, attitude, and skills required
to build a sustainable society (Chikamori et al., 2016).
Education is a solution toward achieving sustainable development.
However, improper learning and educational disparities are also part of
sustainable development issues in almost all countries, regions, remote
areas, minorities, and also in Indonesia. Indonesia consists of various
islands, hills, beaches, and numerous ethnic groups. These factors have
led to a variety of characteristics, conditions, cultures, and differences in
development. There are areas in the country that are categorized as
remote with unique characteristics. In this research, such areas are
referred to as those situated in hilly locales and near provincial or other
countries’borders.
Students in remote zones need proper education. Cajete (Lee, 2015)
stated that indigenous education produces humans that contribute
immensely to their communities. Learning that employs familiar situa-
tions tends to make it easier for students to solve immediate problems.
The combined efforts of indigenous and scientific knowledge permits
the possibility of sustainability at various scales and in the educational
sector (Hill et al., 2020;Tengo et al., 2017). One activity related to stu-
dents' situation is learning materials from indigenous communities. To
compile these learning materials, the teacher needs to be adaptive,
innovative, and creative to suit the students' environment, including the
conditions and circumstances of the facilities. The training of preservice
teachers from the beginning to higher education is essential to produce
quality teachers that understand people's conditions and competence in
such areas. Another preparation is the ability to be adaptive, creative,
and innovative in designing learning based on students' environmental
conditions.
Education for preservice teachers promotes sustainability in the ac-
ademic sector, representing a new paradigm for their preparation. It
helps develop a curricular vision and conversation regarding teacher
education's role in solving global environmental and social justice chal-
lenges (Nolet, 2009).Additionally, designing learning in the context of
* Corresponding author.
E-mail address: niken@upy.ac.id (N.W. Utami).
Contents lists available at ScienceDirect
Heliyon
journal homepage: www.cell.com/heliyon
https://doi.org/10.1016/j.heliyon.2021.e06417
Received 11 April 2020; Received in revised form 6 August 2020; Accepted 1 March 2021
2405-8440/©2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Heliyon 7 (2021) e06417

culture is a specific strategy related to the curricular vision, knowledge of
teaching, disposition, and professional practice of teachers that are
adaptive to the environment familiar to students.
Educational progress comes from forward-looking studies that
embrace students’cultural advantages with diverse experiences of
racism, poverty, trauma, and oppression. A dynamic learning environ-
ment reinforces culture, and the teacher respects the assets discovered in
indigenous knowledge, values, and stories as a model of vitality and
empowerment for all (Malia and Malone, 2017). Therefore, preservice
teachers need to be equipped to use the indigenous environment to
prepare a lesson plan. The impact is that they tend to survive as teachers
in any environment, which affects sustainable education. This article
discusses the various ways to equip preservice teachers to explore and use
artifacts from indigenous communities to prepare their lesson plans.
Subsequently, the solution is to observe the environment and appreciate
the existing culture.
1.1. Preservice math teachers
Teachers are the spearhead of success in learning. Therefore, the
Indonesian government trains them in ongoing learning efforts by
helping them to build strong networks with their peers to improve their
competence (Kyu et al., 2017;Sudja and Yuesti, 2017;Sumaryanta et al.,
2019). Additionally, preservice teachers are properly equipped, and are
agents of change who are trained to adopt the technology of indigenous
knowledge during teaching and learning instructional planning (Kim and
Baylor, 2008).
Preservice teachers need to be appropriately trained to become pro-
fessionals with the ability to prepare learning instruction to help students
master certain abilities and to harness their surrounding environment
(Felder and Brent, 2005). It is essential to understand the environment to
accommodate students’prior education and their indigenous knowledge
abilities. Preservice math teachers need to be observant in designing
learning that accommodates indigenous knowledge.
1.2. The math environment of indigenous communities in education
Although mathematical truths hold everywhere and for everyone, this
does not mean that math education should ignore learners’individuality
or the social and cultural context of education (Bishop, 1997). Hence, we
need to do more than merely inform learners of these truths. We can find
knowledge in the social context from the indigenous community, and
also with math.
Mathematical concepts inherent and practiced in the indigenous
community are known as ethnomathematics; this notion was first intro-
duced by D'Ambrosio (Tutak et al., 2011). The term is derived from a
combination of two words, “ethno”and “mathematics,”where the prefix
indicates the sociocultural context, while the suffix is based on mathe-
matical knowledge such as counting, comparing, sorting, classifying,
designing, playing, weighing, and measurement (Katsap, 2018).
Ethnomathematics in learning encourages teachers and students to
appreciate the diversity of knowledge (Powell, 2009). Further, Powell
(2009) states that the context of community cultural material influences
their knowledge and activities in the world. Students learn the impor-
tance of respecting their knowledge and others, and how all cultural
backgrounds can interact with mathematical knowledge development.
Powell's research (2009) shows examples of various forms in which
mathematical knowledge can be coded differently from academic text-
books (school math textbooks).
Ethnomathematics, through indigenous knowledge, has a positive
impact and is adopted in learning mathematics (i.e., the use of drama-
mediated mathematical knowledge) (Stathopoulou et al., 2015), the
integration of ethnomathematical folklore games in math learning
(Fouze and Amit, 2018), the use of culturally based gender-relevant
teaching (Mogari, 2017;Weldeana, 2015), and integrating ethno-
mathematics into an instructional approach in practice had the greatest
mean gain in the acquisition of creative skills (Ogunkunle and George,
2015). Moreover, indigenous knowledge as material in math learning can
make math interesting and valuable for underrepresented groups in
increasingly diverse populations (Rosa and Orey, 2016). The use of
indigenous knowledge tends to boost students' motivation in learning
math, and reduces feelings of dissatisfaction and inequity (Verner et al.,
2013). Moreover, it encourages respect for culture and math, and leads to
improved learning achievement because it uses indigenous contexts.
Culturally relevant pedagogy is one way to support learning among
indigenous students (Abrams et al., 2013). Students’indigenous knowl-
edge naturally makes it easier to understand math, and tends to accept
learning in a meaningful manner.
1.3. Preservice math teachers’lesson plan for sustainable education
The design of a math lesson plan for sustainable education needs to be
in accordance with the curriculum's learning outcomes and students'
culture. Teaching students from remote areas requires collaborating with
indigenous communities and designing lesson plans in accordance with
their culture. They need to be involved in preparing learning instructions
(Chinn, 2006,2007,2012;Lees, 2016;Owens, 2014). Accordingly,
teachers need to interact with indigenous people, as they are better
prepared to meet students' needs during learning activities (Lees, 2016).
Owens' (2014) research helped teachers, schools, and communities to
implement appropriate and effective professional development, build
partnerships between institutes and societies, revise teaching approaches
and curricula, and to value cultural heritage and aboriginal knowledge.
In other words, teachers’interactions with indigenous people tend to
alter their perceptions, skills, and abilities during teaching or learning
activities.
In other studies, teachers and native Hawaiian instructors worked
together on immersion science for five days. They met several times at
rural schools, universities, and community sites, sharing programs and
developing knowledge (Chinn, 2006). According to Chinn, long-term
professional development that provides learning through cultural im-
mersion, translation, and interdisciplinary instructions aids in estab-
lishing a practical community in which participants are taught as needed
for the relevant growth of the community, place, and standards following
the curriculum and pedagogy.
Chinn stated that preservice teachers carry out observations and
interview indigenous teachers immediately when they arrive at these
locations. This helps to map technologies to visualize and integrate
indigenous-based Hawaiian knowledge with science inquiry; these are
promising instructional strategies (Chinn, 2014).
The teacher designs the engagement of indigenous knowledge in
learning math. Therefore, future math teachers need to be prepared to
achieve the following: a) visualize math incorporated into the real world,
b) investigate the mathematical ideas and practices of their pupils, and c)
discover ways to incorporate it into the curriculum elements belonging to
the sociocultural environment of the pupils in the classroom. However, it
tends to positively motivate and increase the interest and curiosity of
pupils toward math (Bonotto, 2001).
In some cases, preservice teachers that teach indigenous people tend
to be either from developed or remote places. Assuming the teacher's
hometown is an indigenous place, then learning instructions are designed
by criticizing or evaluating his/her teaching and learning, integrating
local knowledge into an established curriculum, or replacing it entirely
and utilizing it to the advantage of the students (Vinlove, 2016).
N.W. Utami et al. Heliyon 7 (2021) e06417
2

However, the teacher is not from a remote area, and learning instructions
are designed by understanding the community through learning from the
students and indigenous people, and asking the inhabitants for feedback
and ideas concerning integrating local knowledge into the curriculum
(Vinlove, 2016).
1.4. Ethics on seeking and drawing upon indigenous knowledge
Conducting research needs to follow ethics. Research involving
humans and animals, both experimental and social research, should use
ethics. Research ethics are concerned with minimizing harm, respecting
autonomy, preserving privacy, and acting equitably (Hammersley,
2015). However, the commodification of indigenous knowledge is often
acquired by less than ethical means. “The commodification of indigenous
knowledge without consent, consideration, or compensation is another
form of exploitation and marginalization of indigenous peoples”(Bat-
tiste, 2016).
However, well-intentioned, indigenous knowledge research is not
enough to take indigenous knowledge without community or committee
approval. The research should protect cultural groups’assets, so research
on indigenous knowledge requires university ethics committee approval
by considering protection issues for the collective. Research that does not
do so may contribute to the continued appropriation and plundering of
indigenous culture, heritage, and knowledge (Battiste, 2016). Core
ethical principles on research related to indigenous peoples and local
communities are respect, the recognition of rights, responsibility as a
scholar, mindfulness, participation, and mutual benefits (Tun
on et al.,
2016). Hence, research on indigenous knowledge must have the uni-
versity committee approval and indigenous community agreements,
respect, recognition of rights, responsibility as a scholar, mindfulness,
participation, and mutual benefits.
2. Methodology
2.1. Research design
A qualitative approach was used due to its suitability for the study to
reveal indigenous knowledge and assist the preservice teachers in
designing math lesson plans. Preservice math teachers need to be trained
to be able to explore indigenous knowledge, which is adopted as material
to design learning instruction. Preservice teachers may take a course or
engage in research activities as research assistants. Preservice teachers’
involvement in the discovery of indigenous knowledge can be achieved
either individually or in small groups.
2.1.1. Research participants
We chose two elderly individuals from the community as research
participants. Additionally, according to the study's purpose, we involved
preservice math teachers—who are members of the indigenous com-
munity, from the border of Yogyakarta and Central Java—as research
assistants. In addition, the indigenous community approved of this
study's activities. We gained university committee approval from the
Institute of Research and Community Service Universitas PGRI Yogya-
karta and indigenous community agreements from Beteng hamlet, Jati-
mulyo, Giri Mulyo, Kulon Progo.
2.1.2. The data collected
The exploration of indigenous knowledge was achieved by observing
and interviewing the indigenous community (Alangui, 2010;Chinn,
2014;Vinlove, 2016). Therefore, artifacts were observed, and elderly
indigenous people were interviewed to acquire indigenous knowledge,
which was utilized as material to design learning instructions. Prior to
that, the researchers clarified that the data collected would be used to
design math lesson plans.
Data were gathered from the indigenous community situated at the
border of Yogyakarta and Central Java, Indonesia. The area is
mountainous, and the inhabitants have some particular indigenous arti-
facts, namely, kentongan (a tool used to summon residents, send out
danger signals, make announcements, etc.), padasan (a tank for water
made of clay, which is used for ablutions), tapih batik (which serves as
fabric for skirts), and so on.
Observation was carried out to identify the artifacts used. We
observed and took pictures to document the artifacts. In addition, daily
activities were also witnessed, while interviews were carried out to
confirm the activities and objects utilized by the inhabitants. The length
of each interview was approximately 30 min per day for two days. We
performed a member-check for data triangulation. The interviews were
recorded and transcribed. The questions included:
- The history and usability of artifacts
- The artifact creation process
- The size of each artifact
During the data collection, we involved preservice math teachers as
research assistants. Their role was to document and record the interview
activities. They also took pictures, observed, and measured the artifacts
under study.
The indigenous knowledge acquired was employed to develop a math
lesson plan; it also served as material in the learning design used.
Indigenous knowledge is either in the form of daily activities, habits, or
artifacts.
2.2. The data analysis
A qualitative procedure was employed for data analysis. This analysis
generated interpretations of data or mathematical values that exist in
indigenous knowledge. The analysis was also linked to the relational
ideas of the artifacts and the math curriculum content. The results of the
analysis were used to develop a math lesson plan.
The preservice teachers engaged in the data analysis. They were
involved in discussions on math object-related indigenous artifacts. They
also engaged in developing lesson plans. In other words, the data analysis
involved the indigenous community.
3. Results
3.1. Indigenous artifacts and mathematical objects related to them
A form of ethnomathematics study is conducted in terms of artifacts
that tend to be discovered in various aspects of people's lives. The basic
needs of humans are food, clothing, and shelter. Based on the aspect of
food, they need to cook and eat. Therefore, artifacts are required in
carrying out processes, going places, etc. In accordance with the context
of clothing, there are certain clothes that indigenous, such as tapih, which
serves as fabric for skirts worn by elderly women. Additionally, there are
various kinds of buildings. One of the buildings is the indigenous home.
Indigenous (Javanese) houses have various styles depending on the strata
(i.e., a balanced roof with right and left sides for a common house,
limasan for a middle house, and joglo for a luxury house).
The homes of indigenous people are built according to numerous
rules (i.e., regarding manufacturing time, measurement, and other ele-
ments). Based on the information obtained from one of the villagers in
the mountainous region:
Nek damel griyo niku wonten petunganipun, kapan le pasang, jumlah
usuke piro. Kabeh eneng petungane. [There are many considerations in
building a house, i.e., when is the right time to build, the number of
ribs. All of that has a calculation.]
(Interview excerpt, March 11, 2020)
Based on traditional elderly individuals, many mathematical values
can be derived. However, the mathematical values that we will discuss
N.W. Utami et al. Heliyon 7 (2021) e06417
3

here are related to geometric shapes. A picture of an indigenous house at
the border of Yogyakarta and Central Java, Indonesia is shown in
Figure 1.
The roofs of the houses in the area are either made of tiles or straw.
The tiles are arranged in a certain pattern to form a roof frame fabricated
into an isosceles trapezoid. This, of course, is used as an example in
teaching the concept of the trapezoid, as well as several other objects.
The roof of the house and the related mathematical objects are shown in
Figure 2. In addition, the roof of the house is used as an enrichment
material in the application of problems encountered on a daily basis.
However, the problem, in this case, is discovering the amount of wood
needed to make the roof frame.
In addition to building homes, other artifacts are solids used for pu-
rification before praying. One of them is the padasan, an object made out
of clay that serves as a water reservoir for the Javanese. Based on the
information obtained from one villager in the mountainous region:
Padasan niki biasane diengge bebersih, bisa cuci tangan, wudlu, mandi
juga bisa. [Padasan is usually used for sacred practices, such as the
washing of hands, ablutions, and for bathing.]
(Interview excerpt, March 11, 2020)
This implies that it serves as a tap and is usually placed in front of the
house or beside the well.
This led to the observation of solids that contain the combined
mathematical values of two truncated spheres. Learning that utilizes
material that deals with the application of daily problems—for example,
how many liters or buckets of water does a padasan contain,
etc.—enriches learning. The padasan is regarded as a metaphor or close
analogy with the truncated sphere. Materials concerning the concept of
Figure 1. An indigenous home on the border between Yogyakarta and Central Java, Indonesia.
Figure 2. The roof of the indigenous house and related mathematical objects.
Figure 3. The padasan and related mathematical object.
Figure 4. The kentongan and related mathematical object.
N.W. Utami et al. Heliyon 7 (2021) e06417
4

the truncated sphere are also carried out on this basis. The padasan
artifact and related mathematical object are displayed in Figure 3.
In addition to the necessities of life, humans, as social beings, also
need to interact with one another. The civic needs of individuals are
dependent on the current rules of society and various artifacts. One of
them is called the kentongan, which is usually located on the cakruk (a
kind of security post); it is a community communication tool made of
wood. In accordance with the information from one of the villagers in the
mountainous region:
Kentongan niki biasane diengge titir nek ono bahaya, ono gempa, ono
maling [Kentongan is usually used for warning against danger,
tremors, and theft].
(Interview excerpt, March 11, 2020)
This means that the kentongan is a communication tool used to inform
people of any sign of possible danger, to gather inhabitants whenever
there is an urgent meeting or community service, etc. The kentongan
artifact and the related mathematical object are depicted in Figure 4.It
has a tube-like shape that is used in learning math, both in the material
Table 1. Indigenous artifacts as learning materials.
Indigenous artifact Mathematical object Learning material
Roof Trapezoid Concept
Concept of the trapezoid
Math problem
The area of the trapezoid
Padasan Truncated sphere Concept
Concept of the sphere
Math problem
The volume and surface area of the truncated sphere
Kentongan Tube Concept
Concept of the tube
Math problem
The surface area of the tube
Table 2. Design of learning activity 1.
Indigenous
artifacts
Description of activity Conjecture of student learning
Roof Teacher poses an example of the trapezoid in daily life (roof)
through the display on the screen. The teacher refers to Javanese
houses that are common, limasan for the middle, and joglo for the
luxurious house.
Some students will imagine the form of a trapezoid from the situation.
Teachers ask students to look for another trapezoid example. Some students will look for another trapezoid on daily life.
Table 3. Design of learning activity 2.
Indigenous
artifacts
Description of
activity
Conjecture of student learning
Roof The teacher poses a contextual problem in the roof area.
Roof area to estimate the minimum amount of tile needed.
Calculating the number of tiles based on the roof area truly helps us to prepare the budget design.
The teacher gives clues and asks key questions to direct students'
minds in inquiry and to find the solutions:
a. How many tiles are on the roof? Count them!
b. Draw the roof on the paper,
cut, and flip the triangle.
Conclude your findings!
Some students will think, based on the situation, about how to
count the tiles.
Some students will discuss the solution to the problem, such as
drawing on paper, counting, and discovering the formula.
The teacher asks two groups of students to present the results of their work. Some students will pay attention to the exposure.
The teacher considers unanswered questions and
helps students to make connections back to quadrilaterals.
The teacher evaluates the process.
N.W. Utami et al. Heliyon 7 (2021) e06417
5

presented at the beginning of this context and in relation to daily
activities.
3.2. Exploring learning materials from indigenous artifacts
We need to be attentive to the mathematical knowledge of indigenous
people. Based on the numerous examples of the artifacts utilized in math
learning, we chose 3 examples, namely, the roof of the house, the
padasan, and the kentongan. Artifacts, mathematical objects, and learning
materials derived from the ethnomathematics of the inhabitants on the
border between Yogyakarta and Central Java are summarized in Table 1.
3.2.1. Math lesson plan with “roof”context
Construction of the lesson plan requires an analysis of the curriculum.
In accordance with the 7
th
grade mathematics learning curriculum in
Indonesia, the artifact “roof”can be adopted at the beginning of learning
as a context related to daily life (see Tables 2and 3).
Relates to the circumference formula and area for various types of
quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid,
and kite) and triangle.
(Permendikbud, 2018)
Based on the curriculum, the lesson plan of math learning for 7
th
-
grade students regarding the trapezoid through the roof is presented as
follows.
In addition, the roof-related trapezoidal contextual problem is pre-
sented. According to the 7
th
-grade math learning curriculum in
Indonesia:
Table 4. Design of learning activity 3.
Indigenous
artifacts
Description of activity Conjecture of student learning
Padasan The teacher poses an example of a sphere and truncated sphere in
daily life through the display on the screen. The teacher refers to
the padasan that indigenous people usually use for sacred
practices, such as washing their hands and ablutions.
Some students will imagine the form of a sphere and truncated
sphere based on the situation.
Teachers ask students to look for another sphere and truncated
sphere example.
Some students will look for the other sphere and truncated
sphere on the daily life.
Table 5. Design of learning activity 4.
Indigenous
artifacts
Description of activity Conjecture of student learning
Padasan The teacher poses a contextual problem of the truncated sphere area.
The truncated sphere area of the padasan is needed to estimate
the minimum number of paint cans needed.
Some students will think based on the situation, how to estimate
the minimum number of paint cans needed.
The teacher give clues and asks key questions to direct the
students' minds in inquiry and to find the solutions:
Compare the area of the truncated sphere with the sphere. How is the comparison?
Hence, could you make a conclusion from the surface
area of the truncated sphere and the sphere?
Some students will discuss the solution to the problem, such as
making comparisons with geometric shapes and discovering the
formula.
The teacher asks two groups of students to present the results of their work. Some students will pay attention to the exposure.
The teacher considers unanswered questions and
helps students to make connections back to the surface area of the sphere.
The teacher evaluates the process.
Table 6. Design of learning activity 5.
Indigenous artifacts Description of activity Conjecture of student learning
Kentongan The teacher poses an example of the tube in daily life (kentongan)
through the display on the screen.
The teacher refers to the kentongan, which is used to inform the
people of any sign of possible danger, to gather the inhabitants
whenever there is an urgent meeting or community service, etc.
(communication tool)
Some students will imagine the form of the tube based on the situation.
The teachers ask students to look for another tube example. Some students will look for another tube on daily life.
N.W. Utami et al. Heliyon 7 (2021) e06417
6

Solve contextual problems related to the area and circumference of
quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid,
and kite) and triangle.
(Permendikbud, 2018)
Based on the curriculum, the lesson plan of math learning for the 7
th
grade regarding the trapezoid through the roof is presented as follows.
3.2.2. Math lesson plan in the “padasan”context
Further, the construction of a lesson plan through the padasan can be
done as a context of the truncated sphere. In accordance with the 9
th
-
grade math learning curriculum in Indonesia, the artifact “padasan”can
be adopted at the beginning of learning as a context related to daily life
(see Tables 4and 5).
Generalize the surface area and volume of various curved side spaces
(tube, cone, and sphere).
(Permendikbud, 2018)
Based on the curriculum, the lesson plan of math learning for
9
th-
grade students regarding the truncated sphere through the padasan is
presented as follows.
In addition, the roof-related sphere contextual problem is presented.
According to the 9
th
-grade math learning curriculum in Indonesia:
Solve contextual problems related to surface area and volume of
arcing (cylindrical, conical, and spherical side space), as well as the
combination of several curved sided spaces.
(Permendikbud, 2018).
Based on the curriculum, the lesson plan of math learning for the 9
th
grade regarding the truncated sphere through the padasan is presented as
follows.
3.2.3. Math lesson plan in the “kentongan”context
Moreover, the construction of the lesson plan through the kentongan
can be done as a context of the tube. In accordance with the 6
th
-grade
math learning curriculum in Indonesia, the artifact “kentongan”can be
adopted at the beginning of learning as a context related to daily life (see
Tables 6and 7).
Compare prism, tube, pyramid, cone, and sphere (Permendikbud,
2018).
Based on the curriculum, the lesson plan of math learning for the 6
th
-
grade students regarding the tube through the kentongan is presented as
follows.
In addition, the padasan is related a tube contextual problem. Ac-
cording to the 6
th
grade math learning curriculum in Indonesia:
Identify prism, tube, pyramid, cone, and sphere.
(Permendikbud, 2018).
Based on the curriculum, the lesson plan of math learning for the 6
th
grade regarding the tube through the kentongan is presented as follows.
All of the presented examples are alternatives that can adopt artifacts
for use in the math lesson plan. The lesson plan, which elaborates on
indigenous people's artifacts, has the potential to connect culture and
mathematics.
4. Discussion
Sustainable education in remote areas depends on the creativity of the
teachers in preparing lesson plans, such as employing artifacts from
indigenous communities. The artifacts of indigenous people need to be
incorporated into math learning materials. The use of familiar objects
(such as indigenous artifacts) makes students feel that their culture is
valued. In addition, it is a more meaningful way of learning math in
accordance with the cultural context. Elaborating on the artifacts of
indigenous people has the potential to connect culture and math.
Indigenous artifacts have a lot of potential that can be used in math
learning. Teachers or preservice teachers should master it. Therefore, it is
urgent to involve preservice teachers in revealing their culture because
they can incorporate their culture into their lesson plan, facilitating their
students' meaningful math learning. Hence, preservice teachers need to
be trained to prepare lesson plans with environmental materials that are
familiar to students. Preservice teachers need to be trained to be adap-
tive, creative, and innovative to promote sustainable education in remote
areas. The research involves preservice teachers as assistants in in-
terviews, observations, and measurements. Additionally, preservice
teachers were invited to discuss the interpretation of the artifacts’
mathematical values and how these artifacts can be used in designing
lesson plans. The concept of involving indigenous knowledge in math
learning for both trained and preservice teachers needs to be included in
ethnomathematically-based education courses (Dawson, 2013;Iluno and
Taylor, 2013;Verner et al., 2013). Training also needs to be conducted
through an ethnomathematics study, that involves indigenous people,
because such an examination would reveal the cultural, social, and po-
litical dimensions of math education (Knijnik, 2002).
The challenge aimed at exploring the indigenous knowledge of
learning materials is to portray mathematical ideas from non-Western
perspectives (Alangui, 2010). However, there is a need to be thorough
and attentive to people's mathematical knowledge. Although the inter-
pretation of mathematical values in indigenous knowledge requires
particular abilities, it is beneficial to learning. It is more valuable and
meaningful to follow the context with which the students are already
familiar.
Examples are artifacts that are made and used in remote areas on the
border between Yogyakarta and Central Java, Indonesia such as the
trapezoid of the roof, the truncated sphere, and the tube-like shape of the
padasan and kentongan materials, respectively. There are still many other
artifacts that may be utilized in learning math in such areas. Further
Table 7. Design of learning activity 6.
Indigenous
artifacts
Description of activity Conjecture of student learning
Kentongan The teacher poses a contextual problem of the tube area as an
example: The tube area of the kentongan is needed to estimate the
minimum number of paint cans needed.
Some students will think based on the situation, how to estimate
the minimum number of paint cans needed.
Some students will discuss the solution to the problem, such as
making comparisons with geometric shapes and discovering the
formula.
The teacher asks two groups of students to present the results of
their work.
Some students will pay attention to the exposure.
The teacher considers unanswered questions and helps students
to make connections back to the surface area of the tube.
The teacher evaluates the process.
N.W. Utami et al. Heliyon 7 (2021) e06417
7

studies are needed to investigate each of these artifacts’mathematical
values in greater depth, as discussed in ethnomathematics research.
The explanation of learning materials from the artifacts discovered
along the border between Yogyakarta and Central Java shows that arti-
facts can be adopted as materials in math lesson plans. Elaborating on
indigenous people's artifacts potentially links cultures and math (Civil,
2014;Naresh and Kasmer, 2018). It also leads to more meaningful math
learning (Sharma and Orey, 2017). Preservice teachers need to be
accustomed to preparing materials for lesson plans in accordance with
the environment that is familiar to the students. They also need to be
adaptive, creative, and innovative in remote areas to produce sustainable
education.
4.1. Limitations of this study
Several limitations must be considered when interpreting the re-
ported results and conclusions. First, there were only two preservice
teachers involved in this study. Therefore, the observation is limited to
certain artifacts. The other artifacts cannot be discussed yet. Second, not
all artifacts are suitable or the same as objects in math. The artifacts are
similar to mathematical objects. More so, the intended use of culture
highlights cultural values. Nevertheless, the emphasis is placed on
contextual problems from indigenous communities.
4.2. Recommendations for future research
Considering that ethnomathematics studies regarding Javanese
indigenous knowledge have increased in the last few years, this study's
repetition is recommended in the future, as many more studies will be
published in the coming years. Research on ethnomathematics studies in
less examined educational stages, such as early childhood, higher edu-
cation, or preservice teachers and teacher training, may also be a sub-
stantial field of study.
5. Conclusion
Indigenous artifacts might be similar to mathematical objects. It is
regarded as a metaphor or close analogy with a mathematical object.
Therefore, indigenous artifacts have an opportunity for sustainable ed-
ucation in remote areas. Hence, teachers or preservice teachers need to
integrate local knowledge into their instruction.
Involving preservice teachers in ethnomathematics studies improves
their capabilities for preparing lesson plans relevant to the student
environment for sustainable education. This methodology develops
preservice teachers' education or teacher training and empowers indig-
enous knowledge. Further, preservice teachers, who are also members of
indigenous communities, would engage in understanding the mathe-
matical values that exist in their indigenous culture. The implication of
this is the increasing number of professional teacher candidates who are
agents of change to be more adaptive wherever they are to teach. Thus,
the quality and quantity of professional teachers’distribution is more
spread evenly.
Declarations
Author contribution statement
Niken Wahy Utami: Conceived and designed the experiments; Per-
formed the experiments; Analyzed and interpreted the data; Contributed
reagents, materials, analysis tools or data; Wrote the paper.
Suminto A. Sayuti, Jailani: Conceived and designed the experiments;
Analyzed and interpreted the data; contributed reagents, materials,
analysis tools or data; Wrote the paper.
Funding statement
This work was supported by the Team of Acceleration of a Reputable
International Journal and the Institute of Research and Community
Services Universitas PGRI Yogyakarta.
Data availability statement
Data included in article/supplementary material/referenced in
article.
Declaration of interests statement
The authors declare no conflict of interest.
Additional information
No additional information is available for this paper.
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