New Paradigm of Mathematics

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Mathematics is a important thing in the world. Definition of mathematics has been given by mathematics expert. Definition of mathematics also very large. Mathematics definition is build as a system that is developed  in a formal form. Formal mathematics is a mathematics that is tought by theacher or lecture, for example mathematics in university and mathematics in school.
 In university, student learn about pure mathematics. Student must prove the formula with axiomas. So, pure mathematics is called axioma mathematics. Here, the material of pure mathematics is to explain mathematics self. It can be called that mathematics is just for mathematics. Students in university is old people. They have good logic. Because of it, they learn mathematics to find where the formula come or to prove the formula.
In the othe hand, there is mathematics school. The matematics school is begin from elementary school until senior high school. Mathematics school is different with mathematics university. In school, students learn aplication of mathematics. Commonly, the students that learn in school is young student. They don’t have enough logic to prove the formula. So, they don’t need to prove the formula.
The problem is about mathematics communication. Theacher must use different way to communicate mathematics in school and in university. Because the sdudent in university is different with the student in school, so he or she must know the condition and psikology of the student. The school student is younger than the university student. Mathematics in university is for chosen people (like mathematics). But mathematics in school is for children, they need friendly mathematics (psikology of children). So, the theacher  adapted herself or hisself  with her or his student to communicate the mathematics material. If the teacher can’t adapted herself or hiseslef with the student, she or he will ignore by the student.
The nature of mathematics (Edward) are:
1.      Mathematics is pattern and relationship
2.      Mathematics is problem solving activity
3.      Mathematics is investigation activity
4.      Mathematics is a main of communication.
There is also addition about the nature of student learn mathematics
1.      Student will learn methematics efectivly if they have good motivation and apreciation
2.      Student will lern mathematics individually
3.      Student can learn mathematics in collaboration with others
4.      Student learn mathematics contextually
After we know the nature of student learn mathematics, we as candidate of theacher must find the good way to teach the student efectivly.
The implication of the nature of the student learn mathematics is the teacher need teaching paradigm. There are two branch of paradigm. The first is old paradigm. The old paradigm of theaching consider the student as empty vesel. The second is new paradigm. It is the contrast of the old paradigm. The students in new paradigm is a seed. If they are given opportunity, then they will grow up and finnally they will get a result.
Today, there is changing paradigm of teaching from old paradigm to new paradigm. So, the teacher use transfer method of  knowledge or ‘give and direct’ to learners . The teacher always give the material to the student and the student always accept the material.  The students never active, they are passive student. The absolute, necessary, and sufficient requirement for teachers in this context is complete mastery of the content. The classic classroom is the teacher lecturing and students listening. The students are silent, passive, and in competition with each other.
The new paradigm of teaching is based on the theory and research that have clear applications to instruction. In the new paradigm of teaching, knowledge is actively constructed, discovered, transformed, and extended by students. The teacher’s effort is aimed at developing students’ competencies and talents; education is a personal transaction among students and between teacher and students as they work together. (Johnson, Johnson, & Holubec, 1998).
There are main point of both paradigm as follow:
The old paradigm of teaching
·         transferring knowledge from teacher to student
·         filling passive empty vessels with knowledge
·         classifying students by deciding who gets which grade and sorting students into categories
·         conducting education within a context of impersonal relationships among students and between teachers and students
·         maintaining a competitive organizational structure
·         assuming that anyone with expertise in their field can teach without training to do so
The new paradigm of teaching
·         knowledge is constructed, discovered, transformed, and extended by students
·         students actively construct their own knowledge
·         teacher effort is aimed at developing students’ competencies and talents
·         education is a personal transaction among students and between teachers and students as they work together
·         all of the above can only take place within a cooperative context
·         teaching is assumed to be a complex application of theory and research
·         that requires considerable teacher training and continuous refinement of skills and procedures (Johnson, Johnson, & Holubec, 1998).

Comparisons of old and new paradigms of teaching
Factor
Old paradigm of teaching
New paradigm of teaching
Knowledge
Transferred from faculty to students
Jointly constructed by students and faculty
Students
Passive vessel to be filled by faculty’s knowledge
Active constructor, discoverer, transformer of own knowledge
Faculty purpose
Classify and sort students
Develop students’ competencies and talents
Relationships
Impersonal relationships among students and between faculty and students
Personal transactions among students and between faculty and students
Context
Competitive/individualistic
Cooperative learning in cla ssroom and cooperative teams among faculty
Assumption
Any expert can teach
Teaching is complex and requires considerable training

Source: http://www.intime.uni.edu/coop_learning/ch9/default.htm

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