By :
lina Dwi Aris Setiani
09301241031
Mathematics Education 2009
A. Introduction
Along with the changing times, we would need for teachers to develop as a learning process in both mathematics education in junior and senior high school with the aim to improve student achievement, especially in math. Currently the quality of education in Indonesia is still very low, it is evidenced by low student achievement in view of the National exam results which we always carried out in each year, especially in mathematics. The low student achievement results can be caused by a lack of understanding of the concepts of mathematics material in schools. For this reason the teacher as an educator needs to do development on the learning process to improve comprehension and mathematics student achievement, especially in math. In an effort to develop learning activities in mathematics at school, teachers should pay attention to some aspects of education that has affect the learning process at school nets. These aspects include lesson plans, student worksheets, small group discussions, Various interaction, student reflection, Various teaching methods, cognitive scheme, student's conclusion, Apperception, assessment, Various teaching media and teaching aid.
B. How to develop teaching learning process of mathematics in junior high school or in senior high school
There are some aspects of process of the teacching learning mathematics that must be developed by the teacher to increase the result study of the student, that are:
1. Lesson Plan
Lesson Plan in the world of education is a tool used by teachers as a guide in their teaching. In other words we can mention that the lesson plan is a requirement of teachers. To develop a lesson plan into a plan of learning that is both effective and efficient, and before the teacher arrange the lesson plan. In the order to lesson plan that was designed and created by teachers can be in accordance with the actual process of learning mathematics, then in an effort to prepare the lesson plan, teachers need to make efforts to develop lesson plans that are prepared in accordance lesson with mathematics learning objectives to be achieved. In preparing the lesson plan should include the introduction of a teacher as a learning activity early in the meeting indicated by raising student motivation and focus the attention of students to participate in the learning process. Teachers also must write a brief description in the form of a brief explanation of the content associated with competencies to be achieved.
With expectations when teaching and learning activities in the beginning students can obtain answers to globally about the content of the lessons to be learned. In writing the procedures and instruments of assessment processes and learning outcomes should be tailored to the indicators of achievement, competence, and refer to the standards of assessment has been established. In selecting and determining the source of learning should be based on the standards of competence and basic competence, teaching materials, learning activities, and indicators of achievement of competencies. In this section the teacher should write all the media in the form of tools, materials, and other resources of learning that will be used during the learning process takes place.
2. Student Worksheet
Student worksheet is a worksheet that contains information and instructions from the teacher to give to the students that contains commands for working on a learning activity in the form of work, practice, or in the form of application of the results of the study to achieve the learning objectives.
Student worksheet has a function, that is that worksheet can be used as a learning tool for students to do well in the classroom, in the practice room and outside the classroom to develop the skills they had before, to apply the knowledge they have acquired previously, to practice their skills in solving problems with various problem solving methods, to construct their own understanding of the concept of the material to acquire new knowledge. There are some purpose of worksheets on the process of teaching and learning in junior high school or in senior high school, as follows:
a. To train students in thinking.
b. To increase student interest in learning.
c. To improve student learning motivation so that learning to be more meaningful and effective and efficient.
3. Small Group Discussion
Small group discussion is a conversation that was done by three or more people, which is done through the process of exchanging thoughts and argumentation to solve problems together. The process of this discussion can be done through group discussion forums conducted by all students in the classroom or may be can be formed by small groups consisting of three until five student. Therefore, in order for the process of learning mathematics at Junior and Senior high school can walk properly, a teacher needs to do a variety of innovations in teaching by applying the method of discussion groups. Method discussion group is a way of delivery the lesson, in this case a teacher provides opportunities to students to hold a communication in order to collect opinions, making conclusions or arrange a variety of alternative problem solving. Through discussion groups students can participate actively. The purpose of Small Group Discussion applied in the learning process are:
1. To utilize the various capabilities that exist or are owned by the students.
2. To provide an opportunity for students to distribute their each opinion.
3. To get feedback from students about the goals that have been formulated has been reached.
4. To help students so that realize and be able to formulate the problems as seen both from his own experience and from school lessons and.
5. To develop students' motivation in learning mathematics.
Using of discussion groups on the learning process will provide a new learning experience, students through this new knoeledge the student can get a variety of information in the lead new idea or in solving problems, students can increase their understanding of important issues, students can develop the ability to think and communicate, students can improve public order in the process of planning and decision-making process, as well as students can foster the spirit of cooperation and responsibility.
Using of group discussion method in teaching mathematics has some weaknesses that can lead to failure of the learning process in achieving the goal of learning. Several weaknesses in the discussion groups,as follow:
1. Discussion groups need more time than the usual way of learning.
2. Can be a waste of time especially if there are negative things such as lack of proper guidance.
3. Sometiimes the process of discussion dominated only by certain people only.
In order for a group discussion can proceed smoothly teachers should provide sufficient guidance on how to solve the problem clearly so that steps can be well understood by students. In order for a group discussion can take place effectively, the small groups should consist of three until five person so that all members of the group can work together in accordance with the duties and responsibilities of each student. Thus, it would be intertwined interactions between students with students and between students and teachers.
Thus all members of the group will participate actively in expressing their opinions or ideas so that his net discussion in each group is not dominated by certain people only. After the discussions in each group ended, the teacher should ask students to present their group's discussion in front of her friends through representative groups. Activities of the presentation can be used as a means to increasing understanding of the concept of the material provided by teachers for students who do not understand or who already understand the concepts of matter such the lesson of mathematics.
4. Various Interaction
Interaction is a process of communication that occurs between two people or more. Interaction is one of the importance of components in the learning process. Through interaction, students can exchange ideas and opinions with peers who are members of one group or with close friends in the classroom. In addition, students also can establish communication with the teacher so the teacher can provide a variety of direction and guidance to students in solving problems. Through the process of interaction of a teacher can understand the condition of their students both in terms of psychological and cognitive aspects, thus the teacher can choose the learning method in accordance with the conditions of their students so that teachers can meet the learning needs by students. Thus the process of learning mathematics can take place with good, effective, and efficient, and as away to achieve the goal of learning mathematics.
The process of interaction in teaching and learning activities consist of three categories, that is whole class, small classes, and individuals.
1. Whole class, before the contains activities teaching and learning takes place conducively, a teacher should provide motivation to students in the form of inducement in the form of questions that relate to the material to be delivered. Then the teacher explains the material to be provided to all students in the classroom.
2. Small classes, after the teacher introduces, explains, and provides clues about the material to be delivered to students, the teacher should divide the students in the class into small groups consisting of three, four, or five people. After teachers make small groups, then teachers should distribute the task to students in the form of problems related to the material being studied. After that, the teacher instructed the students to solve and resolve the problem together.
3. Individuals, when in the discussion groups of students have difficulty in understanding and solving problems together, the teacher should give a good understanding of materials and teachers will have to provide a clear and coherent guidance to students in the group or to each existing student s in the group so that the instructions are students able to understand concepts such material and are able to solve mathematical problems that existed at that question.
5. Various Teaching Methode
Teaching methods can be defined as the way that used to implement a plan that was compiled in the form of a real and practical activities to achieve the learning objectives. There are several methods of learning that can be used to implement learning strategies, including:
a. Method of investigation
With the method of investigation, students can develop a sense of curiosity by conducting research and investigation on the hypothesis made.
b. Practical work Method
Practical work that not only from the cognitivet aspects it’s necessary in the teaching learnig but also skills. With the employ practical in the teaching learning process of mathematics the student will more creative and innovative.
c. Contextual Method
Contextual learning is the concept of learning that helps teachers relate beetween the material with real-world condition in everyday leve. Contextual learning focuses on developing knowledge, understanding, skills of students, and students' contextual understanding of the relationship with the subjects learned in the real world.
d. The expository methode
in the expository method the teachers is not be dominance by the teacher. The teacher only explain the material in the begining of the learning, ang then the teacher give a sample of problem to the all student. In the expository method the student is not only hear and make a summary or notice but also the student choached up to make a exercise and the teacher to countrol the student’s worksheet result.
6. Student Reflection
Reflection is a way of thinking about what is newly learned. Reflection is a student response to the events, activities, or the knowledge they have learned or mastered by the students. Teachers can implement these components by way of reviewing learning materials that have been studied mathematics with students. In addition, the reflection can be used as a way to strengthen students' understanding of mathematical concepts of matter that has not been mastered by the student. Reflection is a summary of the learning that has been delivered by the teacher. Through reflection activities students can do independently writing about a summary of learning outcomes that have been followed.
This reflection activities can be arranged through the presentation. In order for the process of learning mathematics can be running optimally, teachers can develop activities of reflection through the activities of the presentation by using the method of learning the discussion. Through methods of discussion, the teacher divides students into small groups consisting of 3 to 5 people. After that the teacher distributed the worksheet to the students that contains the description of mathematical material with the problem. Through small group is creating interactions that exists between students with students and students with his teacher. From the interaction process students can resolve together through group discussion. After they finished discussing the settlement of the problem through their own understanding , then the teacher asks the student to present the results of their group discussion in front of all students. From the presentations that have been done by individual students, teachers can review the results of their discussions as well as the teacher can choose the right way, effective, and efficient from a variety of ways that express by students through the presentation of the results of the discussions that had been done. Then the teacher explains back how to solve the problems in mathematics to the students clearly and coherently. From the results of the discussions, presentations, and an explanation of teacher students can make a summary of the material as a result of the learning that has been followed.
7. Cognitive Scheme
Cognitive scheme is a sequence of descriptions of material that will be delivered by teachers to students. In this case the teachers make learning framework from scratch and used during the learning takes place so that students can be structured way of thinking and students can more easily understand the material more deeply. Cognitive schemes form the skeleton of a child thought to have a clear understanding of the flow of material that will be on receipt. For that teachers should make this line of thought so that students can take their own conclusions through knowledge they have acquired previously. In addition to cognitive skills of children in reasoning. When the teacher will provide materials to students, the material presented must be coherent in accordance with the order of the material. For example when the teacher will teach students the integral on the base material to be delivered is the differential or derivative. Thus the students would be more easily understand the material.
8. Student’s Conclusion
Student's conclusion is the taking of the conclusions made by students from the results of the discussion of the material that has been submitted by teachers as well as the decision made by the students as a result of the solving problem. Making the conclusion of the activity of mathematical material that has been taught to train students to think critically, analysis, logical, systematic and mathematically. through the process of making the conclusion that the student is done independently by using an understanding and knowledge that they had before, students can easily understand the concepts of mathematics that were still to be abstract. In addition students are also able to remember plot of understanding the concept of mathematical problem solving in long time. And if the student was asked by teachers, friends and others on the origins of the concept, they can answer that question with a quick, clear, coherent, and confident. This is because students are able to construct an understanding of the concept with the knowledge they have acquired previously.
In order for students to be able to draw correct conclusions about the concepts of mathematics lessons given by teachers. The first thing that must be made by the teacher before the teacher carry out learning activities that make our concept clear and coherent according to the flow of materials in accordance with the level of comprehension and thinking skills of students. So that students can easily make a conclusion on the matter of learning outcomes that have been followed. This will improve students' reasoning processes of concepts, laws, principles, and procedures of uraianmateri described by the teacher.
9. Apperception
Appersepton is a way of thinking about what had learned. In other words apperseption can be interpreted as a thinking process that links old lessons with new lessons, as a springboard extent to which students master the lesson a long time so it can easily absorb the new lessons. When a teacher will teach a concept anything about the material on the subjects of mathematics, the teacher should understand that every student has the experience, attitudes and habits are different, in order to explore and connect the experiences, attitudes and habits of students to the concepts that will teachers teach.
10. Assessment
Assessment is the process of collecting various data that can provide a describe of students' learning progress. In the context of teaching learning in the classroom, the assessment was conducted to determine the progress and result of the study of student, diagnosing learning difficulties, providing feedback / improvement of teaching and learning process, and determination of the class increases. Through the assessment can be obtained accurate information about the organization of teaching and learning success of students, teachers, and the learning process itself. Assessment has a very important purpose in learning, including for the grading, selection, knowing the level of mastery of competencies, counseling, diagnosis, and prediction.
In accordance with these goals, the assessment requires the teachers to be directly or indirectly to be able to carry out the assessment in the overall learning process. To assess the student has mastered a variety of competence, and of course, various types of assessment needs to be given in accordance with the competence to be assessed, such as performance/performance, assignments, the work of product, a collection of student work, and a written assessment. So, the purpose of assessment is to provide comprehensive information about the input results studied learners, both views when the learning activities taking place as well as the views of the end result, using a variety of evaluation in accordance with competencies that learners are expected to be achieved. In this case the teacher not only assess students only from the cognitive aspect of the ability of the course that is just the students can answer the question, but also such assessment must reach the affective aspect related to the behavior of students in the classroom and outside the school environment, students discipline in complying with schools rules and active participation of students in cooperation with his friends during in the discussion activities. And in doing a assessment the teacher should be more priority of student's study to construct the comprehension about the concept of the given and does not refer to the exam results.
11. Various Teaching Method and Various Teaching Aid
Teaching media can be defined as all objects become an intermediary in the process of learning. Based on function of learning media consist of teaching aid and facilities. employing the teaching media in the teaching and learning mathematics activities in school is to facilitate the interaction between teachers and students so that the learning activities will take place effectively and efficiently. the teaching aid are learning media containing or carrying characteristics of the concept to be learned. The main function of the teaching aid is to lower the abstractness of the mathematical concepts that are abstract and difficult to understand, with the aim that students are able to capture and understand the truth meaning of mathematical concepts such material. With the look, feel, and manipulate objects or teaching aid then students will have new concrete experiences in the lives of the meaning of the concept of mathematical material or given by the teacher teaches.
In carrying out teaching and learning activities in high school and junior high school mathematics teachers can choose and use appropriate teaching aid of the material to be delivered. For example to teach the material geometry teachers can use learning tools such as whiteboards, built space frame made of steel wire and straw that resembles the shape of space such as cubes, blocks, pyramid, prism and so on. Through this framework teachers can introduced and explain the characteristic of the cube, prism etc. based on the number of ribs, vertex, side, and the properties of the built space.
Facility is a teaching media that serves as a tool to do the activity of teaching and learning. By using these facilities is expected to improve teaching and learning activities. Examples of instructional of teaching media of mathematics can be form a facility such as r ruler, blackboard, a whiteboard, and so on. In addition means that the facility can be form worksheet and job sheet. At the time of implementation of teaching and learning activities teachers can use the worksheet on stage means planting concept and understanding of concepts. While the task sheet is a sheet means which can be used in teaching and learning. In teaching mathematics at a junior high and high school educators can do teaching media development efforts is through the development of computer in learning of mathematics.
C. Conclusion
In an effort to develop learning activities in mathematics in junior and senior high creativity is required to be possessed by every teacher who teaches math. Through high creativity, a teacher can prepare lesson plans in accordance with the standards of competence, basic competence, and indicators of achievement of competencies. In mathematics teaching and learning activities teachers can select and use teaching methods appropriate to students' classroom situations and conditions in accepting new knowledge. Selection and use of learning methods adapted to the material to be delivered. Mathematics learning materials by teachers who were trying to convey to the students should be arranged coherently and clearly so that students can construct their comprehension with their knowledge.
So that students can think logically, systematically, analysis, mathematical, and critical reasoning as well as to improve the process of students, teachers need to train students to make inferences from material that has been taught through discussion groups or individually. To strengthening the memory of students to the concepts he had learned the material teachers can use the method of presentation to train students in communicating with others. Each student should be able to present the results of discussions on how to resolve the issue. Thus creating a meaningful learning, fun, effective, and efficient.
