How to Develop Teaching Learning Process of Mathematics in Junior High School/Senior High School
by
Felisitas Sayekti Purnama Utami (09301241007)
Student of Mathematics Education 2009
Student of Mathematics Education 2009
I. Introduction
During this time, the system of mathematics education at junior high school and senior high schools in Indonesia are still using traditional learning methods. The teacher is seen as the only source of learning. Students are regarded as empty vessels that must always be filled. Teacher is to be authoritarian, frightening, and always transferring his thoughts to the students. Student always passive and does not get involved in learning activities. Formal classes and teachers use the lecture method in teaching mathematics. The teacher explained only teaching materials, give examples, and assign tasks to students. Learning method is not relevant to learning mathematics. Mathematics is the science which is obtained by way of reasoning. Mathematics is formed as a result of human thought associated with the ideas, processes, and reasoning. Teachers should change the method of learning from teacher-centered methods to student-centered methods. Teachers should guide students to discover their own mathematical concepts. In this way, students become more active in learning and students are not easy to forget these mathematical concepts. Teachers should facilitate students in learning mathematics. Learning methods that are applied must be varied. Sources of teaching material are not only from teachers but also from the print media, electronic media, books, internet, neighborhood students, and others. A good teacher should always develop mathematics teaching and learning process.
Teacher can develop teaching learning process of mathematics in Junior High School/Senior High School when understand about lesson plan, student worksheet, small group discussion, various interaction, various teaching method, student reflection/presentation, cognitive scheme, student conclusion, apperception, assessment, various media and teaching aids.
II. How to Develop Teaching Learning Process of Mathematics in Junior High School/Senior High School
1. Lesson Plan
Planning the learning process involves learning the syllabus and the lesson plan. Lesson Plan is translated from the syllabus to guide the revision learners in order to achieve the basic competencies. Each teacher to plan the implementation of a complete and systematic learning that learning takes place in an interactive, inspiring, exciting, challenging, motivating learners to actively participate and provide enough space for the creativity of students. Implementation of structured lesson plan for each of the basic competencies can be implemented in one session or more. Lesson implementation plan contains learning objectives, learning materials, teaching methods, learning resources, and assessment of learning outcomes. The components of the lesson plan are:
a. The identity of the subjects included educational unit, class, semester, courses, subject horse or theme, and the number of meetings.
b. Competency standards are minimum qualifications ladies depicting student mastery of knowledge, attitudes, and skills to be achieved in each class or semester on a subject.
c. Basic competencies to be mastered are the ability of students in course as a reference preparation of indicator of tension in a lesson.
d. Indicators of achievement of competence are a behavior that can be measured or observed to demonstrate achievement of certain basic competence is the reference subjects.
e. Learning objectives which describe the process and expected learning achieved by students in accordance with basic competence.
f. Teaching materials / instructional material is material that is used to achieve learning goals and developed with reference to the learning material in the syllabus.
g. Allocation of time determined in accordance with the purposes of basic competency achievement and learning loads.
h. Method or approach to learning is a model of learning that depend on the characteristic of the chosen approach or strategy, for example, methods for questions, discussion, experimentation, and some models of learning approaches such as contextual approach and cooperative learning model appropriate selection choice of learning methods adapted to the situation and conditions of students, as well as the characteristics of each indicator and competencies to be achieved in each subject.
i. Learning activities included
· Introduction is the initial activity in a meeting intended learning motivating and focusing the attention of learners to participate actively in the learning process.
· Core activity is a learning process to achieve basic competency. Learning activities in an interactive, inspiring, fun, challenge, motivate learners to actively participate and provide enough space for innovation, creativity, and independence in accordance with the talents, interests, and physical and psychological development of learners. This activity is carried out systematically and systemically through the process of exploration, elaboration, and confirmation.
· Closing is activities undertaken to end the learning activities that can be done in the form of summaries or assessment and reflection, feedback, and follow-up.
j. Learning outcomes assessment procedures and instruments namely the assessment process and students learning outcomes that are tailored to the achievement of indicator refers to the competencies and standards of assessment.
k. Source of learning refers to learning resources contained in the standard of competence and basic competences, as well as teaching materials, learning activities, and indicators of achievement of competencies.
In order for mathematics teaching and learning activities meaningful, teachers required to be creative in developing learning and developing the implementation lesson plan. The methods used varied learning so that students play an active role and to construct their own math. By constructing their own math, students will always remember his findings and basic competence was achieved.
2. Student Worksheet
Student worksheets are worksheets created by teachers for students to facilitate students' understanding of material taught. Teachers try to make worksheet students thus enabling students to learn the material independently. Student worksheet is one of the important tools of learning mathematics and be able to help students discover and develop mathematical concepts. Student worksheets form of sheets of paper containing a description of the material, assignments, and training related to the material provided. Students will take an active role in learning. Student worksheet can be given after the teacher explained the material taught in front of all students and dividing the students into several groups. Teachers are responsible to monitor students in the learning process. The structure of student worksheet included:
a. Titles, subjects, semester, and place
b. Instructions to learn
c. Competencies to be achieved
d. Indicator
e. Supporting information
f. The tasks and work steps
g. Appraisal
Student worksheet has many benefits which direct the learning activities, accelerate the learning process, and best learning media owned. A good student worksheets aimed at guiding students to a variety of activities is given and considered the thought process that will be grown on students. With this worksheet, students have a solid concept of the subject matter and interest in the subject matter increases as student worksheets prepared by teachers draw students' attention. Worksheet students must be written in a systematic and coherent. The things done in the writing of student worksheets are:
a. curriculum analyze, competency standards, competency base, indicators, and learning materials.
b. compile a map of the needs of the student worksheets
c. determine the title of student worksheets
d. writing students worksheets
e. determine the assessment tools
3. Small Group Discussion
Discussion is a conversation that contains the exchange of scientific opinion, the appearance of the ideas and the testing of polls taken by some people who are members of the group to seek the truth. Small group discussion method can be used as a method of learning. Discussion method in teaching and learning means to express opinions in the method of deliberation to reach consensus. Students agree to determine the best answer from the problems it faces.
A teacher must think creatively in determining a suitable learning method. Teachers who have described the subject matter in front of the class can override methods of teaching methods with little discussion. All students in the class divided into groups consisting of 3-5 students per group. Within the group, teachers share students' worksheets. The students discuss the issues outlined in the student worksheet. Students are required to participate actively with the expressed opinion among a group of friends. Teachers monitor the discussions and identify the difficulties experienced by students. Teachers discuss these difficulties and offer solutions to problems. Goodness discussion method is able to broaden students 'horizons, can stimulate students' creativity in generating ideas to solve a problem, can develop respect for other people's opinions, and can grow to become more active student participation. Deficiency is probably discussion method will be dominated by discussion of students who like to talk or want to assert themselves, cannot be used on a large group, students have limited information, absorb considerable time, and not all teachers understand how students conduct discussions. In using discussion method the teacher should pay attention to the following requirements:
a. The ability of pupils
b. Problem with the level of difficulty that requires a serious solution to be led by the teacher given to the student-led discussion in turns
c. Teacher guide and control the student discussion
d. Teachers seek the students participated in the discussion
e. All students should have a turn to speak and the other students learn to be patient to listen to the opinion of his friend
4. Various Interactions
Interaction is a form of communication between one people to another. Interactions that occur within a classroom are the interaction between teachers and students and between students and student interaction. Interaction is very important because the presence of interaction, students can construct their own mathematical concepts. Interaction between teachers and students can be divided into the interaction between teachers and all students in the classroom, between teacher-student interaction in a group discussion, and interaction between teacher and every student. Meanwhile, the interaction between students and students can be divided into the interaction between a student with all his friends, the interaction between a student and his friends in the group discussion, and interaction between a student with a student. Interaction between teachers and all students in the classroom occurs when the teacher explains the teaching materials to all students. Interaction between teachers and students in a group discussion occurred during the course of discussion the teacher to monitor students and identify the difficulties experienced by the group discussion. The interaction between the teacher and each student occurs when teachers identify individual difficulties and offer solutions to problems.
The interaction between a student and all his friends occurred when a student is advanced to the front of the class expressed the opinion on the problem or problems that exist in the student worksheet. Any other friends listen to their opinions and provide feedback. Interactions between a student and friend in the group occurred when they discuss solutions to problems outlined in the student worksheet. During the discussion, they are trying to find the best solutions to problems with the deliberations. The interaction between a student with a student occurs when they mutually express opinions and exchange insights. The teacher's role is to build a healthy interaction among the students so that teaching and learning process can proceed smoothly and achieve competency standards.
5. Various Teaching Method
Teaching method is a method used by teachers to teach the material taught to students so that students are easier to understand the material being taught. There are many kinds of teaching methods namely exposition method, discussion method, investigation method, contextual method, lecture method, methods of practice, and others.
a. Lecture method is a method of teaching most often found in the study of non extra. Teachers only determine the order of delivery of material and present it in front of the class. Lecture method has the advantage that can accommodate a large class because each student has equal opportunity to listen to, the costs used are relatively inexpensive, teachers can pressure members to things that are important, and lack of mathematics teaching aids will not disrupt learning. Lecture method also has the disadvantage that mathematics lessons become bored for students because students are passive, students are unable to master the material studied in depth, the knowledge gained through lectures will quickly disappear, and students just memorize mathematical notions.
b. Exposition method which is almost the same as the lecture method in the method of exposition, but the teacher's role is much reduced. Students can ask for trouble and the teacher helps students to find solutions to solving the problem.
c. Practical method of learning that requires students to actively practice solving math problems given by the teacher. Students who are accustomed to working on math problems have been unconsciously instill math concepts in mind.
d. Discussion method is centered on the students because students are required to actively issuing an opinion, ask replied with peers, and concluded as a group problem-solving solution.
e. Contextual learning method is a method that attempted to link learning with real-life teaching materials around the student or real shadows that exist in the minds of students.
Teaching method mathematics continues to grow from day to day. Teachers also need to develop teaching method so that students do not get bored studying mathematics. Teachers are required to design learning creative as possible. By applying various teaching method, the student should be able to find and develop their own math.
6. Student Reflection/Presentation
After the students discuss the problem within each group, students were asked to come forward. Students explain and express his opinion on the matter given in the student worksheet. When a student came forward, all other students will hear the explanation. Stage presentation is to train students to dare to express his opinion in front of other friends and practice of self-confidence. When finished expressing his opinion, other students can provide feedback. This spurred an exchange of knowledge among students. Students who do not agree with his opinion must express their own opinion. In addition, presentation is training students to think critically and creatively. By presenting his work in the future, teachers can identify students understood the material and the material has not yet understood by students.
7. Cognitive Scheme
The scheme is a chart listing the sequence build students understanding of teaching materials provided by the teacher. Cognitive schema contains a coherent description of the material so that students understand what material should be studied in advance so that he has a new understanding of related material taught. In studying mathematics, there is a pre-condition that the material can study the matter further. For example, if students want to understand the concept of dimension three, students must first master the material up flat. The material can be said to be flat wake as a pre condition to study the matter up space. With the cognitive schema, students become much easier to understand the linkages and relationships between the materials that one with another material. If the teacher wrong in describing the material description, students will have difficulty in constructing his thinking.
8. Student Conclusion
Students must share the opinion with other friends. After all students advance to the front of the class to present the results of their discussion, the teacher summarizes the opinions of all students with students about what has been understood and have not understood of learning materials are studied. Reflection is a summary of teacher learning that has been delivered. Teachers provide opportunities for students to draw conclusions based on the opinions of all students. Students can do independent writing activities on a summary of learning outcomes that have been followed.
The conclusion obtained by the students will imprint on the minds of students so that students are not easy to forget. So far, the inference is always done by the teachers so that students do not know the way of inference. As a result, students are only memorizing mathematical formulas to understand but do not understand the intent and meaning of the formula. Conclusions drawn by the teachers will be more easily forgotten by the students.
In conclusion, the student takes a little bit longer. Therefore, teachers must be patient, guiding, and directing students' mindset so it can be a right conclusion. If students are wrong in drawing conclusions, the teacher is obliged to explain where his mistakes and correct errors so that the students' understanding of mathematical concepts to be true.
9. Apperception
Apperception means interprets a thought to integrate and assimilate an observation based on experience that has been owned and thus be able to understand and interpret new knowledge. Apperception is about the students and not teachers. Teachers play an active role that students give new responses associated with the material being taught math. The teacher can give a small problem at the beginning of learning that aims to determine the ability of the students possessed the prerequisites for learning new material. Students are expected to actively express their opinions as far as he knows to understand the new concept of the unknown. Apperception aroused students' interest and attention to something. Therefore, learning is designed in several stages namely:
a. Preparation (preparation): students are prepared to accept the new material by generating material apperception through a test or a discussion so that teachers know the extent of knowledge of students about a problem.
b. Presentation: In this phase teachers provide new learning materials.
c. Association: new material was analyzed and compared with other things associated with that material.
d. Generalization: in this phase of the conclusions drawn are the principles and insights.
e. Application: students are given the opportunity to use and train the new material is learned.
10. Assessment
Assessment is making a record about learning process. Assessment must undercover about student understanding. Assessment is not a discrete process but integral to every stage of teaching, from minute to minute as much as module to module. Informal assessment is going on all the time. Every time a student answers a question, or asks one, or starts looking out of the window, or cracks a joke, he is providing teacher with feedback about whether learning is taking place. It's more an evaluation of the teaching session than about his learning, but the two are inextricable. Assessment reaches back into the rest of teaching: in particular, poorly designed formal assessment regimes can severely hinder student learning and distort the process and subject matter. All assessment is ultimately subjective: there is no such thing as an objective test. Teacher can still make every effort to ensure that assessment is valid, reliable and fair.
A valid form of assessment is one which measures what it is supposed to measure.
a. It does not assess memory, when it is supposed to be assessing problem-solving.
b. It does not grade someone on the quality of their writing, when writing skills are not relevant to the topic being assessed, but it does when they are.
c. It does seek to cover as much of the assessable material as practicable, not relying on inference from a small and arbitrary sample.
The traditional distinction is between summative and formative assessment. Summative assessment is what students tend to focus on. It is the assessment, usually on completion of a course or module, which says whether or not you have "passed". It is or should be undertaken with reference to all the objectives or outcomes of the course, and is usually fairly formal. Considerations of security ensuring that the student who gets the credit is the person who did the work assume considerable importance in summative assessment, which may push in the direction of using conservative approaches such as examinations, which are not necessarily highly valid. All summative assessment can also be formative, if the feedback offered is sufficient.
Formative assessment is going on all the time. Its purpose is to provide feedback on what students are learning: to the student: to identify achievement and areas for further work and to the teacher: to evaluate the effectiveness of teaching to date, and to focus future plans. While grades or marks may assume primary importance in summative assessment, their role in formative assessment is simply to contribute to the feedback process: marks awarded against specific criteria may be much more use than global judgement.
11. Various Media/Teaching Aids
Media are tools that help teachers to facilitate the process of teaching new material to students. Students generally learn mathematics through concrete objects. To understand abstract concepts, students need visual aids as an intermediary or visualization. With the teaching aids, the new material is taught can easily be understood by students. Teaching aids are often called audio-visual tool that can be absorbed by the eyes and ears. Some examples of teaching aids that can be used in teaching are: drawing tables, cube models, blocks, balls, and others. Teaching aids have advantages such as:
a. Growing interest in student learning because the lessons become more interesting.
b. The concept of abstract mathematics presented in concrete form so that students more easily grasp and understand.
c. Clarifying the meaning of learning materials so that students more easily understand
d. Teaching methods will be varied so that students will not get bored easily
e. Creating a more active student learning activities such as: observing, performing, demonstrate, and so on.
f. Use visual aids to stimulate students' imagination and provide a deep impression on the senses to teach because the students are stimulated and engaged in learning.
Teaching aids have flaws such as:
a. A lot of the time required for preparation
b. Funds for the provision of much needed props
Teaching aids are used by the teacher should have the following properties:
a. Durable (made of material that is strong enough).
b. Interesting shapes and colors.
c. Simple and easy to manage (not complicated).
d. Appropriate size (balanced) with the physical size of the student.
e. Can examine mathematical concepts (not complicate the understanding)
f. In accordance with the concept of learning.
g. Can clarify the concept (not complicate the understanding)
h. Demonstration was to become the basis for the growth of abstract thinking concepts for students.
i. If such teaching aids might be useful as much (much)
The process of learning with visual aids is not always able to produce the expected results. The use of visual aids may not clarify the concept and make the students become confused. In choosing props there are things that need to be noticed by teachers namely: objectives, subject matter, teaching and learning strategies, student learning condition, and did not use the media to teach students is too small that it is difficult to see and be noisy. Because the benefits are great, the school should strive to make teaching aids that support learning activities. The teacher was sometimes able to make teaching aids are simple to explain the teaching materials.
III. Conclusion
Most of the teachers in junior secondary school and high school still apply traditional learning methods. The teacher explains the material, give examples, and assign tasks to students. Students are not involved actively in the learning process. This method is not relevant in the learning of mathematics. Students should construct their own thoughts and construct their own math through a variety of learning methods are varied. The teacher must facilitating, motivating, and guide students in learning mathematics. Teachers must develop creative teaching and learning mathematics. In order for teachers to know how to develop mathematics teaching and learning activities, teachers need to know about the components of the development of mathematics teaching and learning activities such as lesson plans, student worksheets, small group discussion, interaction various, various teaching methods, student reflection / presentation, cognitive scheme, student conclusion, apperception, assessment, various media and teaching aids. Hopefully, after the teacher understanding about these components, teachers can change the method of learning mathematics from teacher centered to student centered. Mathematics learning activities becomes more meaningful.
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