This document discusses teaching approaches for mathematics education. It begins with an introduction on the importance of mathematics for students' futures and how they learn mathematics through constructive processes. There are many types of teaching approaches discussed, including constructivism and cooperative learning. Constructivism involves students actively building their own understanding through experiences. Cooperative learning involves putting students in small groups and creating positive interdependence and individual accountability to promote learning. Examples of classroom activities that use these approaches are provided.

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
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Introduction of teaching approches
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Type of teaching approches
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Conclusion of teaching approches
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bibliography
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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.

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