HOW TO DEVELOP TEACHING LEARNING PROCESS OF MATHEMATICS IN JUNIOR HIGH SCHOOL / SENIOR HIGH SCHOOL

By Fitria Yelni

Department of Mathematics Education, Faculty of Mathematics and Science,
Yogyakarta State University

INTRODUCTION

There is a paradigm about teaching learning process of mathematics in the school. Mathematics is a horrified, boring, or ungainly lesson for students. This mindset so annoying and miserable. Why do this situation still happen in mathematics learning? Most of mathematics teachers in Indonesia still implement the traditional mathematics teaching learning process with the single expository method. The teachers explain the material/lesson in front of class and the student must be listen what the teacher said. After that, the teacher give examples and then give the question and the task to the student classically. If this method still be employed by the mathematics teachers, the teacher has many  difficulties to  serve the various needs / demands of the students in learning mathematics, to encourage the low achiement students to improve their achievement, to encourage students to learn actively, to use and develop mathematical props, and to encourage students to learn  through cooperation.

If this paradigm still occured in mathematics teaching learning process in the school, there is no advancement in mathematics learning and student’s achievement. It will assassinate the student’s creativity. So, there must be has effort and method to develop teaching learning process of mathematics in the school to make the student more enjoyable and fun in learning.

HOW TO DEVELOP TEACHING LEARNING PROCESS OF MATHEMATICS IN JUNIOR HIGH SCHOOL / SENIOR HIGH SCHOOL

1.        LESSON PLAN

A lesson plan is a teacher’s detailed description about the instruction of course for a lesson. A lesson plan is developed by a teacher to guide the class instruction. The detail of the plan will vary depending on the preference of the teacher, subject being covered, and the need and/or curiosity of children.

There are many formats for a lesson plan, most lesson plans contain some or all of these elements, typically in this order:

·        Title of the lesson;

·        Time required to complete the lesson;

·        List of required materials;

·        List of objectives, which may be behavioral objectives (what the student can do at lesson completion) or knowledge objectives (what the student knows at lesson completion);

·        The set that focuses students on the lesson’s skills or concept, these include showing pictures or models, asking leading questions, or reviewing previous lessons;

·        An instructional component that describes the sequence of events that make up the lesson, including the teacher’s instructional input and guided practice the students use to try new skills or work with new ideas;

·        Independent practice that allows students to extend skills or knowledge on their own;

·        A summary, the teacher wraps up the discussion and answers questions;

·        An evaluation component, a test for mastery of the instructed skills or concepts, such as a set of questions to answer or a set of instructions to follow;

·        Analysis component the teacher uses to reflect on the lesson itself, such as what worked, what needs improving;

·        A component reviews and reflects on content from the previous lesson.

2.        STUDENTS WORKSHEET

A worksheet should be the ‘spirit’ of the learning process. A worksheet should encourage students to innovate and explore their ideas. It should not only help them an achieving learning objectives but also encourage the students to participate actively in the lesson in the lesson and make it more meaningful.

Utilization of student worksheet is expected to increase the independence of students,
Therefore the development of student worksheet contains the following components:
1. Learning is begins from the realistic things.

2. Invite the active participation of students

3. Enable the development of models

4. Repetition to reinforce understanding.

5. Positive feedback to encourage and enhance students' understanding.

The design of student worksheet is divided into 5 parts, namely the initial, contextual issues, some of the activities, conclusions and exercises. The initial part contains the objectives to be achieved in the student worksheet and student identity. Contextual issues are developed in accordance with the conditions of students who are in the area or neighborhood. Contextual issues was developed by linking the material prerequisite to the material students will be studied. The design of activities is appropriated to the material developed, and so the number of activities that are developed in accordance with the results of flow analysis of student learning, which encourage the students to develop the model. Section of conclusions is present to give students the opportunity to explain their findings during the activity that has been done before, and it expected to become part of formal mathematics for students. At the end, there are the given of exercises. It did to trained  the students tohavetheskilla, in addition to obtaining a good understanding of concepts.

The benefits of students worksheet (LKS) are to provide an opportunity for students to work independently, to gave the chance to the students to cooperate, to provide an opportunity for teachers to develop the various activities,  to provides a useful document for students and provide alternative sources of learning, to gave students the opportunity to conduct discovery.

There are some obstacles in development of LKS: (1)adds to the workload of teachers, (2)require an additional fee, (3)requires knowledge and skills of teachers, (4)requires a continuity of development, (5)requires management techniques / management LKS, and (6)need support so that schools can be carried out comprehensive.

3.        SMALL GROUP DISCUSSION

The teacher can employ various methods to make the mathematics learning more enjoyable for the students. One of them is by divide the class into some of small group discussion. Small group discussion may contain 4-5 students each group. In their group, students try to identify the problem that given by teacher and attempt to solve the problem through the teamwork. So, there is interaction between a student with the other students which built through discussion.

There are some benefit the development of discussion method, that is to gave student the chance to take the initiative, to provide an opportunity for students to think and find the different methods, to train the students to accept the others opinion, deepen understanding of a concept, to related concepts with the other one and to give feedback to the teachers.

The educational benefits of students working cooperatively in groups are well recognised. Among other things,

·      studying collaboratively has been shown to directly enhance learning;

·      employers value the teamwork and other generic skills that group work may help develop; and

·      group activities may help academic staff to effectively utilise their own time.

The obstacles to develop the method of discussion are: (1)the teacher not understand this method yet, (2)this is a new method that the student not receive before, (3)require additional time for the presentation of a material/lesson, (4)material that can be discussed is few, (5)dominated by a brilliant student and (6)not in accordance with the paradigm of learning

4.        VARIOUS INTERACTION

Interaction in teaching learning process is an important matter. Learning activity in the class will be going on if the interaction had built up. In interactions, there are activities that is reciprocal (mutual) and based on mutual need, there is activity rather than expression of feelings, and there is a connection to share of knowledge that is based ‘give and take’, which are all expressed in terms of behavior and actions..

In the class, there are 3 kinds of interaction. These are a whole class interaction, small group interaction and individual interaction.

In a whole class interaction, there is an interaction between teacher and all of students. It maybe occur in the beginning of teaching learning activity when the teacher give an introduction about the lesson that will be taught by the teacher. The teacher explain about what will they learn at that time and what should they do in the teaching learning activity.

After that, the teacher can divide the class into some of small group discussion. In a small group discussion, there is interaction between student in their group. The students try to solve the problem that given by the teacher through a teamwork. So, students can learn more about indirect lesson, such as to accept the others opinion, to think and find the different method, and to take the initiative.

The teacher also come to the small group discussion to control and understand what the  difficulties that the students found. If there are a matter that they not understand yet about the lesson, they can ask the teacher about it and the teacher can explain or give hint to answer the question. It is an individual interaction.

5.        VARIOUS TEACHING METHOD

Many people think that mathematics is very unpleasant, very difficult, and meaningless. They just imagine that mathematics is identically with complicated numbers, many long term equations which are hard to memorize and to understand. Several students moreover think that mathematics such a burden and scary lessons. There are some opinions implanted in students’ mind before learning math. As the consequence, most of the students achieve bad for this lesson. Those opinions are:

a)    Mathematics’ formula is to memorize
This makes the students are lazy to learn and finally they got nothing. But actually mathematics is not a memorizing lesson. It is about concept understanding. Memorizing math formula will be meaningless moreover if they didn’t understand the concept.

b)   Mathematics is an abstract knowledge and has no relation with real life
This term is definitely wrong. The fact shows that math is a very realistic knowledge. It is such an analogue of the real life. It is proved by many inventions and research of mathematics in such sectors as economy, technology, demography, social, and many others where math has a very significant role for it.

c)    Mathematics is boring and rigid; This opinion isn’t true. Although mathematics problem generally has only one solution it allows many ways to reach that solution. It means that mathematics isn’t rigid.

To prevent those opinions, we have to change our mathematics learning teaching process to be more applicative and real. The topic or the way we teach should consider the students’ necessary. We have to implant and ensure that the students love mathematics. It should teachers use a variety of teaching methods in mathematics teaching learning process to enhance creativity, understanding and thinking skills of students. There are many teaching methods can be employed by the teacher, such as:

1. Discussion method (Discussion method)

Discussion method is a method of teaching that is closely related to solving problems (problem solving). This method is also commonly referred to as group discussion (group discussion) and the recitation together (socialized Recitation).

2. Method of demonstration (Demonstration method)

Demonstration method is a method of teaching by way of demonstrating the goods, events, rules, and perform a sequence of activities, either directly or through the use of teaching that are relevant to the subject or the material being presented.

3. Lecture method plus

Plus the lecture method is a method of teaching that uses more than one method, namely the lecture method join with other methods.

a.       Lecture plus question and answer method and tasks (CPTT).

This method is a method of teaching a combination of lectures with question and answer and administration tasks.

This mixed methods should ideally be done in an orderly manner, namely:
1). Delivery of material by the teacher.

2). Provision of opportunities to ask for between teachers and students.
3). Giving the task to students.

b.      Method of lectures plus discussions and assignments (CPDT)

This method is done in an orderly manner in accordance with the order pengkombinasiannya, the first teacher outlining the subject matter, then hold a discussion, and finally gave the task.

c.       Method of demonstration and lecture plus exercise (CPDL)

This method is a combination of activities to describe the subject matter with demonstrated activity and exercise (drill)

4. Recitation method (Recitation method)

Recitation method is a method of teaching where students are required to make a resume with the sentence itself. This method can train students to dare to take the initiative, responsible and independent.

5. Experimental methods (Experimental method)

Experimental method is a method of giving opportunity to the students individual or group, trained to perform a process or experiment so that students find their own knowledge.

6.        STUDENTS REFLECTION / PRESENTATION

After the teaching learning activity, for example by doing small group discussion to study and solve the problem that given by the teacher, the students present their reflection or presentation in front of class. Students explain how to solve the problem in their way. Students from the others group can give opinion, comment, or asking questions if there are some matter which they not understand yet. Each group has chance to present their result of discussion. From all of the students reflection, we can take many new knowledge and the students can share their ideas to the class.

7.        COGNITIVE SCHEME

Cognitive scheme is a teaching content. It contain about what the materials will teach are by the teacher, how many kind of the materials, and how the relationship between each of material is. Cognitive scheme try to give the teaching of material/lesson that encourage the student to construct their own knowledge intact and correctly.

8.        STUDENTS CONCLUSION

After a series of teaching learning process was held, it's time to give students the conclusion from the learning activity. It is important to know the common understanding of what has been acquired by students in various learning activities undertaken. If there are things that each is considered misrepresentation or distortion of understanding, the teacher in charge to rectify the mistake of understanding gained by the students so that students construct their knowledge intact and correctly.

9.        APPERCEPTION

Apperception is the step to determine the extent of preparedness of students and teachers in the learning process to be implemented. readiness here not only in the sense of material readiness, but also readiness in terms of physical, mental, and others. Apperception is very useful, especially for teachers, to identify the extent to which students' initial understanding of the material that will be given, so the teacher can give the appropriate teaching methods and materials which need more emphasis on students.

Apperception also aims to create understanding. If the teacher will teach a new subject matter, need to be connected with things that have been mastered the student or students to relate it to previous experience and in accordance with the need for ease of understanding.
Examples of teachers' efforts to make the connection with the relevant aspects

·      In the beginning of the lesson the teacher to review the extent to which material that has been previously studied can be understood by the student by the teacher asking questions to students, but can also summarize the previous course material.

·      Comparing the old with the knowledge that will be presented. This is done when new material is closely related to the material to be mastered.

·      The teacher explains the concept / understanding. This is necessary because the material to be learned entirely new material.

10.    ASSESSMENT

Assessment is an activity of measurement, quantification and determination of the overall quality of students' knowledge. In this sense, hinted that the assessment should be integrated in the learning process and using a variety of forms.
There are 2 kinds of assessment:

1.      Test
Test is a very important method to obtain information about what students can do and know the students. To ensure authentic results obtained from each student, tests carried out in special circumstances, namely:

a.    Time is limited; students must complete a test or answer the questions in the alotted time.

b.    Without the help from the books, other people or other sources, exeption for the test is an open book test.

c.    Supervision; so that the tests can be run orderly and get authentic results.

Form of tests include multiple choice, true-false questions, match pairs, short answer, structured descriptions, descriptions and performance test. Teachers frequently used the test by combination of several different forms. The portion of each section varies, depending on the level, the subject test and trend test maker.

2.      Non-test
Type of non-test is divided into two parts, namely:

a.       Assessment of the work (product).

1) A written form, usually tangible reports, journals, scientific papers
2) The form is not written; usually shaped like a three dimensional sculpture, yarn structure of conic sections, mathematical space objects (blocks, cubes, tubes, etc.).
If the students' work is collected and viewed progress achieved during a certain period, then the collection is called a portfolio. Portfolios can be used as a discussion with parents to view student progress and achievement.

b.      Attitude

Attitudes and interests of students to a lesson can be measured through observation, fill out the questionnaire or check list.

11.    VARIOUS MEDIA AND TEACHING AIDS

To support the teaching learning process, media tools and equipments needed to be taught material that can be easily accepted by the students and make learning more interesting and enjoyable.
Some forms of learning media including:

a.  Printing materials such as: hand outs, books, modules, student worksheets, brochures, leaflets, wallchart,

b.  Audio Visual such as: video / film, VCDs

c.  Audio such as: radio, cassette, CD audio

d.  Visual: photos, drawings, models / mockups.

e.  Multi Media: CD interactive, computer based, Internet

Benefits of the development of  media and teaching aids are: (1) to provide the various activities, (2) to provide the various teaching methods, (3) to provide variety of contexts and learning atmosphere and (4) to clarify the understanding of concepts.
There are some obstacles to develop the media end teaching aids, that is (1)props are not too relevant to some of the materials in high school, (2) the use of props corpulent time-consuming, (3) skill and creativity required by teachers to develop media and teaching aids, (4) require an additional cost for props and high costs for the development of teaching aids and (5) not in accordance with the prevailing paradigm of learning.