Sabtu, 24 Maret 2012

Realistic Mathematics Education (RME)


INTRODUCTION
Realistic Mathematics emphasizes the construction of the context objects as a starting point for students to acquire mathematical concepts. Concrete objects and objects of environment can be used as a context for learning mathematics in building mathematical connection through social interaction. According to Hans Freudental in Marsigit (2009) mathematics is human activities and should be linked to reality. Thus when students do activities to learn mathematics will occur itself a mathematical process.

CONTENT
The part of Realistic Mathematics Education, among others:
A.    Formal Mathematics
Formal mathematics is agreement in mathematics for use in the learning of mathematics. For example are mathematics symbol, theorems, axioms, formula, and understanding about mathematics.
Based on the book Mathematics for Junior High School grade 2 by Marsigit on page 173, a circle is a set of points that have the same distance to a fixed point. This fixed point is called the centre of circle.
The part of circle, among others:
1.      Centre of circle
The central point of the circle is given the symbol O.
2.      Radii
Radius is the distance between a point on the circle with the centre of circle.
3.      Diameter
Diameter is a line through the centre of the circle and connecting two points on a circle.
4.      Chord
Chord is a line segment that connecting two points on a circle.
5.      Apothem
Apothem is line segment drawn from the centre of circle and perpendicular to the chord.
6.      Sector
Sector is an area bounded by two radii and an arc.
7.      Segment
Segment is an area bounded by a chord and an arc.
8.      Minor arc
Minor arc is the arc that limited the minor sector and minor segment.
9.      Major arc
Major arc is the arc that limited the major sector and major segment.
10.  Minor Sector
Minor sector if its central angle size is less than 1800.
11.  Major Sector
Major sector if its central angle size is more than 1800.
12.  Minor Segment
13.  Major Segment

Circumference of a circle formula is: K = π.d = 2.π.r
With:
K = circumference of a circle
r = radius of the circle
d = diameter of the circle = 2r
π ≈ 3,14
Area of a circle formula is: L = π.r2 =  π.d2
With:
L = area of the circle
r = radius of the circle
d = diameter
π =  ≈ 3,14
B.     Formal Model of Mathematics
Formal Model of Mathematics is a mathematical model of the agreements in the learning of mathematics. Based on the book Mathematics for Junior High School grade 2 by Marsigit, example of formal model of mathematics is like the figure shown below.

Point O is called centre of circle
OR, OT, OP is called radii
TP is called diameter
TR is called chord
OI is called apothem
Area of TRO is called sector
Area of TRI is called segment




TR is called minor arc
TPR is called major arc


           
Source: Marsigit’s book page 173
Figure 1 The circle parts
C.     Concrete Model of Mathematics
Concrete Model of Mathematics is a concrete object that is a model of a topic in mathematics. Based on the book Mathematics for Junior High School grade 2 by Marsigit, example of concrete model of mathematics is like the figure shown below.
       
Source: Marsigit’s book page 173
Figure 2 Tyres and CDs are examples of circle shaped things

D.    Concrete Mathematics
Concrete Mathematics is a real form or the application of the mathematics concepts in everyday life. Based on the book Mathematics for Junior High School grade 2 by Marsigit, example of concrete mathematics is like the figure shown below.
Source: Marsigit’s book page 175
Figure 3 The distance you have passed when walking around the circle fountain is the circumference of a circle

CONCLUSION
The part of Realistic Mathematics Education is formal mathematics, formal model of mathematics, concrete model of mathematics, and concrete mathematics.

REFERENCE
Marsigit. 2009. Mathematics for Junior High School Grade 2. Yudhistira: Yogyakarta.

Marsigit. 2009. “Pemanfaatan Video Tape Recorder (VTR) untuk Pengembangan Matematika Realistik di SMP”. [Online]. Tersedia: http://staff.uny.ac.id. [3 Maret 2012].

Senin, 19 Maret 2012

Developing the Innovative Teaching Learning Process


INTRODUCTION
Mathematics is a subject that is considered part of students as subjects that are difficult to learn. Moreover, by students who are working right brain is more dominant in their daily activities. With this assumption, then the mathematics would be an obstacle in the learning process for most students. Mathematics subjects are not much liked by the students at the school. Most of the students in the school should feel afraid of the mathematic subjects. Therefore, the effort required teachers to be able to make the subjects of mathematics into subjects that are not scary but it is a subject of interest by students at the school.
Mathematics is a lesson that consists of the material count operations like addition, subtraction, multiplication, and division. Mathematics is considered as a hard lesson for students. However, this difficulty can be overcome with a lot of practice at home, with tutoring, and can’t be separated from a parent’s attention.

CONTENT
To develop innovative teaching learning process, it takes several steps, among others:
A.    Preparation
Preparation step include several things, such as:
1.      Curriculum
According to Marsigit, we perceive that curriculum development needs a comprehensive and in-depth study of all the aspects involved, there are at least six principles as a guide:
a.       The chance to learn mathematics for all
b.      Curriculum is not just a collection of subject matters but it should reflect mathematical activities coherently
c.       Teaching learning of mathematics need a comprehensive theory of students activities, their readiness to learn and teacher role of facilitating their learn
d.      The chance to the learner to develop their mathematical concepts
e.       The needs to develop assessment imbedded to teaching learning processes
f.       Employing many kinds of teaching learning sources
Curriculum includes:

a.       Standard competencies
b.      Basic competencies
c.       Objectives
d.      Indicator

2.      Approach / Design
Design of learning includes:
a.       Contextual learning
Is reality-based, outside-of-the-classroom experience, within a specific context which serves as a catalyst for students to utilize their disciplinary knowledge, and which presents a forum for further formation of their personal values, faith, and professional development.
b.      Constructivist
Is the theory that humans generate knowledge and meaning from an interaction between their experiences and their ideas. The Constructivist learning process is experiential learning through real life experience to construct and conditionalize knowledge.
c.       Realistic mathematics
Is a teaching and learning theory in mathematics education that characterized by: the use of contexts, the use of models, the use of students’ own productions and constructions, the interactive character of the teaching process, the intertwinement of various learning strands.
d.      Problem based learning
Is a student-centered pedagogy in which students learn about a subject in the context of complex, multifaceted, and realistic problems.
e.       Cooperative learning
Is an approach to organizing classroom activities into academic and social learning experiences.
3.      Method
Method of learning includes:
a.       Discussion
Is a method in which teachers act as mentors, helpers, appraisers, or discussion leader. In the discussion the students are required to always be actively participating. Students are trained to think critically, be ready with the right to express opinions, to think objectively, and respect others opinions.
b.      Inquiry
Is a method that centered on the students. With the inquiry method, students can acquire knowledge that is not yet know through direct notification by teachers, but students find themselves partially or completely the new knowledge.
c.       Practical work
Is a method in which students are required to do a lot of exercises to memorize and exercises practice. Exercise memorization is an activity that generally emphasizes mathematics fact. Exercise practice is an exercise of considering a number of steps in an activity to arrive at a correct answer. 
d.      Small group discussion
According to Marsigit, the group discussion is based on principles of promoting children’s growth and development through play activities which encourage children to explore, experiment, question, and talk. Teacher’s efforts to facilitate their students to find various patterns of numbers can be seen as consistent with extending the students’ experiences and encouraging social interaction between children. The small group discussion may be thought of as constituting a set of culturally organized activities provided by the teacher who tried to encourage children to communicate their concepts to the others.
4.      Teaching Materials
Teaching materials includes:
a.       Lesson plan
Lesson plan is a step that carried out the teacher where the teacher makes the planning process learning activities in the classroom. The purpose with the lesson plan is expected to be better prepared teachers in teaching, teachers have a reference in learning activities that will be implemented, teachers also can develop lesson plan that engage students so that students not only became a listener only, and thus students will have a role as well as being more actively in learning activities.
b.      Students’ worksheet
Student’s worksheet is one means to help and facilitate in the teaching and learning activities that will form an effective interaction between students and teachers, and can increase student’s activity in improving learning achievement. Student’s worksheet is one type of learning tool for students because the student’s worksheet will help the students to add information about the topic being studied and can increase student’s skill in independent learning.
c.       Hand Out
Hand out is the learning resources which are usually arranged by a teacher the subjects.
d.      Text Book
According to Marsigit, teachers’ competencies of developing textbooks, such as:

1)      Motivation
2)      Theory
3)      Attitude
4)      Practice
5)      Individual experiences
6)      Community experiences
7)      Systemic experiences

Novice taechers’ perception on good textbook for mathematics, such as:
1)      The textbook should be systematic
2)      The textbook should be completed by exercise
3)      The textbook should be understandable, meaningful, and consist of good example
4)      The textbook should be innovative
5)      The textbook should facilitate students’ activities
6)      The textbook should be based on curriculum
7)      The textbook should contain good problem solving
e.       Teaching Aids
Teaching aids is all object and activities which mediates the occurrence of a learning activity.
B.     Implementation
Teaching learning process includes:                                                                    
1.      Apperception
Apperception is the readiness of teachers and students to undergo mathematics learning activities.
2.      Small group discussion
Small group discussion is a group that consists of 3 until 4 students where every student is expected to have their respective roles in the group.
3.      Various method
Teaching method is a way of learning that is used to delivering a material or topic.
4.      Various media
Various media is all object and activities which mediates the occurrence of a learning activity.
5.      Various interaction
Interaction is a mutual relationship between two people or more, and every people involved in an active role. Interactions in learning of mathematics involve the interaction between teachers and students and between students with other students. 
6.      Lesson plan
Lesson plan is a step that carried out the teacher where the teacher makes the planning process learning activities in the classroom.
7.      Student’s worksheet
Student’s worksheet is one means to help and facilitate in the teaching and learning activities that will form an effective interaction between students and teachers, and can increase student’s activity in improving learning achievement.
8.      Student’s reflection
Student’s reflections or presentation is student’s ability for present ideas or opinions in front of the classroom or in front of other person.
9.      Cognitive scheme
The scheme for achieving student’s competencies is an attempt to increase the result of learning maximum. Teachers can provide a handle learning as learning modules that can be used by students to do a lot of exercise. Book module is used as a reference book to run a system of learning mathematics in school.
10.  Conclusion by the students
Is how one student summed up the learning results that have been undertaken on a certain day.
11.  Assessment
Assessment is the process of collecting and processing information to determine student achievement.
C.    Reflection
1.      Teacher’s reflection
Is the ability of teachers to reflect on the learning results that have been implemented.
2.      Observer’s reflection
Is the ability of an observer to express an opinion based on learning thet he/she had observed.
3.      Summaries
A summary of the learning that has been implemented.

CONCLUSION
To create the innovative teaching learning mathematics, it is necessary to teaching methods and teaching materials are varied to avoid monotony of learning to use only one method of learning and one teaching materials.  

REFERENCES
Marsigit. “Supporting Evidences and Monitoring To Develop School-Based Curriculum for Junior High School Mathematics In Indonesia”. [Online]. Tersedia:  http://staff.uny.ac.id/sites/default/files/penelitian/Marsigit,%20Dr.,%20M.A./Marsigit_Article_Indonesia_Support_Evidences%20Develop%20School%20Based%20Curr_for%20Math%20JHS.pdf.  [3 Maret 2012].

Marsigit, Shisumi. “Stimulating Primary Mathematics Group-Discussion”. [Online]. Tersedia: http://staff.uny.ac.id. [3 Maret 2012].

Marsigit. 2010. “Developing Teacher Training Textbooks for Lesson Study in Indonesia”. [Online]. Tersedia:  http://staff.uny.ac.id/sites/default/files/penelitian/Marsigit,%20Dr.,%20M.A./Marsigit_Paper_Develop%20Textbook_APEC%20Confer_17_21%20February_2010_Tokyo_0.pdf.  [3 Maret 2012].