Theory of
Cognitive Development Jean Peaget
Jean Piaget's theory provide
restrictions on intelligence, knowledge and students’ relationship with the
environment. Intelligence is a continuous process of forming the necessary
structures in continuous interaction with the environment. knowledge
is highly subjective when an individual is still
baby and in early childhood and will
be objective when
enters adulthood. Jean Piaget, designing models that
describe how humans understand the world by collecting and organizing
information.
According to Piaget (in Woolfolk:
2009) cognitive development is affected by maturation, activity and social
transmission. Then Piaget divides cognitive development of children into four
main periods are correlated with and more sophisticated with age:
1.
Sensory-motor period (years 0-2)
According to Piaget, baby born with
some innate reflexes as well as and encouragement to explore their world. The
scheme was originally formed through the differentiation of the innate reflexes.
2.
Preoperational period (ages 2-7 years)
In this stage, children learn to use
and represent objects with images and words. Their thinking still egocentric (the
child difficult to see from others' viewpoints.)
3.
Concrete operational period (years 7-11)
In this stage a child has been able
to sort certain objects by size, shape or other characteristics, then the child
will begin to classify, to consider, understand, and observe an object.
4.
Formal operational period (11 years of age to
adulthood).
Characteristics of this stage is the
acquisition of the ability to think abstractly, reason logically, and draw
conclusions from available information. In this stage, someone can understand
such things as love, logical proof, and value.
According to Piaget (in Sugihartono,
2007: 109-110), the human mind has a structure called a schema or cognitive
structure. By using the scheme, a person can process and identify the stimuli
receives so that they can put it in a category/ corresponding concept.
By
using the scheme, someone can adapt and
coordinate their environment to form new schemata
through assimilation process (taking an
information from the outside world
and then adjust the
pre-existing structures) and accommodation (individual
adjustment to a new thing), which are both regulated by equilibration (adjusting
continuity between assimilation and accommodation).
Implications of Piaget's view of
learning is the teacher must adapt the learning process is carried out with the
cognitive stages of the students. Because if there is no adjustment between the
two, teachers and students will have difficulty in teaching and learning and
the learning objectives will not be achieved.
Piaget
believes that good education is education that involves the child to experiment on their own, in a sense: 1.) Try everything to see
what happens; 2) Manipulate signs and symbols; 3) Asking
the question; 4) Find their own
answers; 5) Match what he had found at some point with what he found at
the other; 6) Comparing the
findings with the findings of others.
Realistic Mathematics Education (RME)
Realistic Mathematics Education (RME) is a mathematics
learning approach developed by Freudenthal in Netherlands. Gravemeijer (1994:
82) said Realistic mathematics Education is rooted in interpretation of Mathematics as an activity,
such as problem-solving activities, find and organize the subject problem.
Learning mathematics means doing mathematics, of which everyday life problem
solving is an essential part.
Other concept in realistic mathematics
education is state by Treffers (in Fauzan, 2002: 33-34). The key idea of RME
is Children should be given the opportunity to reinvent mathematics under the
guidance of an adult (teacher). In Addition, the formal mathematical knowledge
can be developed from children's informal knowledge.
The statements above describes a perspective
of mathematics learning placed as a process for students to find their own
mathematical knowledge based on informal knowledge they have. In this view of
mathematics is presented not as “a finished good" that can be moved by the
teacher into the minds of students.
Freudenthal mentions two types of Mathematization in mathematics learning:
1.
Horizontal mathematization, involves going from the world of life into the world of symbols, the examples are identification, formulation and visualization problems with different ways by students.
2.
Vertical mathematization means moving within the world of symbol, the example of vertical mathematization are presentation of the relationships in the formula, refine and adjust the mathematical model, using different models, the formulation of mathematical models and generalization.
According
Soedjadi (2001: 3), there are five characteristics in the learning of
mathematics:
1. Using the context, means that the environment around
us or the knowledge that has been owned by students can be used as a part of
contextual learning materials for students.
2. Using the model, means that the mathematical problems
or ideas can be expressed in the form of model from the real situations that
lead to the abstract level.
3. Using the contributions of students, means that the
concept of problem solving or discovery is based on the idea of students'
contribution, in this case the students play a full part in the learning
process.
4. Interactive, means that learning activities are built
by the students' interaction with students, students with teachers, students
with the environment and so on, so that communication or interaction among
class members to stay awake and facilitate the learning process because there
is no boundary or divider that prevents them to interact.
5. Intertwin, which means that teachers can use the
different topics that can be integrated so as to bring an understanding of a
concept at once.
In realistic mathematics learning, someone can build their own knowledge
through the process of active learning. A concept does not instilled through
the process of transferring, but someone who is learning should be given the
freedom and encouragement to express their thoughts and construct knowledge for
themselves. In addition, it is also necessary for interaction in the realistic
mathematics learning, both among students, teachers and students, and so on.
The implications of the social aspect that is high enough in the
learning activities of students, then teachers need to determine appropriate
teaching methods and in accordance with those requirements. One method of
teaching that can meet these objectives is the inclusion of a discussion in the
learning activities of students.
Discussion activity is deemed able to encourage and to expedite
interaction between students. In addition, the negotiation and evaluation
between students and teachers are an important factor in this constructive
learning.
Constructivism Theory
Constructivist theory is defined as
generative learning, which acts to create a meaning of what is learned. Constructivism
better understand learning as a human activity to build or create knowledge by
giving meaning to the knowledge in accordance with their experience.
Constructivism approach has some common concepts such as:
1.
Active learners build knowledge based on existing
experience.
2.
In the context of learning, students should develop
their own knowledge.
3.
The importance of fostering knowledge actively by
students through the interplay between past learning with new learning.
4.
The most important element in this theory is student actively build their knowledge by comparing
new information with existing understanding.
5.
The imbalance is a major motivating factor learning.
6.
Teaching materials are provided to have a docking with
the student experience to attract students.
There are two forms of
constructivist, the construction of psychological (cognitive) and social
constructivist. Cognitive constructivist emphasis on knowledge, confidence,
self-concept, or identity who is focused on the people psychological live. In
other words, cognitive constructivist focus on how individuals use the
information, resources, and assistance of others to build and improve mental
models and strategies in solving the problems they faced. In the learning, teacher
intend to transfer concepts, ideas, and the knowledge of something to students,
it will be interpreted and constructed by students themselves through the
experience and knowledge. Social constructivist emphasis on the social
interaction that occurs, the cultural, as well as activities that determine the
development and individual learning to a problem. In social constructivist, learning environment is
influenced by a complex, real and suitable to be applied in the learning
process. For example, the assignment to students to understand and gather
information on various livelihood around him.
In an effort to implement
constructivist learning theory, Tytler (in Sugihartono, 2007: 115) put forward
several suggestions relating to the design of learning, as follows: (1) provide
an opportunity for students to express his ideas with his own language, (2)
provide an opportunity for students to thinking about his experiences to become
more creative and imaginative, (3) provide an opportunity for students to try
new ideas, (4) provide experiences that relate to the idea that has been owned
by the student, (5) encourage students to think about changing their ideas, and
(6 ) creating a conducive learning environment.
Sources:
Anita Woolfolk. Educational Psychology. Edisi Bahasa
Indonesia. Yogyakarta: Pustaka Pelajar, 2009.
Fauzan,
A. 2001. “Pengembangan dan Implementasi Prototipe I & II
Perangkat Pembelajaran Geometri untuk Siswa
Kelas IV SD Menggunakan Pendekatan RME”.
Paper presented at the National Seminar of Realistics Mathematic
Education (RME) in UNESA Surabaya, 24
February 2001.
Gravemeijer, K. 1994. Developing
Realistic Mathematics Education. Utrecht: Freudental Institute. Retrieved:
http://ironerozanie.wordpress.com/2010/03/03/realistic-mathematic-education-rme-atau-pembelajaran-matematika-realistik-pmr/
Siswoyo,
Dwi, dkk. 2008. Ilmu Pendidikan.
Yogyakarta: UNY Press.
Soedjadi,
R.. 1999. Kiat Pendidikan Matematika di Indonesia. Jakarta: Dirjen
Dikti Depdikbud.
Sugihartono, dkk. 2007. Psikologi Pendidikan. Yogyakarta: UNY Press.
