Internalizing Religious Values into Ethno-Mathematics as an Effort
to Strengthen Character Building: An Ethno-Mathematics
Integration Study
Muniri
and Galandaru Swalaganata
Department of Mathematics Education, State Islamic Institute of Tulungagung,
Jl. Mayor Sujadi Timur No. 46, Tulungagung, Indonesia
Keywords: Internalization, Ethno-Mathematics, Islamic Values, Educational Character
Abstract: The undesirable fact of ignoring the cultural noble values in society inspired the emersion of mathematics
basic concepts. Mathematics is always there to provide simple formulation when the society face problems
in daily life. The existence of values in mathematics such as independent, critical, logical, and creative has
implicitly shaped our national character. The heritages such as inscriptions, pyramids, religious sites and
their ornament, calendar, batik, woven, weaving and so on are real examples of knowledge contribution
including mathematics. Internalizing religious (Islamic) value was felt necessarily embellished into ethno-
mathematics learning which includes the required value to develop the noble values and strengthen
individual character in community, nation, and state life. This article aims to spread the ideas through
illustrating the ethno-mathematics concept planting combined with the religious value as a step to build the
character, the noble student individuals (akhlakul karimah) just as our hope.
1 INTRODUCTION
Some serious efforts have been done by the
government as an independent and dignity nation
shown by discussions, seminars, and symposium
with main theme “strengthening character
education”. This is evidenced their curriculum
changes every decade ranging curriculum 1974 to
2013. Various curriculum innovations have been
carried out to fulfill and answer the challenges of
times and generations in the future. This form of
innovation has created a variety of distinctive
features in providing answers to challenges at certain
times, such as (i) an effort to motivate students
actively in learning packaged in curriculum CBSA,
(ii) an efforts to increase the competency of students
nationally, then applied based curriculum
competence, (iii) to foster the competency diversity
and character of students locally, packed in the
education unit level curriculum, and finally (iv)
2013 curriculum which emphasizes on strengthening
character education. Alteration and renewal the
curriculum above, indicates that the government is
serious in facilitating potential development for
future generations to the nation's dignity.
Harmonization of the heart (ethics), sense
processing (aesthetics), thought-processing (logic-
literacy), and physical/sports (kinesthetics) are
efforts made to strengthen character education
(Yunus, 2013). This harmonization involves the
support of all elementer (school, families, and
communities). Thus, it can achieve of the value of
the character, such as religious attitude, honesty,
tolerance, discipline, hard work, independent,
creative, love of the homeland, communicative,
friendly, caring, and responsibility. 2013 curriculum
is focusing on the formation and development of the
character/ morality students through strengthening
character education program. The crystallization of
value character above, include religious, nationalist,
independent, cooperation (gotong royong), and
integrity. Therefore, those notions are presented into
teaching and learning which are integrated and
connected with local wisdoms.
Mathematics subjects are still classified as
popular subjects in school. Even public interest in
mathematics remains one of the benchmarks for
predicting one's intelligence and success in the
future. Therefore, mathematicians and mathematical
education experts try to present mathematics easily,
466
Muniri, . and Swalaganata, G.
Internalizing Religious Values into Ethno-Mathematics as an Effort to Strengthen Character Building: An Ethno-Mathematics Integration Study.
DOI: 10.5220/0008523804660473
In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 466-473
ISBN: 978-989-758-407-7
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
such as presented by many circles both in terms of
composition, order of presentation of objects,
concepts, principles, and procedures as well as in
terms of the implementation of concepts, principles
and procedures in answering any problems that
arise.
Mathematical concepts should not be studied and
understood separately from real life contexts
including in culture. It causes mathematics seems
like only a set of symbols, formulas, calculation and
reasoning techniques do not mean anything, and
seem to have no benefit in human life. This situation
has an impact on the lack of interest in learning and
mastering mathematics.
Kusaeri (2017) said that the existence of
mathematics to provide solutions to problems in
accordance with the context and age in social life.
Like the presence of geometry that developed in
ancient Egypt, due to the desire of the farmers in
dealing with the problem of measuring agricultural
land that is located along the Nile in the form of a
rectangle, which then developed the emergence of
new knowledge, such as measuring triangles,
pentagons, and so on. Indeed, the existence of other
simple mathematical activities has been carried out
since ancient times or prehistoric times, such as
simple visual counting activities of objects around
them. One of the proofs has been done by
archaeologists in the form of simple calculation
systems, measurements and shifts of objects in
certain societies in ancient times. The discovery of
several bones that have notches at regular intervals,
where the aim of the notch is possible to indicate the
number of hunted animals killed by the hunter, and
how to track their pet.
From the above opinion it can be concluded that
every community group is familiar with
mathematics even though some of them are not
aware of it. This shows that the mathematical culture
in certain community groups has taken place
massively even though the mathematical concepts,
principles and procedures are not obtained from
school learning.
Mathematical culture can generate advanced and
high-character community activities or vice versa
that the progress of a society can generates
mathematical activities. This is consistent with the
opinion of Gerdes (1994, 1996) that ethno-
mathematics describes as the study of ideas and
concepts that using visualization of the developing
cultural context, so that mathematics can be learn as
knowledge that has many functions in life and
character of a nation.
Good character or morality is a basic value of
religion (Islam). God sent prophets and apostles as
deliverers of revelation exemplified by good morals.
Prophet Muhammad SAW. in one of the hadiths said
"innamaa buitstu liutammima makaarimal morality"
means "Verily I (Muhammad) was sent to perfect
morals." Based on the context of this hadith
according to Maksudin (Maksudin, 2013) explains
that actually morals in human beings already exist
(fitrah), therefore there is the term "perfect", which
means that in nature human beings have morals,
both to God (Allah), and to others human. Naturally,
human know something that is good and bad,
something that is right and false, which is useful,
and which is bad based on the nature of belief
(qolbu) and knowledge (reason).
Almawardi in his book "Adab ad-Dunya wa al-
Din" as quoted by Miskawaih (1999) says "dharuroh
fi ad-din al-aql wa li al-aqli ad-din al Ashli" which
means that religion is necessary for the ratio, and the
ratio is the basis of religion. While similar thing also
expressed by Albert Einstein "religion without
science is blind and science without religion is lame
"(Miskawaih, 1999). The opinion inspires us that
religion and science absolutely must be synergized
because essentially derived from the same source,
it’s from the God (Allah). The basics acquisition of
knowledge (read: science and technology) has been
described in the Qur'an in Al-Alaq verses 1-5, which
reads (Agama, 1990):
This means (i) Read: In the name of your God
who created, (ii) Created man from clot, (iii) Read:
and your Lord is the most Generous, (iv) He who
taught by the pen, (v) Taught man what he never
knew,
The above verse teaches knowledge bound by a
strong monotheism (bismirobbikal ladzi kholaq) and
(warobbukal akrom). A read command can be
interpreted in a broad sense reviewing, analyzing,
studying, research, discussion, question, discover,
prove, test hypotheses, and so on. That five verses of
the Qur'an which fell first on top, giving a message
not only to study one science of religion, but a read
command is also to examine various other
knowledge such as engineering, industry, animal
husbandry, agriculture, and even mathematics
(falaqiyah, faraid, charity, buying and selling, and
so on). Furthermore, through read command not
only acquire knowledge, but also gain magnificence
(warobbukal Akrom) which is due to the functioning
Internalizing Religious Values into Ethno-Mathematics as an Effort to Strengthen Character Building: An Ethno-Mathematics Integration
Study
467
of all the human senses, the thought (brain) and the
flavor/ mind (heart), which in turn formed by itself
personality steady and decorated by a positive
character or a noble character (Mulyono, 2003).
Therefore, this paper attempts initiated by
illustration ideas of ethno-mathematics concept is
designed based on the value of religion (Islam) as a
breakthrough step to form characters (akhlakul
karimah) just as our hope.
2 RESEARCH METHOD
This paper is a review of library research that carry
out research from literature in the form of books, as
well as research reports, journals, and articles which
have a relation with the issues to be studied. This
article discusses the internalization of Islamic values
in ethno-mathematics as an effort to shape the
character of the nation through the formation of
student character. Thus, the data in this study were
obtained from various sources of literature relating
to ethno-mathematics, Islamic values, and national
character.
3 RESULTS AND ANALYSIS
Some experts give general understanding and
specifically to mathematics. One of the experts is
Hudojo (1998) said mathematics is abstract ideas
which are given symbols that are hierarchically
arranged and their reasoning is deductive, so
learning mathematics is a high mental activity.
Whereas Ramdani (2006) said that mathematics is
seen as the science of logic regarding the form,
composition, magnitude and other related concepts
with a large number which is divided into three
fields, namely algebra, analysis and geometry. Thus,
based on these two opinions, it means that
mathematics can play a role in activity or acting in
daily life through thinking and reasoning and skill in
communicating.
3.1 Culture and Character
In a study of the history of the development of
mathematics from the Mesopotamia, Egypt, and
Greece cannot be separated from the high value of
local culture. The exist values indicate higher the
civilization of the community. Thus, it is not
excessive if there is a hypothesis that character can
be born from culture and culture that can give birth
to good character. The term culture in Islam is
known as al Saqaafah or culture, while the character
comes from the word al-akhlaq which means good
behavior. The figure who is the role model of
mankind is God's chosen man, namely Muhammad
SAW as a model in life and life in the world to the
hereafter. Read: (wainnaka la ala khuluqin adhim).
Or read (laqad kana lakum fi rasulillahi uswatun
hasanah).
Images of human figures expected Indonesia has
been reflected in man chosen (perfect man) as the
reference every Muslim is the personality of the
Prophet Muhammad. He has four characters, that is
sincere (siddiq), trustworthy (amanah), extended
(tabligh), smart (fatonah). Through these four
characters, he was able to change the incredible
world. According Rukiyati (2013) that the existence
of four of these characters are manifestations of
human perfection from three sides (i) mind, (ii) the
soul, and (iii) the morality or "thinking, feeling and
action”. Furthermore, he asserted through four (iv)
of this noble nature, man is guaranteed to be tough,
strong physical, and psychological (healthy brain,
healthy heart, and healthy body). Accordingly, the
four characters of Mohammad are adopted as the
educational goal as well as three notion’s Bloom
proposal (cognitive, affective, and psychomotor).
Abdurrahman (1995) said that through the
example of the Prophet Muhammad would give birth
to a human who has the mature moral integrity,
stable, mature personally and socially. This is
demonstrated through the nature Sidiq (sincere) and
Fathonah (smart) reflects a personal quality as a
human being, whereas through the nature of Tabligh
(communication skills) and Amanah (trustworthy)
reflects the quality of human figure socially.
Manifestations of these two aspects of maturity
(personal and social) that are the core values that are
referenced from the human figure perfectly the
figure of the Prophet Muhammad bringer of the
message of God inspired the character education in
Indonesia which derived into 18 indicators of the
character education as shown in Table 1.
The term culture is often interpreted as a pattern-
intact human behavior and the products of mindset,
oral, patterns of action, and artifacts that depends on
a person's ability to learn, which aims to convey
knowledge to the next generation through a variety
of means and tools, language, and patterns of
reasoning (Mega, 2016). Thus, the means of cultural
values is a matter that cannot be separated from the
life of a society, because culture is an integral and
complete from various embodiments and behavior in
public life.
ICMIs 2018 - International Conference on Mathematics and Islam
468
Culture and characters sometimes appear and
develop in specific social communities (Hammond,
2000). Its existence appearance sometimes is
natural, which is facilitated by God as ethnicity,
race, skin color, the diversity of languages, and
more. While the other part can exist because it was
created by community groups, such as the arts,
customs, language and formal education. Suparlan
(1981) defines culture as the whole of human
knowledge which is used to interpret, to understand
the environment, and to create and promote
behavior. Medium culture is the result of activities
and the creation of the mind (intellect) of man, such
as trust, art and customs.
Based on some of these definitions, it can be
concluded that an understanding of the culture is
something that can affect the level of knowledge,
ideas of the human mind that is abstract. While the
culture is the form of objects produced by humans
can be behavioral and objects are real, as is the
custom, language, equipment life, religion, art, and
others, all of which is intended to help humans the
continuity of social life.
3.2 Philosophy of Ethno Mathematics
Etymologically, D'Ambrosio (1985, 1999; 2006)
initially defines ethno-mathematics as mathematical
practices carried out by groups certain cultures, such
as certain tribal societies, labor groups, children of
the group a certain age, professional grade and so
on. In other words, ethno-mathematics develop from
local culture that is associated with mathematical
thinking, so that it can evolve based needs and
problems faced through a cultural context. While the
paradigm and direction of development of ethno-
mathematics suggested by Rosa and Orey (2000;
2011), states the mathematical concepts embedded
in cultural practices, focused on the realization that
everyone develop a unique method to understand
and change the reality of the cultural community.
The paradigm of cultural diversity can be uniquely
interaction between languages with their habits on
the environment. Such as planting in agriculture,
trade, business activity, weaving, carpentry, etc.,
which eventually gave birth to the mathematical
forms that vary because of cultural activities using
mathematical ideas and concepts through
quantitative considerations, relational and spatial
aspects of their lives. These conditions show that
mathematic has indeed united in life and culture of a
society.
Studies have shown that there is a link between
mathematics and culture, as was done by Clements
(Karnilah, 2013). It can be seen from the results of
meeting s of the International Community of
Mathematics Education which states that issues
related to culture will inevitably interact in the
learning process of mathematics. It also reflects on
all the objects and mathematical concepts.
Therefore, the development ethno-mathematics can
be directed to activities, ideas, and concepts and
mathematical contexts associated with elements of
cultural or human creations.
3.3 Mathematical Ideas
The term idea of mathematical often inspired by
some of the facts of nature created by the God
(Allah) as the form of mountains, caves, sea, sand,
trees, flowers, fireworks, the expanse of the earth,
rivers, rocks, fish, birds, etc. These facts may be
either natural scientific facts and inspired a
mathematical idea developed into a certain culture
and civilization that are reflected in the activities of
life through work activities to meet the needs of their
own lives. As well as the caves for shelter from the
scorching sun and rain inspire them make a home.
Mountains inspire art brick buildings such as the
pyramids of Egypt. Piles of rocks inspiring places of
worship such as the temple buildings, temples and
places of worship of humanity.
Table 1: 18 indicators of characters education.
Foundation
Aspect
Attitude
Characteristic Value
Derivatives Value
Religious
Personal
Sidiq (Sincere) and
Fathonah (Smart)
Honestly, curiosity,
creativity, reward
achievement, happy reading.
Sincere: Believe, faith and piety,
self-respect, honest, sportif.
Fathonah: Creative, innovative,
critical, initiative, productive,
disciplined, meticulous, visionary,
problem solver, self-contained.
Social
Tabligh (Able to
communicate or
care) and Amanah
(Trustworthy)
Friends / communicative,
democratic, tolerant, national
spirit, love of country, love
of peace, social care, care for
Tabligh: Care, compassion,
concern, sympathy, empathy,
helpful, clever grateful, patient,
humoris, friendly, neat, responsive.
Internalizing Religious Values into Ethno-Mathematics as an Effort to Strengthen Character Building: An Ethno-Mathematics Integration
Study
469
the environment,
responsibility, hard work,
self-contained.
(a) (b)
Figure 1: Interpretation between (a) mountain and (b)
curve in mathematics.
The curve (see Figure 1) is a symbol of a
person's life, sometimes a person who gets lucky to
be interpreted being positioned above the curve and
vice versa. It is implied that the curve is as the
journey of life. It means that every life is never flat.
But there is also the concept of mathematical ideas
can inspire a civilization or vice versa, for example
geometry such as square, triangular, irregular
pentagon, a regular hexagon, circles, cubes, blocks,
pyramid and prism (Figure 2), ball even a curve to
the number system.
(a) (b)
Figure 2: Interpretation between (a) pyramid and (b) prism
in mathematics.
(a) (b)
Figure 3: Interpretation between (a) Ka’ba and (b) Square
and circles in mathematics.
As seen in Figure 3 the activity in the Ka'ba is
ritually surrounds the sharia commanded by Islam in
performing tawaf Haj and Umrah. However, tawaf
can be understood our focus in reaching the target or
goal, it also means the way to enhance the desired
destination point.
According to Ascher and Ascher (1997),
mathematical ideas covering with numbers, logic,
spatial configuration, and the combination or
composition in the system and structure. Ascher
recognize that there are two aspects in mathematic
activities, namely, to understand the relationship
between mathematical ideas and habits of life as
well as how to modify the learning of mathematics
so internalized the ideas in this lesson. Some ideas
of mathematics used in arts and culture can be
developed in the architecture is the concept
tessellation. The tessellation means repetitive
drafting a model or form that meets a field, which is
in the study of mathematics known as tiling. Some
concepts tessellation in mathematics are the form of
a regular polygon, congruence, cubes, blocks and
circles.
Application of the principles of tessellation
encountered in everyday life, such as in engineering
tile installation (manufacture of ornaments mosque,
temple or house), fabric pattern, batik, design
patterns for wallpaper, painting, weaving, carving,
and others.
The idea of ethno-mathematics is a mutual
influence between mathematics and social and
cultural life, economy, architecture. The emergence
of mathematical ideas continued to grow along with
the development of society, from the ancient
primitive societies age, pre-history to the public in
modern civilization. Every socio-cultural
development of the basic idea is always to be found
mathematically describe in a context, it means
implicitly mathematics come to give color to build
positive character in society.
In fact, it can be found a few examples of
naturally occurring teselasi, namely beehive,
cobweb, leaves and flowers as shown in Figure. 4.
ICMIs 2018 - International Conference on Mathematics and Islam
470
(a) (b)
(c) (d)
Figure 4: Interpretation between (a) broccoli and (b)
triangles, hexagons, snowflakes in mathematics, (c) spider
web and (d) parabola.
Some definitions related to tessellation also
expressed by O'Daffer (2008) as follows:
• Regular Tessellation "Such a tessellation, made
up of congruent regular polygons of one type, all
meeting edge to edge and vertex to vertex is
called a regular tessellation ".
• semiregular tessellation “A tessellation formed
by two or more regular polygons with the
arrangement of the polygons at each vertex the
same ".
• A Semi Regular Tessellation “A tessellation is
a regular Semi tessellation of regular polygons
that has exactly two or three different
arrangements about its polygon vertices ".
In other words, for practice tessellation (to tile)
there are three regular polygons are triangle, square,
and hexagonal irregular. The important thing should
be owned by a semi-regular tessellation is formed by
irregular polygons and each peak in the polygons
should coincide.
3.4 Some Examples of Mathematical
Ideas and Culture of Islamic Values
3.4.1 Mosques and its ornaments
Some Muslim artists distribute works of art through
nature painting, or geometry painting through the
period and a ruler, in order to obtain attractive
shapes, until he found a complex pattern (R.
Cromwell, 2009). Ornaments used on the walls of
the mosque is a form of cultural and intellectual
geometry with the calculation of the figures
carefully and thoroughly (Lu & Steinhardt, 2007).
Its characters are formed is a mental attitude that is
innovative, creative, critical, visionary. Moreover,
one Islamic geometry art is girih. Girih is decorating
with tessellation or tiling technique of Persian. There
are at least three elements that are the bending lines,
symmetry and repetition.
Figure 5: The mosque involves the concept of a triangle,
rectangle, beams, pyramid and prism.
Figure 6: Ornaments of mihrob structured geometry based
tiling/semi-regular tessellasion. (Rohayati, Karno, &
Chomariyah, 2017)
3.4.2 Webbing
According Hoenigman (Mega, 2016) mentions that
the woven art is a form of culture, which is included
in the artifacts. Matting firstly is used by human
which is to help in their everyday lives. There are at
least three types of materials used in webbing,
namely bamboo, pandanus, and rattan. Each material
has strong characteristics and philosophy. The
following pictures Local webbing culture is an
expression of human civilization as.
(a) (b)
Figure 7: (a) A concept of circle woven, (b) Woven square
and rectangular form
3.4.3 Weaving
Weaving is a technique in the manufacture of fabrics
made with the simple principle a square or a
rectangle, by combining the lengthwise and
crosswise yarns, usually made of wood fibers,
cotton, silk, and more. Weaving art is closely related
to knowledge systems, culture, beliefs, the natural
environment, and a system of social organization in
Internalizing Religious Values into Ethno-Mathematics as an Effort to Strengthen Character Building: An Ethno-Mathematics Integration
Study
471
the community. Because of the social culture in a
diverse society, the art of weaving in each area have
differences. Therefore, it has a characteristic and is
part of the representation of the people's culture.
Mental attitude or character developed is
independent, tenacious, resilient, and visionary.
Figure 8: Example of weaving sajadah. (Prabawati, 2016)
3.4.4 Indonesian Batik
Batik is a craft that has high artistic value and has
become part of the culture of Indonesia (especially
Java) for a long time. Batik tradition was originally a
hereditary tradition, so occasionally a recognizable
motif batik originated from a family or even batik
may indicate the status of a person.
Along with the times, batik is now a valuable
commodity and prestigious not only for purposes of
dress, such as clothes and gloves, but also a
decoration and a prayer rug to pray. The moral being
offered is persistent, tenacious, independent,
visionary, honest, economical, creative, initiative,
etc.
(a) (b) (c)
Figure 9: Example of (a) The combination of flowers,
natural painting, (b) sajadah, (c) The combination of the
concept of fractal pentagon, circle.
3.4.5 Music and Percussion
Percussion word comes from the Latin term
percussio means hit and percussus (noun, meaning
"punch"). Percussion is musical instrument that
produces sound by being hit, beaten, shaken, rubbed,
or other actions that make the objects vibrate with a
device, a stick (stick), as well as with his bare hands,
or complaint with other objects that produce sound.
To simplify the classification, a percussion
instrument called also with percussion instruments
or percussion instruments, such as tambourines,
extension, violin, tambourine, and so on. Some
developed moral message is caring, cooperation,
dynamic, responsibility, respect, creative,
innovative.
(a) (b) (c)
Figure 10: (a)The concept of rows in the art, (b) A
combination of tube concept, (c) The draft tube.
4 CONCLUSIONS
Based on the discussion and analysis above,
mathematical ideas inspired, explored, constructed
from natural phenomena provided by God the
Almighty (Allah SWT) in the form of natural
panoramas such as mountains, trees, flowers,
beehives and spiders, ravines, and river. In addition,
it is also inspired by the activities of human
activities in meeting their own needs, such as
farming, trading, handicrafts, transportation
equipment and sophisticated equipment such as
airplanes and computers. So that the mathematical
concepts also have many implications in solving
problems in everyday life and sustaining the
perfection of other sciences, this is in accordance
with the term mathematics as Queen of Sciences as
well as mathematics is a servant, namely as its
servant.
Despite cultural creation continues to change
rapidly, mathematics is always relevant in
supporting the change in civilization. Mathematics
puts forward logical thinking which always goes in
line with the common sense of the human mind.
That means that mathematics always develops from
time to time and the wider its scope is in accordance
with the development of common sense of the
human mind. For this reason, it is no exaggeration to
say that mathematics has contributed and played a
significant role in realizing human civilization.
REFERENCES
Abdurrahman, N. 1995. Ushul al Tarbiyah al-Islamiyah fi
al-Baiti wal al Madrasah wal al-Mujtama.
(Shihavuddin, Trans.). Jakarta: Gunan Insani.
Agama, K. 1990. Al-Qur’an and Translation. Kingdom of
Saudi Arabia.
ICMIs 2018 - International Conference on Mathematics and Islam
472
Ascher, A. 1997. Ethnomathematics. In
Ethnomathematics: Challenging Eurocentrism in
mathematics education (pp. 25–50). New York: State
University of New York Press Albany.
D’Ambrosio, U. 1985. Ethnomathematics and its place in
the history and pedagogy of mathematics. For the
Learning of Mathematics, 5(1), 44–48.
D’Ambrosio, U. 1999. Literacy, Matheracy, and
Technocracy: A Trivium for Today. Mathematical
Thinking and Learning, 1(2), 131–153.
https://doi.org/10.1207/s15327833mtl0102_3
Gerdes, P. 1994. Reflections on Ethnomathematics. For
the Learning of Mathematics, 14(2), 19–22. Retrieved
from http://www.jstor.org/stable/40248110
Gerdes, P. 1996. Ethnomathematics and Mathematics
Education. In International Handbook of
Mathematical Education (pp. 909–943). Dordrecht:
Kluwer Academic Publiser.
Hammond, T. 2000. Ethnomathematics: Concept
Definition and Research Perspectives. Columbia
University. Retrieved from
http://srlweb.cs.tamu.edu/srlng_media/content/objects/
object-1234476000-
b6fdd344454299ac478700e4deb6e040/2000
Hammond.pdf
Hudojo, H. 1998. Mengajar Belajar Matematika. Jakarta:
Departemen Pendidikan dan Kebudayaan Direktorat
Jenderal Pendidikan Tinggi Proyek Pengembangan
Lembaga Pendidikan Tenaga Pendidikan.
Karnilah, N. 2013. Study Ethnomathematics: Penanggalan
Sistem Bilangan Masyarakat Adat Baduy. Universitas
Pendidikan Indonesia.
Kusaeri, K. 2017. Historigrafi Matematika; Rujukan
paling Otoritatif Tenatng Sejarah Perkembangan
Matematika. Yogyakarta: CV Matematika.
Lu, P. J., & Steinhardt, P. J. 2007. Decagonal and Quasi-
Crystalline Tilings in Medieval Islamic Architecture.
Science, 315(5815), 1106–1110.
https://doi.org/10.1126/science.1135491
Maksudin. 2013. Pendidikan Karakter Non-dikotomik
(Cet. 1). Yogyakarta: Pustaka Pelajar.
Mega, B. 2016. Ethno-mathematics: As Stepping Stones to
Learning Mathematics. In National Seminar of
Mathematics and Learning.
Miskawaih, I. 1999. Menuju Kesempurnaan Akhlak: Buku
Dasar Pertama tentang Filsafat Etika. Bandung:
Mizan.
Mulyono, A. 2003. Pendidikan bagi Anak Berkesulitan
Belajar. Jakarta: Rineka Cipta.
O’Daffer, P. G. 2008. Mathematics for Elementary School
Teachers. Pearson Education.
Orey, D. C. 2000. The Etnomathematics of the Sioux tipi
and cone. In Mathematics Across Culture: The History
of non-Western mathematics (pp. 239–252).
Dordrecht: Kulwer Academic Publishrs.
Prabawati, M. N. 2016. Etnomatematika Masyarakat
Pengrajin Anyaman Rajapolah Kabupaten
Tasikmalaya. Jurnal Pendidikan Matematika, 5(1).
R. Cromwell, P. 2009. The Search for Quasi-Periodicity in
Islamic 5-fold Ornament. The Mathematical
Intelligencer, 31, 36–56.
Ramdani, Y. 2006. Kajian Pemahaman Matematika
Melalui Etika Pemodelan Matematika. MIMBAR,
Jurnal Sosial Dan Pembangunan, 22(1), 1–14.
Rohayati, S., Karno, K., & Chomariyah, W. I. 2017.
Identifikasi Etnomatematika pada Masjid Agung di
Yogyakarta. In Prosiding SEMPOA (Seminar
Nasional, Pameran Alat Peraga, dan Olimpiade
Matematika). Yogyakarta.
Rosa, M., & Orey, D. 2011. Ethnomathematics: the
cultural aspects of mathematics. Revista
Latinoamericana de Etnomatem, 4(2), 32–54.
Rukiyati, R. 2013. Urgensi Pendidikan Karakter Holistik
Komprehensif di Indonesia. Jurnal Pendidikan
Karakter, 3(2).
Spradley, J. P. 2006. Metode Etnografi. Yogyakarta: Tiara
Wacana.
Suparlan, P. 1981. Kebudayaan, Masyarakat, dan Agama:
Agama sebagai Sasaran Penelitian Antropologi. In
Majalah Ilmu-ilmu Sastra Indonesia (Indonesian
Journal of Cultural Studies) Juni Jilid X Nomor 1.
Jakarta: Fakultas Sastra Universitas Indonesia.
Yunus, R. 2013. Transformasi Nilai-Nilai Budaya Lokal
Sebagai Upaya Pembangunan Karakter Bangsa. Jurnal
Penelitian Pendidikan, 14(1).
Internalizing Religious Values into Ethno-Mathematics as an Effort to Strengthen Character Building: An Ethno-Mathematics Integration
Study
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