There are many views about Mathematics
learning in school. However, there are many theories that it is less
appropriate when applied at the international level. In this time we will learn
about the criterias of international level of educational practice, adapted
from Paul Ernest. There are nine views of this criterias.
The first is about the nature of Mathematics.
Paul Ernest said that mathematics are a body of knowledge, science of truth,
structure of truth, and social activity. Mathematics is a science that contains
a truth. Further Ebbut and Straker (in Marsigit, 2009) expressed the essence of
mathematics as follows:
- Mathematics is a search for patterns and relationship
- Mathematics is a creative activity, involving
imagination, intuition and discovery
- Mathematics is a way of solving problems
- Mathematics is a means of communicating information
or ideas
The second is the value of
Mathematics. In general, values influence attitudes and behavior of someone
on something. About the moral value in the mathematics learning, people often look
at the good side or bad side. Value includes consideration of the elements that
bring an individual ideas about what is right, good, or desirable. Just like a
pragmatic theory which states that the truth of a statement of the criteria
measured by whether the statement is functional in practical life. It is mean
that a statement is true, if the statement or the consequences of that
statement has practical uses for human life.
The
third is about society's view of education. Nowadays people begin
to realize the importance of
an education. In
the era of globalization, they must have adequate
education in order not to lag
behind other segments of society.
In this case mathematics education is also experiencing the impact of globalization.
Need a few
changes in it, especially
in the face of society's view that more advanced, and
embrace a belief system. People are starting to think about humanity, freedom,
justice, and democracy.
This is what should bring a change in the
mathematics learning such as how
to develop and
manage the knowledge,
teaching, learning, and schooling.
The
fourth is about learning theory. In
mathematics education, it is known as a constructivist
learning paradigm. Constructivism paradigm states that mathematics as a fallible human activity, not a collection of the external correct absolute structure to the human. Mathematical truth and
the truth of mathematical objects must be
realized as a result of construction or how
to construct. Constructivism
holds the opinion that every world
experience, depending on the context and unique and can not be accessed by other individuals.
Piaget (Sugihartono, 2007) suggests that
cognitive development is not an accumulation of separate
pieces of information, but rather
is the construction of a mental framework
by the students to
understand their environment,
so students are free
to construct their own understanding. The principles of constructivism in learning
including the following:
1. Understanding
is built by the students
themselves both personally and socially,
2. Knowledge
can not be transferred from teacher to student, but only with the
liveliness of the students themselves
to reason,
3. Students
actively construct continuously so that it always changes the concept towards
the concept of a more detailed, complete, and in accordance with
scientific concepts
4. Teachers act as facilitators.
The fifth is the nature of students
and students ability. Every student are different from other students, this is
what makes them unique. In a learning process every student has different
motivation, intelligence, emotions, backgrounds, and circumstances of
psychology. Level of maturity among students in the classroom is different, so
the teacher must be able to overcome the psychological state of a variety of
students in the learning process. Characteristics of effective learning are
when learning process can respond to special needs students (Sugihartono, 2007:
28). In
one class, each
student has different ability in learning. There are a high and low ability to understand the material. Teachers should pay
attention to it. How to cope with
students who have
such low capacity,
motivate and help when experiencing difficulties
in learning. So that students are able to catch up.
The
sixth is the
nature of teaching
learning of Mathematics. On mathematics learning, most teachers still use
the teacher-centered system.
So that students are not given the opportunity to grow
and develop the knowledge, because in the learning process teacher has a
full role. Mathematics learning
system should be centered on the students. Students are allowed to build their own knowledge, so they will grow as expected, without
any coercion. Here the teacher acts as facilitator
in the learning and
facilitate students when encountering learning difficulties.
Teachers also need
to understand the learning styles
of each student, whether
auditory, visual or
kinesthetic. In order to implement appropriate learning styles and poses no boredom
in class.
The seventh is the nature of
teaching learning resources. Learning resources can be everything around us. In
mathematics we are learning to use the teaching aid to facilitate students in
understanding the material. The use of the board, reference books, the internet
and calculators can also facilitate the learning process.
Related to the resources of teaching, Ernest (1991, in Marsigit 2009) suggested
that due to the learning should be active, varied, socially engaged and
self-regulating, the theory of resources has three main components :
1. the
provision of a wide variety of practical resources to facilitate the varied and
active teaching approaches;
2. the
provision of authentic material, such as newspaper, official statistics, and so
on for socially relevant and socially engaged study and investigation; and
3. the
facilitation of student self-regulated control and access to learning
resources.
The eighth is Assessment. Assessment is any systematic procedure for
collecting information that can be used to make inferences about the
characteristics of people or objects. Assessment can and should provide
information that both enhances instruction and promotes learning (Reynolds,
2010). The function of the Assessment are to: 1) Describe the extent a student
has mastered a competency. 2) Evaluating student learning outcomes in order to
help students understand themselves, make decisions about next steps, both for
the selection of programs, personality development. 3) Finding it difficult to
learn and the possibility of student achievement that can be developed. 4) Find
the weakness and lack of an ongoing learning process in order to improve
subsequent learning process. 5) Controls for teachers and schools on the
progress of students' progress.
The ninth is the diversity. In mathematics learning in the classroom, we not
only face the same students, but also the diverse students. They not only come
from one culture, but also from different cultures. We must implement a system
of multiculturalism in learning. Moreover, taking the theme of learning should
not also mention specific ethnic. Capture the theme can be widely and do not
depend on local culture.
Sources:
Marsigit.
2009. Philosophy of Mathematics Education. Retrieved:
Reynolds,
C. R., Livingston, R. B., & Willson, Victor. 2010. Measurement and
Assessment in Education Second Edition. New Jersey: Pearson.
Sugihartono,
dkk. 2007. Psikologi Pendidikan. Yogyakarta: UNY Press.
