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

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Type of teaching approches

3 - 13

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Conclusion of teaching approches

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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 mathematics

(National Council for Teachers of Mathematics (NCTM), 2000 ).

Mathematics is a discipline that trains the mind to think in a logical and systematic

problem solving and decision making. Mathematical properties of naturally promote

meaningful learning and challenge students' thinking. The concept of learning mathematics

known as a constructive process in which students build and shape knowledge in

mathematics 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

environment 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 abilities

of their students, and then design lessons that challenge these abilities.

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

congratulate 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 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.

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 contextual

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 conditions. 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 unfamiliar

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 instructional

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

activities 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

instrument 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 information

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,

enthusiasm 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.

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