A. Introduction
Today, mathematics is object that be afraid by students. From national examination, we know that achievement in mathematics education in junior high school still low. The achievement of mathematics education is affected by teaching and learning process. Teaching learning process is important thing that must be consider. In teaching and learning process, teacher must consider students ability, students difference, method of teaching, etc. Usually, teaching and learning process contain of introduction, main curse, and conclution.
B. How to develop teaching and learning process of mathematics in Junior High School
How students learn? How teacher supporting students? So, we need to develop teaching and learning process of mathematics in Junior high school. We need to change treacher centered learning to the students centered learning. And teacher need to not only consider the result of the course, but also the process of the course. There are some aspect that must be consider to develop teaching and learning process of mathematics:
1. Lesson plan
Planning is key of success activity. Every activity that have good plan have greater possibility to be success. So that education. To have good education we need planning. Before teacher teach their students, actually teacher must create lesson plan. Lesson plan is not only to report to the accessor or school but actually lesson plan must become the key of teaching learning process. Teacher make lesson plan to have illustration how will their teaching and learing process will be done. Not only that, lesson plan also conduct of assesment. So, what is lesson plan? And how to develop mathematics lesson plan in junior high school?
Lesson plan is a plan for learning made by teacher that describe procedure and teaching management to reach one or more basic competence. Lesson plan can be used by teacher as general guide to implement teaching and learning process. Lesson plan will help teacher to organize standard material and anticipate students and constraints that may be face in teaching and learning process. Without lesson plan, a teacher will have difficulties in teaching learning process. Usually, teacher that have little experiences need lesson plan that more detail than teacher that have more experiences.
Lesson plan contain of some aspect:
a. Basic competency.
Competency that formulate in lesson plan must clear. Competency will be easy to monitor if competency is more concrete.
b. Standard material
Standard material that develop must appropriate with the students ability and needs, contain functional value, and appropriate with condition and the needs of environment and region.
c. Learning activity
Learning activity is stage that will done by teacher and students to finish standard material that have been planned. The stage usually contain of introduction, main material, and closing.
d. Teaching method
A teaching method is characterised by a set of principles, procedures or strategies to be implemented by teachers to achieve desired learning in students (Liu & Shi in Peter Westwood, 2008).
e. Learning media
Learning media is all of tools that can deliver information from teacher to the students. Through media, students can see, read, hear, or the three of them in understanding material. Electronics tools can be used as learning media.
f. Learning resources
Learning resources that can be used in teaching learning mathematics process are textbook, models, diagram, computer program, etc.
g. Time allocation
Time allocation is amount time that needed by teacher and students to do the stage of learning activity.
How to develop mathematics lesson plan? There are some stage to develop mathematics lesson plan:
a. Designing the instruction that appropriate with students need. So, teacher need to k now students ability, background, learning experiences, ability to work together, etc.
b. Identify the purpose of the lesson that teacher want the students to achieve.
c. Identify the objectives that teacher hope their students will achove. Objectives are behavioral in nature and performance.
d. Describe teaching method.
e. Describe assassment
2. Students worksheet
Students worksheet is worksheet that made by teacher to guide students thinking.
By using students worksheet, we wish that students worksheet will help students to make sense of the contents. The key to develop good students worksheet are:
a. the content of the worksheet must serve the essential purpose.
b. Students worksheet not only contain of problems but also contain of guide to reach the basic concepts.
c. Make students worksheet that make students ineteresting
d. Relate the material with real life
The purpose of students worksheet:
a. Focusing students attention
b. Bridging the gap between watching and doing
c. Encouraging students to communicate their mathematical ideas
d. Delivering and or summaarizing content efficiently
3. Small group discussion
Smlal group discussion start with divide students in group. Each group contain fo 3, 4, or 5 students. In divide students to a small grooup, we need to consider some aspects. First, every member of the group must have heterogen ability.
Implementation of small group discussion start with teacher give the problems. Then every group must solve that problem. In small group discussion, students can share their ideas with other. Students that have more ability can develop their understanding by explain the material to the other. And students that have low rank ability can helped by the others. Teacher can move around and support the students. Teacher can give question yang stimulate students thinking so that students more understand about the material. They can share about materials. After each group have solved their problem that given by teacher, every group must choose their representative to present their result in small group discussion in front of the class. After all group have presented their result, teacher can investigate their result. Note that teacher must not mistaken the students. Teacher must give good response to the students. But, teacher also must give information about the right concepts. Sometimes, some students needs to have clarification from the teacher if their concepts, formula, and their discussion result was correct.
The advantages of small group discussion:
a. Improve interaction betwen students with other and between students and teacher
b. See the thinking pattern of the students
c. Improve students creativity
d. Make teaching and learning process more fun
e. It is motivate the students because students can get feedback from teacher and the others
The important points to develop small group discussion are:
a. When teacher divide students into small group, please made the member of each group to have heterogen ability
b. Teacher let students to explore their knowledge. Teacher let students to do effort to solve the problem. If students make mistake, teacher no need to became angry and mistaken the students but teacher need to give question that make students conscious about their mistake and students can understand the right concepts.
c. Sometimes teacher need to give success experience to the students so that students became confident.
d. Teacher need to appreciate students opinion and give good response to the students
e. Teacher need to support the students if they start to confuse and teacher give clue to the students.
4. Various interaction
There are three various interaction:
a. Whole class
Whole class is interaction that done by teacher in front of all the students. Usually, in the beginning of the lesson, teacher introduce material that will be learn. The keys of good whole class teaching are:
1) Teacher must look students in the eye so that students can really understand the material. Another advantage of see students in the eyes are teacher will know students responds, did students understand? Confuse, or sama sekali tidak paham.
2) Teacher must give stimulate question that become point utama the material. Trough stimulate question, students will curious and think more deeply
b. Group discussion
Group discussion happen when teacher divide students in the class to soe group. Usually, teacher give problems to every group so taht the member can share their idea.
The keys of interaction in good group discussion are:
1) Give problem that make students motivated to solve it.
2) Mix students that have low rank ability with high rank ability ( member of the group are heterogen)
3) Teacher give support and hint to the group.
4) Teacher give stimulate question to the group.
5) Teacher appreciate students effort
c. Individual
Individual interaction between teacher and a student happen when a students that have difficulties ask to the teacher. Individual interaction also can happen when student interact with other student.
5. Various teaching method.
As we know, today almost all teacher use classical method to teach. The cycle of classical method is explanation, giving example, giving problem, and then evaluation.
But actually there are some teaching method that can be implemented:
a. Expository:
In expository method, teacher’s role is as center of the learning. Teacher explain the material. Teacher expalain the definiton, principles, and concepts of the subject. After that, teacher give example. Students follow the pattern that teacher set. In this method, students did not find their own facts.
b. Discussion method
Discussion method is teaching method that faced students to the problem. The main purposes of those method are to solve the problem, answer the question, add and understand students knowledge.
The special quality of discussion method are stimulate students creativity, stimulate students to share the ideas to solve problem, and stimulate students to share their opinion. Discussion also melatih students to appreciate opinion of another person.
Stage of discussion method:
1) Determine the goal
2) Determina type of discussion that will be done appropriate with the goal
3) Determine problem that will be discussed
c. Investigation
An investigative approach to teaching mathematics, as well as employing investigational work in the classroom, literally investigates the most appropriateways in which a teacher can enable concept development in students. Mathematical investigation seemed to involve students in loosely-defined problems, asking their own questions, following their own interests and inclinations, setting their own goals, doing their own mathematics and, moreover, having fun.
The benefit of investigation:
1) Students can identifying and expressing their own problems for investigation.
2) Students can expressing their own ideas and developing them in solving problems.
3) Testing students ideas and hypotheses against relevant experience.
4) Students rationally defending their own ideas and conclusions and submitting the ideas of others to a reasoned criticism.
d. Practical work
Mathematics is abstract. To solve its abstaction, teacher can use practical work as the method of teaching. In mathematics practical work, students practice about the material based on setting that teacher gave. The practice is based on the material. Students can work in better way only if they thoroughly understand the concepts. Practical work can develop creativity and understanding among the students.
e. Contextual teaching and learning
Contextual teaching and learning is concepst of learning that help teacher relate the course with real life. It is encourage students to make relation between their knowledge and its application. In contextual teaching and learning, teacher try to relate the material with previous material so that students have meaningfull learning.
There are some approaching of contextual teaching and learning:
1) Problem based learning
2) Authentic instruction
3) Inquiry based learning
4) Project based learning
5) Work based learning
6) Service learning
7) Cooperative learning
The key that must teacher do in implementatio of contextual teaching and learning:
1) uses real-world problems as a context for students to learn about critical thinking and problem solving skill and to acquire knowledge of the concept that the essence of the subject matter. In this case the students involved in the investigation to solving the problem of integrating skills and concepts from various subject matter content. The role of teachers in this study is to present a problem, ask questions, facilitates the investigation and dialogue.
2) More emphasis on practice, both in the laboratory and in the community and the world of work (business).
3) Learning should be able to establish relationships with community schools.
Therefore, every teacher must be able to see a variety of potential people who could be utilized as learning resources, and become a liaison between the school environment.
Therefore, every teacher must be able to see a variety of potential people who could be utilized as learning resources, and become a liaison between the school environment.
4) Need to develop a democratic climate and open learning through integrated learning, participatory and the like.
5) Need to develop a learning model 'moving class', for each field of study, and the classroom is a laboratory for each field of study, so that in a classroom equipped with various facilities and learning resources needed for learning and learners can learn in accordance with the interests and capability.
6. Students reflection
Reflection is process of reviewing an experience of practice in order to describe, analyse, evaluate and so inform learning about the pactice. When students reflect, they thoughfully consider an experience.
Actually, students reflection done by presentation. After students solve the problem individually or in group discussion, students can presents their result in front of the class. Students explain why they get those result, the thinking process, and way to solve them.
At students reflection, other students can ask the question, and comment.
7. Cognitive schema
Cognitive schema is the organization of knowledge about particular concept. People uses cognitive schema to do adaptation and coordination with environment. There are three process in pembentukan cognitive schema:
a. Asimilation: process integrating new information to the cognitive schema. It is happen when new information is agree with previous knowledge
b. Accomodation: adaption cognitive schema in new situation. It is happen when new information can not directly assimilated with cognitive schema because new information is different with previous knowledge.
c. Disequilibrium and equilibrium
Accomodation begin when new information not suitable with previous knowledge, at this process happen disequilibrium. Then, the cognitive schema reconstructed so that suitable with previous knowledge or happen equilibrium, then the new information can be accomodate then assimilated to be new knowledge.
First stage to know students cognitive development is looking students behaviour when they interact with object or another person. Based on piaget, students of junior high school have reach formal operational stage. Because of that, junior high school students have develop abstract thinking and logs to solve the problem.
8. Students conclution
Students conclution is conclution that made by students after the lesson. Students can share what they have learn in this lesson and share the concept that they just learn. After heard students conclution, teacher will know the understanding level of the students. If students conclution is right, teacher may be can belive that the lesson is make studets understand but if students conclution is not goor or not right, teacher must not let it go. Teacher must inform the right material. Students conclution also let teacher know if students consider the lesson or not.
9. Apperception
Apperception is help that teacher give to the students to know the students readiness.
The purpose of the apperception is to know students readiness in physic and psychological to learn the material. Appercetion can be done by giving tematic apperception test or by ask the students about previous material that needed or became basic in current material.
The importance of apperception:
a. To know from where teacher must start the lesson
b. To help students remembering the previous lesson
c. To identify which material in previously that students didi not understan so that teacher can help them.
10. Assesment
Assesment is process of collecting students information. The purpose of assessment is to know how far the understanding of students. It is also to know the effectively of teaching method.
Usually, teacher used test to do assesment. But actually there are some ways to obtaining information on students progress like interviewing, investigation, etc.
Assessment help teacher to immediately improve their lesson because through assessment teacher can know students difficulties and effectiveness of the teaching method.
The purposes of the assessment are:
a. To know the students progress
b. To know the effectiveness of the teaching method
c. To know students difficulties
d. To motivate teacher and students
There are two type of assessment:
a. Formative
Formatie assessment is valuable because it is allows a teacher to make immadiate adjustments to the program of instruction when necessary. The common ways of conducting formative assessments are by
(1) interviewing students,
(2) observation of students a work,
(3) appraising work sample, homework, and portofolios,
(4) giving quiz and informal testing
b. Summative
Summative assessment done in the end of the semester. It comes too late to influence the current teaching cycle. (Peter Westwood, 2008)
11. Media and teaching aid
Learning media is tool that can inform the students about the material. Through learning media, students can seee, read, hear, or three of them in menyerap information that disampaikan by teacher. Teaching aids are intended to support the teacher in teaching learning process.
The important thing that must be consider is that uses of teaching aid must be satisfied with the purpose. The correct teaching aids need to be developed and teaching aids need to be employed correctly in class.
There are some teaching aid that can be used in mathematichs teaching and learning. In using teaching aids we must consider the material. Different material may be has different teaching aids. In example, if the lesson is about square and square root, we can use nail board and hand-rubber as teaching aids. If we learn about phytagorean theorem, we can use sipat thread, stake, sticks, and measurement tools
Teaching aids are useful to:
a. Students can visualise or experience something that is impratical to see or do in real life
b. Engage students other senses in the learning process
c. Improve students motivation
d. Facilitate different learning style
e. Focus with what is important
C. Conclution:
To develop teaching and learning process of mathematics in junior high school, teacher must consider some aspects: lesson plan, students worksheet, small group discussion, various interaction, various teaching method, students reflection, cognitive schema, students conclution, apperception, assessment, various media and teaching aid.
Every aspect must be used effectively because each aspect affected teaching learning process.
D. References
Westwood, Peter. 2008. What Teacher Need to Know. Australia: Camberwell, Vic. : ACER Press,
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