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SEMESTER 1 SESI 2014 / 2015 
TREND AND ISSUE IN EDUCATION FOR MATHEMATIC SCIENCE (SME 3023) 
DISCUSSION ISSUES ON TEACHING APPROACHES. 
DISEDIAKAN OLEH : 
NAMA NO. MATRIK PROGRAM 
ATINA HASANAH BT MOHD GHAZALI D20121058406 ISMP ( EKONOMI ) 
NUR SHUHADA SURIA BINTI SHA’ARI D20121058472 ISMP ( EKONOMI ) 
FATIN AMIRA BINTI YUNUS D20121058529 ISMP ( EKONOMI ) 
KUMPULAN KULIAH : A 
PENSYARAH : DR MOHD FAIZAL LEE BIN ABDULLAH
No. 
Details 
Page 
1 
Introduction of teaching approches 
2 
2 
Type of teaching approches 
3 - 13 
3 
Conclusion of teaching approches 
14 
4 
bibliography 
15 
INTRODUCTION
The main goal of an education system is to improve students understanding of basic 
concepts learned. In the present era of technology, labor background to science and 
mathematics is indispensable for the opportunity and choice to determine the future of these 
individuals will be increased if the individual is proficient or proficient in mathemat ics 
(National Council for Teachers of Mathematics (NCTM), 2000 ). 
Mathematics is a discipline that trains the mind to think in a logical and systemat ic 
problem solving and decision making. Mathematical properties of naturally promote 
meaningful learning and challenge students' thinking. The concept of learning mathemat ics 
known as a constructive process in which students build and shape knowledge in mathemat ics 
by linking new knowledge or concepts acquired knowledge or concepts that are already on 
them. 
One teacher teaching methods is an important component in the session teaching and 
learning. The method has been designed with good performance will bring the desired results. 
A teacher needs to have a creative nature that can be built through experience. Teaching and 
learning mathematics becomes effective when student-centered. Creative elements need to be 
applied in teaching and learning principles involving teachers, environment and teaching 
methods. Teachers need to be knowledgeable, took the initiative and understand what and how 
to teach and why and how students should learn math. Cheerful and conducive environme nt 
will also stimulate students to learn mathematics. That why there are many type teaching for 
mathematic. 
TYPE OF TEACHING APPROCHES
Constructivism 
 Definition of Constructivism. 
Constructivism is basically a theory -- based on observation and scientific study 
-- about how people learn. It says that people construct their own understanding and 
knowledge of the world, through experiencing things and reflecting on those 
experiences. When we encounter something new, we have to reconcile it with our 
previous ideas and experience, maybe changing what we believe, or maybe discarding 
the new information as irrelevant. In any case, we are active creators of our own 
knowledge. To do this, we must ask questions, explore, and assess what we know. 
In the classroom, the constructivist view of learning can point towards a number 
of different teaching practices. In the most general sense, it usually means encouraging 
students to use active techniques (experiments, real-world problem solving) to create 
more knowledge and then to reflect on and talk about what they are doing and how their 
understanding is changing. The teacher makes sure she understands the students' 
preexisting conceptions, and guides the activity to address them and then build on them. 
 Principles of constructivism 
1. Posing Problems of Emerging Relevance to Students 
o Time vs. Coverage: Constructivist teachers seek to ask big questions to 
give students a chance to think about it, and lead them to the resources 
to answer it. 
o Learning for Transfer is an intellectual activity that must be nurtured and 
modeled. Unfortunately, most curriculum for secondary students is 
departmentalized, fragmented, relies heavily on memorization, and 
hence, does not support transferability. 
o The Value of Changing One’s Mind - changing students’ minds is an 
invaluable element of the learning process. 
2. Structuring Learning Around Big Ideas 
o Much of traditional education breaks wholes into parts and then focuses 
study on the parts; many students, however, have difficulty building
wholes from parts. Most of us need to see the whole before we are able 
to make sense of the parts. 
o When concepts are presented as wholes, students seek to make meaning 
by breaking the wholes into parts that they can see and understand; they 
construct (constructivism) the process and understanding rather than 
having it done for them. 
3. Seeking and valuing students points of view 
o Students points of views are windows to their reasoning. The 
acknowledgement that other perspectives exist implies relativity and 
merit, and casts doubt on many of the other “truths” we accept without 
reflection. 
4. Adapt Curriculum to Address Students’ Suppositions 
o This principle implies that teachers need to know the cognitive abilit ies 
of their students, and then design lessons that challenge these abilit ies. 
So while we might assume adolescents are functioning at the formal 
operational level, many may still be at the concrete operational level. 
5. Assessing Student Learning in the Context of Teaching 
o Rather than view assessment as a way to determine what is “right” or 
“wrong”, or as a tool to evaluate individual students, assessment is used 
as an entry point for intervention and planning on how to lead students 
to construct new understandings, knowledge and skills. 
 Example question. 
o Application of Integration 
o Area under the curve 
Find the volume if the area bounded by the curve y=x3+1, the x-axis and the 
limits of x=0 and x=3 is rotated around the x-axis.
Cooperative 
 Definiton of cooperative. 
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.) and feel proud and jointly 
celebrate when a group member is recognized for achievement. (We all congratula te 
you on your accomplishment!). 
 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 and 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 and 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 and 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 and 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 and 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: www.KaganOnline.com 
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 origina l 
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. 
 Example question. 
o Divide students into 4 or 5 people per group and make sure students discuss the 
questions given with friends and make presentation in front of the class after 
they complete answer the question.
Contextual 
 Definition of contextual 
Contextual learning is a proven concept that incorporates much of the most 
recent research in cognitive science. It is also a reaction to the essentially behaviorist 
theories that have dominated American education for many decades. The contextua l 
approach recognizes that learning is a complex and multifaceted process that goes far 
beyond drill-oriented, stimulus-and-response methodologies. (Dan, 1999) 
 Element of contextual 
1. Relating. 
o Learning in the context of life experience, or relating, is the kind of contextual 
learning that typically occurs with very young children. For toddlers, the 
sources of learning are readily at hand in the form of toys, games, and everyday 
events such as meals, trips to the grocery store, and walks in the neighborhood. 
(Dan, 1999) 
o The curriculum that attempts to place learning in the context of life experiences 
must, first, call the student’s attention to everyday sights, events, and conditio ns. 
It must then relate those everyday situations to new information to be absorbed 
or a problem to be solved. 
2. Experiencing. 
o Experiencing—learning in the context of exploration, discovery, and 
invention—is the heart of contextual learning. However motivated or tuned-in 
students may become as a result of other instructional strategies such as 
video, narrative, or text-based activities, these remain relatively passive 
forms of learning. And learning appears to “take” far more quickly when 
students are able to manipulate equipment and materials and to do other 
forms of active research. (Dan, 1999)
3. Applying. 
o Applying concepts and information in a useful context often projects 
students into an imagined future (a Teaching Mathematics Contextually: 
The Cornerstone of Tech Prep 5 possible career) and/or into an unfami liar 
location (a workplace). In contextual learning courses, applications are often 
based on occupational activities. (Dan, 1999) 
4. Cooperating. 
o Cooperating—learning in the context of sharing, responding, and 
communicating with other learners—is a primary instructional strategy in 
contextual teaching. The experience of cooperating not only helps the 
majority of students learn the material, it also is consistent with the 
realworld focus of contextual teaching. (Dan, 1999) 
5. Transferring. 
o Learning in the context of existing knowledge, or transferring, uses and 
builds upon what the student already knows. Such an approach is similar to 
relating, in that it calls upon the familiar. (Dan, 1999) 
 Example question. 
o By relating common experiences to new problems, students gain an 
appreciation for the power of mathematics and its ability to model the real 
world.
Mastery 
 Definition of mastery 
Mastery learning uses differentiated and individualized instruction, progress 
monitoring, formative assessment, feedback, corrective procedures, and instructiona l 
alignment to minimize achievement gaps (Bloom, 1971; Zimmerman & Dibenedetto, 
2008). The strategy is based on Benjamin Bloom’s Learning for Mastery model, which 
emphasizes differentiated instructional practices as strategies to increase student 
achievement. Drawing from the principles of effective tutoring practices and learning 
strategies, mastery learning uses feedback, corrective procedures, and classroom 
assessment to inform instruction. Rather than focusing on changing content, this 
strategy endeavors to improve the process of mastering it. 
In a mastery learning classroom, teachers follow a scope and sequence of 
concepts and skills in instructional units. Following initial instruction, teachers 
administer a brief formative assessment based on the unit’s learning goals. The 
assessment gives students information, or feedback, which helps identify what they 
have learned well to that point (diagnostic) and what they need to learn better 
(prescriptive). Students who have learned the concepts continue their learning 
experience with enrichment activities, such as special projects or reports, academic 
games, or problem-solving tasks. Students who need more experience with the concept 
receive feedback paired with corrective activities, which offer guidance and direction 
on how to remedy their learning challenge. To be effective, these corrective activit ie s 
must be qualitatively different from the initial instruction by offering effective 
instructional approaches and additional time to learn. Furthermore, learning goals or 
standards must be aligned with instruction (or opportunities to practice), corrective 
feedback, and evaluation. 
 Element of mastery. 
1. Specifically explain to students what will be learned and clarify how it will be 
assessed. 
o Teachers must make clear to students regarding what will be learned on that day 
and how the evaluation will be conducted. Among the important aspects that 
need to be clarified include the title of the lesson, the objectives to be achieved, 
the skills taught, the values are applied and the ratio or assessment instrume nt 
to be used in learning.
2. Allow students to learn at their own pace. 
o Based mastery learning, students should be given the opportunity to learn 
according to their interests, abilities and cognitive level of their own. In 
addition, students were also given the responsibility to control the pace of their 
learning in stages. This means that students will only be moved or shifted to the 
next level when captured early stage. For example, in a subject, students will 
only be transferred to the unit 2 after successfully master unit 1. 
3. Monitor student progress and provide a response along with appropriate remedies. 
o Teachers need to monitor the achievement of every student throughout the 
teaching and learning session was held. Monitoring can be done with more 
specific with how to measure student ability and achievement for each learning 
activity. Among the measures that monitoring can be done is to ask questions 
orally with students or provide the questions or the structure of objectives that 
need to be answered by the students. In this way the teacher can monitor student 
achievement to determine the best way to help the students concerned. 
4. Testing to ensure that final learning criterion is reached. 
o To determine whether the objectives or learning outcomes to be achieved 
materializes end or vice versa, teachers need to carry out an assessment to 
students at the end of teaching and learning. Assessment forms can also be 
provided either orally or in writing, for example using a worksheet or training. 
 Example question. 
o Differentiation 
o Teacher show the solution to the student.Student are given the similar question 
to test their understanding. 
Self access.
 Definition of self access . 
Self-study is the status of the individual who is willing to receive informa t ion 
from the environment with an open mind. Pupils should be in a quiet and safe to make 
students ready to learn optimally. 
Teachers need to assess the readiness of students and examine the level of 
achievement of learning or enrollment that has been done before starting teaching in 
the classroom. This serves to ensure that teaching is more effective to start. 
 Type of self access 
There are three types of learning readiness, the first is cognitive readiness. 
Involve cognitive mental state of readiness of pupils to understand, think and 
interpreting a new learning environment. This can be achieved by promoting mental 
activities such as investigate, gather information and solve problems 
Willingness to learn next, affective readiness. It is closely linked with emotions 
or feelings to unleash the potential of the individual. If students are in a relaxed state 
and not tense, acceptance of the teaching is more effective. If the student is emotional 
rather, the student will be difficult to accept the contents of the lessons taught by the 
teacher. This problem can also be said with attitude, curiosity, diligence, enthusia sm 
and human values in students themselves 
The last type is the willingness to learn is a psychomotor physical readiness. 
Manipulative skills, gross motor or kinesthetic movement such as running and fine 
motor finger movements involved in this aspect. Normally, this will depend on the age 
and maturity of the individual, activities - activities such as physical education, art and 
crafts can be seen again this difference 
 Example question. 
o Formulating algebraic expression 
o Nimal bought sugar and tea powder from a boutique. The price of sugar is Rs. 
X and that of tea powder is Rs. Y. write an expression for the remainder, if the 
gave Rs. 500 to the vendor. 
CONCLUSION OF TEACHING APPROCHES
In the face of globalization in education, teachers need to be prepared with knowledge 
and diversification strategies and teaching methods to make classes more interesting turn can 
produce an effective P & P. 
Student-centered teaching strategies should be given priority when conducting R & D 
in order for students to participate actively. The method is very suitable ongoing discussion 
because this method involves all pupils to give their views and ideas so as to build social 
relationships among students. 
In addition, task-based teaching strategies also can not be ignored. This is so because 
these strategies can be member the opportunity to students to apply what they learned. 
Simulation method must be implemented by teachers to provide opportunities for pupils to 
dramatize the situation is almost the same in accordance with the actual situation. In addition, 
the simulation method can generate creative thinking and enhance student proficiency.
BIBLIOGRAPHY 
Azimah. (n.d.). Pengajaran Masteri dalam Matematik Sekolah Rendah. Retrieved december 
2014, 2014, from blogspot: http://azaiza.blogspot.com/2011/04/pengajaran-masteri-dalam-matematik. 
html 
Class Activities that use Cooperative Learning. (n.d.). Retrieved december 12, 2014, from 
Kagan Publishing & Professional Development: http://www.kaganonline.com/index.php 
Clemente Charles HUDSON and Vesta R. WHISLER. (2000). Contextual Teaching and 
Learning for Practitioners. SYSTEMICS, CYBERNETICS AND INFORMATICS , 54 - 58. 
Gray, A. (n.d.). Contructivist Teaching and Learning . Retrieved december 2, 2014, from 
SSTA Research Centre Report : 
http://www.saskschoolboards.ca/old/ResearchAndDevelopment/ResearchReports/Instruction/ 
97-07.htm# 
HAFIZZULLAH, S. K. (n.d.). PEMBELAJARAN MASTERI. Retrieved december 2, 2014, 
from Murid dan amalan belajar, model sistem behavioral.: 
http://seribuimpianhafiz.blogspot.com/p/pembelajaran-masteri_23.html# 
Horton, L. (1979). Mastery Learning : Sound in theory but.. Educational Leadership , 154 - 
156. 
Hull, D. (1999). Teaching Mathematics contextually. United States of America: CORD 
Communications, Inc. 
IBRAHIM, A. B. (n.d.). AMALAN PEMBELAJARAN KOPERATIF OLEH GURU 
MATEMATIK. Retrieved december 2, 2014, from my-rummy: http://www.my-rummy. 
com/Amalan_Pembelajaran_Kooperatif_oleh_Guru_Matematik.html 
IDROS, M. A. (n.d.). TEORI PEMBELAJARAN KONSTRUKTIVISME DAN KESEDIAAN 
BELAJAR. Retrieved december 2, 2014, from blogspot: 
http://sharapsikomtpm.blogspot.com/2012/08/teori-pembelajaran-konstruktivisme-dan.html 
koon, t. s. (1998). konstruktivisme : pedagogi bilik darjah bestari. jurnal keningau , 1 - 7. 
NGASIMAN, N. H. (2012, jun 16). KESAN KAEDAH PEMBELAJARAN KOPERATIF 
TERHADAP PENCAPAIAN. pp. 1-47. 
ridhuan, m. (n.d.). STRATEGI & KAEDAH PENGAJARAN. Retrieved december 2, 2014, 
from blogspot: http://cikgumadrid.blogspot.com/2011/09/kerja-kursus-pendek-murid-dan-alam. 
html 
Zimmerman, B. J., & Dibenedetto, M. K. (2008). Mastery learning and assessment: 
Implications for students and teachers in an era of high-stakes testing. Psychology in the 
Schools, 45(3), 206-216. 
Bloom, B. S. (1971). Mastery learning. In J. H. Block (Ed.), Mastery learning: Theory and 
practice (pp. 47–63). New York: Holt, Rinehart & Winston.
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Teaching approches

  • 1. SEMESTER 1 SESI 2014 / 2015 TREND AND ISSUE IN EDUCATION FOR MATHEMATIC SCIENCE (SME 3023) DISCUSSION ISSUES ON TEACHING APPROACHES. DISEDIAKAN OLEH : NAMA NO. MATRIK PROGRAM ATINA HASANAH BT MOHD GHAZALI D20121058406 ISMP ( EKONOMI ) NUR SHUHADA SURIA BINTI SHA’ARI D20121058472 ISMP ( EKONOMI ) FATIN AMIRA BINTI YUNUS D20121058529 ISMP ( EKONOMI ) KUMPULAN KULIAH : A PENSYARAH : DR MOHD FAIZAL LEE BIN ABDULLAH
  • 2. No. Details Page 1 Introduction of teaching approches 2 2 Type of teaching approches 3 - 13 3 Conclusion of teaching approches 14 4 bibliography 15 INTRODUCTION
  • 3. The main goal of an education system is to improve students understanding of basic concepts learned. In the present era of technology, labor background to science and mathematics is indispensable for the opportunity and choice to determine the future of these individuals will be increased if the individual is proficient or proficient in mathemat ics (National Council for Teachers of Mathematics (NCTM), 2000 ). Mathematics is a discipline that trains the mind to think in a logical and systemat ic problem solving and decision making. Mathematical properties of naturally promote meaningful learning and challenge students' thinking. The concept of learning mathemat ics known as a constructive process in which students build and shape knowledge in mathemat ics by linking new knowledge or concepts acquired knowledge or concepts that are already on them. One teacher teaching methods is an important component in the session teaching and learning. The method has been designed with good performance will bring the desired results. A teacher needs to have a creative nature that can be built through experience. Teaching and learning mathematics becomes effective when student-centered. Creative elements need to be applied in teaching and learning principles involving teachers, environment and teaching methods. Teachers need to be knowledgeable, took the initiative and understand what and how to teach and why and how students should learn math. Cheerful and conducive environme nt will also stimulate students to learn mathematics. That why there are many type teaching for mathematic. TYPE OF TEACHING APPROCHES
  • 4. Constructivism  Definition of Constructivism. Constructivism is basically a theory -- based on observation and scientific study -- about how people learn. It says that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences. When we encounter something new, we have to reconcile it with our previous ideas and experience, maybe changing what we believe, or maybe discarding the new information as irrelevant. In any case, we are active creators of our own knowledge. To do this, we must ask questions, explore, and assess what we know. In the classroom, the constructivist view of learning can point towards a number of different teaching practices. In the most general sense, it usually means encouraging students to use active techniques (experiments, real-world problem solving) to create more knowledge and then to reflect on and talk about what they are doing and how their understanding is changing. The teacher makes sure she understands the students' preexisting conceptions, and guides the activity to address them and then build on them.  Principles of constructivism 1. Posing Problems of Emerging Relevance to Students o Time vs. Coverage: Constructivist teachers seek to ask big questions to give students a chance to think about it, and lead them to the resources to answer it. o Learning for Transfer is an intellectual activity that must be nurtured and modeled. Unfortunately, most curriculum for secondary students is departmentalized, fragmented, relies heavily on memorization, and hence, does not support transferability. o The Value of Changing One’s Mind - changing students’ minds is an invaluable element of the learning process. 2. Structuring Learning Around Big Ideas o Much of traditional education breaks wholes into parts and then focuses study on the parts; many students, however, have difficulty building
  • 5. wholes from parts. Most of us need to see the whole before we are able to make sense of the parts. o When concepts are presented as wholes, students seek to make meaning by breaking the wholes into parts that they can see and understand; they construct (constructivism) the process and understanding rather than having it done for them. 3. Seeking and valuing students points of view o Students points of views are windows to their reasoning. The acknowledgement that other perspectives exist implies relativity and merit, and casts doubt on many of the other “truths” we accept without reflection. 4. Adapt Curriculum to Address Students’ Suppositions o This principle implies that teachers need to know the cognitive abilit ies of their students, and then design lessons that challenge these abilit ies. So while we might assume adolescents are functioning at the formal operational level, many may still be at the concrete operational level. 5. Assessing Student Learning in the Context of Teaching o Rather than view assessment as a way to determine what is “right” or “wrong”, or as a tool to evaluate individual students, assessment is used as an entry point for intervention and planning on how to lead students to construct new understandings, knowledge and skills.  Example question. o Application of Integration o Area under the curve Find the volume if the area bounded by the curve y=x3+1, the x-axis and the limits of x=0 and x=3 is rotated around the x-axis.
  • 6. Cooperative  Definiton of cooperative. 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.) and feel proud and jointly celebrate when a group member is recognized for achievement. (We all congratula te you on your accomplishment!).  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:
  • 7. 1. Positive Interdependence (sink or swim together) Each group member's efforts are required and indispensable for group success and 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 and 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 and 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 and 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 and make decisions about what behaviors to continue or change.
  • 8.  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: www.KaganOnline.com 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 origina l 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
  • 9. 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.  Example question. o Divide students into 4 or 5 people per group and make sure students discuss the questions given with friends and make presentation in front of the class after they complete answer the question.
  • 10. Contextual  Definition of contextual Contextual learning is a proven concept that incorporates much of the most recent research in cognitive science. It is also a reaction to the essentially behaviorist theories that have dominated American education for many decades. The contextua l approach recognizes that learning is a complex and multifaceted process that goes far beyond drill-oriented, stimulus-and-response methodologies. (Dan, 1999)  Element of contextual 1. Relating. o Learning in the context of life experience, or relating, is the kind of contextual learning that typically occurs with very young children. For toddlers, the sources of learning are readily at hand in the form of toys, games, and everyday events such as meals, trips to the grocery store, and walks in the neighborhood. (Dan, 1999) o The curriculum that attempts to place learning in the context of life experiences must, first, call the student’s attention to everyday sights, events, and conditio ns. It must then relate those everyday situations to new information to be absorbed or a problem to be solved. 2. Experiencing. o Experiencing—learning in the context of exploration, discovery, and invention—is the heart of contextual learning. However motivated or tuned-in students may become as a result of other instructional strategies such as video, narrative, or text-based activities, these remain relatively passive forms of learning. And learning appears to “take” far more quickly when students are able to manipulate equipment and materials and to do other forms of active research. (Dan, 1999)
  • 11. 3. Applying. o Applying concepts and information in a useful context often projects students into an imagined future (a Teaching Mathematics Contextually: The Cornerstone of Tech Prep 5 possible career) and/or into an unfami liar location (a workplace). In contextual learning courses, applications are often based on occupational activities. (Dan, 1999) 4. Cooperating. o Cooperating—learning in the context of sharing, responding, and communicating with other learners—is a primary instructional strategy in contextual teaching. The experience of cooperating not only helps the majority of students learn the material, it also is consistent with the realworld focus of contextual teaching. (Dan, 1999) 5. Transferring. o Learning in the context of existing knowledge, or transferring, uses and builds upon what the student already knows. Such an approach is similar to relating, in that it calls upon the familiar. (Dan, 1999)  Example question. o By relating common experiences to new problems, students gain an appreciation for the power of mathematics and its ability to model the real world.
  • 12. Mastery  Definition of mastery Mastery learning uses differentiated and individualized instruction, progress monitoring, formative assessment, feedback, corrective procedures, and instructiona l alignment to minimize achievement gaps (Bloom, 1971; Zimmerman & Dibenedetto, 2008). The strategy is based on Benjamin Bloom’s Learning for Mastery model, which emphasizes differentiated instructional practices as strategies to increase student achievement. Drawing from the principles of effective tutoring practices and learning strategies, mastery learning uses feedback, corrective procedures, and classroom assessment to inform instruction. Rather than focusing on changing content, this strategy endeavors to improve the process of mastering it. In a mastery learning classroom, teachers follow a scope and sequence of concepts and skills in instructional units. Following initial instruction, teachers administer a brief formative assessment based on the unit’s learning goals. The assessment gives students information, or feedback, which helps identify what they have learned well to that point (diagnostic) and what they need to learn better (prescriptive). Students who have learned the concepts continue their learning experience with enrichment activities, such as special projects or reports, academic games, or problem-solving tasks. Students who need more experience with the concept receive feedback paired with corrective activities, which offer guidance and direction on how to remedy their learning challenge. To be effective, these corrective activit ie s must be qualitatively different from the initial instruction by offering effective instructional approaches and additional time to learn. Furthermore, learning goals or standards must be aligned with instruction (or opportunities to practice), corrective feedback, and evaluation.  Element of mastery. 1. Specifically explain to students what will be learned and clarify how it will be assessed. o Teachers must make clear to students regarding what will be learned on that day and how the evaluation will be conducted. Among the important aspects that need to be clarified include the title of the lesson, the objectives to be achieved, the skills taught, the values are applied and the ratio or assessment instrume nt to be used in learning.
  • 13. 2. Allow students to learn at their own pace. o Based mastery learning, students should be given the opportunity to learn according to their interests, abilities and cognitive level of their own. In addition, students were also given the responsibility to control the pace of their learning in stages. This means that students will only be moved or shifted to the next level when captured early stage. For example, in a subject, students will only be transferred to the unit 2 after successfully master unit 1. 3. Monitor student progress and provide a response along with appropriate remedies. o Teachers need to monitor the achievement of every student throughout the teaching and learning session was held. Monitoring can be done with more specific with how to measure student ability and achievement for each learning activity. Among the measures that monitoring can be done is to ask questions orally with students or provide the questions or the structure of objectives that need to be answered by the students. In this way the teacher can monitor student achievement to determine the best way to help the students concerned. 4. Testing to ensure that final learning criterion is reached. o To determine whether the objectives or learning outcomes to be achieved materializes end or vice versa, teachers need to carry out an assessment to students at the end of teaching and learning. Assessment forms can also be provided either orally or in writing, for example using a worksheet or training.  Example question. o Differentiation o Teacher show the solution to the student.Student are given the similar question to test their understanding. Self access.
  • 14.  Definition of self access . Self-study is the status of the individual who is willing to receive informa t ion from the environment with an open mind. Pupils should be in a quiet and safe to make students ready to learn optimally. Teachers need to assess the readiness of students and examine the level of achievement of learning or enrollment that has been done before starting teaching in the classroom. This serves to ensure that teaching is more effective to start.  Type of self access There are three types of learning readiness, the first is cognitive readiness. Involve cognitive mental state of readiness of pupils to understand, think and interpreting a new learning environment. This can be achieved by promoting mental activities such as investigate, gather information and solve problems Willingness to learn next, affective readiness. It is closely linked with emotions or feelings to unleash the potential of the individual. If students are in a relaxed state and not tense, acceptance of the teaching is more effective. If the student is emotional rather, the student will be difficult to accept the contents of the lessons taught by the teacher. This problem can also be said with attitude, curiosity, diligence, enthusia sm and human values in students themselves The last type is the willingness to learn is a psychomotor physical readiness. Manipulative skills, gross motor or kinesthetic movement such as running and fine motor finger movements involved in this aspect. Normally, this will depend on the age and maturity of the individual, activities - activities such as physical education, art and crafts can be seen again this difference  Example question. o Formulating algebraic expression o Nimal bought sugar and tea powder from a boutique. The price of sugar is Rs. X and that of tea powder is Rs. Y. write an expression for the remainder, if the gave Rs. 500 to the vendor. CONCLUSION OF TEACHING APPROCHES
  • 15. In the face of globalization in education, teachers need to be prepared with knowledge and diversification strategies and teaching methods to make classes more interesting turn can produce an effective P & P. Student-centered teaching strategies should be given priority when conducting R & D in order for students to participate actively. The method is very suitable ongoing discussion because this method involves all pupils to give their views and ideas so as to build social relationships among students. In addition, task-based teaching strategies also can not be ignored. This is so because these strategies can be member the opportunity to students to apply what they learned. Simulation method must be implemented by teachers to provide opportunities for pupils to dramatize the situation is almost the same in accordance with the actual situation. In addition, the simulation method can generate creative thinking and enhance student proficiency.
  • 16. BIBLIOGRAPHY Azimah. (n.d.). Pengajaran Masteri dalam Matematik Sekolah Rendah. Retrieved december 2014, 2014, from blogspot: http://azaiza.blogspot.com/2011/04/pengajaran-masteri-dalam-matematik. html Class Activities that use Cooperative Learning. (n.d.). Retrieved december 12, 2014, from Kagan Publishing & Professional Development: http://www.kaganonline.com/index.php Clemente Charles HUDSON and Vesta R. WHISLER. (2000). Contextual Teaching and Learning for Practitioners. SYSTEMICS, CYBERNETICS AND INFORMATICS , 54 - 58. Gray, A. (n.d.). Contructivist Teaching and Learning . Retrieved december 2, 2014, from SSTA Research Centre Report : http://www.saskschoolboards.ca/old/ResearchAndDevelopment/ResearchReports/Instruction/ 97-07.htm# HAFIZZULLAH, S. K. (n.d.). PEMBELAJARAN MASTERI. Retrieved december 2, 2014, from Murid dan amalan belajar, model sistem behavioral.: http://seribuimpianhafiz.blogspot.com/p/pembelajaran-masteri_23.html# Horton, L. (1979). Mastery Learning : Sound in theory but.. Educational Leadership , 154 - 156. Hull, D. (1999). Teaching Mathematics contextually. United States of America: CORD Communications, Inc. IBRAHIM, A. B. (n.d.). AMALAN PEMBELAJARAN KOPERATIF OLEH GURU MATEMATIK. Retrieved december 2, 2014, from my-rummy: http://www.my-rummy. com/Amalan_Pembelajaran_Kooperatif_oleh_Guru_Matematik.html IDROS, M. A. (n.d.). TEORI PEMBELAJARAN KONSTRUKTIVISME DAN KESEDIAAN BELAJAR. Retrieved december 2, 2014, from blogspot: http://sharapsikomtpm.blogspot.com/2012/08/teori-pembelajaran-konstruktivisme-dan.html koon, t. s. (1998). konstruktivisme : pedagogi bilik darjah bestari. jurnal keningau , 1 - 7. NGASIMAN, N. H. (2012, jun 16). KESAN KAEDAH PEMBELAJARAN KOPERATIF TERHADAP PENCAPAIAN. pp. 1-47. ridhuan, m. (n.d.). STRATEGI & KAEDAH PENGAJARAN. Retrieved december 2, 2014, from blogspot: http://cikgumadrid.blogspot.com/2011/09/kerja-kursus-pendek-murid-dan-alam. html Zimmerman, B. J., & Dibenedetto, M. K. (2008). Mastery learning and assessment: Implications for students and teachers in an era of high-stakes testing. Psychology in the Schools, 45(3), 206-216. Bloom, B. S. (1971). Mastery learning. In J. H. Block (Ed.), Mastery learning: Theory and practice (pp. 47–63). New York: Holt, Rinehart & Winston.