Ethnomathematics is the First Reflection Lectures
People just do not understand the mathematics of the schools, but also from the cultural environment that is affected. Ethnomathematics designations proposed by D'Ambrosio (1984) in his article titled Ethnomathematics delivered at the opening of an international conference of mathematics education in Adelaide Australia, and in journals (D'Ambrosio, 1985) entitled Ethnomathematics and iits place in the history and pedagogy of mathematics. For the learning of mathematics 5 (1), 44-48. Ethnomathematics to refer to different forms of mathematics with school mathematics as a result of the influence of existing activities in an environment that is influenced by culture. This translation of scientific articles work Terenzinha Nunes (The Institute of Education of London) entitled Ethnomathematics and Everyday Cognition contained in the book Handbook of Research on Mathematics Teaching and Learning (editor: A. Douglass Groows, publisher: Macmillan, New York in 1992) . This paper presents two different views of cultural influences on the activities of mathematics and mathematical problem solving.
a. Two Views on Culture and Mathematics
Years of education and mathematics education researchers to focus on activities in the classroom as the main setting in the learning of mathematics. Based on a Survey (Cockcroft, 1986) and analysis of mathematical knowledge of children (Carraher, Carraher & Schliemann, 1985, 1987; Ginburg, 1977; Ginburg, Posner & Russell, 1981; Hughes, 1986; Resnick, 1984) suggests that many mathematical knowledge acquired outside of school. The fact that mathematical knowledge can be acquired outside of school led to a new variable in the analysis of mathematical learning. D'Ambrosio (1984, 1985) uses the term "ethnomathematics" to refer to different forms of mathematics with mathematics in school as a result of activities in an environment surrounded by cultural influences. The purpose of the use of mathematics in an environment that is influenced by different cultures in the mathematics classroom penekananya to learn to know something (learning to know about), learning to do (learning to do), learn to animate (learning to be), learn how to learn (learning to learn), and learn to socialize among their peers (learning to live together) .
The use of mathematics outside of school is obviously related to the environment, such as building a house, change money at the Bank, considering the results of production, determining the geometric patterns of harmony, sell and buy goods, and so on. Application of mathematics is often very different from the mathematics learned in school. In everyday life at home, in the kitchen mothers often measure the contents with a spoon or cup, while at school in particular by measuring the content of liters or cubic meters. Besides mathematics in everyday life are common among different regions with each other in a system such as numeracy or arithmetic means are used. The differences in the use of mathematics can be seen in depth or which appears on the surface structure depends on what view of mathematical knowledge is used.
Two different approaches to assess the influence of culture on mathematical knowledge can be identified from the literature. The first view adopted Stigler and Baranes (1988) which states that mathematics is not universal, formal domain of knowledge but as symbolic representatives of the assembly formed by the influence of culture and procedures for agencies to manipulate it. For example, in child development, their representatives and incorporate these procedures into their cognitive systems, and processes that occur in the context of forming social activities. Mathematical skills learned in school is not formed on the basis logically abstract cognitive structure, but to forge out a combination of knowledge and skills acquired earlier, and enter a new culture. The second view (Nunes, 1992) states that understanding cultural influences on learning mathematics should involve both the analysis of the differences between specific solutions to the reality of mathematics and recognition of the precepts of logic (logical invariants) that underlie these differences. Cultural differences exist not only because of opposition in the culture. In a culture, differ in the use of mathematics depends on its purpose. Research in mathematics education can take the meaning of the analysis of various solutions on the same problems that exist simultaneously within a single culture. In some cultures there is a written presentation and Lesan, it's like two practices in arithmetic simultaneously (Red & LAVE, 1981). Research shows that the use of mathematics in the same culture differ in kind but in other ways and other differences in the relationship between the presentation and use of provisions in the application of mathematics.
b. Counting Principles and Contributed Development of Culture in Counting System
Counting and measuring is a way to present selected aspects of objects and situations. So that one can measure the dimensions need to choose what will serve as a scale, for example, a group of objects to be counted or the length or weight when measured. Counting and measuring activities usually lead to a broader purpose. For example, people counting the money in your pocket to see if enough available money to buy something. People measure tablecloth table to determine who will be selected to cover it. Activities such as these that make counting and measuring meaningful in everyday life.
Calculate and measure a variety of activities are fundamentally different, but both seem based on logic. Through analysis of how children develop counting skills, and Galistel Gelman (1978) stated four principles of logic that must be met if an activity would be classified as an activity count. These principles are as follows: (1) provides one-one correspondence between objects and labels calculated to compute, (2) set the labels to calculate the fixed sequence, (3) recognize that no relevant sequence of the order that their objects are calculated, and (4) using kekardinalan principle, namely using the label last for many objects present in the set. The fourth principle is expressed as a strong logic, and are considered free of the culture and the possibility of an inborn.
Systems using the principles of logic has led to limited use. Absence of an organized system of numeracy in the culture, people would have trouble in the fourth obey this principle. How many labels that can be remembered in a fixed order (principle-2). Without counting system numeracy activities will be limited to small numbers and the system can go invinity numeracy.
Although the principle of free-2 calculations may be culturally specific system of number-2 tergabtung in the culture. Important work of Lancy (1983), Save (1991), and other people to explain how cultural differences on the issues addressed in the calculation of the memory dialing. Overwhelmed and Oksagmin Papuanugini developed a system of counting the memnabtu they set a fixed sequence by using the names of body parts in the calculation of the label. For example, pointing one thumb, index finger shows two middle fingers show number 3, and so on. The use of body parts to the calculation as the conventional solution to the problem of cultural memory dialing. Body parts are named and the order in which to be agreed. Some selected parts of the body does not have a clear label identity in western culture. As the three sites and six locations on the arm between shoulder and neck. The use of both this section and systematically labeled these calculations can be up to 68.
This does not mean the only solution and the best in this matter. In the UK the solution of this problem using a system call to memory the basic numbers labels are built. Number of words used in the UK is provided in the original sequence generation in systematic combinations. Number of words to do with one another to 12. But after 13 there is a label that helps labelr-label fixed sequence. Start number 13 there are cues that establish the following labels. Cues are even more evident from 21, when used recursively to generate the calculation of the number of words. Generalization words matter in this show relates to the introduction of a basic system of calculation.
Based on the counting system in a grouping scema used to re-organize the calculation. To define a number system is the basis for choosing a system unit agreement (some conventional units for a mixed base system) used in the calculation. According to Luria (1969) a system of basic numeracy involves the calculation of natural objects organized in a group-2 in the conventional units of the new calculation. And adhering to the semantic structure of a complex system based on numeracy. Numbers 343 states there are 3 groups of a hundred, four groups of tens, and units of the group. In order to grasp the meaning and memperumum label number to infinity subject should not think about the objects of nature are only considered fairly. They also must understand the meaning of meaning in the structure of number systems. They give great importance to attribute this difference is that the compute-2 natural objects without understanding the basic system is done by the right brain. Where understanding is based on the basic system is controlled by left-brain system. As a summary of the calculation system put in both on an invariant principles of logic and in particular on the part of the culture for the implementation of these principles-2. Not all cultures find common solutions to the challenge to keep the label-2 numbers in a fixed sequence. Differences in the various solutions they relate to the skills of large numbers. Systematically counting the body parts are one type of solution to keep the words to count in a fixed sequence. But this section has a limited range. The use of a counting system is a part of culture that can solve problems in the calculation of memory dialing. Based system allows to calculate the infinite, an impossibility with no basis to use the systems of the body. Of view of psychology, based on the count involving the introduction of the concepts of arithmetic units. In a basic system of arithmetic units is not just a natural object but also a group-kelomnpok konsvensional of objects that show the basis of the system. Besides culturally dependent nature of the source we call a basis, the use of unit-2 arithmetic is not so simple as the conventional void of logic. Basic counting system is supported by the concept of a unit that is partnership both calculation and size.
Market day for the use of Java, pon, wage, kliwon, legi, and Pahing in learning math is a simple example application ethnomathematics . The market today can be used to apply the concept of base number. For example, if the right Anga birthday on Wednesday, wage then a year later (through a leap year) his birthday on the day of what? We know, a leap year has 366 days, which when divided by 7 residue 2, and when divided by 5 so that the trace of 1 year after the wage is Friday Kliwon Wednesday.
According to that raised in the lectures held yesterday, created a chart that links ethnomathematika with various other sciences. This shows the relationship between various sciences with other sciences which were interconnected and need each other. The following chart:
Formal math Model math Model concrete Concrete (example) |
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Philosophy Ideology Political geography |
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Have method spiral, it can be descriptive qualitative that have 4 component is recording, transcription, categorizalitation and analyse (conclution/theory) |
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1. Formal 2. Formal Model 3. Concret Model 4. Concrete (mathematics context) |
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The mechanism after the Mataram kingdom managed to break the resistance of the coastal local authorities who have the support community schools, finally arises a new problem of how to create stability for the government of Mataram. Namely how to create a form of intellectual culture which can reduce the tension between cultural environment and Javanese pesantren. This effort was initiated by changing the calculation of leap years Saka, a Java-year Sultan Agung's to fit the Hijri month based on circulation. Adapted month name to the Islamic calendar; Islam is a weekly day be reunited with the names of the day Javanese, for example, Wage Monday, Tuesday POND, Saturday Pahing and so on. Thus, the calculations in Java can be received with relief by the public schools. Only for the benefit of royal ceremonies ongoing, year-Java as the Saka year is to preserve his first initial, the year 78 AD.
Space and time as the original place where it is not understood in the same way universally. Understanding of space and time are formed on the public side of thinking that allows people to communicate their mutual existence. Bring together people construct this understanding through social institutions and public symbols, such as, calendar system, event celebrations, rites of life, the creation of settlements and territorial administration. Java has a number of different traditions when the time is constructed as a single linear progress that accumulated along the path of development that flows constantly and could not return. Not always precede the beginning of the end, as the array-array mystical song tells "(puppets performing) is over even though he (the mastermind) had not yet started (wus wisan Durung mucuki) '. (Zoetmulder, 1991:288).Compared to Bali, Java, more open to the construct of linear time, as introduced by Islam and the West (Lombard, 1996, vol 2). There are specific directions on looping timeline, but sometimes the direction is not prominently displayed. The widespread use of sengkalan / kronogram which is the form of a series of words or figures (eg Semar or Togog) which can be interpreted as numeric that indicates the number of years is one marker of the desire to mark something in the time frame is moving forward but at the same reluctance to explicitly show that year, so can easily be sorted and counted another track that has been pursued.
Spatial formulation is present in one complete set. Becker defines the spatial formula-based three-in puppet stage: scenes of the great assembly hall meeting at the beginning, a scene in nature in the middle and at the end of the war. Although persistent dramaturgical structure is very flexible to divide and develop the play. We find a similar formulation of the completeness of the petungan, the calculation method used to formulate the Java numeric aspects of a space, in particular domestic space. Way that is also used to formulate this time based on the completeness of a set of elements are repeated. Although the results of the dimensions of building elements, petungan not result in the proportion and scale of particular space that can be felt. As stated na cyclical calendar system, petungan show what kind of space (and not the space for what is) right. The concern is the welfare of this counting system which emitted a space and suitability for a particular designation. In determining the size of the building elements, petungan using a physical size of the building owners such as foot, span, cubit and fathom. The use of physical force shows that the space is basically the extension being the owner. Character of a number of size can be mathematically formulated into 5x + n with multiplier x is any number and n is a constant determinant of the character. Characteristics of the space formed as defined in the constant n is more concerned with the suitability for a space to pass judgment on the character of the positive / negative. There is no number n is so good that is suitable for all purposes and vice versa should always be avoided. Number n = 1, which is symbolized as the most prosperous Sri-were only intended for residents living behind the house even though these numbers have all the characteristics of the superior division of the kingdom of Mataram have become two of the mid-18th century, which divided the two kings is a count of the number of some scattered in various places so it does not form a unit area of the whole region bounded clear. Male authority in shaping the space and control the territories are represented in a symbolic phallus (male genitalia) who suggests a close relationship between power and fertility. Ilham Sultan Agung, third king of Mataram to the creator of Tarikh-Jawi, inspiration Pompilus King Numa and Julius Caesar as Pontifex Maximus as the creator of the Tarikh Ancient Rome, the inspiration of Pope Gregory VIII as 1582 AD Tarikh pendekrit correction, inspiration Kanjeng Sinuhun Paku Buwana VII in creating Pranotomongso Jawi, inspirational philosopher Confucius (Confucius) in creating the Tarikh Lunar and so on, certainly not inspired wantahan (vulgar). Era as a time for the system handles a variety of people, must have been created / decreed after the "inspiration" which is transcendental to nature "fourth dimension", as well as through the sophistication of accuracy or sophistication of thought and astronomic calculations and very macrocosm, and driven by "The energy radiation Doyo linuwih" (RPEDL) specific. Because, as is known in every model creation chronicle or the system calendar, always followed by various "supplements" details of the dimensionless 'astrofalakiah'. For example, the scope of our era, will be found in astrology, palmistry and others. In the Tarikh Lunar, then count the King of creation PATKWA falakiah ramalpenujuman Hi Hok (Fu Hsi) was already used since the 59th century. Then the "supplement" Tarikh Jawi, nor is it the complete game. Perhaps even the most complete. This can be see in many Primbon Jawi. In contrast to the level of epistemology and ontology in the creation of system Tarikh dimension, the dimension of the creation of "supplements" this would seem more mysterious, and even dis-dis-epistemologik ontologik. We take the example for instance in the "supplement" Tarikh Jawi. MARKET DAY and recycling element within Primbon Jawi has given index or so-called valence NEPTU. Thus each individual and each DAY MARKET been given by the valence-specific valence 'legend'. Although there has been rationalization of the calculation of reference formulation ketemunya NEPTU legend, but apparently not as scholarly as legitimatif never Cultural Aspects in Java Patterns of Domestic and Public Architecture 23 occurred among the experts Tarikh appreciation for menjumbuhkan Jawi (adjust) epistemoloi and ontology descriptions in " legitimate ". Valence-valence SAPTOWORO on the cycle, ie day Dite = Sunday, neptu = 5; Soma = Monday, neptu 4; Anggoro = Tuesday, 3 neptu; Buda = Wednesday, neptu 7; Respati = Thursday, neptu 8; Sukra = Jum " at, neptu Tumpak = 6 and Saturday, neptu 9. At MARKET, which belong to the group PONCOWORO cycle, then each was largely a valence: POND = 8; Legi = 5; Pahing = 9, Pon = 7 and Wage = 4. Contemplation or combined cycle between the PONCOWORO SAPTOWORO met (her "crush") in Selapaan cycle = 35 days, which means a repeat of the same again MARKET DAY and it, like 35 days ago. Another sophistication of the system's creation Tarikh Jawi Agug Hanyokrokusumo Sultan, among others, is to dilengkapinya various elements of the parameters of the cycle. Perhaps this is caused by "inspiration-calculation" certain, so that various levels of this dauran siklusitas interconnected with other cycle (ie at the time of Mash Windon). As we know, in every single tiger or 8-year-Jawi, all siklusitas cycle, the cycle Windu, YEAR, MONTH, DAY and MARKET, would return the same as before. Only Khurufan cycle are not repeated, because the distance daurnya reach 120 years old. Sengkalan or Sangkala to show time. The definite article the, or used for personification of something, namely kalaatau time.So to show the time or in the event.For example, "Hand Yakso Satataning Jalmo ', which is sengkalan for Cakil Buto, which means that Buto Cakil have two hands like a human. Sengkalan made puppet shows in Cakil Buto, the year 1552 Saka or 1630 AD. "Sanga Cudda Candrama Horse ', which indicates the year written by a professor KitabBharata Yudha Panuluh in the year 1079 Saka or 1641 AD. Support the Buwana stage is also derived from the letters sengkalan pa-murda = 8; song, empty, suwung = 0; letter gamurda = 7; Buwana = 1, then Stage Support the Buwana built in Saka 1708, or 1782 AD. Sengkalan was also found to Support the Stage punck Buwana called "Naga Janma Tinitihan Muluk '. That is, the dragon = 8; grandiose = 0; titihan = 7; janma = 1. 1708 also means that a warning was founded by Sampeyan Dalem stage Ingkang Sinuhun Paku Buwana III.Persatuan two words into one new word, a new form, for example garwadan sigaraning words - life or soul mates, cups and katakata nancang-thought, or binding thoughts, tales of the words dipaido - ora mengeng, or blamed - disputed - was not going to grumble. (Boediono, 2008; 138-139, Tiknopranoto, ...: 76). pancawara (Pahing, Pon, Wage, POND, Legi) come into play. In the chronicle of Java, there is a distinction in the name of each, namely: Alip, Ehe, Jimawal, Je, Dal, Be, Wawu, Jimakir. Cycle or cycle from year to year Alip Alip for eight years called the next eight years. Eight years of the original understanding was ten years old, because it means tiger ten. Associated with the entry of the day pancawara kurupyang accommodate the coupling of the chronicle saptawara used in Java, can be explained as follows: Taking into account the leap year (Wuntu years), eight years of age 2835 days. That number is divisible by 35. Number 35 is the multiplication 7 (number of days saptawara) and 5 (the number of days pancawara). Therefore, each dated one month the first year Alip, saptawara and falls on the same day pancawara. First noted that the beginning of the year falls on Java Jum "at Legi. Of course as a new era, the first year is the year of Alip. So-called kurup Awahgi kurupnya, as an abbreviation of Alip-JumuwahLegi. In AH quruf course quruf Jam'iyah name. In fact Java has changed kurup chronicle before reaching 128 years old. Kurup Awahgi only 120 years old, later replaced by kurup Amiswon, short-POND Alip-Thursday, which is only 72 years old. Then replaced again with kurup Aboge, short-Rebo Alip-Wage, lasted for 120 years. The latter is kurup Asapon, short-Tuesday-Alip Pon.Penambahan Wuntu one day in the year (leap) in the Great, which is twelve months, together with the chronicle AH. Normal year (not leap) year Wastu called. The placement of a leap year berbedaialah (wuntu). In a leap year chronicle of Java (wuntu) located in the 2 (Ehe), year 5 (Je) and year 8 (Jimakir). With a leap year which is located in the 8 (Jimakir), then the cycle or the cycle of leap years, which in the Hijri era lasted 30 years, in the chronicle of Java to 32 years, or 4 tiger. Fourth year of tiger dalam32 has its own name:A. The first is called Adi tiger tiger;2. The second is called windu windu Kuntara;3. Windu to the three so-called tiger Sangara,4. The fourth is called tiger tiger Sancaya.Ethnomathematics a mathematical mindset that grow and develop in a particular culture. Through mathematical mindset, the culture was able to understand and find solutions for problems encountered in each activity. Builder is one of the cultural groups who use mathematics in their daily work, although they are not aware of it. From the observations, obtained several examples ethnomathematics growing and developing the culture of building workers in Bali, namely:
(1) use pythagoras’s theorem to make right angle (2) the concept of a circle in a circular (3) use the concept of diagonal rectangle in determining the center of point (4) use the concept of the field geometry,(5) use the concept of comparison in determining the gradient and high tugeh,(6) use the concept of reflection symmetry in the folding and making ornaments of the building.
Builders on average do not learn mathematics through formal channels, to get these concepts rather than mathematical school. They get it from experience and association with fellow seprofesinya. This suggests that the "content" and "spirit" of mathematics exist everywhere, including in a specific cultural groups such as the builder. Learning mathematics can benefit from these ethnomathematics, primarily as a source of learning mathematics. In addition to improving students' motivation and confidence in learning, the use of the culture of learning can also have relationship between mathematical concepts learned to real world situations of students. So that the student learning more meaningful.
Reference
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