my assignment

PREFACE
Our gratitude is pronounced presence of Allah SWT because of His blessings and guidance I was able to complete the task of this group in the form of papers and can be presented at the Mathematics Learning Strategies course. In this paper we discuss about the constructivist approach.
A discussion of this material actually requires a long description. However, because of our limitations and so forth, then the discussion we may still relatively simple. We feel that a lot of shortcomings in the task of making this paper. For that we expect criticism and constructive suggestions from readers.
Further, I would like to thank those who helped us in solving this task, so this job is completed and ready for presentation.
Hopefully this paper can provide benefits to us and also to the reader.













TABLE OF CONTENTS

PREFACE ................................................ ..............................................
TABLE OF CONTENTS ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..
CHAPTER I. INTRODUCTION
1.1. Background
1.2. Limitation Problem
1.3. Goal Writing
1.4. Methods of Writing
CHAPTER II. DISCUSSION
2.1.Definition of Constructivism ... ... ... ... ... ... ... ... ... ... ............
2.2.Characteristics of Constructivist Approach ... ... ... ... ... ... ... ... ... ... ... ... ....
2.3. Constructivism in Mathematics Education approach ... ..
2.4. Study Mathematic according constructivism
2.5. Constructivism in Mathematics learning
2.6.Implementation in learning Mathematic
2.7.Constructivism in Mathematic learning Evaluation
2.8.Posision of constructivist in another approach
CHAPTER III. CLOSING
2.1. Conclusion ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
2.2. Suggestions ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..
REFERENCES ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

CHAPTER I
INTRODUCTION
A. Background
When people would do something, then that person should set goals to be achieved. To achieve that goal one chooses the right approach in order to obtain optimal results, effective and efficient.
Though it has been stated by Nisbet (1985) that there is no true way of learning, and The best way of teaching, because every people differ in their intellectual abilities, attitudes, and personality so that they adopt approaches to study different characteristics.
From this we can state that unlicensed individuals to choose the manner and style of his own to teach, but at least there are certain characteristics in a particular learning approach yng typical compared with other approaches. One example of an existing approach that is konstrukrtivisme approach.
In this constructivist approach to the role of teachers as mentors and teaching in the learning activities. Therefore, teachers prefer the liveliness of sisiwa untu channel new ideas that fit with the material presented to enhance students' skills in private.
B. Limitation Problem
In the discussion of this paper, the authors limit the issues to be discussed, including:
1.Understanding constructivism
2. The characteristics of constructivism approach
3. Constructivist approach
C. Goal Writing
The purpose of writing this paper is to:
1. Increase the knowledge of readers about constructivism approach in learning mathematics, which is one approach to learning mathematics.
2. Understand and can apply the constructivist approach.
3. To fulfill the task of Mathematics Learning Strategies course.
D. Writing Methods
In writing this paper the authors use the methods of literature study.




















CHAPTER II
DISCUSSION
A. Definition of Constructivism
Constructivism is learning to be generative, ie act of creating something of meaning from what is learned. Constructivism is not a new idea of what passed in our lives as long as it is set and the coaching experience by experience. This causes a person has knowledge and become more dynamic.
Constructivism states that knowledge will be arranged and woke up in the mind of his own students when he tried to organize his new experience based on an existing cognitive framework in mind. Thus knowledge can not be moved away from the brain degan someone
teacher students. Each student must build knowledge in his brain own.
Constructivist approach is an approach to the learning process where students are active in seeking knowledge. Constructivist approach is radically different from the traditional approach where the teacher is someone who always follow the answer.
In constructivist class students who are empowered by their knowledge of themselves. They shared strategies, and its completion with a debate between one another, to think critically about best way to resolve a problem.
Some general concepts of constructivism approach,are:
a. Students actively build knowledge based on existing experience.
b. In a learning context, students should develop their own knowledge.
c. Provided teaching materials need to have regard to the experience of students to attract students.
d. The importance of fostering knowledge actively by the students themselves through a process of mutual influence between the previous learning with new learning.
e. Imbalance is the main factor of learning motivation.
f.The most important element in this theory is that someone is actively developing her knowledge by comparing new information with existing understanding.
Based on his understanding of constructivism Piaget, Kamii (1989.1994) has demonstrated how primary school students can find their own procedures in solving multidigit problems in integers. So from this discovery means that when students are not taught algorithms such as carrying and borrowing their knowledge of number and value of place is far superior than students who were taught atoran algorithm.
Werrington and Kamii extend this work in classes 5 and 6 primary schools and describe a learning approach by using fractional division without teaching algorithm of multiplying and dividing. In this classroom teachers do not teach the child how to resolve the issue, but presented the problem and encourage students to find their own way of solving problems. When students give answers, the teacher does not directly justify or condemn the students' answers, but she encourages students to exchange thoughts or ideas until agreement is reached.
B.Characteristics of Constructivist Approach
As for the characteristics of constructivist approach are:
a. With the approach of constructivism, the development of knowledge for learners can be done by students themselves through research or direct observation so that students can deliver new ideas conformed to the experience by discovering the fact that according to the study of theory.
b.Between knowledge-knowledge that exist, there must be linkages with the existing experience on the student.
c. Each student has an important role in determining what they learn.
d. The role of teachers as mentors by providing material or concept of what will be learned and provide opportunities for students to menalisis accordance with the material being studied.




C. Constructivism in Mathematics Education Approach
Learning math is not a process of packing carefully knowledge, but about organizing an event, where this activity is widely interpreted to include activities and thinking konteptual (Cobb, 1991)
The essence of learning math by learning theory of constructivism
According to the constructivist theory of learning students must learn to be mentally active to build the structure of knowledge based on cognitive maturity he has.
In other words, students are not expected as the small bottles that are ready to be filled with a variety of science according to the will of teachers.
Relative to the above, Tasker (1992:3) suggested three emphasis in learning theory of constructivism, namely:
1. Student's active role in constructing knowledge significantly.
2.The importance of making links between ideas in the construction significantly.
3. Connections between ideas premises of new information received.
Wheatley (1991:12) supports the above opinion by asking two key principles of learning with constructivist learning theory, namely:
a.Knowledge can not be passively, but actively by the students' cognitive structures.
b.Cognitive function is adaptive and helps the organization through real experience possessed child.
Both the above understanding emphasizes how the importance of active involvement of children in the process of association of ideas and construction science through the environment.
Even specifically Hudoyo (1990:4) said that someone would be easier to learn something when the study was based on what is already known to others. Therefore, to study a new mathematical content, learning experiences that last from one will affect the process of learning these mathematic.
In addition to the emphasis and specific stages that need to be considered in learning theory of constructivism, Hanbury (1996:3) find a number of aspects in relation to learning mathematics, namely:
1.Students construct mathematical knowledge by integrating their own ideas.
2. Mathematics becomes more meaningful because students understand.
3.Strategies students more valuable.
4.Students have the opportunity to discuss and exchange experiences and knowledge with her friends.
In an attempt to implement constructivist learning theory Tytler (1996:20) proposed few sara related to learning design, as follows:
a.Provide opportunities for students to express his ideas with his own language.
b.Provide opportunities for students to think about his experience to become more creative and imaginative.
c. Provide opportunities for students to try new ideas.
d.Giving experiences related to the ideas that have been owned by students.
e.Encourage students to think about changing them.
f.Creating a conducive learning environment.
Some experts have been describing constructivist teaching and learning indicators based on Constructivism. Confrey (1991) states:
"... ... As a constructivist when I taught math, I do not teach students about the mathematical structure of the object is there in this world. I teach them, how to develop their cognition, how to see the world through a set of quantitative lens which I trust will provide a powerful way to understand the world, how it reflects the lens to create lenses that are stronger, da how to appreciate the role of lens in the play develop their culture.
I try to teach them to develop them to develop an intellectual tool that is mathematics. "
This reflects that the math is just all the tools to think, the main focus of mathematics learning is to empower students to think construct mathematical knowledge has ever been found by previous scholars.
D.Study Mathematic according constructivism.
1. Hudojo (in Hermayani, 2008) says that learning is an active process to develop schemata that related knowledge is like a gossamer and not just a hierarchically structured "Teachers play a role helping students find the facts, concepts, principles for themselves rather than give a talk or control all activities. " In relation to the learning of mathematics in high school, who must think student actively formulate concepts and take the meaning.

Nickson says that learning mathematics in the view of constructivism is to help build the learning of mathematics concepts, mathematical principles with their own abilities through a process of internalization that principle or concept and transform it woke up again and the information obtained into a new concept or principle.

According Hudojo (in Hermayani, 2008), there are three characteristics that must be raised in the process of learning mathematics in the view of constructivism are as follows:
1. Students must be actively involved in learning. Students learn mathematics in meaningful work and thinking;
2. New information must be included with the old information so that together with the schemata (cognitive structures) owned by the students;
3. Learning based on problem-solving orientation.

Constructivism Experts say that when students try to complete tasks in class, then the mathematical knowledge is actively constructed (wood and Cobb in Suherman, 2003). In addition, constructivism other experts also say that the constructivist perspective, learning mathematics is not a process of "packaging" knowledge carefully, but about organizing an event, where this activity is widely interpreted to include activities and conceptual thinking (Cobb in Suherman, 2003). Cobb also defines that learning mathematics is a process whereby students actively construct mathematical knowledge.

Constructivist Experts agree that learning mathematics involves active manipulation of meanings rather than just numbers and formulas alone. They refused to understand that mathematics is learned in a linear pattern collection. Each stage of learning involves a process of research on the meaning and delivery recitation skills in a way that there is no guarantee that students will use math skills in a setting the intelligent. In relation to learning, learning is seen as an active process and constructivist in which students try to solve problems that arise as they participate actively in the practice of mathematics in the classroom (Cobb in Suherman 2003)

Confrey (in Suherman, 2003), offers a powerful construction in mathematics. In constructing he identified ten characteristics of powerful construction student thinking. Powerful construction is characterized by:
1. A structure with the size of internal consistency.
2. An integration between the various concepts.
3. Convergence between the various forms and contexts.
4. The ability to reflect and explain.
5. A continuity of history.
6. Depend on kinds of symbol system.
7. A match thing with the experts opinion.
8. A potential to act as a tool for further contruction.
9. As a guide for the next action.
10. An ability to justify and defend it

All the powerful features of the above can be used effectively in the learning process in class. According Confrey (in Suherman, 2003), students who study mathematics are often just set up a criteria for their evaluation of their construction. As a result, knowledge of mathematics become isolated from the rest of their experiences that are constructed from their action in the world in a spontaneous and interactive patterns. Therefore, students' views about the 'truth' when students learn mathematics needs to get control experts and the public becomes incomplete. In this case the role of teachers and other students is to justify the role of student thinking in mathematics.

One of the fundamental in mathematics according to the constructivist learning is an approach with unexpected responsibilities previously with an astute interest in studying the character, authenticity, the story and its implications. View of constructivism in the learning process requires a shift from the role of teacher as an authority on science to the role of teachers as facilitators and mediators who are creative. Thus, here teachers are required constantly to explore in managing learning, packing material presented in textbooks in such a way that appeals to students and act as facilitator and mediator in a managed learning. One of the most important principle in psychology teacher education is not merely to provide knowledge to students but students must construct their own knowledge in his mind. In this process teachers can help in ways of teaching so that information becomes very meaningful and very relevant for students, by providing opportunities for students to discover or implement their own ideas, encouraging students to be aware of and consciously use their own strategies for learning. "Constructivist theory views students constantly checking new information against old rules and revise the rules if it does not fit anymore".

In addition, according to constructivists that substantively, learning mathematics is problem solving process. (Cobb, Thompson, and von Glaserfeld, in Suherman, 2003). Constructivism has focused exclusively on the process by which individual students actively construct their own mathematical realities. (Cobb et.al, in Suherman, 2003) ,
E. Constructivism in Mathematics learning.
In learning teachers not just provide knowledge to students. Students must construct their own knowledge in his mind. Teachers only help to make the information more meaningful and relevant for students by demonstrating the opportunity for students to use strategies they have to learn. Based on the results of Piaget's research (in Hermayani, 2008) concluded that the knowledge developed in the child. Piaget also says that knowledge is constructed as an effort to organize the learners' experiences with these schemes or cognitive structures that have been there before the children themselves. Furthermore, constructivist theory views students constantly checking new information against old rules and explore the rules if it does not fit anymore.

Some experts have been describing constructivist teaching and learning indicators based on constructivism. Confrey (in Suherman, 2003) states that:

... ... As a constructivist when I taught math, I do not teach students about the mathematical structure of the object is there in this world. I teach them, how to develop their cognition, how to see the world through a set of quantitative lens which I believe will provide a powerful way to understand the world, how it reflects the lens to create lenses that are stronger, and how to appreciate the role of the lens in the play development of their culture. I try to teach them to develop an intellectual tool that is mathematics.

This above is just reflecting that mathematics as a tool for thinking. Where the main focus of mathematics learning is to empower students to think construct mathematical knowledge has ever been found by previous experts.

Suparno states that knowledge construction process is characterized by, among others, as follows:
1. Learning means to form meaning. Meaning is created by students from what they see, hear, feel and experience. Construction in this case have been influenced by the notion that he had.
2. Construction knowledge is a continuous process. Every time dealing with a phenomenon or a new issue, held reconstruction, either strong or weak.
3. Learning is not the activities of collecting facts, but rather a development of thought with a load of new understanding. Learning is not the result of development, but the development itself, a development that requires the invention and the rearrangement of one's thoughts.
4. The learning process is actually happening at the time a person in doubt as scheme stimulate further thought. Situation of imbalance (disequilibrium) is a good situation to spur learning.

These characteristics provide a reference that in mathematics each student must construct his own knowledge and have their own way to understand and to know the peculiarity in him, including their advantages and disadvantages in understanding things. This means that students are actively thinking, formulating concepts, and take the meaning. The teacher's role here is to help make the construction process is run for students to form knowledge. Furthermore, Piaget (in Ratumannan, 2002) asserted that the human mind has a structure called schemata or cognitive structures. With this cognitive schemata or structures a person to adapt and coordinate their environment, forming new schemata, namely through the process of assimilation and accommodation. Assimilation is the absorption of new information in mind. While the accommodation is a rearrangement of the structure of the mind because of new information, so that information has a place, Reseffendy (in Ratumanan, 2002)

According to Davis (in Hermayani, 2008) view of constructivism in mathematics-oriented:
1. Knowledge is built in the mind through a process of assimilation or accommodation.
2. In mathematical work, each step learners faced with the "what".
3. New information associated with the experience of the world through a logical framework to transform, organize and interpret their experiences.
4. Center of learning is how learners think, not what they say or write. So that process of knowledge construction going on in the minds of their own students through the process of internalization.

In other words, if some information (knowledge) recently introduced to the students and knowledge in accordance with the cognitive structures that have been held, then the knowledge that will adapt through a process of assimilation and forming new knowledge. However if the new knowledge that was introduced was not in accordance with students' cognitive structure there will be an imbalance (disequilibrium), then the restructured cognitive structure will be adjusted to the new knowledge or a balance (equilibrium) (in Ratumanan, 2002)

Based on the above understanding, then according to the constructivist approach may mean that learning is an active process of meaning formation by the students themselves to new sensory input based on cognitive structures that have been previously owned.
F. Implementation of Constructivism in Learning Mathematic.
Mathematical concepts hierarchically structured, structured, logical and systematic way starting from the simplest concepts to the most complex concepts. In mathematics there is a topic or concept as a basic preconditions for further understanding the topic or concept. According to substantively constructivist, learning mathematics is problem solving process.
In this case the main focus of mathematics learning is to empower students to construct knowledge of mathematical thinking that has ever been found by previous experts. Evaluation in constructivist mathematics learning occurs during the learning process took place (on-going assessment).


G. Constructivism in Mathematic learning Evaluation
To describe the evaluation of learning, need to be clarified how the different between assessment and evaluation. According to Webb (1992) evaluation in education is a systematic investigation about the value or merit of a destination. Included in the evaluation is the collection of systematic evidence to help decision about:
1.student learning,
2.material development,
3.program.
Wood gives a general definition of assessment as follows:
Assessment is considered as providing a thorough consideration of an individual function in describing the broadest sense in a variety of qualitative and quantitative evidence and therefore up to the test of cognitive skills with paper-pencil techniques for a number of people.
Webb and Briass adds that:
Assessment in mathematics is the process of determining whether the student knows. It is a part of mathematics teaching activity, namely checking whether students understand, get feedback from students, then use this information to guide the development of their learning experience.
Although there is discrepancy between the evaluation and assessment is meant here is the way teachers assess (assess) student achievement study mathematics. Evaluation in constructivist approach to mathematics learning occurs throughout the learning process occurred (on-going assessment). From the beginning to the end of the teachers monitor student progress, students' understanding of a mathematical concept, help shape and oversee the construction of knowledge (mathematics) created by students.
H. Posision of constructivist in another approach.
According to Burton (1993) looked at the traditional view of mathematics as knowledge and skills that are strictly defined (a) learning through transmission, (b) learn in a manner that compliant (compliant), (c) assess students through using paper and pencil tests without the need visible. Constructivist view of learning reject the contrary made by the traditional view and put the responsibility to learn from teacher to pupil. Furthermore, Burton (1993) proposes that the responsibility of the teacher in the learning process is to:
 Stimulate and motivate students
 Provide experiences to foster understanding
 Diagnose and resolve student complaints
 Evaluate
Kamii (1990) adds that "the reality of children constructing their own knowledge of mathematical logic does not necessarily lead to that the role of teachers just sit and do nothing, otherwise the role of teacher to be no immediate and more difficult than the traditional classroom.
The purpose of constructivist approach can be formulated as follows:
A teacher of mathematics should promote and encourage the development of every individual in the classroom to reinforce the construction of mathematics, for submission of questions (posing), constructing, exploring, solving, and justification of mathematical problems and knsep-concept of mathematics. Teachers are also expected to try to strive to develop students' ability to reflect and evaluate the quality of their construction (the students).















CHAPTER III
CLOSING
3.1 CONCLUSION
 Constructivist approach is a learning process that explains how knowledge is constructed in the minds of learners. Knowledge is actively developed by the students themselves and not passively received from people around him.
 Constructivist view of learning mathematics is to help build the learning of mathematics concepts, mathematical principles with their own abilities through a process of internalization of that principle or concept and transform it awoke again and the information obtained into a new concept or principle.
 . According to the constructivist approach, learning is an active process of meaning formation by the students themselves to new sensory input based on cognitive structures that have been before owned
 Giving homework with constructivist approach, because it can provide a motivation for students to understand a concept as a whole through the work assignment with the conditions and situations that are not only stare to the classroom and the limited time in the learning process.
3.2 SUGGESTION
The advice can be given regarding the approach according to the Constructivism is the learning of mathematics in teacher learning can not merely provide knowledge to students. Students must construct their own knowledge in his mind.







REFERENCES
Suherman, Erman. 2003. Contemporary Mathematics Learning Strategies. New York: JICA
http://wikipedia.org
http://www.answers.com/topic/learning-theory-constructivist-approach
http://id.shvoong.com/sosial-sciences/education/1997674-pendekatan-pembelajaran-matematika-konstruktivis-dan/
http://onengdalilah.blogspot.com/2009/04/modelpembelajaranmatematika- dalam.html
http://techonly13.wordpress.com/2009/07/04/pembelajaran-matematika