To be able to civilizing the mathematics to achieve excellence of nation is required comprehention about the meaning of mathematics in various dimensions. Materially, mathematics can be concrete objects, pictures or models kunus, colorful symbol of big numbers or small, and so on. In formally mathematics be able form of pure mathematics, mathematical axiomatic, formal mathematics or mathematics deductively defined. Normatively, the objects of mathematics in the form of meaning contained in the formal objects. The Meanings expressed by the mathematical material and the formal mathematics that will then produce value of mathematics. In metaphysics, mathematics showed various levels of meaning and value dimensions that can only be achieved by metacognition. Pragmatically, we can explain that mathematics is the set of truth values consisting of the theorems and proofs. Mathematical acculturation is an implication of awareness of the importance of reflection activities through the study of mathematics and mathematics education in various dimensions. Thus the mathematical acculturation implies how far we are able to perform activities in a range of intentions, attitude knowledge, skills and experience of mathematics, mathematics education and mathematics learning. Explicitly civilize mathematics based on:
1. Knowledge of mathematics in various dimensions, including the nature, justification, and events.
2. Mathematical objects in various dimensions which include the nature and and its parentage.
3. The use of formal mathematics, including its effectiveness in science, technology, and other sciences.
4. Practices of mathematics in various its dimensions in generally including the activities of mathematicians or activities of mathematics from elementary school students.
Hartman (1942) patternize that anything about the object of thought, including mathematics, always has a value includes 4 (four) things: value because of its meaning, value because of its benefit of purpose, value because of its function and value because of its uniqueness. Civilize math in school have an comprehension aspects of the nature of school mathematics, the essence of mathematics education, the essence of the value of mathematics, the essence of studying mathematics, the nature of mathematics teaching and learning process, the nature of the acculturation of school mathematics. Based on various views about mathematics and how to learn it is expressed by the ethnic group of social constructivisist and the ethnic group of absolutist with their opinion and studying, thus the essence of learning mathematics is meet a subjective and objective mathematical knowledge through social interactions to test and represent the new knowledges.
To get and learn mathematics objective, students needs to develop procedures for example: follow the steps made by others person, making an informal step, determining the initial step, using the steps that have been developed, defining the steps that can be understood other people, comparing the various steps, and adjusting step. Through these steps, it is expected students will acquire mathematical concepts that have been actualized in him, so it can be said that the characteristic of mathematics is subjective. Social interaction is occur between students and teachers can provide criticism for the rectification of the concepts, so the students will get improvement concepts. Acculturation of mathematics can contribute to the nation through innovation excellence of learning mathematics that is done continuously.
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