By : Rosa Ardiyati (09301241032)
Regular Mathematics Education 2009
Mathematics Education Department, Faculty of Mathematics and Natural Science
Yogyakarta State University
Learning Mathematics means doing Mathematics itself. In order to do that as a teacher has a big role in bringing the students to some kind of atmosphere so that the student can enjoy their time while they learn Mathematics. There a many things that should be concerned by a Mathematics teacher so that teaching learning process can be done perfectly.
In developing teaching learning process, at least there are many things that must be concern by the teacher. Those are lesson plan, student’s worksheet, small group discussion, various interactions, various teaching methods, various media, various teaching aids, student’s reflection/ presentation, cognitive scheme, student’s conclusion, apperception, and the last is assessment. All of those things are important to the learning process because of they include the process from the beginning of the lesson (making the plan: lesson plan) until the end of the lesson (assessment, e.g. presentation, exam, etc). Furthermore, speaking of the development of the teenager (we can say in junior or senior high school’s age), it needs many stimulus to improve their way to think. And it include the way to think in learning Mathematics. We can’t apply the same way of teaching Mathematics like when they are in elementary school. Their brain has improved. And that’s means we as the teacher have to improve our teaching learning in order to help them to improve their mind.
These are some explanations about things to develop in order to teaching learning process of Mathematics, especially in junior or senior high school.
1. Lesson Plan
Making a lesson plan is the first step in teaching learning process. And it’s a important step actually, because it consist of the whole plan of the teaching learning process. In formal description, we can say a lesson plan is a teacher's detailed description of the course of instruction for one class. First thing about lesson plan is it’s for only one class which is usually not be concerned by most of the teacher. Most of the teacher uses the same lesson plan to different classes. Each class have different potential and skill, so the teacher should make a different lesson plan.
There are few elements in lesson, those are title of the lesson, time allocation, the list of the material, or sometimes we can also write the standard competence and the basic competence before it. Also we have the list of objective (behavioral and knowledge objective) which is we call it indicators, the instructional component, the summary of the materials, and the last is evaluation. All of those elements are important to help the teacher manage the lesson. And it can be seen as the directive when the teacher do the lesson.
There are many benefits in making lesson plan, those are the learning process become more manageable because the teacher already planned it well, and through lesson plan the teacher can share their ideas to another teacher, the lesson can be well prepared, so the lesson can run efficiently and many other benefits.
Furthermore, in order to improve the student’s skill, good lesson plans also have to focus on what student need. What they need so they can improve their skill and knowledge, especially in learning Mathematics. And don’t forget to make a note while and after the lesson (as a teacher), so that the teacher can evaluate whether the lesson plan is good or need to be fix in some element, so the next session of the lesson can be better.
2. Student’s Worksheet
In senior high school and junior high school, the student already familiar with student’s worksheet. Even in elementary school, the student already has given this worksheet. Most of the teachers use this worksheet; prove the importance of this worksheet in developing teaching learning, especially in learning Mathematics. The student’s worksheet usually contains a lot of exercises, so that the student can improve their knowledge after the teacher explains the material.
3. Small Group Discussion
Every student in a class is unique. So there is no 2 student that exactly have the same skill, potential and talent. That makes the teacher has to find a way to make this heterogenic class still become efficient in teaching learning process. The teacher can do that through small group discussion. In small group discussion the teacher split the class into many group that each group only consist of 3-4 people, so that every student can communicate effectively to another in their group. Then the teacher gives them some problem or topic to be discussed. It will be different if the teacher does this in whole class method. In whole class or classical method the student tend to be more individually in solving the problem, whereas the students also need another idea to help them in solving the problem. Or maybe some students who have less understanding about the problem can be helped by sharing the problem by their peer in small group.
4. Various Interactions
There is one thing that very important in learning process, in this case is learning Mathematics. That is interaction. Every learning process involves interaction in the process. The traditional way of teaching uses one interaction. That is the teacher to the whole class, which is called classical interaction. There are many other ways to interact in learning process. Those are student to another or we called it peer to peer, this interaction makes them possible to interact with their colleagues. And there is interaction between some students (in a small group) to the teacher, this interaction usually used in small group discussion, so that the teacher can communicate with the student more efficiently. These various interactions should be used in order to make the whole lesson more interesting for the student. Because using one single interaction in whole time might make them bored and barely improved.
5. Various Teaching Methods
Every material in Mathematics needs different approach so that the student can understand it well. That means the teacher should employ different teaching methods in the learning process. In the traditional learning method, the teacher only use one one single methods, that is expository method. The teacher explains the material, giving some example, then exercises or homework, another explanation and then exam. That makes the student become passive.
First method is lecturing. Sometimes there are materials that can be better if it’s explained by the teacher itself than using another method. Usually the teacher use this method to teach some topic that hard to understand or we can say it advance.
The second is presentation. The subject of the presentation is not the teacher, but the student. In this method the teacher help the student to construct their ideas about the topic so that the student can make a presentation about the topic. This method can acknowledge the speaking skill of the student and also how they share their ideas to another. Usually this method can be used in some topic that easy to understand. So that the student can learn from textbook or other sources without teacher’s help. But the teacher still has responsibilities, that is at the end of the presentation the teacher make a short conclusion about the presentation and explain some addition information about the topic and explain it if the is something wrong about the material of the presentation.
The third is demonstration and experiment. In mathematics learning doing this method may need more expenses due to the teaching aids that we need. But using this method really helps the student to understand the topic. The students need to make visualization about the topic. And doing demonstration and experiment help them to do that. The topic that usually needs to be demonstrated for example is geometry, probabilities, Cartesian diagram, and many others.
The fourth is problem solving method. First step to do this method is the teacher gives the student a problem or some problem that can be solved by their own ways. Of course the difficulties of the problem should be suitable by their knowledge. Then every student must be has different ways to solved the problem. And at the end of the lesson the teacher teach the formal way to solve the problem. Thus the student can understand the topic more meaningful.
And actually there are still many other methods that can be employed in learning Mathematics. And those methods can be hold in different meeting so that the students become more creative and not only focus on one way to learn Mathematics. Use different methods in learning also prevent student from boring.
6. Student Reflection/ Presentation
Student reflection or presentation should be hold in order to develop mathematics learning. Reflection make the student can understand the material deeply, beside just listening what the teacher explain. And present their work can help them to improve their speaking skill and can make the whole class become more active.
7. Cognitive Scheme
Cognitive scheme is one of the things that should be concern by the teacher. Without that scheme the knowledge that the student get won’t be contextual. We can say the application of cognitive scheme is making a mind mapping. Thus, the student can make a mapping about what they have learned. And one thing that’s necessary about cognitive scheme is the teacher should begin the learning from what the students know, then develop it to what should they know, and how could they know.
8. Student’s Conclusion
At the end of the learning process, what students know is the most important result of the learning. Because learning is about teaching the students from don’t know the topic become knowing the topic. So student’s conclusion is really matter in the learning process. What teacher should do in order to make the student make a proper conclusion after the learning process is make a good plan in every lesson. Then in the learning process the teacher should not be too dominant, so that the student can have their time to conclude with their own ways.
9. Apperception
What is apperception? Apperception means readiness. And who should be ready? That is the student. The teacher’s role here is to help the student to construct their mind so that they can be ready for the topic. One important thing about construct the student’s mind is the teacher should begin from what they know before the teacher introduces them to the topic.
For example the teacher gives few questions that lead to the topic. So the teacher can acknowledge the understanding or how far the students know about the topic that will be learned. If the lesson has much time allocation, the teacher can hold the apperception to be better one. For example in topic calculate the area of a arbitrary rectangle. First, the teacher gives them the problem. And the students should solve the problem by their own way. This method can construct their ideas, because every student will have different point of view in solving the problem. Maybe it will be better if the class is split into some group, so the student can share their ideas to another. And the teacher move around the class so he/she can help the student, maybe by giving them hints in solving the problem. After few minutes some of the student come forward to the class and present their work. By this, the other student can find that there are many different ways to solve the problem. Then at the end of the lesson, the teachers teach them the proper way which is more efficient to solve the problem. By doing this apperception, the students are not only get their knowledge one way from only the teacher, but also through their ideas, then it will be completed by the explanation of the teacher.
10. Assessment
Assessment means to record or we can say evaluate. Assessment holds from the beginning of the learning process. Usually the teacher only holds the evaluation at the end of the lesson. Whereas the process of the learning also important. Doing the assessment means make a note for the whole class and each student (individually). The way to evaluate the student can be through exam, student’s presentation and demonstration, paper, homework, and etcetera. The benefits of the assessment for the student actually are for evaluate their improvement in learning, and for the teacher is to evaluate the process of learning, whether it has already well or need to be fixed in some element.
11. Various Media and Teaching Aids
There are a lot of media and aids to developing mathematics learning. In conventional method, the teacher only uses few media that is blackboard and textbook. In this way of learning the student tend to think that the knowledge is only come from the teacher, which is wrong. In this modern era, the media of learning can be various. There are LCD, aids, internet, group discussion, seminar, and etcetera. Through LCD, the teacher can use some PowerPoint presentation, Flash Presentation, Video, or just few images to help the student improve their knowledge and understanding the topic. Not only media, but there are teaching aids which is also important. Teaching aids can be some homemade craft or some aids already have been provided in some store. These teaching aids help the student visualize the topics. Because sometimes there are some topics that hard to understand if the student are not see it as a real thing, and that the benefit of the teaching aids.
Learning Mathematics and maybe it satisfy by other subject, is about the process of the learning. We can’t concern in only few part of the process. For example only focus on the assessment and worksheet. If we just concern with only few of that process it means that the learning won’t be done well. The student can’t reflect their ideas while the learning, because the teacher doesn’t really concern about student’s reflection/ presentation. The teachers just use the conventional ways to do the learning. And that is teacher center, which is not suitable anymore to be done in this modern era. Because now we already have the new international trend which is student center, so that teacher employs various ways to teaching and the role of the teaching is not as the only source of knowledge but as the one who helps the students to understand the knowledge through many things.
