How to Learning Teching of Mathematics

Rachma Hanan T.
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P.Mat Internasional


How to Learning Teching of Mathematics

I. Lesson Plan
A lesson plan is a teacher's detailed description of the course of instruction for one class. A daily lesson plan is developed by a teacher to guide class instruction. Details will vary depending on the preference of the teacher, subject being covered, and the need and/or curiosity of children.

Developing a lesson plan
While there are many formats for a lesson plan, most lesson plans contain some or all of these elements, typically in this order:
-Title of the lesson
-Time required to complete the lesson
-List of required materials
-List of objectives, which may be behavioral objectives (what the student can do at lesson completion) or      knowledge objectives (what the student knows at lesson completion)
-The set (or lead-in, or bridge-in) that focuses students on the lesson's skills or concepts—these include   showing pictures or models, asking leading questions, or reviewing previous lessons
-An instructional component that describes the sequence of events that make up the lesson, including the teacher's instructional input and guided practice the students use to try new skills or work with new ideas
-Independent practice that allows students to extend skills or knowledge on their own
-A summary, where the teacher wraps up the discussion and answers questions
-An evaluation component, a test for mastery of the instructed skills or concepts—such as a set of questions to answer or a set of instructions to follow
-Analysis component the teacher uses to reflect on the lesson itself —such as what worked, what needs improving
-A continuity component reviews and reflects on content from the previous lesson

II. Small Group Discussion
In this session, student can learn how to exchange their ideas with other. If you want students to learn critical thinking skills or be able to synthesize several sources of information into a coherent perspective, you need to model those processes and give students a chance to practice them.
For example, teachers who sometimes encounter something that they do not understand or for which they do not already have a rehearsed answer, should use that opportunity to demonstrate how they gain understanding or solve problems. And if they also involve the students in that process, they are providing a valuable lesson about how one thinks in the discipline. Students also need time to reflect on what they are learning, clarify what they do not understand in a non-judgmental environment, and have meaningful discussions about how they fit what they are learning into their construct of the world.
If you want students to be able to have intelligent discussions, you need to model that behavior. In other words, don't just talk to the students, but engage them in a two-way exchange that lets them explore ideas rather than just answer questions. And when you are presenting new information, remember that the students need some time to think before you expect them to voice their thoughts.

It helps to prepare a background for small discussion groups.
(a synthesis of information from several sources and my own experiences)
-Make a safe place. Students will not contribute to a discussion if they are afraid that they will be ridiculed for what they say. This needs to be done by an explicit statement and by demonstration.
-Have clear objectives for the discussions and communicate them clearly. Are the small groups meant to discuss specific assigned readings? Are they where students ask questions to clarify what they do not understand (and if they have no questions are they all excused)? Are these "mini lectures" in which you are presenting new information?
-Formulate and communicate your expectations of the students. Will they be graded on participation? This is not usually a good incentive because it's difficult to coerce participation and students have the impression that participation can never be graded fairly, anyway. It's better if they form more intrinsic reasons for participation such as a feeling of responsibility to the group or because it's fun and interesting. Also, let students know that a discussion is not a series of two-way exchanges between the instructor and each student. Some students have not had much experience with group discussions and do not really understand what is expected of them.
-Avoid yes/no questions. Ask "why" or "how" questions that lead to discussion and when students give only short answers, ask them to elaborate. Also, avoid questions that have only one answer. This isn't "Jeopardy" and students shouldn't be put into the position of trying to guess which set of words you have in mind.
-Don't fear silence. This may be the most difficult thing to do but it's absolutely essential. When we are responsible for facilitating a discussion, we tend to feel that a lack of response within one or two beats is stretching into an eternity. But even if you have posed a very interesting question or situation, the students will need some time to think and formulate a response. If you have very reticent students, you can try asking them to write down one or two ideas before you open up discussion. Or try handing out a list of discussion topics at the end of the session for the next session to give them time to think. Even so, there may be times when there is just no response. That's when you need to re-state the topic, use a different example, take only a part of it at a time, or throw out a "what if" scenario or devil's advocate proposition. But the important thing is to learn to bide your time and bite your tongue and wait for the students to respond.
-When possible, set up the room for discussion. A circle works best, especially if the group can sit around a table. If you can't re-arrange the furniture, then move around the room, sit among the students; become a discussion participant rather than a teacher.
-Get to know the students' names and who they are. Students are more likely to be engaged with the group if addressed by name rather than by being pointed at. If you know the interests, majors, experiences, etc. of the students, it becomes much easier to think of ways to involve them. For example, if you ask "Jane" to contribute a perspective based on her semester in Rome, you're more likely to get her involved in the discussion than if you ask if anyone wants to say something about the Coliseum.
-Provide positive feedback for participation. If a student is reluctant to speak up and then makes a contribution that just lies there like a dead fish, that student is not likely to try again. If you can't think of anything better, thank the student for his/her contribution. But it's much better to build on what the student has said, add an insight, ask others how they would respond to what the student said, and otherwise weave that contribution into the fabric of the discussion. Feedback can be a good means of getting through a lull in the discussion also. A recap of what has been discussed so far lets students know that you heard what they said, helps to reinforce main points, and often stimulates further discussion.
-Show enthusiasm for the subject. You can't expect students to become interested in a discussion topic for which the instructor shows no enthusiasm. This usually means that the instructor has not done his/her homework, a part of which is to think about what is interesting, why the subject is worthwhile or relevant, personal experience with the subject, how the topic relates to current events, etc. If you are interested in the subject, then you will be interested in discovering what your students think and feel.
-Teach your students how to participate. Many of them may have had little or no experience with small group discussion, and most of those who have experience have never been taught how to do it well. There are all kinds of resources in the library in the Speech/Communications area about small-group discussion. -You could prepare a handout for your students or assign a project (preferably in small groups) that involves their preparing information for the rest of the group about small-group communications.
-Ease students into discussion. One tactic is to arrive at the classroom early and engage the first students to arrive in "chit chat" about the weather, a recent sports event, something in the news, etc. The point is to get students comfortable and talking so that as you ease them into the subject for the day, you are not making a sudden demand for performance. You will also be establishing the idea that discussion is a natural process, not cruel and inhuman punishment, or something with which they have no experience.
-Clarify for yourself how you see your role as a discussion facilitator. If you are uncomfortable, your students will also be uncomfortable. So don't try to make yourself into the "Great Communicator" if you are not. Are you more comfortable with a prepared list of topics and questions or do you like a more free-wheeling atmosphere? Do you feel that some topics are strictly off limits or do you feel that you can manage even very "touchy" topics by keeping the discussion relevant and on course? Are you able to give over enough control to the students so that they feel some ownership and responsibility to making the course work?
-Provide opportunities for students to talk to each other in smaller, unsupervised groups so that they get to know each other and become comfortable with sharing ideas. You can do this with small "break-out" groups which are assigned a specific task about which they will report to the larger group. You can assign group projects, encourage the formation of small study groups, or have the class form interest groups which are responsible for contributing something related to their particular interest periodically. The point is to encourage interaction that is not under the watchful eye of the instructor and helps students to become comfortable with each other.
-Manage both process and content. This is often rather difficult at first but becomes much easier with practice. Good discussion is as much about process as it is about content and if you concentrate on one but neglect the other, you are likely to have problems. The tendency is to become caught up in the content and forget to encourage quiet students to contribute or forget to minimize your own contributions. But concentrating too much on making sure everyone contributes or on acknowledging and rewarding contributions can allow the conversation to stray too far afield or become mired in a tangle of irrelevant minutiae. To a great extent, you will need to take your cues from the students. While you are part of the discussion, you have the added responsibility of monitoring it as well. During the course of a class session, you will probably have to do some of each.
-Bringing students into the process of the course and even having them contribute to content does not mean that you have to give over total control. It's still your course and your responsibility to inform the students what information they should study, how they will be expected to demonstrate their knowledge and understanding, and your standards for performance. It is their responsibility to read, study, participate, and perform. When you ask students to participate, you are not asking them to simply voice their unformed and uninformed opinions. At the developmental stage for most freshmen and sophomores, students tend to believe fervently that everyone has a right to his/her opinion. Unfortunately, the corollary, for them, is that therefore all opinions are equal. Part of your mission, therefore, is to help them understand the difference.
-Listen, learn, and adapt. There is no single prescription for all groups. Much like individual people, groups have individual characters and you will need to adapt your style to them as much as is comfortable for you. If you can be open to those differences, they will become part of what makes teaching an interesting challenge year after year after year.

III. Various Method of Teaching
A teaching method comprises the principles and methods used for instruction. Commonly used teaching methods may include class participation, demonstration, recitation, memorization, or combinations of these. The choice of teaching method or methods to be used depends largely on the information or skill that is being taught, and it may also be influenced by the aptitude and enthusiasm of the students.
Methods of Teaching Instruction
Explaining
Explaining, or lecturing, is the process of teaching by giving spoken explanations of the subject that is to be learned. Lecturing is often accompanied by visual aids to help students visualize an object or problem.
Demonstrating
Demonstrating is the process of teaching through examples or experiments. For example, a science teacher may teach an idea by performing an experiment for students. A demonstration may be used to prove a fact through a combination of visual evidence and associated reasoning.
Collaborating
Collaboration allows students to actively participate in the learning process by talking with each other and listening to other points of view. Collaboration establishes a personal connection between students and the topic of study and it helps students think in a less personally biased way. Group projects and discussions are examples of this teaching method. Teachers may employ collaboration to assess student's abilities to work as a team, leadership skills, or presentation abilities.
Learning by teaching
In this teaching method, students assume the role of teacher and teach their peers. Students who teach others as a group or as individuals must study and understand a topic well enough to teach it to their peers. By having students participate in the teaching process, they gain self-confidence and strengthen their speaking and communication skills.

IV. Various Method of Interaction
Interaction is a way of framing the relationship between people and objects designed for them—and thus a way of framing the activity of design.

V.       Various Method of Teaching Aids/ Media
As we all know that today's age is the age of science and technology. The teaching learning programmes have also been affected by it. The process of teaching - learning depends upon the different type of equipment available in the classroom.

Need of Teaching Aids

1) Every individual has the tendency to forget. Proper use of teaching aids helps to retain more concept permanently.
2) Students can learn better when they are motivated properly through different teaching aids.
3) Teaching aids develop the proper image when the students see, hear taste and smell properly.
4) Teaching aids provide complete example for conceptual thinking.
5) The teaching aids create the environment of interest for the students.
6) Teaching aids helps to increase the vocabulary of the students.
7) Teaching aids helps the teacher to get sometime and make learning permanent.
8) Teaching aids provide direct experience to the students.

Types of Teaching Aids
There are many aids available these days. We may classify these aids as follows-

1.  Visual Aids
The aids which use sense of vision are called Visual aids. For example :- actual objects, models, pictures, charts, maps, flash cards, flannel board, bulletin board, chalkboard, overhead projector, slides etc. Out of these black board and chalk are the commonest ones.

2. Audio Aids
The aids that involve the sense of hearing are called Audio aids. For example :- radio, tape recorder, gramophone etc.

3. Audio - Visual Aids
The aids which involve the sense of vision as well as hearing are called Audio- Visual aids. For example :- television, film projector, film strips etc.
Importance of Teaching aids

Teaching aids play an very important role in Teaching- Learning process. Importance of Teaching aids are as follows :

1. Motivation
Teaching aids motivate the students so that they can learn better.

2. Clarification
Through teaching aids , the teacher clarify the subject matter more easily.

3. Discouragement of Cramming
 Teaching aids can facilitate the proper understanding to the students which discourage the act of cramming.

4. Increase the Vocabulary
   Teaching aids helps to increase the vocabulary of the students more effectively.

5. Saves Time and Money

6. Classroom Live and active
   Teaching aids make the classroom live and active.

7. Avoids Dullness

8. Direct Experience
   Teaching aids provide direct experience to the students


VI. Cognitive Scheme
Types of schema include:
Person Schema. Schema about the attributes (skills, competencies, values) of a particular individual. This often takes the form the personality we attribute to that person.
Event schema (cognitive scripts). These are processes, practices, or ways in which we typically approach tasks and problems. They are the programs we call upon when faced with a certain stimulus. These are behaviorally oriented
Role schema. These schema contain sets of role expectations, that is, how we expect an individual occupying a certain role to behavior.
Self-schema. Generalizations about the self abstracted from the present situation and past experiences. This is essentially one's self concept which is in essence perceptions of oneself in terms of traits, competencies, and values (see Laura's notes on Self Concept Based Motivation). Self-efficacy is a type of self schema that applies to a particular task.
Functions of Schema
They are used frequently for the following:
1. Evaluation. When we evaluate individuals occupying a certain role (e.g., doctor, accountant, actor, artist), we compare their behavior to our culturally derived role schema for that role.
2. Role playing. In assuming a certain role, the role schema often becomes our scripts as to how to behave.
3. Identification. We often identify and categorize individuals by the role they assume. We use these role schema to help us place individuals into a certain category by matching their observed behavior with our role schema.
4. Prediction. Once an individual is placed into a category (role) we tend to assume he or she will behave in accordance with the role schema and use this as basis to predict future behavior of this person.

VII. Student Work Sheet
Student Worksheet is sheets consist of taks that have to do by the students. Student worksheet usually in the form of sign, steps how to solve a task. The advantages of student worksheet are:
1. For teacher to make easy study process
2. For students to make they can study by themself and how to comprehending the written task
The structure of worksheet :
1. Title
2. Student sign or student clue
3. Competency
4. Supporting information
5. Task and steps
6. assesment

VIII. Student presentation
Student can explain  the problem and how to solve it.
The purpose of Student Presentation
to learn what work-based learning is;
to understand why it is important to participate in work experiences before graduating from college;
to know their rights and responsibilities as interns with disabilities;
to develop strategies for appropriately disclosing their disabilities and requesting effective accommodations;
to become familiar with adaptive technology that will provide them with access to computers; and
to identify key personnel and support-services offices that will be able to assist them on a typical college campus.

IX. Student Conclusion
In this part, student can make a conclusion about what they have learn before.

X. Classsroom based Assesment
The characteristic of assesment and evaluation is to collect information about the student for successful in the future.
The principe of assesment
Harmonize it with target-----Ascertaining and result-----entangling-----use various method.
Class Technique and Task
1.Pre Course : Interpretation Norm-referenced and criterion-referenced interpretation.
2. In-Course : Achievement Test and Diagnostic Test and Portofolio
3. End-Course : Summative Test, Final Achievement Test.