Dosen Pengampu:
Prof. Marsigit, M.A (Yogyakarta State University)
Prof. Ruyu Hung, Ph.D (National Chiayi University)
Makalah Ilmiah tentang Ontologi, Epistemologi, dan aksioma Pendidikan Matematika Dasar
Yogi Ageng Sri Legowo (19706261008)
A. INTRODUCTION
The first sentence of Kant, which was enshrined by his pupil in "Pedagogia" in 1803 read
"El hombre es la única criatura que ha de ser educada."
which means that humans are the only creatures that must be educated. In this sentence Kant wants to explain that human nature is different from animals from the point of view of the ability and need for learning. Animals naturally have the instinct to survive from the moment they are born. Even though they need their mothers to feed them, their instincts in avoiding danger, for example when a baby is born birds have an instinct not to scream so that they do not become predatory food is a survival technique that is not taught and does not need to be taught by the mother. This is different from humans, to be a civilized human being, humans need other humans to wake him up. Thus the background of the emergence of Education which aims to civilize society.
Kant (1803) which states the discipline of changing animals into humans, and vice versa humans without discipline will be led by the animal's impulse (lust), the best way for humans to avoid this barbarism is to get accustomed from an early age to submit to the teachings of reason. Similar to the concept of Kant, Educating children to discipline in mathematics is from an early age, since he is sensible. So it is appropriate if mathematics is taught since a child is in elementary school age.
The problem then arises when students as subjects of learning feel afraid of the object of learning, namely mathematics learning. Yet according to Carl Friedrich Gauss, mathematics is the queen and at the same time a servant of knowledge. Analogy as a steward can mean that mathematics is the basis of other sciences so mastering it is a prerequisite for being able to study several other fields of science.
In this paper we will discuss about ontology, epistemology and axiology. Mathematics education in elementary schools and the study of the position of mathematics as a steward of science.
B. ONTOLOGICAL, EPISTEMOLOGY, AND ACTIONOLOGY
Before studying the nature of mathematics education in elementary schools based on ontology, epistemology, and axiology, it is best to first understand what ontology, epistemology and axiology are.
1. Ontology
Originally the word, ontology comes from the words "ontos" and "logos". Ontos has the meaning of a form while the meaning of logos means knowledge (Adib, 2011: 69). Whereas in Sosanto (2011: 91) states that ontology has the root word "on" the same as being, and "logos" is the same as logic. Which has a theoretical meaning about "being about being". So that it can be interpreted in a term that ontology is the science that discusses the nature that exists, which is reality, both physical / concrete, and spiritual / abstract.
2. Epistemology
Originally the word, Epistemology comes from the Greek from the word "epistem" which means knowledge or science. While "logos" which also means knowledge. Epistemology is a branch of philosophy that investigates the origin, structure, methods, and validity of knowledge. Epistemology is closely related to the source of knowledge and its method of acquisition.
The deepening of the problem in the epistemology approach is to answer the questions: (1) what is knowledge ?; (2) what is the source and basis of knowledge ?; (3) Is that knowledge the result of observation, experience, or reason? And (4) Is that knowledge a certain truth or is it only conjecture?
In epistemology, there are several theories of the validity of knowledge, namely:
a. Theory of Coherence of Validity. This theory says that a statement or proposition is valid if the proposition has a relationship with ideas and propositions that can also be logically proven in accordance with the provisions of logic.
b. Correspondence Validity Theory. This theory says that a knowledge is valid if the propositions are in accordance with the reality that is the object of knowledge. This validity is closely related to truth and sense certainty. So, the validity of knowledge can be proven directly.
c. Pragmatic Validity Theory. This theory says that a knowledge is valid if it has the consequences of the usefulness or is really useful for those who have that knowledge.
d. Semantic Validity Theory. This theory emphasizes the meaning and meaning of a proposition. Propositions must show meanings and meanings that refer to reality by pointing out tangible characteristics.
e. The theory of excessive logical validity. This theory says that a proposition that has different terms or terms but contains the same information does not need to be proven anymore, or it has become an excessive logical form. For example: a circle is a circle.
3. Axiology
Axiology comes from the Greek term namely: axios which means appropriate or reasonable and logos which means knowledge. Axiology is a branch of philosophy of science that talks about the purpose of science itself and how humans use it. Axiology is related to the usefulness of science. This is in accordance with the definition of axiology in the Big Indonesian Dictionary which means the use of science for human life; or study of values, especially ethics. Value itself is interpreted as something that is held in high esteem.
There are two basic axiological categories, namely (1) objectivism and (2) subjectivism. Both of them are branched into each of two ethical approaches, namely: (1) intuitive value theory, (2) rational value theory, (3) natural value theory and (4) emotive value theory (Hamdani, 2011: 24-25).
C. ONTOLOGY OF PRIMARY MATHEMATIC EDUCATION
Understanding the nature of Mathematics education in primary schools must begin first by understanding the nature of mathematics, and the nature of education in primary schools. This is important to do to form a comprehensive definition of the nature of mathematics education in elementary schools.
The Nature of Mathematics
The term mathematics comes from the Greek word "mathein" or "manthenein" which means "to learn". Ruseffendi defines mathematics as symbolic language, deductive science, the science of regular patterns, and organized structures, ranging from undefined elements, to defined elements, to axioms or postulates, and finally to the proposition.
Mathematics uses deductive thinking patterns in obtaining truth. This means that mathematical truths originate from previous truths and ultimately to undefined elements. With this mindset, mathematics is known as a way or method of thinking and reasoning. Mathematics is consistent, so mathematics can be used as a way of making decisions, namely through mathematical logic.
At the beginning of its development mathematics is a tool to solve the problems of the difficulties of everyday life through real natural objects in the surrounding environment. Then mathematics develops through abstraction and idealization into a science. What is built is more a social process than an individual process. This is because:
1. Individual thoughts about initial difficulties that arise will be formed by communication or conversation.
2. All individual thoughts are subsequently shaped by social thought.
3. Mental functions are collective (eg problem solving groups)
Therefore, it can be said that the whole process of thinking and learning is shaped by the social experiences experienced by each individual (Martin, 2009: 77).
The Nature of Education in Primary Schools
In understanding Education, we will use the philosophy of constructivism. In the philosophy of constructivism, learning is defined as the process of building students' knowledge through the process of assimilation and connecting experiences they have had. Suparno (1997: 61) characterizes the process as follows:
1. Learning means forming meaning.
2. Construction is defined as a continuous process.
3. Learning is not an activity of gathering facts, but developing thought.
4. The actual learning process takes place when a person's scheme is in doubt which stimulates further thinking.
5. Learning outcomes are influenced by students' experiences with the learning environment.
6. The results of one's learning depends on what students already know: in the form of concepts, goals and motivation.
This constructivism approach is very close to the concept of a mathematics learning process which is done in stages and is influenced by previous mathematical experience and knowledge.
Mathematics Education in Primary Schools
According to Wein (1973), mathematics education is a study of aspects about the basic properties and history of mathematics and the psychology of learning and teaching which will contribute to the understanding of teachers in their assignments with students, together study and analysis of school curricula, principles which underlies the development and practice of their use in the classroom.
Education in elementary schools based on Piaget's theory of learning enters the Concrete operation stage (7 - 12 years). At this stage the child begins to think rationally in the beginning. Children begin to have logical operations that can be applied in concrete problems. Dahar (2011: 138), operations in this period were related to personal experience. Children cannot use abstract operations, such as hypotheses and verbal propositions.
The mathematical operations that are able to be completed by children in stages: (1) Combinativity or classification, which is an operation that combines two or more classes into large groups. For example, all boys + all girls = all children. (2) Reversibility, i.e. any logical or mathematical operation can be negated by the opposite operation. For example, all children - all girls = all boys. (3) Association, operations that combine classes in any order. For example, (1 + 3) + 5 = 1 + (3 + 5). (4) Identity, i.e. an operation in which there is a zero element which when combined with any element or class does not produce change. For example 10 + 0 = 10. (5) Matching, which is to arrange a series of sequence objects, for example wooden toys or sticks according to the size of the object. The child can only do this activity as long as the problem is a concrete problem.
D. EPHEMOLOGICAL OF PRIMARY MATHEMATIC EDUCATION
According to Ernest, mathematics is knowledge that is built not found. Mathematics as a science is mathematics that is intact in its deductive axiomatic system or structure. This means that mathematical truth is obtained by using deductive reasoning and then a series of consistency truths are arranged that lead to the final conclusions (Soemoenar, et al., 2007: 1.19).
E. AXIOLOGICAL OF PRIMARY MATHEMATIC EDUCATION
Axiological review is related to the value and usefulness of mathematics education in elementary schools. The most basic value of mathematics education for elementary school students is its ability to train and teach intelligence. Through mathematics education students are taught to always be oriented towards solving problems through simplification of problems through the language of mathematics, students can have the ability of logic and make decisions correctly.
Besides the direct impact on students, knowing the characteristics of mathematics education and the characteristics of elementary school education of teachers will be more appropriate in choosing models, methods and approaches according to needs.
The shift in learning and learning paradigms that are now more appropriate using the constructivism approach have a major impact on the changing roles of students and teachers in the classroom. Students as subjects of learning play an active role in the classroom, while teachers as motivators, facilitators and mediators try to create a learning environment that is conducive to student learning.
F. CONCLUSIONS
Philosophy can not be separated from the scope of life, including in studying the field of mathematics education. Philosophy is needed by humans to answer questions that arise in various fields of human life. The answer is the result of thinking that is systematic, integral, comprehensive, and fundamental.
The philosophy of mathematics education includes three things, namely: the purpose and value of mathematics education, learning theory, teaching theory. The purpose of mathematics education should include social justice through the development of democratic thinking in critical mathematics. Students should develop the abilities they have to analyze mathematical problems.
Mathematics education is able to provide reinforcement to students, this means students think mathematics in everyday life and are able to use it as a practical application of mathematics. Strengthening students in mathematics education has three dimensions, namely (1) students have mathematical abilities, (2) students have the ability to use mathematics in daily life, and (3) students believe in their abilities.
REFERENCES
Adib, Mohammad. 2011. Filsafat Ilmu: Ontologi, Epistemologi, Aksiologi, dan Logika Ilmu Pengetahuan. Yogyakarta: Pustaka Pelajar.
Dahar, Ratna Wilis. 2011. Teori-teori Belajar & Pembelajaran. Jakarta: Erlangga.
Hamdani. 2011. Filsafat Sains. Bandung: Pustaka Setia
Martin, W. 2009. Paul Ernest's Social Constructivist Philosophy of Mathematics Education. Disertasi University of Illinois at Urbana Champaign.
Marsigit, Ilham R., & Mareta M. M.2014. Filsafat matematika. Yogyakarta: UNY press
Rink, F.T. 1803. Immanuel Kant. Pedagogia. www.philosophia.cl/ Escuela de Filosofía Universidad ARCIS.
Susanto A. 2011. Filsafat Ilmu: Suatu Kajian dalam Dimensi Ontologi, Epistemologis, dan Aksiologis. Jakarta: Bumi Aksara.
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