TEACHING MATHEMATICS
All
praise is to Allah, Lord of the Universe, and may peace and blessings be upon
His beloved Prophet Muhammad (S.A.W), on the household of the Prophet, and on
his faithful companions. I feel deeply indebted to Him for lending me the
required strength to complete this task. Out of many topics, I choose Teaching
Mathematics as the title of this assignment. As an introduction, Mathematics
reveals hidden patterns that help us understand the world around us. Now much
more than arithmetic and geometry, mathematics today is a diverse discipline
that deals with data, measurements, and observations from science; with
inference, deduction, and proof; and with mathematical models of natural
phenomena, of human behavior, and of social systems. That is why Mathematics is
also known as “The Mother of Science”.
Mathematics holds
the definition of “the abstract study of topics such as quantity, structure, space and change”[1].
There is a range of views among
mathematicians and philosophers as to the exact scope and definition of mathematics. . When
mathematical structures are good models of real phenomena, then mathematical
reasoning can provide insight or predictions about nature. Through the use of abstraction and logic,
mathematics develop from counting, calculation, measurement and the systematic
study of the shapes and motions of physical objects. Practical
mathematics has been a human activity for as far back as written records exist. The research required to solve
mathematical problems can take years or even centuries of sustained inquiry.
I choose teaching
mathematics because Mathematics is used
throughout the world as an essential tool in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics, the branch of mathematics concerned with
application of mathematical knowledge to other fields, inspires and makes use
of new mathematical discoveries, which has led to the development of entirely
new mathematical disciplines, such as statistics and game theory.
As for the students, “Mathematics will help
them to navigate their lives in this ever-so-complex
modern world”. They may think
that this subject is not much of a use now but as they grow older, they will
soon realize that Mathematics is very important especially when it comes on dealing
with taxes, loans, credit cards, purchases, budgeting, and even shopping. From
other perspective, we need to prepare
our students for further studies in math and science. Not everyone ultimately
needs algebra, but many do, and teens don't always know what profession they
might choose or end up with.
Apart from that, I personally think that
students have to not only learn Mathematics, but love this subject too so that
they can see the beauty of Mathematics, or at the very least avoid thinking
negatively about this particular subject. In addition, Mathematics education is
also very important in order to enable
the students to understand information around us. In today's world, this
includes quite a bit of scientific information. Being able to read through it
and make sense of it requires knowing big and small numbers, statistics,
probability, percent.
Besides knowing that Mathematics
has very important role to our daily life, we should acknowledge that
Mathematics is also used in conducting and performing religious rituals in
Islam. Besides the Quranic inducement and appreciation on scientific knowledge,
there are five main aspects of religious rituals in Mathematics is applied
compulsory. For example, the regulation of lunar calendar whereby its periods
are based on the moon, the regulation of the time of five daily prayers which
its period is determined by the sun, The distribution of inheritance (which involves
some skills in arithmetic and first degree algebraic equations). The geometry
of Islamic decorative art (which involves various geometrical designs and
skills).
Another references of Mathematics
in Quran is the word ‘land’ appears 13 times in the Quran and the word ‘sea’
appears 32 times, giving a total of 45 references. If we divide that number by
that of the number of references to the land we will get the figure
28.888888888889%. The number of total references to the land and sea,45 divided
by the number of references to the sea
in the Qur’an,32 is 71.1111111111%. Miraculously, these figures
represent the exact proportions of land and sea on the Earth today.
There are several
motivation factors of teaching Mathematics. Teaching Mathematics is a challenge, a responsibility, and an
opportunity. Learning to teach Mathematics occurs through a variety of means:
the study of a wide variety of Mathematics, pedagogical preparation within a
mathematical context, formal clinical preparation in education, an extended
internship, and continual experiences as a student, learner, and problem solver
in Mathematics.
For too many teachers, “[2]Mathematics
instruction is a “show and tell” job”. Since we have a reasonably good idea of
the logical organization of Mathematics, we try to develop that logical
organization student by essential verbal method. Mathematics become a game of
proposition and symbol of manipulation with well-define rules and close
officiating. In our concern with the details and rigor of the game, we too
often forget the application and uses of Mathematics. We may forget that man
invented Mathematics to help him understand the phenomenon in the physical
world, and help him to process information obtain from physical, social and
cultural situation. When a person is allowed to learn Mathematics, that is to
abstract his own Mathematical models from physical context, he develop concepts
according to logical rules. inductive
processes are used more frequently than deductive processes from discovering
patterns in Mathematics and forming Mathematics concepts.
Everyone
aspiring to be a Mathematics teacher is aware of the demand for qualified
teachers at the secondary level, but there is an even greater need for quality Mathematics
teachers—teachers who care about both students and Mathematics, teachers who
have a broad and deep understanding of Mathematics, and teachers who are
thoroughly professional. The responsibilities are great, but the rewards are
even greater.
There are many effects or impact from teaching and learning
Mathematics. One of them is the ability of solving problem that involve
thinking in mathematical way. For example, For example, historically,
philosophers describe geometry as playing a critical role in the developlement
of 'proof' and 'logic' as a form of thought which is very precise and comes
with a strong guarantee that there is reliability and 'truth' in the
connections. Pedagogically, many people believe that the learning of geometry
(if taught in an appropriate fashion) gives the individual a strong model of
what truly reliable reasoning (proof) is all about. Some even believe that
practicing such exact reasoning will have an impact on how one reasons and
solves problems in other areas.
A second example would be the
necessity of mathematics for the quantitative reasoning and the study of
patterns in science. While, in principle, there is no guarantee that these
precise games played in mathematics will actually 'fit' the objects and
relationships studied in science, there is an 'unreasonably' good fit of these
patterns (appropriately chosen) with the patterns found in science. Simply put,
much of engineering, physics, etc. would not be possible without the way that
parts of mathematics allow us to take one set of measurements and predict other
events (measurements) with amazing accuracy.
Methods of teaching
Mathematics can be varied depends on the objectives such as conventional
approach, rote learning, exercises, problem solving and relational approach.
Conventional approach is the gradual and systematic guiding through the
hierarchy of mathematical notions, ideas and techniques. Starts with arithmetic and
is followed by Euclidean geometry and elementary algebra taught
concurrently. Requires the instructor to be well informed about elementary mathematics,
since didactic and curriculum decisions are often dictated by the logic of the
subject rather than pedagogical considerations. Other methods emerge by
emphasizing some aspects of this approach.
Secondly, the rote learning approach. This method of teaching
is based on mathematical results,
definitions and concepts by repetition and memorisation typically without
meaning or supported by mathematical reasoning. A derisory term is ‘drill and kill’. In traditional education, rote learning is
used to teach multiplication tables, definitions,
formulas, and other aspects of mathematics.
Next is exercise
approach. This method is the most effective among all methods. It involves the reinforcement of mathematical skills by completing large
numbers of exercises of a similar type, such as adding vulgar
fractions or solving quadratic equations. Since
mathematical questions have the same pattern of answers, doing a lot of
exercise will definitely help the students to improve their result in
Mathematics as this subject cannot be mastered by just reading the answers.
A teacher can also use problem solving approach. This
methods highlights the cultivation of
mathematical ingenuity, creativity and heuristic thinking
by setting students open-ended, unusual, and sometimes unsolved problems. The
problems can range from simple word problems to
problems from international mathematics competitions such
as the International
Mathematical Olympiad. “[3]Problem
solving is used as a means to build new mathematical knowledge, typically by
building on students' prior understandings”.
Lastly the relational
approach. It uses class topics to solve everyday problems and relates the topic
to current events. This approach
focuses on the many uses of math and helps students understand why they need to
know it as well as helping them to apply math to real world situations outside
of the classroom.
There are many ways of teaching and learning Mathematics.
Both teachers and parents hold the responsibilities on ensuring that the
children do not hate this subject as some born to love Math and some don’t.
There is a large amount of kids who have at one point felt their brains explode
when practicing “times tables.” They often wonder Why do we have to learn this
stuff? It’s so boring! What they often don’t recognize is that math is used
every day in many ordinary situations. Why don’t they recognize math in
“action?” Because it doesn’t present itself in the form typically seen in a
math class.
So how do we help our children learn math without drilling
them with flash cards or having them endlessly solving a series of number
problems? Firstly, Involve the young child in problem–solving by doing some “mental arithmetic.”
For example, ask the child, “If I have 2 cups of water and I need a total of 6
cups for the family, how many more cups do I need?” For older children ask, “If
I get a 20% discount on this item, how much will I be paying?”.
Next, encourage your
child to estimate calculations. When estimating, always use numbers that make
it easier to solve problems quickly in their head. For example, when adding 98
+ 43, it is easier to use 100 + 40 to get a close approximation very quickly.
Notice that 98 is 2 less than 100, and 43 is 3 more than 40. So now we simply
subtract 2 and add 3 to get the exact answer. Often use the first and second
method in order to sharpen their calculating skills in Mathematics.
While accuracy is
important, always be patient when the child comes up with a wrong answer. You
will find that a wrong answer is a way to discover what he/she may not
understand. Armed with that knowledge, you can help him/her learn “Number
Sense” and the concepts involved. Communicate mathematically with the children
by explaining how you arrived at an answer, and listen to them explain to you
how they solve real–life math problems. Whether the answer is right or wrong,
by calmly listening, parents and teachers help them to become more
self–confident. After all, they are just learning. We cannot expect them to be
right every time. At the same time, our encouragement will instill in them a
positive attitude towards math.
An Islamic scholar,
Muhammad Ibn Musa Al-Khawarizmi, the father of algebra was a mathematician and
an astronomer. “[4]He
emphasised that he wrote algebra book to serve the practical needs of the
people concerning matters of inheritance, legacies, partition, lawsuits and
commerce.”
While Al Biruni was
among those who laid the foundation for modern trigonometry. He was a
philosopher, geographer, astronomer, physicist and mathematicians. Al Biruni
carried out geodesic measurements and determined the Earth’s circumference in a most ingenious
way. “[5]With
the aid of Math, he enabled the direction of Qiblat to be determined from
anywhere in the world”.
Meanwhile,
Galileo
Galilei said that the universe cannot be read until we have learned the
language and become familiar with the characters in which it is written. It is
written in mathematical language, and the letters are triangles, circles and
other geometrical figures, without which means it is humanly impossible to
comprehend a single word. Without these, one is wandering about in a dark
labyrinth.
Albert Einstein
stated that “as far as the laws of mathematics refer to reality, they are not
certain; and as far as they are certain, they do not refer to reality”. Taking Einstein's work a stage further, he showed how
mathematics can be used in a predictive way, with a
very high degree of accuracy. His works are fundamental to space science and
our understanding of the movements of planets, stars and galaxies over time.
Development of the mathematics of Einstein's general theory
of relativity led scientists to predict the existence of black holes in outer
space, which subsequent analysis of space research data seems to confirm.
In conclusion, More must be done to help both weaker and stronger pupils in
maths. The increasing importance of science and technology in everyday life and
for success in many careers highlights the need for a strong foundation in
mathematics. I personally think that in Mathematics is something that should
not be ignored and neglected as most of our daily routines involves the use of
Math whether it is realized or spontaneously occur. Without having the
knowledge in Mathematics, nothing can be done or produced in developing a
country.
Therefore, both parents and teachers are responsible of
teaching and exposing the children into Mathematics. However, parents should
not assign the task of teaching Mathematics to their children fully to the
teachers when it is part of their job too. Aside from teachers, parents are the
biggest source of encouragement to the children. They should understand that
children
don’t hate Math. “[6]They
hate being confused and intimidated by math. With understanding comes passion.
And with passion comes growth—a treasure is unlocked.”
[1] Peter Sullivan - Teaching
Mathematics: Using Reasearch-informed Strategies - Australian Council for
Educational Research - page 2 - 2002
[2]
Charles Dodgson – The Mathematics Teacher - National Council of Teachers of
Mathematics – page 468 - 1974
[3] Peter Sullivan - Teaching
Mathematics: Using Research-informed Strategies - Australian Council for
Educational Research - page 12 - 2002
[4] Ali Abdullah Al Daffa – The Muslim
Contribution in Mathematics – Croom Helm Ltd, London - page 19 - 1997
[5] Ali Abdullah Al Daffa – The Muslim
Contribution in Mathematics – Croom Helm Ltd, London - page 26 - 1997
[6] Leon Woloski – Healthy Megazines -
River Publishing for Holland and Barrett - page 17 - 2012
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