By Anniltal Manzilah
09301241028
Mathematics Education of 2009
I. Introduction
As we know, in Indonesia, teacher prefer
employing traditional method to a modern one. It’s not so good because in
traditional method, the teacher always explain, explain and explain the
students about the matter. This is not so good because by employ this method,
the teacher have killed the student’s creativity. The students just have to
listen and write what the teacher said, and the teacher treat the students like
an empty vessel so that teacher can fill them more and more. It will make the
student be a passive participant. The student is not too dare to ask some
questions or ask clearer explanation.
To improve this condition, we have to reform
all of the teaching learning components. We can make changes in the lesson
plan, student’s worksheet, use small group discussion method, employ various
interaction, implement various teaching methods, ask students to make a
reflection everyday, understanding the cognitive schema, let the student to
make a conclusion, understanding the apperception, assessment, and start using
various media and teaching aids. We can make the students understanding the
matter easily if wecan make a nice and fun condition of teaching learning
process.
II. How to Develop
Teaching Learning Process of Mathematics in Junior and Senior High School
1. Lesson plan
Lesson plan is the planning made by the
teachers contains about standard competency, basic competency, indicator, the
matter will be tought, the method will be employed, the assessment or
evaluating system, etc. Lesson plan is made individually by each teacher, so
that every teacher have a different lesson plan that will be used or will be
implemented in their class.
Lesson plan is made everyday, so the teacher
can evaluate the teaching-learning process to improve the quality of teaching-learning
activities. There are standard competency and basic competency in lesson plan.
Standard competency is chapter or an achievement that the teacher or maybe
goverment want the students to mastered. Well, and basic competency is not the same
as. Basic competency is more specific than standard competency. The steps that
can be taken in making lesson plan are:
1.
Take a unit of learning that will be tought
2.
Make and determine standard and basic competency
3.
Determine the indicators
4.
Organize the time allocation
5.
Formulate learning objectives
6.
Determine and learn the materials
7.
Organize the methods that will be employed
8.
Arrange the learning activities that will be run
9.
Determine the assessment techniques and evaluating system
Beside that, lesson plan contains indicator
and the matter will be tought too. Indicator is the ability that should be
reached by the studets. Then, the matter is what subject or chapter that will
be tought by the teacher in the class. To make it seems easier for you, I’ll
give you an example. For example, a teacher make a lesson plan for mathematics
subject. The standard competency is about Logic, that is how to use
mathematical logic in problem solving that related to complex pronouncements.
The basic competency can you make is: students understand about mathematics
pronouncement and it’s negation, students can determine the propriety value of
the pronouncement, etc. And then, the teacher must determine the indicators,
it’s like students understand mathematical pronouncements and can make example
of it. The matter that able to write in this lesson plan is about the
definition of mathematics pronouncements, conjunction, disjunction,
implication, biimplication, etc. And the last step, the teacher should plan
about tha method and evaluating system that will be employd in his class. Tha
teacher can employed more than just one method. The teacher may start his class
with a short introduction employ expository method, and the use problem based
learning, or perhaps he can employ discussion method for the next. The
evaluating system is different for each method. In discussion method, the
teacher should appraise student’s active, the question from each students, how
the discussion going on, etc. After the teacher
did their lesson plan, they have to evaluate if the lesson plan run well
or otherwise. If the lesson plan didn’t run well, may be the teacher should
change the teaching method, or teaching strategy. By this way, teachers will
understand how far their students understand the subject, and the difficulties
that had to the students to improve the quality of learning activities.
2. Student’s
Worksheet
Student’s worksheet, usually called LKS in
Indonesia, is a worksheet for students to measure hhow far they understand the
matter tought by the their teachers. As we know, student’s worksheet usually
given to students as a long list of tasks. I think that it’s not too effective
to know how far the student’s understanding. Till the day, teachers always give
a theory about mathematics, give their students some examples, and last, give
them a lot of tasks. It’s exposition method. But our students is not like an
empty vessel. We can’t treat them like an empty glass and fill more and more.
How many teachers in Indonesia that understand this problem? Especially for
elementary school’s teacher. They are the determinator of the characteristic of
students. If we always employ this method, we don’t ever get a creative
students or a smart one. We just produce machines. And our students is not
machines. Why don’t we give them a chance, an opportunity to develop their
ability? Why don’t we give them a problem and just look how they solve it?
It’s much better to make them more creative.
If we always train them to be craeive in problem solving, although they forget
the subject, they will always employ the way of thinking, that is critical,
logic, and creative. I have a little example how to give a good student’s
worksheet to train their creativity. For example, we are the teachers will be
start the class. We enter the class, give a short introduction, in this case is
about triangle. We can make or bring a picture of a triangle and show that to
the students. We can asking the students to make a paper or the simpler one
about the picture. Let them make and show up their perception about the
picture. Let them construct their knowledge about triangle. The thing that we
should do is just moving around and controlling the students or maybe we can
help the students if they found a problem in making a perception. After they
make and write their perception about the picture, we can ask some students to
show up and present their perception in front of class. Let the other students
enjoy the show. Don’t ever stop the show before it’s over. Ask 5 or more
students to show up, and then let the other students to give a comment or maybe
a question about their friend’s perception. In this moment, we can answer and
straighten the perception if it’s not right. In other meeting, ask the other
students to show up. We have to give a same chance for all students. If the
students is cannot to work individually, we can split them to a small groups.
Let them discuss the picture we gave, or in other case, we can give them a
problem. It will train them to be creative and critical.
Beside that format of student’s worksheet,
there are another format that could develop the student’s ability. I will
explain in a simple example. This worksheet’s format is a reflection. After we
end the teaching-learning process, we can ask our students to write a
reflection about the subject and anything they got that day. It will help them
to focus of attention along the class. So, student’s worksheet is not only a
list of question given to the students, buat it can be given in many format to
develop our student’s creativity, to make them critically, to train them to
find a strategy in solving a problem. By this way, we can train their mind
better.
3. Small Group
Discussion
Small Group discussion is a kind of
interaction in class. Small group discussion run by split the students in a
small group of some students to discuss a problem or a task that given by the
teacher. Small group discussion is good to run if we employed problem solving
learning or problem based learning. Because in this case, students need to
discuss to their friends to find the best way or the simple strategy to solve
the problem. Small group discussion will trai our students how to working in
group, how to help each other in finding solutions of the problem, etc. The
goal of employing small group discussion are:
1. To provide an opportunity forour students to
take their initiation in solving the problems. Small group discussion give the
students more chance to improve their character, to develop their imagination
to solve the problems.
2. To deepen the student’s understanding. By
discuss with their small group, students will more understand the matter.
3. To give the students an opportunity to think
and determine a strategy to solve the given problems.
In the implementation of this small group
discussin, we need an active students. But at the fact, our students is almost
passive ones. So, the obstacles of small group discussion’s implementation are:
a. Teacher’s perception about this method is less.
The teachers usually employ the traditional method because they don’t wanna to
make difficulties to their selves to learn more about the modern methods.
b. Small group discussion requires additional
time. Of course, that’s right. In small group discussion, we will ask the
students to discuss thw given problem with their small group, and then show up
and present their discussion result in front of class.
c. Small group discussion method usually
dominated by brilliant students. That’s right too. To employ this small group
method, we need active students, so the passive ones will be covered by the
active and smart students. But it’s can be solved. We can give a little
question to each member of the small group to make certain that al of the
member in the group is understanding well about the matter.
d. Evaluating system of small group discussion is
more complex. This is the reason why almost teacher don’t employ this method.
The teacher find a simple evaluating format, and find it in exposition method.
In small group discussion, teachers sholed know and understanding the
characteristic of each students to make the evaluating easier.
4. Various
Interaction
There are three interaction can
be run in class, that are whole class, small group discussion, and individually
one. Whole class is interaction of the students or a students to all of the
class. For example, in exposition method, the teacher stand up in front of
class and explain more and more about the matter. It’s a whole class
interaction. But, whole class interaction is can employ not only in exposition
methods. We can combinate the methods to make a fun and nice learning so that
the students will not feel bored in class. Although we employ discussion
method, we still allowed to run whole class interaction, maybe in introduction,
or when we straighten the student’s perception. The goal of whole class
interaction are:
1. To covered all of the students. For example,
when the teachers gonna to give a problem to solve by all of the students.
Before split the students in small groups, the teacher can run whole class
interaction to explain what the problem is and how to make a small group
discussion.
2. Take a short time. If the teacher explained
the problem in each small group, it will spend many times. So that, teacher
sould run whole class iinteraction.
The next interaction is small group
discussion. Small group discussion run by split the students in a small group
of some students to discuss a problem or a task that given by the teacher.
Small group discussion is good to run if we employed problem solving learning
or problem based learning. Because in this case, students need to discuss to
their friends to find the best way or the simple strategy to solve the problem.
Small group discussion will trai our students how to working in group, how to
help each other in finding solutions of the problem, etc. The goal of employing
small group discussion are:
1. To provide an opportunity forour students to
take their initiation in solving the problems. Small group discussion give the
students more chance to improve their character, to develop their imagination
to solve the problems.
2. To deepen the student’s understanding. By
discuss with their small group, students will more understand the matter.
3. To give the students an opportunity to think
and determine a strategy to solve the given problems.
The last interaction is individually one. In
this interaction, teacher or a student only talk or meking interaction to another
one. For example when there is a student that give a question to the teacher or
to another student that presenting his/her presentation. The goal of individual
interaction is to make certain that all of the students understood the matter.
If there is a student that don’t undrestanding about a presentation, we have to
train him/her to give a question, so that all of the class can understand the
matter well. Individual interaction will make teacher understanding deepen
about the characteristic of each student. For this three various of class
interaction, we cannot employ an interaction only, but we have to combine all
of the varians to increase the learning quality.
5. Various
Teaching Method
There are so many teaching methods in
teaching-learning process, such as:
1. Exposition Method
This is a traditionnal or convention method in teaching-learning. The
characteristics of this method are:
a. The students are passive, it’s causes that the
students just listen. Listen and listen to the teacher’s explanation
b. The teacher treat their students as an empty
vessel, so that they fill them more and more
c. The class is very formal. The teacher standing
in front of class and never stop of talk and the students sit to listen the
teacher’s explanation
d. The teacher is one and the only one sources of
learning. The students must listen and record or make a note waht the teacher
explain
e. The teacher always talk and chalk only
f. The structure are to explain, give students
examples and finally give them tasks
g. The teacher tends to be otoritarian
This method is not compatible to employ
without combination with the other method. Exposition is good only to make a
whole class interaction, so that the information can covered all of the
students.
2. Discussion Method
Discussion method is a way to organize, to manage learning activities with
problem solving or problem based learning. Discussion method is participate by
all of the students, and it’s good to develop colaboration each other. Small
group discussion run by split the students in a small group of some students to
discuss a problem or a task that given by the teacher. Small group discussion
is good to run if we employed problem solving learning or problem based
learning. Because in this case, students need to discuss to their friends to find
the best way or the simple strategy to solve the problem. Small group
discussion will trai our students how to working in group, how to help each
other in finding solutions of the problem, etc. the characteristics of
discussion method is the role of teacher is to facilitate the student’s need to
learn mathematics.
3. Ask and Answer Method
Ask and answer method is a way to manage learning process by produce and
giving students some questions to help them to think critically in
understanding the matter. This method will be run effectively if the matter is
amazing and make the students interested to solve and learn more.
4. Giving task method
Giving task method is a step to teach or present the matter by giving the
students task. But it is better if we give the students task in front, so it’s
like a student’s worksheet. Before we explain about the matter, we can ask the
students to make a paper about the matter that will be tought, so that the
students have a knowledge about what’the matter that will be learn. This task
can be give in groups, so that the teacher can employ small group discussion
and train their students about colaboration.
Beside the methods above, there are still many others, like games method,
experimental method, etc.
6. Student’s Reflection
Student’s refelection is like a resume or a summary of the day. So, after
the teacher close his/her presention that day, let them to follow us in all,
but give them a chance to make hers/his refelection as the evaliauion of
teaching processs. Teacher can’t manipulate the student’s refelection. Because
this reflection is a tool to evaluate how the teaching-learning run, and how to
improve it.
The implementation of student’s reflection is to: give the student a chance
for meking improvotation in teaching-learning process. By write the reflection
honestly, they can show up their difficulties, what’s the matter that they
can’t understand, etc. the teachers is also can understand the student’s
difficulties so that teachers can help the student to solve their difficulties.
For example, I got an English subject on my third semester. My lecturer is
teach well. In every meeting, after the class closed, he always asking us to
make a reflection and give them at the next week. By this way, he can
understand our difficulties in learning English and know the students that have
a good English.
7.
Cognitive Schema
Cognitive Schema- the organization of knowledge about a particular
concept. The schema contains the features or attributes that are associated
with a category membership. (Sims & Lorenzi, 1992). The Types
of schema include:
1. Person Schema. Schema
about the attributes (skills, competencies, values) of a particular individual.
This often takes the form the personality we attribute to that person.
2. Event schema (cognitive scripts). These are processes,
practices, or ways in which we typically approach tasks and problems. They are
the programs we call upon when faced with a certain stimulus. These are
behaviorally oriented
3. Role schema. These
schema contain sets of role expectations, that is, how we expect an individual
occupying a certain role to behavior.
4. Self-schema. Generalizations about the self abstracted from
the present situation and past experiences. This is essentially one's self
concept which is in essence perceptions of oneself in terms of traits,
competencies, and values (see Laura's notes on Self Concept Based Motivation).
Self-efficacy is a type of self schema that applies to a particular task.
The
functions of cognitive schema are:
1.
To evaluate. When we evaluate individuals occupying a certain
role (e.g., doctor, accountant, actor, artist), we compare their behavior to
our culturally derived role schema for that role.
2.
Role playing. In assuming a certain role, the role schema
often becomes our scripts as to how to behave.
3.
To identify. We often identify and categorize individuals by
the role they assume. We use these role schema to help us place individuals
into a certain category by matching their observed behavior with our role
schema.
4.
To predict. Once an individual is placed into a category
(role) we tend to assume he or she will behave in accordance with the role
schema and use this as basis to predict future behavior of this person.
8.
Student’s Conclusion
Student’s conclusion is the
conclusion of every student about a matter. This conclusion is mean a concluson
about a subject, or teaching-learning process. The subject’s conclusion is
student’s right. So the teacher can’t determine and just fill them like an
empty vessel, because they have rights to make their conclusion about the
matter. They can sort by theirselves what’s the matter that important for them,
what’s the solving strategy that looks easier to do, etc. If a teacher give the
students problem to solve, let them make and create their strategy to solve the
problem. Even if the way, the steps or the strategy is complicated, just let
them. Because how complicated the strategy is, the strategy is found by their
selves, so that they can understand the steps well.
For example, in small group
discussion, after the students discuss the problem with their grouup, we will
ask some groups to present their result, their strategy in solving the
problems. From the groups that presented their solving strategy, I’m sure that there
are differences in each group. The teachers can’t judge a strategy is
complicated or wrong, even if the teachers have a simpler one. Because the
conclusion is the student’s right. So, let them look and pay attention to the
presenter group and give them a chance to choose and determine which strategy
that they think they can do well.
As same as like a solving strategy,
the conclusion of teaching learning process is the student’s right too. The
students should be given a chance to evaluate how good the teaching-learning
process, and let them speak up about their conclusion, so that the teachers can
make improvitation anytime the students find a difficulties about a teaching
method.
9.
Apperception
In psychology, apperception
is "the process by which new experience is assimilated to and transformed
by the residuum of past experience of an individual to form a new whole. In short, it is
to perceive new experience in relation to past experience. It originally means
passing the threshold into consciousness, i.e., to perceive. But the percept is
changed when reaching consciousness due to the contextual presence of the other
stuff already there, thus it is not perceived but apperceived.
Apperception is
a general term for all mental processes in which a presentation is brought into
connexion with an already existent and systematized mental conception, and
thereby is classified, explained or, in a word, understood; e.g. a new
scientific phenomenon is explained in the light of phenomena already analysed
and classified. The whole intelligent life of man is, consciously or
unconsciously, a process of apperception, in as much as every act of attention
involves the appercipient process.A rich child and a poor child walking
together come across the same ten dollar bill on the sidewalk. The rich child
says it is not very much money and the poor child says it is a lot of money.
The difference lies in how they apperceive the same event – the lens of past experience through which they see
and value (or devalue) the money. But it’s in psychology. There some differences
about apperception in psychology, philosophy, and epistemology. In philosophy, Leibniz introduced the concept of apperception into the more
technical philosophical tradition,although he used the word practically in the
sense of the modern attention, by which an object is apprehended as "not-self"
and yet in relation to the self. And last, in epistemology,
apperception is "the introspective or reflective apprehension by the mind
of its own inner states.
10.
Assessment
Assessment is include how to evaluate, how to record, how
to uncover the student’s understanding about the matter. The goals of
assessment are:
1. To help the teacher making a standard value for student’s achievement
2. To help the teacher to know the good students
3. To help the teacher to determine or employ better teaching-learning
strategy
4. To help the teacher identifying what’s the student need in learning process
The instruments that can
be used in assessment process are:
1.
Group Discussion
In discussion, the
students will be asked to discuss each other(or maybe teacher can split the
students in small groups) to discuss about the solutions of the problems given.
2. Problem Analysis
In this instrument, the students will be given a problem and asked to
analyze the problem in their perception and then find or create strategy to
solve the problem.
3. Presentation
The students (in a small group or individual) asked to show up their minds
and their perception or maybe solutions about a given problem.
4. Test of creative thinking
In this instrument, students are given some questions contains problems and
then they asked to determine r create a strategy to solve. It is not about the
solutions, but the strategy students create.
5. Individual test
It is like an examination, but the format is not multiple choise. The
teacher give some writen questions contains problems to solve, or asked the
student to make a writing about a matter.
11. Various Media
In teaching learning process, the teacher should use various media. To
learning mathematics, students can’t only use a textbook. They need another
sources. As same as teaching activities. The teacher can’t only talk and chalk,
because it will make the students feel so bored about mathematics. So, teacher
must use various media in teaching learning acivities, such as whiteboard, or
sometimes can use LCD projector, and etc. It head for:
1. Provide variety activities
2. Provide various teaching methods
3. Provide various context and learning atmosphere
4. Make the learning activities to be nice and fun
5. To deepen the student’s understanding
6. Make the matter easier to understood by the the students
But it is not as easy as the theory to implement various media in
teaching-learning process. That’s cause:
1. Using various media requires a lot of time
2. Need creative and professional teacher
3. It requires more costs
It’s why the various media is cannot implemented yet. Because some schools
is not too dare to give additional expence to increase teaching learning
quality. And we also don’t have many creative teachers yet. The teachers in our
country prefer employing exposition methods to try another one.
12. Various Teaching Aids
Beside various media, there is various teaching aids. Teaching aids is the
aids that teacher use to make students understand the matter easily. It can
forms a model of cube, tube and the others, or picture about the matters. For
example, we can use marbles to make the elementary students in understanding
about operating systems such as addition, substraction, etc. To be underlined,
teachers should use a familiar things so that the students can understand
easily, especially for elementary students. In junior or senior high school, teacher
don’t need to use marbles because it’s not appropriate with the matters in
senior or junir high school. For high school students, teacher can use a
picture of something related to the matter and ask the students to explain
about the picture. For example, teacher will give a matter about triangle and
rectangle. Taecher can use a palm leaf rib, or pipe and then ask the students
to make a design of triangle and rectangle. By this way, teaching learning
activities will be niceand funnier so that the students can understand the
matter easily because the enjoy their learning activities.
The obstacles of
implementing various teaching aids are:
1. It’s spend more times
2. It’s requires a creative teachers
3. And it’s need additional costs to set aside the aids
But, it still can run.
Even if there are no additional costs from the school, teacher still can run
this method, but teachers must be more creative to make aids from unuseful
things.
III.
Conclusion
From the explanation
above, they know that to increase the teaching learning quality, we must take
changes of learning components, from the lesson plan till the teaching learning
activities. The teacher should be more creative in teaching activities and
facilitate the student’s need to learn mathematics. Beside, the teacher must
employs various methods of teaching and use various media and aids in teaching
activities. But, the changes is not easy to do, because there are some
obstacles in practicing the changes. Those are:
1. The changes requires creative and professional
teacher. It means that we should give training to the teachers so that they can
take the changes and handle the class better.
2. The changes spend more times in teaching learning process. For example in
discussion and presentation. Discussion method is good, but it’s take more
time. The teachers must be find the solution how to employ discussion method in
short time.
3. The changes need more costs. Using various media and aids will take more
costs, but it can be solved by using unuseful things and recycle its to be
reused.
4.
