Mathematics was stretch along the history. Mathematics begins from practical definition until proof then built systematically. Mathematics that was built systematically then developed to be formally system. The formally system is learned by students of university. They learn about definition, axiom, proving, and soon. Mathematics that learned by students of university called pure mathematics and mathematics that learned by young students called school mathematics.
Mathematics that taught on young students is different with mathematics that taught in university. As candidates of teachers, we should communicate mathematics to young students well. We cannot teach the students with pure mathematics because they cannot accept it. The objects of study are different. When we at school, we need mathematics that good, friendly and suitable with the children’s world. First, we have to understand about the aspect of children education.
Ebbut and Strarke (1995) give definition about school mathematics, that are:
1. mathematics is search for pattern and relationship,
· it’s mean that school mathematics give students the opportunity to discovery and investigation to determine patterns of relationships,
2. mathematics is investigation activity,
· encourage the initiative and provide an opportunity to think differently,
3. mathematics is problem solving activity,
· provide an environment that stimulates learning math mathematical problem. Help students solve mathematical problem using his own ways and find information which is needed to solve mathematical problems. It’s can develop the ability and skills to solve problems.
4. mathematics is mean communication
· Encourage students to recognize the nature mathematics, make examples of the nature of mathematics, explain the nature of mathematics, to justify the need for math activities, read and write mathematics.
The natures of students learn mathematics will be effective if students have:
1. motivation from themselves,
2. students able to collaboration,
3. student able to learn mathematics individually, and
4. students able to learn mathematics contextually.
There are two types of mathematical paradigm. They are old paradigm or called traditional paradigm and new paradigm or called constructivism paradigm. The teachers have to teach the paradigm of teaching. In the past, teachers taught the students with traditional paradigm. This paradigm puts students as empty vessel. It is use method transfer of knowledge or gives and direct. The student cannot explorer their ability because the teachers just give the lesson and not let the students to explorer the lesson by themselves. It makes students become passive. The students inclined to follow their teachers. Of course it’s not make progression for the students. So that, this paradigm now not used by teachers.
Now, almost teachers use the new paradigm or constructivism paradigm. What is meant of constructivism? The term refers to the idea that learners construct knowledge for themselves as he or she learns. Constructing means is learning, there is no other kind. In this paradigm, the students are like seeds. If they were given by opportunity, they will grow and grow. So, at the time they will be bearing fruits. On this paradigm, teachers just become facilitators. The students should be active than before. Students can explore their ability in the lesson. First, students have to solve the problems of mathematics by themselves, and the truth is subjective. Then they will ask it to the teachers. The teachers will give explanation about the problems, and then they get objective answer.
Besides that, teachers should develop technology. Technology is very helpful to teach the students. In recent years, the technology is precociously. Teachers should follow it. So, teachers can teach the students well.
References
http://www.exploratorium.edu/IFI/resources/constructivistlearning.html
http://marsigitpsiko.blogspot.com/2008/12/hakekat-matematika-sekolah-dan-siswa.html
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