Mathematics is the mother of science, so it is studied and applied by all of the lesson. All of the people also studied it, from the younger people until the older people. Every level of schools studies about it, since entering elementary school, junior high school, senior high school, until university. After we graduate from university, we still need mathematics. We cannot escape from mathematics because mathematics is so important to be study.
So what the teachers need to teach their student? They need the paradigm of teaching
Let’s start with the question about the nature mathematics! First, we must know about the nature of mathematics. What is it? Start with the meaning of mathematics. The mathematician can define the meaning of mathematics through the history. Philosophers define mathematics to the simple mathematics and prove it, and it builds systematically as the system that develops as formal mathematics. Mathematics for university consists of system, axiom, definition, n making theorem. Moreover, the nature of mathematics is how to make someone not bore with it and it can plant mathematics for mathematics.
Many problem that showed for us as the teacher, the problem is how to develop or to build communication with the students. Mathematics for the younger student and older student is different. Younger student think about something concrete and the older people think about something abstract. It is so different between mathematics in university and mathematics in school. In university, they learn about something abstract and it developed with the axiom and a lot of proof. In contrast to mathematics in school, they learn not to prove, they learn about something concrete, daily objects, and example.
The other problem is if we are a teacher and we must teach about mathematics, we need to adapt or to know the psychology of our student. As a teacher, we must adapt the student’s world. This is some example why we must know the student’s world, if parent say like child, so it’s caused the parent want to understand the children’s world, or the designers must know about girl’s fashion to know the girl’s world so they can design some thing that girl like. If the teachers cannot adapt, they will be avoided.
According to Ebutt and Straker (1995), teachers do not use axiomatic mathematics definition, but they must use mathematics as school mathematics. With this definition, the student will like mathematics. The following is the nature of School Mathematics by Ebutt and Straker :
1. Mathematics is a search of pattern or relationship
In this point, the student should be motivated to determine their pattern or relationship between in material to the other material. Therefore, the students have a freedom to determine their own pattern or relationship with their method. In the last, the student will be more understanding with the teacher’s explanation.
2. Mathematics is problem solving activity
What is the goal learn mathematics? The goal of learning mathematics is to find the solution of each problem. As we know that mathematics happen in daily life situation, inevitably and in real life situation, pencil and paper do not always come in handy. So learning must be meaningful, so number should be make useful and sense. But remember when the students solve the problem, they have another way to solve it. So these activities is useful to develop the student’s thinking.
3. Mathematics is investigation activity
What do you think about mathematics as investigating activity? It means that to solve the problem of mathematics, we must investigate it. When investigating it, the students have many ways to solve the problems. They use their pattern or relationship that it depends of their understanding about the material. So this activity will develop the student’s creativity, so many ways that they can use. These activity can make the student think that mathematics is so easy and not rigid or limited with one ways, but mathematics can be solve with many ways.
4. Mathematics is learning of communications
Mathematics as learning of communications works to:
- Encourage students to make examples of the nature of mathematics
- Encourage students to explain the nature of mathematics
- Encourage students to justify the need for mathematics
- Encourage students to discuss mathematical problem
- Encourage students to read and write mathematics
According to the nature of school mathematics in above, teacher must know about the nature of student learn mathematics. So what is it?
1. Mathematics students learn effectively is by good motivation and perception
How can the student get a good motivation and perception? It depends of the teaching method. The teacher must inspire, challenge and stimulate the students by the teaching method. However, we must know the psychology of our student because students have different character so the teacher must different way to be motivated each students.
To encourage students to become self-motivated independent learners, the teacher can do the following:
- Give frequent, early, positive feedback that supports students' beliefs that they can do well.
- Ensure opportunities for students' success by assigning tasks that are neither too easy nor too difficult.
- Help students find personal meaning and value in the material.
- Create an atmosphere that is open and positive.
- Help students feel that they are valued members of a learning community.
2. Students learn mathematics individually
Students examine their own mathematics. He studied according to his understanding. Sometimes he is abstracting events in everyday life into the concept of mathematics. Every student has different ways of learning mathematics. It can be seeing directly when the students solve with a case of mathematics. It will be looked different way of solving the problems between students with the other students. This is not blame for mathematics is essentially investigative activity.
3. Students learn mathematics in collaboration with the other
Learning mathematics with the other can make us more expected to understand math. In-group, the students can exchange their ideas and if they have some problem, they can solve it together.
4. Students learn mathematics contextually that bound by space and time
Students will be better understand math if teachers pass them contextually. Young student learn about something concrete and daily living that close to them. With the experience, they develop their ability to understand abstract concept, axiom, prove, reason logically, manipulate symbol and generalize. Teacher can give the example that close to daily live so the student know the application of mathematics in daily live not only just calculate the formula.
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
Constructivism : constructing meaning and making sense of numbers
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
The differences between the old paradign and the new paradigm is like the table below
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 classroom and cooperative teams among faculty |
Assumption | Any expert can teach | Teaching is complex and requires considerable training |
With the differences, we can know that the new paradigm is more effective that the old paradigm, so what do you think again. Let's to use the new paradigm.....
References :
