HOW TO DEVELOP TEACHING LEARNING PROCESS OF MATHEMATICS IN JUNIOR HIGH SCHOOL AND SENIOR HIGH SCHOOL
By
Hafizh Praditya Mahardika/09301241001/Pend. Matematika 2009
A. Introduction
As we all know that education in Indonesia has not been good enough. The education has not shown the progress of relevant. Of course the indication of problem can be derived from many factors. It can be from the teachers, the students, the school, the material, and also the method of learning process. Although the curriculum in Indonesia has been good enough but unfortunately the realization of the curriculum has not been good. As School Based Curriculum, actually that curriculum has good content and purpose which to develop learning process in the class by creating meaningfull learning. But once again there is nothing relevance one factor with others, like the teachers cannot apply, the students do not want to learn, and many other. In the other case developing learning process be expected can also develop education in Indonesia, especially mathematics lesson.
In Junior and Senior High School mathematics still considered monster by the student in their learning process in the class. Mathematics considered difficut lesson, both of the material and its delivery by the teacher, so that it is can affect their achievement in mathematics. The obstacle of student’s learning of mathematics come from inside and outside factor. The inside factor like motivation and spirits. The outside factor fasilities and infrastructure, monotown method, and wrong way of study. The students felt do not geting anything from learning process in the class, because they do not understand the teacher’s explanation. Here the teacher plays an important role that almost influential because the teacher create ideas which organize learning process. The meaningfull learning process can develop student’s achievement in mathematics. There are many way to make meaningfull learning process, it is like lesson plan, student’s worksheet, small group discussion, various interaction, various teaching method, student’s reflection, cognitive scheme, student’s conclusion, apperception, asessment, various media and teaching aids. The essentially of its in the aplication by the teacher.
B. How to Develop Teaching Learning of Mathematics
Teacher’s attempt to create meaningfull learning process can brings the student to active, creative and innovative. Its attempt course needs participate from the student and the environment. It is teacher’s attempt to develop teaching learning process of mathematics:
1. Lesson Plan
What is lesson plan? Lesson plan is kind of skenario created by the teacher to see plan of learning process. Its contain when, where, and how learning process should be. Lesson plan make details description of intruction process in the class that depending on the teacher, subject being covered, and the need. The activity during make lesson plan such as makes observation paper, list of required material and suitable media, determine evaluation component, prepare the journal to examine learning progress, and make summary. By lesson plan both of the teacher and the student will ready more and more before learning process begin because they can describe what needed to make meaningfull study. Also by lesson plan the teacher can determine time needed to explain about the material or allocation time and know where get its resources, see the indicator, determine a good activity that suitable used to explain the material, determine what suitable assigment and guide make the syllabus. With lesson plan the teacher also can anticipate many probability problem arround teaching in the class, for example the student actually has been not understood yet about a chapter so the teaher can repeat their explanation without distrub the next intruction. So the learning process seem perfect with lesson plan so that create meaningfull learning process atmosphere.
2. Student’s Worksheet
Student’s worksheet is set of task or assigment from the teacher which purposed to create student’s motivate for studying. Beside that student’s worksheet also shaped summary of material which packed by clearly so that possible the student can learn it indepedently. With student’s worksheet they have a duty to did it, example find solve about the problem. By its the student will be familiar with problems and its solve, so that they were habitually to thinking. Student’s worksheet is important learning tools of mathematics because with all problem contain in its student will think and finally find the developing concept of mathematics. The student otomatically will build interation among same student and also the teacher and understand how important interaction activity to build concept of mathematics. With using student’s worksheet in learning process in the class will open chance to student to follow active in learning process, so that the teacher can observe activity in the class. Student’s worksheet have some benefit, it is like build student’s motivate, build student’s esteem, increase student activity, make student always thinking, and soon. But student’s worksheet also have some obstacles, it is like increase workload to the teacher, an additional cost from both of the teacher and the student, the student will boring if the student just do the worksheet, and soon. There are many step to make student’s worksheet:
· Doing analisize to curriculum
· Arrange map of needs
· Determine the title
· Write the student’s worksheet
· Determine evaluation tools
3. Small Group Discussion
It is kind method by teacher of assesing personality and term suggests a discussion among a group of person. Usually consist few member, 5-8 member of student who will express opinion or solve about topic of current issue or lesson matter or problem in mathematics. Firstly, the teacher explanation in whole class about something, then the teacher asked the student to make small group to discuss with note member consist variation of student, from jenius student until moderate student, the purpose is make siclus of thinking so that each member give their own result. After that usually every group get own allocation in discuss topic. Example, the teacher give problem about shown prove of the theorm, then each group have different answer or proof . Here, the teacher just as the fasilitator who provides directing about steps to prove it. With small group discussion student will learn:
· Be assertive: an assertive person is direct, honest carreful about not hurting others ‘self-respect’.
· A patient listener: listening to another person is one way of showing appreciation.
· Right language: words can make friends and right words at the right time make the best result.
· Be analytical: it is necessary to make relevant points which can be suppurted with fact and analytical logic.
· Be good leader: in every discuss activity always leader, here the leader give each member part of discussion fairly according member’s abbility.
If any member of the group criticizes or disapproves a point , it is unwise to get upset or react sharply, in the case the criticism is flimsy, the same can be pointedout politely. In the small group discussion also many benefits, it is like:
· Provides chance to expose
· Language skills
· Academic knowledge
· Leadership skills
· People handing skills
· Team work
· General knowlegde
4. Various Interaction
In learning process the teacher give some problem to the student, then the student can solve it in three kind of interaction: individual, group, and whole class. In the individual, the student try many way from resoursce to solve that problem with the teacher provides their own way. Here, the student do interaction with the teacher individual. There are share each steps from the student using their own thinking to the teacher. If individual interaction held between student and teacher so if the student make wrong steps the student do not feel embarashing to anyone, instead the student get their self-esteem. In the case of group, should the teacher make different member of group every begin new chapter. The purpose is create various interaction to each member, because with different member every new chapter make different atmosphere in the student, so they do not feel just certain student who become member to certain group. With new member, new leader, and new topic will build good teamwork in the every case. Their conection among member of the class also has been expanded. In the case interaction whole class is interactions either individually or group with all student in the class. Activities may include presentation or just solve the problem. Interaction in whole classroom through bring many benefit to student’s self esteem. Corret or wrong of student’s answer are matters for later, here the most important is the presence of interaction that can generate student’s spirit and motivate.
5. Various Teaching Method
Why the teacher needs not just one method to teaching learning of mathematics? As we all know that mathematics is a lesson need logic and do it or do math to understanding. If the teacher just using one method so has been firmed that learning process will be failed. So that to teaching learning of mathematics the teacher needs various teaching method, it is like discovery method, problem solving method, expository method, presentation method, discussion method, precesing method, and soon. If one method felt less suitable so the teacher still have many others where used to apply suitable method with thw material. For example problem solving method, it has superiority like:
· Train the student to disign a invention
· Creative thinking
· Identify and conduct investigation
· Evaluate the result of observation
· Stimulate the development of student progress
· Can create school education more relevant
But there weakness on problem solving method, it is like:
· Some subject is very dificult to immplement this method
· Allocation requires a longer time compared with other learning method
That is just example to various teaching learning process one of all kind method and answer why the teacher needs not just one menthod.
6. Student Reflection
Also called student presentation. Tha main frame of this part is almost similar with small group discussion and various interaction, just diference in presentation is the student must share their opinion in front of the class, either individually or group. First the teacher give problem in front of the class. And then asked to the student to solve it then the student give their mind to solve that problem. With presentation the student will attept to prepare that presentation as well as they can. They will try to:
· Know the problem
The student will study more and more to prepare their presentation until they understand so they have mainset about the point of problem. It is very importan remember point of that problem will rising the concept of that problem until they finally get concept of the material.
· Explanation to other
As we all know that the best way to learn is explain it, because with explain we will more and more understanding.
· Make summary
Before the student expose their presentation, firstly they make summary so that easy when explain the point. With summary the student will simple to remember it.
7. Cognitive Scheme
To develop teaching learning process the teacher must see the cognitive sceme factor in the student. The level of student thinking influence to abillity in image or describe something. Here, student’s cognitive scheme is different among the student. In level elementary school course have different level cognitive scheme with junior high school, also junior high school different with senior high school. So if tha material in the senior high school cannot apply in both of junior high school and elementary school, because diferent cognitive scheme. For example, if student in junior high school image a cat, they will get that cat have four legs, beautiful feather, big eyes, until details. But how if kid? The kid cannot image or mention body of the cat competely. It show that kid’s cognitive shceme have not like the student have, so to extend the material to the student must consider level of their cognitive scheme so that they can received well. As we all know that mathematics have connection among one concept with other concept. Learning process just application old concept with new concept. If student’s cognitive scheme has been not received yet so will happend lost concept, both of old and new concept. So cognitive scheme very influence to learning process of mathematics.
8. Student’s Conclusion
In the learning process, conclusion by the student self is very important because they own who make the way and the scheme. They hold their understanding with their conclusion. The teacher give problem and then the student try to find the solve. They effort to find the steps, find the way, find why the problem solved by certain step, until find other way as possible. One student is different with other, so there are many different conclusion but still have one content. The teacher must teach how the student make their own conclusion because not most of student can do it. Steps to make conclusion is like
· Understanding the material
· Make summary by them self
· Find the key word
· Make sketch
· Try to solve problem by them self
Here the teacher as fasilitator again who provides directing student’s conclusion in order to the student do not make wrong understanding and finnaly make wrong conclusion.
9. Apperception
Apperception is introduction before lesson begin. Apperception used by the teacher to give an image about the material, where the resources, and suitable assigment for that material. In many cases where the student could not catch the lesson. It is used to examine student’s readyness in follow the lesson. Apperception is thus a general term for all mental processes in which a presentation is brought into connexion with an already existent and systematized mental conception, and thereby is classified, explained or, in a word, understood. A new phenomenon is explained in the light of phenomena already analysed and classified. The whole intelligent life of man is, consciously or unconsciously, a process of apperception, in as much as every act of attention involves the appercipient process. The teacher must give few explanation about next material used to stimulant the student in order to give an image. For example the teacher give a question or quiz about the areas of triangle, then the student will think for several minute to find the solve so ottomatically their mind will be ready. There are steps to transcendental the apperception:
· All experience is succession of a variety of contents
· To be experience at all
· Unity of experience therefore implies a unity of self
· The unity of self is as much an object of experience as anything is
· Experience both of the self and its object
10. Assessment
Assessment used to record student understanding about the material has been explanated by the teacher. Assessment about the student understanding done as evaluate step to examine how far progress learning. Assessment can focus on the individual learner, the learning community it is like class, workshop, or other organized group of learners, the institution, or the educational system as a whole. Assessment design of test items should be based on the student outcomes. The first step in designing the assessment is to analyze the teacher’s learning situation by outlining goals and objectives, then the determining the type of learning those outcomes represent. The term assessment is generally used to refer to all activities teachers use to help students learn and to gauge student progress. Though the notion of assessment is generally more complicated than the following categories suggest, assessment is often divided for the sake of convenience using the following distinctions:
· Summative and formative
Summative assessment is generally carried out at the end of a course or project. In an educational setting, summative assessments are typically used to assign students a course grade. Summative assessments are evaluative. And formative assessment is generally carried out throughout a course or project. Formative assessments are diagnostic.
· Objective and subjective
Objective assessment is a form of questioning which has a single correct answer. Subjective assessment is a form of questioning which may have more than one correct answer
· Referencing
· Formal and informal
Formal assessment usually implies a written document, such as a test, quiz, or paper and its geven score on student’s works. Therefore informal assessment usually occurs may include observation, inventories, checklists, student’s rating, performance and portfolio assessments, participation, self evaluation, and discussion.
11. Various Media
Media is tools used to help the teacher at teaching process. The teacher needs media to teach the matter that difficult if explain by manual or traditional method. Here, media plays important role and give many contribution in develop learning process either make easy explanation by the teacher or abridge the student receive the lesson. The media in learning process devide to electronic media and non-electronic media. Electronic media is like used VTR, computer, LCD and non electronic media is like paper, black board, etc. VTR used to help the teacher prepare presentation, assigmet, lesson plan, and many other. Traditional learning process do not used any media except just preaching and preaching. So the student feels boring and of course get nothing from learning process. Student’s worksheet also order in learning media, its usefull to make the student work indepedenly. Presentation media view points of the material explaned by the teacher, so the student will be easy to understand mean from discussion. Classroom, chairs, and tables also media physic but its more inclining to facilities.
12. Various teaching aids
Teaching aids is tools used to make some aid to the teacher in confront learning problem. Kind of teaching aids are demonstartion tools and experiment tools. Almost the teacher feel diffiult in explanation without make demonstration tools, the material like geometry needs real shape as model from the abstract. Example in chapter the cube, the teacher must create realize cube models in order to the student more understanding in the case looking for the areas, the volume, the diagonal, also connect between the cube with the pyramid. With real model, the student will easy to find many thing about the cube and its formula applied. The experiment tools used in the section problem solving learning. The student will do observe about the something problem and have to need any tools using. With experiment tools they will know apllied the theory to the realize, so that they more and more understanding.
C. Conclusion
To develop teaching learning of mathematics process there are many way to do it, like lesson plan, student’s worksheet, small group discussion, various interaction, various teaching method, student’s conclusion, student’s reflection, cognitive scheme, appeception, assessment, various media and teaching aids. The point of all is how the teacher realize it.
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