Selasa, 13 Maret 2012

IDENTIFY DESIGN OF INNOVATIVE TEACHING LEARNING PROCESS OF MATHEMATICS

Diposting oleh Fa di 04.45 0 komentar

Nowadays there are two kind of teaching methods in Indonesia; they are traditional method and innovative method. Traditional method usually called as formal mathematics. And the teacher who used this method called as the absolutism, the teacher only speaking in front of the class and determines everything that must be done by the students. This method is very old, but there is still some teacher who used this method. It is very uncomfortable for students, since by this method there is no interaction between teacher and students. The second teaching method is innovative learning. This method asks teacher roles as the facilitator for student. Teacher is not as the main source for students anymore. By this method also students can be active and they can promote their own knowledge since they can experiment everything around them.
There are big dipole way of teaching between many teachers, they are traditional—progressive; authoritarian – democratic; classical – individual; transfer of knowledge – cognitive development; structured – unstructured; teacher centered – student centered; teacher directed – student initiative; dependent – independent; grade oriented – process oriented. This big dipole way of teaching makes Cocroft Report (1982:132 in Marsigit) (1) said that teacher have to get many method for any intelligence level, they are exposition methods, discussion methods, problem solving, investigation, exercise, and application.
When a teacher used traditional way of teaching, it will make students do not like mathematics lesson. So, teacher have to pay attention to the essence of student:
1.      Cognitive aspects
a.       Students will be study when they have their own motivation
b.      Students study by their own way
c.       Students can study by themselves or discuss with another friends
d.      Students need different contexts and situation to study
2.      Affective aspects
3.      Psychomotor aspects
So, to develop the motivation of students to study mathematics, teachers have to change and innovate their way of teaching from traditional teaching into innovative teaching.
There are some characteristics of innovative learning. Some of them are the development of students’ worksheet, learning resources, various methods of teaching, various interactions, various teaching aid, and small group discussion.
1.      Developing Student’s Worksheet
One of the characteristics of innovative learning is developing student’s worksheet. It caused the paradigm of learning is learning mathematics is doing some exercises. So we need teaching aids, and on of teaching aids is student’s worksheet.  Student’s worksheet or LKS is a worksheet that contains the information and command/instruction from teachers to students to do a learning activity in the form of work, practice, or in form of the application of learning outcomes to achieve a goal.
A good student’s worksheet must complete the characteristics of worksheet, which is student’s worksheet can promote students to construct their own knowledge of mathematics. On developing student’s worksheet, teacher can use discovery methods, they are structure guide discovery and unstructured guide discovery. So, a student’s worksheet is not only collection of many exercises.
Then, there are four steps in developing good student’s worksheet:
a.       Determining the instructional aims by analyzing the students by identify who are our students and knowing the character of our students
b.      Collects the materials that we need based on instructional aims
c.       Arranging the students worksheet, at least there are materials, tasks, and exercises
d.      Checking the student’s worksheet is it consistent with the instructional aim or not.

2.      Developing Learning Resources
Learning resources are all good sources of data, people, and the particular form that can be used by learners in learning, either separately or be combined to facilitate learners in achieving learning goals or achieve a certain competence.
There are two types of learning resources:
-          Learning resources are designed (learning resources, by design), the learning resources that are specifically designed or developed as a component of an instructional system to provide facilities directed learning and formal.
-          Learning resources are used (learning resources, by utilization), the learning resources that are not designed specifically for the purpose of learning and its existence can be found, implemented and utilized for the purposes of learning. This learning resources may take from:
a.       Message: information, teaching materials, etc
b.      People: teachers, students, etc
c.       Materials: books, pictures, etc
d.      Tools or equipment : computer, white board, etc
e.       Approaches, methods, techniques of solving problems
f.       Environment: class, library
Thus, we can conclude that learning resources can be come from many ways, not only based on books and teacher’s note like traditional methods.

3.      Developing and Implementing Various Methods of Teaching
During learning process, teachers have to use various methods of teaching, because if teacher only use one method of teaching, they students will be bored and can’t get the materials well.
There are many teaching methods, and some of them are:
a.       Assessment provides educators with a better understanding of what students are learning and engages students more deeply in the process of learning content
b.      Cooperative Learning involves students working in groups to accomplish learning goals
c.       Interactive Lectures provide short activities that can break up a lecture
d.      Jigsaws are an option when you have several related data sets you would like students to explore. In a jigsaw, each student develops some expertise with one data set, then a few classmates about it
e.       Quantitative Writing engages students with numbers by asking them to analyze and use quantitative data in written reports and arguments.




4.      Developing and Implementing Various Teaching Aids
Teaching aids is a tool used by teachers, facilitator, or tutors to help learners improve reading and other skills, illustrate or reinforce a skill, fact, or idea and relieve anxiety, fears, or boredom, since many teaching aids are like games.
The aim of teaching aid is to motivate the students to apply his full attention to materials. There are many kinds of teaching aids; they are mathematics card, interactive presentation, worksheet, etc.

5.      Developing and Implementing Various Scheme Interaction
During learning process, there are many interactions between teacher and students, and between student and student. These interactions must be happened in a class, because except material, students also develop social skills. There are three types of interaction in the class:

a.       Whole class
The teacher gives some problems to the students in class, then the teacher give a chance to students to answer the problems.
b.      Small group
Teacher dividing into some small groups, and then they discuss the problem in groups. Teachers monitor the students and give some clue about the answer.
c.       Individual
Teacher observes each student and gives attention to the students with low ability
So, during learning process, these interactions must be developed by teacher to anticipate students’ boredom.

6.      Developing and Implementing Small Group Discussion
During learning process, teacher can use small group discussion because small group discussion is one of characteristics of innovative learning. In small group discussion, teacher can develop many skills, not only materials, because during small group discussion, students feel freely to presenting their idea to their members.
The steps of small group discussion are: 1) teacher divide the students become some groups consist of 4-5 members; 2) teacher give some problems to students; 3) students discuss the problem together in the groups; 4) teacher monitor the students, are they get some difficulties on solve the problems; 5) teacher gives some clue about the solution; 6) students get the solution.
When teacher used small group discussion, he/she spent half of each mathematics period to let students work in the group. But sometimes, one group has been done the task, and another group has not done it. So, teacher can take other exercises to the group who has been done.
When we identify the constructivism teaching learning process we also must pay attention on the spiritual, philosophy, paradigm, theories, notion and the rules of our environment thus we can determine the culture, system, design, management, and model of teaching learning process in mathematics.

Selasa, 06 Maret 2012

ETHNO MATHEMATICS

Diposting oleh Fa di 06.21 0 komentar

Every country has its own culture. There is a different culture between Indonesia and Malaysia, also between Indonesia and Japan. There’s also different culture between one province and another province in Indonesia. It is because Indonesia is a country with thousands of islands spanning out from the West (Aceh, Sumatra) to the East (Merauke, Irian Jaya). It is located between two oceans, the Pacific and Indian, and two continents, Asia and Australia. The population would be about 350 million residents. In fact by 2011, the population had grown to 375 million. Those different cultures we usually called as ethnology.
Mathematics learning process is also different between one country and another country. It depends on the culture of the country. For example, in Europe we can use mathematics problem based on four seasons. But we can’t do this in Indonesia, since Indonesia only has two seasons. This difference usually called as ethno mathematics. Ethno mathematics consists of the culture of mathematics, mathematical culture, the uncultured of mathematics, and also the context of mathematics.
In mathematics education, ethno mathematics is the study of the relationship between mathematics and culture (D'Ambrosio, 1999, 146). Often associated with "cultures without written expression" (D'Ambrosio, 1997, may paraphrases Ascher 1986), it may also be defined as "'the mathematics which is practiced among identifiable cultural groups'" (Powell and Frankenstein, 1997 quoting D'Ambrosio). It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethno mathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two. (1)
Ethno mathematics comes from the philosophy of mathematics that affected to the paradigm of mathematics. This paradigm then developed into two kinds of theories. The first theory is about history, psychology, anthropology, and sociology. The second theorem is about mathematics. Then this two theories combined together become ethno mathematics that developed into mathematical context (formal mathematics, model of mathematics, model concrete, and the concrete of mathematics. Ethno mathematics also be in ice berg theorem.
The final project of studying ethno mathematics is a small research in mathematics learning process that’s affected by the culture of a country. This research based on a theory. Then from the theory we can uncover the culture phenomena, so we get the data and develop it into a construction of research and we can make a new theory. This research must contain of the unity, concept, method, scope, relationship, structure, subject, characteristics, value, and timeline.
The example of ethno mathematics around the world is on numerals. These are some explanation of the numerals in some countries: (1)
1.      English
For instance, in English, there are four different systems. The units words (one to nine) and ten are special. The next two are reduced forms of Anglo-Saxon "one left over" and "two left over" (i.e., after counting to ten). Multiples of ten from "twenty" to "ninety" are formed from the units words, one through nine, by a single pattern. Thirteen to nineteen, and in a slightly different way twenty-one through ninety-nine (excluding the tens words), are compounded from tens and units words. Larger numbers are also formed on a base of ten and its powers ("hundred" and "thousand"). One may suspect this is based on an ancient tradition of finger counting. Residues of ancient counting by 20s and 12s are the words "score", "dozen", and "gross". (Larger number words like "million" are not part of the original English system; they are scholarly creations based ultimately on Latin).
2.      German
The German language counts similarly to English, but the unit is placed first in numbers over 20. For example, "26" is "sechsundzwanzig", literally "six and twenty". This system was formerly common in English, as seen in an artifact from the English nursery rhyme "Sing a Song of Sixpence": Sing a song of sixpence, / a pocket full of rye. / Four and twenty blackbirds, / baked in a pie.
3.      French
In the French language as used in France, one sees some differences. Soixante-dix (literally, "sixty-ten") is used for "seventy". The words "quatre-vingt" (literally, "four-twenty", or 80) and "quatre-vingt-dix" (literally, "four-twenty ten" 90) are based on 20 ("vingt") instead of 10. Swiss French and Belgian French do not use these forms, preferring more standard Latinate forms: octante for 80 and nonante for 90.
4.      Mesopotamia
In ancient Mesopotamia the base for constructing numbers was 60, with 10 used as an intermediate base for numbers below 60.
5.      West Africa
Many West African languages base their number words on a combination of 5 and 20, derived from thinking of a complete hand or a complete set of digits comprising both fingers and toes. In fact, in some languages, the words for 5 and 20 refer to these body parts (e.g., a word for 20 that means "man complete"). The words for numbers below 20 are based on 5 and higher numbers combine the lower numbers with multiples and powers of 20. Of course, this description of hundreds of languages is badly oversimplified; better information and references can be found in Zaslavsky (1973).
Then, some examples of ethno mathematics in Indonesia are:
1.      The role of mathematics in Yogyakarta palace
2.      The role of mathematics in Javanese culture
3.      The role of mathematics in ‘wayang’ culture
4.      The role of mathematics in Borobudur and Prambanan building
5.      The role of mathematics on the counting of someone death
6.      The role of mathematics in fengshui
7.      The role of mathematics in Javanese calendar
8.      The relation of mathematics and forecasting
9.      Irrational mathematics
10.  The relation of mathematics and horoscop
11.  The role of mathematics on Javanese ‘primbon’.

 

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