## Senin, 08 Desember 2008

### The Application of Problem Based Learning in Mathematics Learning

The Application of Problem Based Learning in Mathematics Learning

By: Wahyudi

A. Background

Mathematics is a base science that is used as an equipment to learn other sciences. Therefore, mastering toward mathematics is absolutely required.and the concepts have to be comprehended correctly and early. They are due to the mathematic concepts are a causality network. Where a concept is compiled based on a previous concepts, and will be a further base concept. Thereby the understanding of incorrect concept will cause at the fault in understanding of further concepts ( Antonius Cahya Prihandoko, 2006).
Mathematics studies an abstract structure and a guide relation in it. It means that mathematics learning intrinsically is a learning concept, structure concept and looks for the relationship between them (the concepts and structure). The characteristic of an axiomatic deductive mathematics must be known by teacher so that they can learn mathematics correctly, from the simple concepts to complex concepts.
Based on reality above, hence the correct mathematic learning is required in inculcating mathematics concepts in Elementary school. Where the purpose of mathematics learning in base education is to prepare the student in order to get ready to face the changes situation in life and in a world which always grow up through an action based on an logical, rational, stall, careful, honest, efficient, and effective thinking ( Puskur, 2002). Despitefully, the student is expected to be able to apply mathematics and mathematics thinking in daily life to learn a various sciences which emphasis at the settlement of natural existence and student behaviour foming and skill in applying mathematics .
According To Brissenden (1980:7) the Iesson of mathematics at student is followed by arrangement of activity by teacher and each study activity contains two fundamental characteristics. Firstly, explains which gambling, management type this teacher applies activity of accross the board class, either individually and also group of learning. Second, activity by compiling expansion rule of study stages;steps metematika. This thing can be done by depicting some topics in study. Initial step done by teacher is attention at expansion effort of mathematics with formation of concept and outline from the subject.
Relation between procedural and conceptual of vital importance. Conceptual knowledge referred to concept understanding, while procedural knowledge referred to skill to do an algorithm or procedure finalizes the problem of mathematicses. According To Sutawijaya ( 1997:177), comprehends just concept insufficient, because in practice everyday life of student requires mathematics skill.

One of way which can be done to execute the study is done by using study method appropriate. One of study method which can be applied is study with Problem Based Learning. Applying of method problem based learning is not only increases result of learning but also supplies educative participant empirically learning finalizes problem according to Iesson matter self-supportingly. Reason of using of Problem Based Learning is as follows:
1) To draw near the students at study of mathematics with development of
situation of real world.
2) Can assist the students to develop idea and skilled thought in stall to obtain
life efficiency ( life skill).
3) Places student as subject and study object.

Problem based learning designed to develop:
1. Ability integrates ( federating) knowledge owned, then bases special knowledge
context
2. Ability takes decision at the same time develops critical position and idea
3. Self-supporting ability to learn and heartens to learn along the life
4. Efficiency interpersonal, kolaborasi, and communications
5. construction of His own cognate structure and skillful evaluates
6. Behavior and ethics which professional

B. The Application of Problem Based Learning
Common characteristic is from Problem Based Learning namely problem as a beginning of study. The planning problem that is as an issue comes from the dilemmatic problem of the environment that is used to attract the learners’ enthusiasm. Problem must be adapted for base interest, matter, and learning result which wish to be reached.
According To Duch ( CUTSD 1997: 2) good problems can succeed study. Good problems planning is:
1)Some facts happened in real world in tidy in the form of problem map which can draw
student enthusiasm.
2)Chooses one of fact which many studied by mass media to become the root of the
matter at discussion a study.
3)Can motivate the students in compiling strong argument based on some information
and also reference which they obtain.
4)Can peep out position is each other cooperation between students to study and also
finalizes the problem.
5)Initial question presented at problem can become guide of all students to take role
in discussion. This question must: ( a) haves the character of open to various
knowledge areas and also comments; ( b) can be attributed to basic knowledges
before all and also all valueses various aspects as a form of contribution of
expansion of problem or solution; ( c) focused on issues which can invite debate or
unresolved completely.
6)Can motivate the students to involve in analytical and critical thinking process.
7)Every specific units from expansion of the root of the matter must can be reunited
to become form of understanding a study matter.

Educative participant before all has owned knowledge base, efficiency, trust, and concepts. When educative participant given on to problems of reality which dilematis hence they will pay attention to, organizes, interpretation, and gets information and also new knowledge. Applying of problem based learning in education assists pembelajar to connect things does they know, they need to reachs level of better idea ( better thinking).

( Teacher & Educational Development, University of New Mexico School of Medicine ( 2002: 3-4).
Beginning of applying activity of problem based learning namely makes preparation of problem based learning in mathematics study. According To Wood ( 1995: 5-120) preparation of problem based learning is:
1.Determines topic or study direct material.
2.Determines problems issues is real world [by]
3.Compiles desire list of educative participant to learn comfortably
4.Presentation design of problem to be able to guide educative participant
5.Determines allocation of time and study meeting schedule
6.Organizes group of learning
7.Learning resource design
8.Balmy learning area design to develop " Process Skill" educative participant.
9.Assessment format design of process and result of learning
Applying of problem based learning ( get started) started with:
1.Recognition of problem based learning at instructor
2.Specifies applying rule of the game of problem based learning. This research
applies interaction type between groups ( group interaction). educative Tutor and
participant cooperated develops study.
3.Specifies hope or purpose of applying of problem based learning to increase ability thinks is logical and positive position of student to mathematics.
After problem presented at educative participant, hence study takes place in process of tutorial. Teacher stands as tutor. One problems in debate by some groups. Tutor called as also instructor, moderator, fasilitator, or leader. Tutor comes from educator. Tutor responsible assists group of identifying performance mistake, digressing opinion, motivates member of group of communicating, and is each other evaluates result of job(activity step by step. Tutor prepares balmy space to process study ( Harsono, 2004: 26-29).

The role of tutor in process of problem based learning is:
1.Process controller
a.Acted as doorman and time custodian.
b.As officer without dropping sanction to educative participant.
c.Interference if there is conflict among educative participant.
d.Pushs the happening of balmy situation that to execute of group dynamics.

2.Observer behavior of group
a.Pushs the happening of interaction of group, bravery, and approval.
b.Pushs educative participant to develop individual quality.
c.Assists educative participant to involve ability and realizes their weakness.
d.Pushs educative participant as change agent in group
e.Acts as role model.
3.Problem billows
a.Pushs the happening of active participation, concentration of attention, and
discussion is more life.
b.Reexamines all result of discussion, returns question of educative participant to
be replied x'self by them, gives comment and suggestion, and stimulates to think
for example trying to develop hypothesis.
c.Pushs educative participant to study and defines again explanation of the, makes
relationship or concept bearing, process etcetera.
d.Pushs educative participant to analyse, makes synthesis and evaluation about
problem or data, and summarizes result of discussion.
e.Assists educative participant in the case of identification source and learning
matter. ( Harsono, 2004: 31-32)

Educative Teacher activity and participant in tutorial as follows:
1. Educative Participant Activity
a.Identifies knowledge and efficiency owned.
b.Identifies problem and digs relevant information source.
c.Investigates and interpretation of information which collected.
d.Learning self-supportingly ( self-directed learning) ( Harsono, 2004: 35-42)
e.Prioritizes some alternative of problem solutions.
f.Integrates, opinion to select solution of problem.
(Cindy L. Lynch, Susan K. Wolcott, and Gregory E Huber, 2001: 2-5)
g.reflection of X'self ( Teacher & Education Development, University of New Mexico School of Medicine, 2002: 26 & 29).
Educative participant activity ( a, b, c, e, and f) refers to " steps for better thinking: a developmental problem solving process" from Cindy L. Lynch, Susan K. Wolcott, and Gregory E Huber).

2. Teacher Activity as Tutor
a.Makes study centrally at educative participant.
b.Area design motivating educative participant to learn.
c.Leads the time and process tutorial.
d.Applies effective question.
e.Arranges group dynamics.
f.Provides constructive feedback.
(University of New Mexico School of Medicine, 2002: 1-35)
g.Evaluation result of educative participant learning at cognate domain

References

Don Woods (1997). Problem-based Learning, especially in the context of large classes. Matter is accessed on 14 Augusts 2008, from http://chemeng.mcmaster.ca/pbl/pbl.htm
Dairy Advisory Teams (1998). Problem Solving and Action Planning. Matter is accessed on 12 June 2008, from http://www.das.psu.edu/das/dairy/teams/problem-solving
Duch, B., Groh, S. and Allen, D. (2001). 'Why Problem-Based Learning?' in The Power of Problem-Based Learning, Duch, B., Groh, S. and Allen, D. (eds), Stylus, Virginia. Matter is accessed on 14 Augusts 2008, from http://www.paulhazel.com/docs/pbl.htm
Harsono. (2004). Pengantar Problem Based Learning. Yogyakarta: Fakultas Kedokteran UGM.
Lynch, Wolcott. (2001). Helping Your Students Develop Critical Thinking Skills. Matter is accessed on 15 Augusts 2008, from http://www.idea.ksu.edu/papers/Idea_Paper_37.pdf.
Teaching with Technology Initiative. (2002). Problem-Based Learning. Matter is accessed on 15 Augusts 2008, from http://twt/pbl/45/htm.