Download - 48354022 5-pillars-in-mathematics
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.