MANAGING THE TEACHING LEARNING PROCESS OF MATHEMATICS

Managing the teaching learning process of mathematics is a practical approach that is important for mathematics teachers to help them on managing material, students, and class. There are twelve kinds of managing the teaching learning process of mathematics:

1.      Developing Lesson Plan

Lesson Plan is teacher’s detailed description of the course of instruction for one class. In Indonesia, we called lesson plan as RPP (Rencana Pelaksanaan Pembelajaran) A daily lesson plan is developed by a teacher to guide class instruction. Detail will vary on the preference of the teacher, subject being covered, and the need or curiosity of the children. There may be requirements mandated by the school system regarding the plan.

A well-developed lesson plan reflects interests and needs of students. It incorporates best practices for the educational field. The lesson plan correlates with the teacher’s philosophy of education, which is what the teacher feels in the purpose of educating the students.

Also, when teacher develop lesson plan, the teacher must know the contents of lesson plan:

-          Identity and Information of school, class, subject, time allocation, etc.

-          Aim of the material

-          Competency that will be developed during the learning process

-          Description of the competency

-          Learning resources that most used during learning process

-          Teaching contents or material that will be studied.

So, from explanations above, I think that on developing lesson plan, teacher must pay attention on the meaning of lesson plan, that lesson plan developed based on the teacher, students’ needs, and school mandate. So, it must be different between one teacher and other teachers. Also teacher must pay attention on the contents of lesson plan. So lesson plan can be work well to teachers and students.

2.      Developing Student’s Worksheet

One of the characteristics of innovative learning is developing student’s worksheet. It caused the paradigm of learning is learning mathematics is doing some exercises. So we need teaching aids, and on of teaching aids is student’s worksheet.  Student’s worksheet or LKS is a worksheet that contains the information and command/instruction from teachers to students to do a learning activity in the form of work, practice, or in form of the application of learning outcomes to achieve a goal.

A good student’s worksheet must complete the characteristics of worksheet, which is student’s worksheet can promote students to construct their own knowledge of mathematics. On developing student’s worksheet, teacher can use discovery methods, they are structure guide discovery and unstructured guide discovery. So, a student’s worksheet is not only collection of many exercises.

Then, there are four steps in developing good student’s worksheet:

a.       Determining the instructional aims by analyzing the students by identify who are our students and knowing the character of our students

b.      Collects the materials that we need based on instructional aims

c.       Arranging the students worksheet, at least there are materials, tasks, and exercises

d.      Checking the student’s worksheet is it consistent with the instructional aim or not.

3.      Developing Learning Resources

Learning resources are all good sources of data, people, and the particular form that can be used by learners in learning, either separately or be combined to facilitate learners in achieving learning goals or achieve a certain competence.

There are two types of learning resources:

-          Learning resources are designed (learning resources, by design), the learning resources that are specifically designed or developed as a component of an instructional system to provide facilities directed learning and formal.

-          Learning resources are used (learning resources, by utilization), the learning resources that are not designed specifically for the purpose of learning and its existence can be found, implemented and utilized for the purposes of learning. This learning resources may take from:

a.       Message: information, teaching materials, etc

b.      People: teachers, students, etc

c.       Materials: books, pictures, etc

d.      Tools or equipment : computer, white board, etc

e.       Approaches, methods, techniques of solving problems

f.       Environment: class, library

Thus, we can conclude that learning resources can be come from many ways, not only based on books and teacher’s note like traditional methods.

4.      Developing and Implementing Apperception

Psychologically apperception is the process by which new experience is assimilated to and transformed by the residuum of past experience of an individual to form anew whole. In sort, it is to perceive new experience in relation to past experience. In education, we usually called apperception as students’ readiness to learn.

Apperception must be done by the teacher when they want to teach the material. Apperception can provide the basis of students to learn new material, so the apperception can provide ease in learning. Before starting new lesson, teachers should try to connect first with lesson material that has been mastered by the students of knowledge that has been known from the past or the lessons of experience.

Teacher can know how far students facilitate to do apperception by take some exercises before the lesson begins or after teacher have done the material.

5.      Developing and Implementing Various Methods of Teaching

During learning process, teachers have to use various methods of teaching, because if teacher only use one method of teaching, they students will be bored and can’t get the materials well.

There are many teaching methods, and some of them are:

a.       Assessment provides educators with a better understanding of what students are learning and engages students more deeply in the process of learning content

b.      Cooperative Learning involves students working in groups to accomplish learning goals

c.       Interactive Lectures provide short activities that can break up a lecture

d.      Jigsaws are an option when you have several related data sets you would like students to explore. In a jigsaw, each student develops some expertise with one data set, then a few classmates about it

e.       Quantitative Writing engages students with numbers by asking them to analyze and use quantitative data in written reports and arguments.

6.      Developing and Implementing Various Teaching Aids

Teaching aids is a tool used by teachers, facilitator, or tutors to help learners improve reading and other skills, illustrate or reinforce a skill, fact, or idea and relieve anxiety, fears, or boredom, since many teaching aids are like games.

The aim of teaching aid is to motivate the students to apply his full attention to materials. There are many kinds of teaching aids; they are mathematics card, interactive presentation, worksheet, etc.

7.      Developing and Implementing Various Scheme Interaction

During learning process, there are many interactions between teacher and students, and between student and student. These interactions must be happened in a class, because except material, students also develop social skills. There are three types of interaction in the class:

a.       Whole class

The teacher gives some problems to the students in class, then the teacher give a chance to students to answer the problems.

b.      Small group

Teacher dividing into some small groups, and then they discuss the problem in groups. Teachers monitor the students and give some clue about the answer.

c.       Individual

Teacher observes each student and gives attention to the students with low ability

So, during learning process, these interactions must be developed by teacher to anticipate students’ boredom.

8.      Developing and Implementing Small Group Discussion

During learning process, teacher can use small group discussion because small group discussion is one of characteristics of innovative learning. In small group discussion, teacher can develop many skills, not only materials, because during small group discussion, students feel freely to presenting their idea to their members.

The steps of small group discussion are: 1) teacher divide the students become some groups consist of 4-5 members; 2) teacher give some problems to students; 3) students discuss the problem together in the groups; 4) teacher monitor the students, are they get some difficulties on solve the problems; 5) teacher gives some clue about the solution; 6) students get the solution.

When teacher used small group discussion, he/she spent half of each mathematics period to let students work in the group. But sometimes, one group has been done the task, and another group has not done it. So, teacher can take other exercises to the group who has been done.

9.      Developing and Implementing Student’s Presentation

After students have done their work, teacher will let them to presenting their work. The following guidelines will help mathematics teacher implement the use of student presentation in the class:

Before oral presentation

a.       Provide students with an orientation on how to work. Decide on the topics that will be covered by student reflection

b.      Decide on what teacher want to learn about students’ mathematical knowledge of the topics

c.       Decide on how teacher want to record and grade students’ oral presentations

During oral presentation

a.       Remind students that they must communicate their ideas clearly

b.      Point out that teacher will be taking notes on what they say or do

c.       Observe and listen as students make their presentation

d.      When students completes their presentation, ask probing questions for clarifications as well as to check the understanding

e.       Throughout the presentation, record students’ statements and actions. Take note of the use of diagrams and graphs, as well as student’s apparent of confidence

f.       Ensure that student’s misconceptions are addressed by teacher or the class by the end of the presentation.

After oral presentation

a.       Quickly record any additional comments about specific events from the presentation

b.      Make decisions about scores after considering comments and notes

c.       Make an instructional decision based on teacher’s finding.

10.  Developing and Implementing The Cognitive Scheme

Developing and implementing the cognitive scheme is an approach on learning, where students interact with their environment by exploring and manipulating object, wrestling with a number of questions and controversy, or conduct experiments. The basic idea of this theory is that students will easily recall a concept if the concept comes from the student’s own knowledge.

The concept of cognitive development of children representing three forms of representation:

a.       Enactive: knowledge gained from the motor activity of children who do are like concrete direct experience or activity

b.      Iconic: the period when the child’s knowledge is obtained through a dish or other graphic images such as films and static image

c.       Symbolic: a stage where the child is act to understand or build knowledge through a process of reasoning by using symbolic language such as words or other abstract symbols.

The example of developing and implementing cognitive scheme is teacher teach  first, before they teach

11.  Developing and Implementing Student’s Conclusion to do Reflection

This approach allowed some creative thinking brainstorming for new ideas. Students are encouraged to take part in full because all ideas equally recorded. This method describes the knowledge and experience of the group. Usually, one idea proposed by an individual could spark other idea. Actually, the overall goal of this method comes with new ideas or a combination of new ideas. To start a brainstorming session, the teacher must create or choose one issues to be discussed, the procedures to be followed. However, they must be ready to intervene when the process take place with no feeling of dropping their opinion, the session will run smoothly if the following steps be maintained:

a.       All ideas welcomed

b.      The students neither are nor allowed to criticize every idea put forward.

12.  Developing and Implementing Assessment

After teacher check how far the students’ apperception and most of students have been got their apperception, then teacher can get some assessment for students. The goal of assessment is to monitoring the students’ progress in understanding materials. This method requires the students’ creation to answers or products which demonstrate their knowledge or skills. This differs from traditional testing methods which require students to select a single correct answer or to fill in the blank.

Some important think on assessing students are:

a.       Students should be active participants, not passive “selectors of the single right answer”

b.      Intended outcomes should be clearly identified and should guide the design of a performance task

c.       Students should be expected to demonstrate mastery of those intended outcomes when responding to all facets of the task

d.      Students must demonstrate their ability to apply their knowledge and skills to reality-based situations and scenarios

e.       A clear, logical set performance-based activities that students are expected to follow should be evident

f.       A clearly presented set of criteria should be available to help judge the degree of proficiency in a student’s response.