1.0 INTRODUCTION

Mathematics is a way of organizing our experience of the world. It improves our

understanding and enables us to communicate and make sense of our experiences.

It also gives us enjoyment. By doing mathematics we can solve a range of practical

task and real-life problems. We use it in many areas of our lives. In mathematics we

use ordinary language and its own special language and operation. As a teacher, we

need to teach students to use both this languages. We can work on problems within

mathematics and we can work on problems that use mathematics as a tool.

Mathematics not only can describe and explain but also predict what might happen.

In Malaysia, mathematics is perceived as an important subject in general.

Therefore, mathematics education has undergone tremendous changes according to

the needs of the country in the course of nation building. Learning and teaching skills

are important in order to help us to improve the uses of mathematic in our daily life.

There are five pillars in teaching and learning mathematics that are problem solving

in mathematics, communication in mathematics, mathematical reasoning,

mathematical connections and application of technology. Through this task, we will

go deeply for each pillar.

1.1Problem-Solving in Mathematics

What is a problem in mathematics? According to Lester (1977), problem

arises when pupils who intend to carry out a certain task but are unable to

find any known algorithm to work it out. From the general point of view, a

problem is any task in which you are faced with a situation is not obvious and

immediate. When the problem existed, there must be a way to solve the

problem. Problem-solving in mathematics can be referred as an organized

process to achieve the goal of problem. The aim of problem-solving is to

overcome obstacles set in the problem. In order to overcome these obstacles,

solving mathematics problems often require pupil to be familiar with the

problem situation and be able to collect the appropriate information, identify a

strategy or strategies and use the strategy appropriately.

There are two types of problems solving, which are routine problem and

non-routine problem. Routine problem is a type of mechanical mathematics

problems that apply some known procedures involving arithmetic operation,

formulae, laws, theorems or equations to get the solutions. Meanwhile, non-

routine problem is a unusual problem situation in which you do not know of

any standard procedure for solving it. The process of problem-solving needs

a set of systematic activities with logical planning, including proper strategy

and selection of suitable method for implementation.

There are several types of problem-solving models such as Model

Process of Problem-Solving: Dewey, Polya’s Model and Lester’s Model. In

solving any problems, it helps to have a working procedure. Based on Polya’s

Model, problem solving in mathematics could be implemented in four stages.

Firstly understand the problem, read and re-read the problem carefully to find

all the clues and determine what the question is asking you to find. Secondly

plan the problem-solving strategy to look for strategies and tools to answer

the question. Thirdly try it and lastly look back and see if you've really

answered the question. Sometimes it's easy to overlook something. If there

are mistake, check the used plan and try the problem again.

1.2 Communication in Mathematics

Communication is an essential part of mathematics. It is a way of sharing

ideas and clarifying understanding. The communication process also helps

build meaning and permanence for ideas and makes them public (NCTM,

2000). When students are challenged to think and reason about mathematics and to

communicate the results of their thinking to others orally or in writing, they learn to

be clear and convincing. Other than that, listening to others’ thoughts and explanation

about their reasoning gives students the opportunity to develop their own

understandings about mathematics. Conversations between peers and teachers will

foster deeper understanding of the knowledge of mathematical concepts. There are

many ways to start a conversation. Open-ended questioning is an important way for

teachers to encourage meaningful conversation between teachers and students. As one

student share ideas about a task, other students are exposed to mathematical thinking

from their peer group, and these comments carry a different connotation from those of

the teacher. When children think, respond, discuss, elaborate, write, read,

listen, and inquire about mathematical concepts, they reap dual benefits

which is they communicate to learn mathematics, and they learn to

communicate mathematically (NCTM, 2000).

1.3 Mathematical Reasoning

The traditional view of teaching is that students learn whatever the teacher

teaches within a straightforward transmission of knowledge. A teacher’s

explanations were accepted without question and processes were practiced

until they became habitual. In short, the students in the classroom were not

involved actively in the lesson. If the class is open to ideas and suggestions,

accepting any rational point from students and allows time for students to try

hard to find solution to a problem, it helps them develop their reasoning skills.

Exploring, justifying, and using mathematical conjectures are common to all

content areas and all grade levels. Through the use of reasoning, students

learn that mathematics makes sense. Reasoning mathematically is a habit of

mind, and like all habits, it must be developed through consistent use in many

contexts and from the earliest grades. At all levels, students reason

inductively from patterns and specific cases. Increasingly over the grades,

students should learn to make effective deductive arguments as well, using

the mathematical truths they are establishing in class. By the end of

secondary school, students should be able to understand and produce some

mathematical proofs logically rigorous deductions of conclusions from

hypotheses and should appreciate the value of such arguments.

1.4 Mathematical Connections

Mathematics is not a set of isolated topics but rather a web of

closely connected ideas. When student study mathematics, they will see and

experience the rich interplay among mathematical topics, between

mathematics and other subjects, and between mathematics and their own

interests. By making mathematical connections will allow students to better

understand, remember, appreciate and use mathematics in their lives. An

emphasis on mathematical connections helps students recognize how ideas

in different areas are related such as, connection between math and art,

connection between math and music, connection between math and

architecture and connection between math and nature. Students should

come both to expect and to exploit connections, using insights gained in one

context to verify conjectures in another. For example, elementary school

students link their knowledge of the subtraction of whole numbers to the

subtraction of decimals or fractions. Middle school students might collect and

graph data for the circumference (C) and diameter (d) of various circles.

Teachers are exhorted to teach in ways that will encourage the

making of useful mathematical connections by their students. Learners might

make connections spontaneously. The implied role for teachers is to act in

ways that will promote learners’ making of mathematical connections

(Thomas & Santiago, 2002). In conclusion, There are many connections

between mathematics and other aspect of our lives. As we discover these

connections mathematics gains meaning and beauty.

1.5 Application of Technology

Information technology refers to the use of computers and software to

convert, store, protect process, transmit, and retrieve information.

Computational theory, algorithm analysis, formal methods and data

representation are just some computing techniques that require the use of

mathematics. Mathematics was one of the earlier subjects to make use of the

computer in the classroom. Mathematical tools have advanced from the

abacus and Quipu, an Incan base-10 counting system made of knotted fibers,

to the calculators and computers of today. These tools can be used in the

classroom to promote higher-level thinking and highlight the links between

taught concepts and their real-world applications.

The range of instructional technology applicable to mathematics is vast,

and at times, overwhelming. A multitude of hardware, software, and online

offerings can be implemented in both conventional and novel ways to

complement the many content, process, and technological standards of

successful math instruction. (by Ales, Ragon).

2.0 CONCLUSION

As a conclusion, it is important to us to improve our knowledge about

mathematics. This is because we use mathematics in many areas in our lives. There

are five pillars in learning and teaching mathematics which can help student to

understand mathematics better. First pillar is problem-solving in mathematics that

tells us about the teaching strategy used to solve mathematics problems. There are

many types of problem-solving and problem-solving’s model. Second pillar is about

communication in mathematics. Through this pillar, we can know that

communication is an essential part of mathematics. Communication in mathematics

is a way of sharing ideas and clarifying understanding. Third pillar is mathematical

reasoning. Through the use of reasoning, students can learn that mathematics

makes sense. Next pillar is about mathematical connection which tell us

mathematics have connections between other area. The last pillar is about

application in technology. As we all know, there are many successful

implementations of technology in mathematics that we use recently, as example,

computer and calculator. Overall, five pillars in mathematics can helps mathematics

education to improve teaching and learning skills among teachers and students.

3.0 REFLECTION

Based on the task given, I’ve learn that mathematics is a way of

organizing our experience of the world. It improves our understanding and

enables us to communicate and make sense of our experiences. To improve

our knowledge and skills in mathematics, there are five pillars in teaching and

learning mathematics that can help us to play role in helping the nation to

achieve Vision 2020. Problem-solving in mathematics can be referred as an

organized process to achieve the goal of a problem. The ultimate goal of any

problem-solving program is to improve students' performance at solving

problems correctly. From this fact, I know about two types of problem-solving

and several problem-solving models. Communication in mathematics it is a

way of sharing ideas and clarifying understanding. Students and teachers must

have good communication to ensure the process of learning become more interesting.

Mathematical reasoning is a habit of mind, and like all habits, it must be

developed through consistent use in many contexts and from the earliest

grades. Several problem-solving strategies address reasoning and proof such

as, finding and using the pattern, accounting for all the possibilities, working a

simpler problem, breaking a problem up in easier pieces and so on. In

mathematical connection, it will allow students to better understand,

remember, appreciate and use mathematics in their lives. Application of

mathematic in technology can be used in the classroom to promote higher-

level thinking and highlight the links between taught concepts and their real-

world applications.