Thursday, 27 October 2011

RPH Matematik

Rancangan Pengajaran Harian
Rancangan Pengajaran 2 : 2.2 Mengenal Simbol

Matapelajaran              :Matematik
Kelas                           : Tahun 1 Gemilang
Tarikh                          : 5 Mei 2011
Masa                            : 9.10 am – 9.40 am (30 minit)
Jumlah Murid                : 25 orang
Bidang                          : Nombor dan Operasi
Objektif                       : 2.2.Mengenal dan menggunakan simbol ‘+,  ‘ dan = .

Hasil Pembelajaran      : Di akhir pembelajaran,murid dapat;
a.       Dapat menggunakan dan mempelbagaikan perbendaharaan kata dalam kontek tambah dan
b.      Dapat mengenal simbol tambah, dan sama dengan.
c.       Dapat menulis ayat matematik bagi operasi tambah dan
Peralatan dan Bahan yang digunakan:
1)      Kad perkataan
2)      Kad simbol
3)      Lembaran kerja

Pengetahuan Sedia Ada Murid:
1.      Murid telah mengenal simbol nombor dan nilainya.
2.      Murid pernah melihat simbol tambah (+), dan sama dengan (=) di dalam kehidupan seharian mereka.

Aktiviti Pengajaran Dan Pembelajaran
Aktiviti Guru
Aktiviti Murid
Set Induksi
(5 minit)
Pengertian Tambah dan Tolak

1.  Guru menunjukkan dua kumpulan buah rambutan
2.Guru meminta murid   memerhatikan apa yang dilakukannya
a)Memasukkan lima biji buah
   rambutan ke dalam bakul
b)Menambah tiga biji buah
   rambutan lagi ke dalam bakul
1.Murid menunjukkan minat.
2.Murid memerhatikan apa yang dilakukan oleh guru.
Murid mengira keseluruhan buah.


Keseluruhan kelas

Langkah 1
(8 minit)

Langkah 2
(7 minit )
Tambah ialah
a.   Nilai yang berganda
b.   Semakin banyak
c.  Simbol tambah

Membentuk ayat membawa maksud tambah dan sama dengan
1. Guru menunjukkan sejumlah     buah rambutan di dalam bekas.

2.   Guru meminta murid mengira jumlah buah rambutan yang ada di dalam bekas.

3. Guru memaparkan kad perkataan yang membawa maksud tambah.
i. Lima biji buah rambutan bubuh(maksud tambah) lagi tiga
biji jadi lapan biji.

4.Guru mengulang aktiviti menggunakan objek lain dan murid membentuk ayat-ayat yang sesuai membawa maksud tambah

1. Guru memaparkan kad perkataan yang membentuk ayat yang membawa maksud tambah
2.Guru menggantikan perkataan yang membawa maksud tambah dengan perkataan tambah dan perkataan jadi kepada sama dengan

Lima biji buah rambutan bubuh tiga biji buah rambutan jadi lapan biji
Ayat Gantian
Lima biji buah rambutan tambah tiga biji buah rambutan sama dengan lapan biji buah rambutan
3.Guru mebimbing murid sehingga kesemua murid memahami perkataan yang membawa maksud tambah dan sama dengan
4.Guru mengulang aktiviti 1 hingga 5 menggunakan kad perkataan lain

1.Murid membuat pemerhatian bilangan buah rambutan di dalam bekas tersebut.
2.Murid mengira jumlah buah rambutan yang ada di dalam bekas dan yang akan dimasukkan

3.Murid memerhatikan kad perkataan yang dipaparkan dan mendengar penerangan guru
4.Murid memberi respon dengan membentuk ayat menggunakan objek lain

1.Murid memerhatikan kad perkataan yang ditunjukkan oleh guru
2.Murid memberikan respon dengan menyatakan perkataan bubuh mesti diganti dengan perkataan tambah dan perkataan jadi mesti diganti dengan sama dengan

3.Murid menyatakan ayat yang betul selepas perkataan bubuh dan jadi kepada tambah dan sama dengan
4.Murid melibatkan diri dalam aktiviti 1 hingga 5

Teknik Penyoalan didalam kumpulan

Aktiviti Pengukuhan
(5 minit)
2. Lembaran Kerja

1. Guru memberikan lembaran kerja sebagai latihan pengukuhan.

1.Murid mendengar penerangan guru dan bersoaljawab dengannya.
2.Murid menerima lembaran kerja dan cuba menjawabnya dengan bimbingan guru.
Tugasan invidu

Refleksi/ Penutup
(5 minit)
a.       Merupakan nilai sesuatu objek yang semakin banyak jika disatukan
1.Guru menerangkan kepada murid tentang pengertian tambah dan kegunaannya di dalam kehidupan seharian.

1.Murid mendengar penerangan guru dan bersoaljawab mengenai tajuk

Sunday, 2 October 2011



Cooperative Learning
Cooperative learning is a successful teaching strategy in which small teams, each with students of different levels of ability, use a variety of learning activities to improve their understanding of a subject. Each member of a team is responsible not only for learning what is taught but also for helping teammates learn, thus creating an atmosphere of achievement. Students work through the assignment until all group members successfully understand and complete it. 
Cooperative efforts result in participants striving for mutual benefit so that all group members:
  • gain from each other's efforts. (Your success benefits me and my success benefits you.)
  • recognize that all group members share a common fate. (We all sink or swim together here.)
  • know that one's performance is mutually caused by oneself and one's team members. (We can not do it without you.)
  • feel proud and jointly celebrate when a group member is recognized for achievement. (We all congratulate you on your accomplishment!).
Why use Cooperative Learning?
Research has shown that cooperative learning techniques:
  • promote student learning and academic achievement
  • increase student retention
  • enhance student satisfaction with their learning experience
  • help students develop skills in oral communication
  • develop students' social skills
  • promote student self-esteem
  • help to promote positive race relations
5 Elements of Cooperative Learning
It is only under certain conditions that cooperative efforts may be expected to be more productive than competitive and individualistic efforts. Those conditions are:
1. Positive Interdependence (sink or swim together)
  • Each group member's efforts are required and indispensable for group success
  • Each group member has a unique contribution to make to the joint effort because of his or her resources and/or role and task responsibilities
 2. Face-to-Face Interaction  (promote each other's success)
  • Orally explaining how to solve problems
  • Teaching one's knowledge to other
  • Checking for understanding
  • Discussing concepts being learned
  • Connecting present with past learning     
3. Individual & Group Accountability ( no hitchhiking! no social loafing)
  • Keeping the size of the group small. The smaller the size of the group, the greater the individual accountability may be.
  • Giving an individual test to each student.
  • Randomly examining students orally by calling on one student to present his or her group's work to the teacher (in the presence of the group) or to the entire class.
  • Observing each group and recording the frequency with which each member-contributes to the group's work.
  • Assigning one student in each group the role of checker. The checker asks other group members to explain the reasoning and rationale underlying group answers.
  • Having students teach what they learned to someone else.
 4. Interpersonal & Small-Group Skills
  • Social skills must be taught:
    • Leadership
    • Decision-making
    • Trust-building
    • Communication
    • Conflict-management skills
5. Group Processing
  • Group members discuss how well they are achieving their goals and maintaining effective working relationships
  • Describe what member actions are helpful and not helpful
  • Make decisions about what behaviors to continue or change
Class Activities that use Cooperative Learning
Most of these structures are developed by Dr. Spencer Kagan and his associates at Kagan Publishing and Professional Development. For resources and professional development information on Kagan Structures, please visit:
1. Jigsaw - Groups with five students are set up. Each group member is assigned some unique material to learn and then to teach to his group members. To help in the learning students across the class working on the same sub-section get together to decide what is important and how to teach it. After practice in these "expert" groups the original groups reform and students teach each other. (Wood, p. 17) Tests or assessment follows.
2. Think-Pair-Share - Involves a three step cooperative structure. During the first step individuals think silently about a question posed by the instructor. Individuals pair up during the second step and exchange thoughts. In the third step, the pairs share their responses with other pairs, other teams, or the entire group.
3. Three-Step Interview (Kagan) - Each member of a team chooses another member to be a partner. During the first step individuals interview their partners by asking clarifying questions. During the second step partners reverse the roles. For the final step, members share their partner's response with the team.
4. RoundRobin Brainstorming (Kagan)- Class is divided into small groups (4 to 6) with one person appointed as the recorder. A question is posed with many answers and students are given time to think about answers. After the "think time," members of the team share responses with one another round robin style. The recorder writes down the answers of the group members. The person next to the recorder starts and each person in the group in order gives an answer until time is called.
5. Three-minute review - Teachers stop any time during a lecture or discussion and give teams three minutes to review what has been said, ask clarifying questions or answer questions.
6. Numbered Heads Together (Kagan) - A team of four is established. Each member is given numbers of 1, 2, 3, 4. Questions are asked of the group. Groups work together to answer the question so that all can verbally answer the question. Teacher calls out a number (two) and each two is asked to give the answer.
7. Team Pair Solo (Kagan) - Students do problems first as a team, then with a partner, and finally on their own. It is designed to motivate students to tackle and succeed at problems which initially are beyond their ability. It is based on a simple notion of mediated learning. Students can do more things with help (mediation) than they can do alone. By allowing them to work on problems they could not do alone, first as a team and then with a partner, they progress to a point they can do alone that which at first they could do only with help.
8. Circle the Sage (Kagan) - First the teacher polls the class to see which students have a special knowledge to share. For example the teacher may ask who in the class was able to solve a difficult math homework question, who had visited Mexico, who knows the chemical reactions involved in how salting the streets help dissipate snow. Those students (the sages) stand and spread out in the room. The teacher then has the rest of the classmates each surround a sage, with no two members of the same team going to the same sage. The sage explains what they know while the classmates listen, ask questions, and take notes. All students then return to their teams. Each in turn, explains what they learned. Because each one has gone to a different sage, they compare notes. If there is disagreement, they stand up as a team. Finally, the disagreements are aired and resolved.
9. Partners (Kagan) - The class is divided into teams of four. Partners move to one side of the room. Half of each team is given an assignment to master to be able to teach the other half. Partners work to learn and can consult with other partners working on the same material. Teams go back together with each set of partners teaching the other set. Partners quiz and tutor teammates. Team reviews how well they learned and taught and how they might improve the process.
How do cooperative and collaborative learning differ from the traditional approach?
Cooperative and collaborative learning differ from traditional teaching approaches because students work together rather than compete with each other individually.
Collaborative learning can take place any time students work together -- for example, when they help each other with homework. Cooperative learning takes place when students work together in the same place on a structured project in a small group. Mixed-skill groups can be especially helpful to students in developing their social abilities.
The skills needed to work together in groups are quite distinct from those used to succeed in writing a paper on one's own or completing most homework or "seatwork" assignments. In a world where being a "team player" is often a key part of business success, cooperative learning is a very useful and relevant tool.
Because it is just one of a set of tools, however, it can easily be integrated into a class that uses multiple approaches. For some assignments individual work may be most efficient, while for others cooperative groups work best.
Research suggests that cooperative and collaborative learning bring positive results such as deeper understanding of content, increased overall achievement in grades, improved self-esteem, and higher motivation to remain on task. Cooperative learning helps students become actively and constructively involved in content, to take ownership of their own learning, and to resolve group conflicts and improve teamwork skills.
What are the benefits of cooperative and collaborative learning?
Benefits from small-group learning in a collaborative environment include:
  • Celebration of diversity. Students learn to work with all types of people. During small-group interactions, they find many opportunities to reflect upon and reply to the diverse responses fellow learners bring to the questions raised. Small groups also allow students to add their perspectives to an issue based on their cultural differences. This exchange inevitably helps students to better understand other cultures and points of view.
  • Acknowledgment of individual differences. When questions are raised, different students will have a variety of responses. Each of these can help the group create a product that reflects a wide range of perspectives and is thus more complete and comprehensive.
  • Interpersonal development. Students learn to relate to their peers and other learners as they work together in group enterprises. This can be especially helpful for students who have difficulty with social skills. They can benefit from structured interactions with others.
  • Actively involving students in learning. Each member has opportunities to contribute in small groups. Students are apt to take more ownership of their material and to think critically about related issues when they work as a team.
  • More opportunities for personal feedback. Because there are more exchanges among students in small groups, your students receive more personal feedback about their ideas and responses. This feedback is often not possible in large-group instruction, in which one or two students exchange ideas and the rest of the class listens.
How can I use cooperative and collaborative learning in conjunction with other educational techniques?
Since cooperative-learning techniques revolve around the use of a particular tool -- small groups -- they can be used with almost any other educational strategy.Many of the other teaching techniques detailed in previous workshops include small-group learning activities. The cooperative-learning techniques described here will help you and your students make the best use of these small-group activities.
Some types of cooperative learning (like those demonstrated in this workshop) have been developed in concert with the theory of multiple intelligences, so they work very readily with this strategy. In small groups, students can share their strengths and weaknesses and use the group activities to develop a variety of their intelligences.
Cooperative activities involve the construction of new ideas based on personal and shared foundations of past experiences and understandings -- so they naturally apply some of the principles of constructivism. Learners also investigate significant, real-world problems through good explorative questions, and as a result these groups can easily be used for an inquiry-based approach.
They can also help students meet national, state, or local standards. Cooperative and collaborative activities can have many different objectives, ranging from mastery of basic skills to higher-order thinking. Because the specifics of a cooperative-learning project depend on the objectives of the particular teacher, the teacher can easily orient the project toward meeting these standards.
Cooperative Learning Structures and Techniques
NOTE: This content is taken from materials presented at The University of Tennessee at Chattanooga Instructional Excellence Retreat, May 1996. Barbara J. Millis, PhD, Associate Director for Faculty Development, United States Air Force Academy, Facilitator.
Three-step Interview
Three-step interviews can be used as an ice breaker for team members to get to know one another or can be used to get to know concepts in depth, by assigning roles to students.
  • Faculty assigns roles or students can "play" themselves. Faculty may also give interview questions or information that should be "found."
  • A interviews B for the specified number of minutes, listening attentively and asking probing questions.
  • At a signal, students reverse roles and B interviews A for the same number of minutes.
  • At another signal, each pair turns to another pair, forming a group of four. Each member of the group introduces his or her partner, highlighting the most interesting points.
Roundtable structures can be used to brainstorm ideas and to generate a large number of responses to a single question or a group of questions.
  • Faculty poses question.
  • One piece of paper and pen per group.
  • First student writes one response, and says it out loud.
  • First student passes paper to the left, second student writes response, etc.
  • Continues around group until time elapses.
  • Students may say "pass" at any time.
  • Group stops when time is called.
The key here is the question or the problem you've asked the students to consider. It has to be one that has the potential for a number of different "right" answers. Relate the question to the course unit, but keep it simple so every student can have some input.
Once time is called, determine what you want to have the students do with the lists...they may want to discuss the multitude of answers or solutions or they may want to share the lists with the entire class.
Focused Listing
Focused listing can be used as a brainstorming technique or as a technique to generate descriptions and definitions for concepts. Focused listing asks the students to generate words to define or describe something. Once students have completed this activity, you can use these lists to facilitate group and class discussion.
Example: Ask students to list 5-7 words or phrases that describe or define what a motivated student does. From there, you might ask students to get together in small groups to discuss the lists, or to select the one that they can all agree on. Combine this technique with a number of the other techniques and you can have a powerful cooperative learning structure.
Structured Problem-solving
Structured problem-solving can be used in conjunction with several other cooperative learning structures.
  • Have the participants brainstorm or select a problem for them to consider.
  • Assign numbers to members of each group (or use playing cards). Have each member of the group be a different number or suit.
  • Discuss task as group.
  • Each participant should be prepared to respond. Each member of the group needs to understand the response well enough to give the response with no help from the other members of the group.
  • Ask an individual from each group to respond. Call on the individual by number (or suit).
One Minute Papers
Ask students to comment on the following questions. Give them one minute and time them. This activity focuses them on the content and can also provide feedback to you as a teacher.
  • What was the most important or useful thing you learned today?
  • What two important questions do you still have; what remains unclear?
  • What would you like to know more about?
You can use these one minute papers to begin the next day's discussion, to facilitate discussion within a group, or to provide you with feedback on where the student is in his or her understanding of the material.

Paired Annotations
Students pair up to review/learn same article, chapter or content area and exchange double-entry journals for reading and reflection.
Students discuss key points and look for divergent and convergent thinking and ideas.
Together students prepare a composite annotation that summarizes the article, chapter, or concept.
Structured Learning Team Group Roles
When putting together groups, you may want to consider assigning (or having students select) their roles for the group. Students may also rotate group roles depending on the activity.
Potential group roles and their functions include:
  • Leader - The leader is responsible for keeping the group on the assigned task at hand. S/he also makes sure that all members of the group have an opportunity to participate, learn and have the respect of their team members. The leader may also want to check to make sure that all of the group members have mastered the learning points of a group exercise.
  • Recorder - The recorder picks and maintains the group files and folders on a daily basis and keeps records of all group activities including the material contributed by each group member. The recorder writes out the solutions to problems for the group to use as notes or to submit to the instructor. The recorder may also prepare presentation materials when the group makes oral presentations to the class.
  • Reporter - The reporter gives oral responses to the class about the group's activities or conclusions.
  • Monitor - The monitor is responsible for making sure that the group's work area is left the way it was found and acts as a timekeeper for timed activities.
  • Wildcard (in groups of five) - The wildcard acts as an assistant to the group leader and assumes the role of any member that may be missing.
Send-A-Problem can be used as a way to get groups to discuss and review material, or potential solutions to problems related to content information.
·  Each member of a group generates a problem and writes it down on a card. Each member of the group then asks the question to other members.
·  If the question can be answered and all members of the group agree on the answer, then that answer is written on the back of the card. If there is no consensus on the answer, the question is revised so that an answer can be agreed upon.
·  The group puts a Q on the side of the card with the question on it, and an A on the side of the card with an answer on it.
·  Each group sends its question cards to another group.
·  Each group member takes ones question from the stack of questions and reads one question at a time to the group. After reading the first question, the group discusses it.
·  If the group agrees on the answer, they turn the card over to see if they agree with the first group's answer.
·  If there again is consensus, they proceed to the next question.
·  If they do not agree with the first group's answer, the second group write their answer on the back of the card as an alternative answer.
·  The second group reviews and answers each question in the stack of cards, repeating the procedure outlined above.
·  The question cards can be sent to a third, fourth, or fifth group, if desired.
·  Stacks of cards are then sent back to the originating group. The sending group can then discuss and clarify any question
Variation: A variation on the send a problem is to use the process to get groups to discuss a real problem for which there may be no one set answer.
  • Groups decide on one problem they will consider. It is best if each group considers a different problem.
  • The same process is used, with the first group brainstorming solutions to a single problem. The problem is written on a piece of paper and attached to the outside of a folder. The solutions are listed and enclosed inside the folder.
  • The folder is then passed to the next group. Each group brainstorms for 3-5 minutes on the problems they receive without reading the previous group's work and then place their solutions inside the folders.
  • This process may continue to one or more groups. The last group reviews all the solutions posed by all of the previous groups and develops a prioritized list of possible solutions. This list is then presented to the group.
Value Line
One way to form heterogeneous groups, is to use a value line.
  • Present an issue or topic to the group and ask each member to determine how they feel about the issue (could use a 1-10 scale; 1 being strong agreement, 10 being strong disagreement).
  • Form a rank-ordered line and number the participants from 1 up (from strong agreement to strong disagreement, for example).
  • Form your groups of four by pulling one person from each end of the value line and two people from the middle of the group (for example, if you had 20 people, one group might consist of persons 1, 10, 11, 20).
Team Expectations
Some of the common fears about working with groups include student fears that each member will not pull their weight as a part of the group. Students are scared that their grade will be lower as a result of the group learning vs. learning they do individually. One way to address this issue is to use a group activity to allow the group to outline acceptable group behavior. Put together a form and ask groups to first list behaviors (expectations) they expect from each individual, each pair and as a group as a whole.
Groups then can use this as a way to monitor individual contributions to the group and as a way to evaluate group participation.

Guided Reciprocal Peer Questioning
The goal of this activity is to generate discussion among student groups about a specific topic or content area.
  • Faculty conducts a brief (10-15 minutes) lecture on a topic or content area. Faculty may assign a reading or written assignment as well.
  • Instructor then gives the students a set of generic question stems.
  • Students work individually to write their own questions based on the material being covered.
  • Students do not have to be able to answer the questions they pose. This activity is designed to force students to think about ideas relevant to the content area.
  • Students should use as many question stems as possible.
  • Grouped into learning teams, each student offers a question for discussion, using the different stems.
Sample question stems:
  • What is the main idea of...?
  • What if...?
  • How does...affect...?
  • What is a new example of...?
  • Explain why...?
  • Explain how...?
  • How does this relate to what I've learned before?
  • What conclusions can I draw about...?
  • What is the difference between... and...?
  • How are...and...similar?
  • How would I
  • What are the strengths and weaknesses of...?
  • What is the best...and why?
Cooperative Learning References
  • Solomon, R., Davidson, N., & Solomon, E. (1992). Handbook for the Fourth R: Relationship Activities for Cooperative and Collegial Learning . (Volume III). Columbia, MD: National Institute for Relationship Training, Inc.
  • Bossert, S.T. (1988). Cooperative activities in the classroom. Review of Educational Research, 15, 225-250.
  • Bruffee, K.A. (1993). Collaborative learning: Higher education, interdependence, and the authority of knowledge. Baltimore, MD: The Johns Hopkins University Press.
  • Cohen, E.G.: (1994). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research, 64, 1-35.
  • Cooper, J. (1990, May). Cooperative learning and clooege teaching: Tips from the trenches. The Teaching Professor, pp 1-2.
  • Davis, J.R. Better teaching, more learning. Phoenix, AZ: The Oryx Press.
  • Kagan, S. (1992). Cooperative learning (2nd ed.). San Juan Capistrano, CA: Resources for Teachers.