1.0 Introduction
Learning mathematics is a
key fundamental in every education system that aims to prepare citizens for a
productive life in the 21st century. Mathematics ia a body of
knowledge which is although created by human beings, often seems to have a
necessity of its own and to offer access to a truth which many claim to be real
and fundamental. Its own beauty, elegance and precision may sometimes appear to
be cold or inhuman and yet even very young children can gain great pleasure
from working and solving problems within its domain. Mathematical knowledge may
often seem to have a highly personal nature as if we had created if for
ourselves. However, mathematics is usually taught to large groups of pupils who
are asked to arrive at a common understanding of an accepted body of knowledge.
At the individual level,
mathematics underpins many aspects of our daily activities. It supports
learning in many fields of study, whether it is in science or in business. A
good understanding of basic mathematics is essential wherever calculations,
measurements, graphical interpretations and statistical analysis are necessary.
The learning mathematics also provides an excellent vehicle to train the mind,
and develop the capacity to think logically, abstractly, critically and
creatively. These are important 21st century competencies that we
must imbue in our students, so that they can lead a productive life and be
life-long learners. Furthermore, it is vitally important for all countries in
this highly competitive global economic environment, yet there are continued
difficulties in developing a successful education system which supports all
pupils to reach their mathematical potential.
Mathematics is an
important subject in our national curriculum. The curriculum must engage with
the 21st century learners who are digital natives comfortable with
the use of the technologies and who work and think differently. The learning of
mathematics must take into cognizance the new generation of learners, the
innovations in pedagogies as well as the affordances of technologies. It’s the
goal of the national mathematics curriculum to ensure that all the students
will achieve a level of mastery of mathematics that will serve them well in
their life, and for those who have the interest and ability, to pursue
mathematics at the highest possible level.
Students begin to learn
mathematics from the day they start formal schooling, and minimally up to the
end of the secondary school. This gives every child at least 10 years of
meaningful mathematics education. Students have a different starting points.
Not all will have the same interests and natural abilities to learn
mathematics. Some will find it enjoyable, others will find it challenging. Some
will find the formulae and rules bewildering others may find the theorems and
results intriguing. Therefore, it is important for the mathematics curriculum
to maximize student potential. Curriculum review and design is ongoing work.
The quality of the curriculum is as much in its design as in its
implementation. Teachers, who are the frontline of the curriculum delivery,
must believe in the value of the changes. Support, resources and training will
be provided to build capacity in our teachers. All these will be part of the
continuous effort to deliver the best mathematics curriculum for the students.
2.0 The
conceptual of a good mathematics teacher from a global perspective.
Good mathematics teaching is an
important factor affecting teachers own teaching and students mathematics
achievement well. A good mathematics teacher can be thought to need some
qualities that are connected to their view of mathematics. The view consists of
knowledge, beliefs, conceptions, attitudes and emotions that can be divided
into two main components which is the view of their own as a learner and
teacher of mathematics and the view of mathematics and its teaching and
learning.
Not all students like mathematics, but
good mathematics teachers have the power to change that. A good mathematics
teacher can help students who have traditionally struggled with mathematics
begin to build confidence in their skills. For students who usually bored with
numbers, a good mathematics can breathe a new life into the subject. Teachers
who are good in teaching would makes their class a place where students want to
be.
2.1
Knowledge of Mathematics
A good mathematics teacher has an extensive knowledge of
mathematics. They have taken multiple course in algebra, geometry, statistics,
calculus and other areas of mathematics at the college level and possibly even
graduate level. These knowledge allows them to confidently explain the concepts
and processes to the students. They should also have enough confidence in their
abilities as a learner and teacher. Teachers are not constantly consulting the
answer key in the back of the teacher’s guide to help student solve the
problems. These confidence boosts their credibility and helps students trust in
their ability to teach what students need to know. Such a teacher needs to be
aware of students possible misconceptions, therefore teachers needs to have a
sufficient knowledge of the context of teaching and knowledge of the goals of
education.
2.2
Leadership
A
skilled mathematics teacher is seen as a leader in their classroom and in the
school. The students respect them not only for their knowledge of mathematics
but also for their overall attitude and actions. Students also can tell the
teachers respects them well. Moreover, teachers have control over the
classroom, laying out clear rules and expectations for student to follow. When
students misbehave, discipline is consistent and fair.
2.3
Planning And Evaluating A Mathematics Lesson
Preparing a plan in advance of the
lesson has two main advantages for a teacher. The advantages are it helps to
clarify and to structure teachers thoughts about what it is teachers trying to
teach and how teachers intend to achieve it. The aspect that need to be discussed
are about what is the topic?, to whom, where and when ?, how will the teacher
teach the topic? Teaching and learning activities and more. In many ways,
planning a lesson is similar to developing a piece of mathematics. Although the
finished product appears concise and logical, its development is a creative
interaction between objective, tasks, and practicalities in the quest for an
effective learning experience. The lesson plan engage students and help them
feel confident in their mathematical abilities.
2.4
Using Information and Communications Technology ( ICT )
Next is the teachers who consider the
affordances of ICT to help students learn. ICT tools can help students
understand mathematical concepts through visualizations, simulations and
representations. Stimuli such as videos, graphic images aid in maintaining a
high level of attention. It can also support exploration and experimentation
and extend the range of problems accessible to students. The ability of using ICT
is a part of the 21st century competencies. It is also important to
design learning in ways that promote the development of other 21st
century competencies such as working collaboratively and think critically about
the mathematical solution.
2.5 Teaching Strategies
A
good mathematics teachers understand that students learn in a different ways. Teachers
keeps up with the best practices in math education and regularly incorporates
them into their instruction to help all the students learn. They would
understand there multiple ways to solve problem and uses those alternate
strategies to help struggling student understand and solve the difficult
concepts. Through this it would develop student’s confidence in their ability
to do mathematics and to confront unfamiliar tasks. Furthermore, while teachers
are explaining and demonstrating, teachers can also probes student’s understanding
of the process by asking questions and giving feedback to the students who response
the questions. Teachers also can use the students’ response to modify their explanation
and demonstrating so that students are better able to follow the process. Using
additional examples if necessary and assign work to students to do on the spot
also the teaching strategies.
2.6
Connecting Teaching Content to Real Life
Teachers who linked the teaching
content to real-life situations and give students opportunities to discover
mathematics knowledge from these situations. A good mathematics teachers help
students to experience the developmental process of mathematics knowledge as
well as to understand the origins of mathematics. Students have a chance to
discover mathematics knowledge in real-life situations. Through this connecting
process, it would not facilitate students’ understanding of relevant
mathematics knowledge because most students think that mathematics is abstract
and useless. By introduce new teaching content we could let them appreciate the
fact that mathematics is related to and taken from real.
2.6 Creating
a Favorable Teaching Atmosphere
Furthermore, the teachers who create
and enjoyable teaching atmosphere and motivate students’ learning interests are
also a good mathematics teacher. The teacher who are humorous and good at
creating an enjoyable classroom environment are able to conduct a good
mathematics lesson which made students feel at ease rather than to have a
stressful environment. Moreover, the teachers who care about the students
mathematics learning interests and know how to inspire and cultivate their students
learning interests. The teachers also needs additional pedagogical knowledge to
understand student’s thinking in order to be able to arrange meaningful
learning situations. Students’ attitudes towards mathematics are shaped by
their learning experiences. Making the learning mathematics fun, meaningful and
relevant does a long way to inculcating positive attitudes towards the subject.
2.7
Encouraging Students’ Active Participation
Another aspects of good mathematics
teaching is that the teachers give opportunities to students to conduct
self-exploration and teachers should encourage them to participate in such
activities. Students have opportunities to conduct some exploration on
teacher-constructed situations, demonstrate their problem solving methods, make
relevant analogies and be involved in some other activities. For example group
discussions activities, students operations and more. Working in groups solving
problems cooperatively also provides scaffolding opportunities.
Students will interact with others to
develop new ideas and as a result it will encourage them to share ideas and
results, compare and evaluate strategies, challenge results, determine the
validity of answers and negotiate ideas on which they all can agree. The
students be given plentiful opportunities and time to discover their thoughts,
to look for problem solving solutions, or to discover mathematical rules
through their own explorations. Besides, teachers should also create a learning
zone to challenge students, so as to continuously stimulate their curiosity and
thirst for knowledge and make them actively learn and explore. Teachers should
not explicitly tell all the learning point and problem solving methods.
2.8
Developing Mathematics Students To Think
The
ability to developed students’ mathematics thinking, mathematics method and
their ability to think and reason mathematically were thought of fundamental
components of a good mathematics teaching which is highly emphasizes by every
teacher. Teacher use the various teaching strategies to inspire student’s
thinking, guide them to think mathematically and to explore problem solving
methods. When the student answer a problem incorrectly, teachers should not
allow them to quit. Teachers encourages them to figure out where they went
wrong and keep working at the problem until they get the correct answer,
providing support and guidance needed. By giving practices also be able to increase
students thinking skill which is they will develop habits and strategies that
will help them be better and more independent learners.
2.9
Questioning Sessions
One aspects of the mathematics classroom that many take
time to find their feet with is the way which teacher phrase questions that had
been set as an exercises. Contextual questions build the skill, with different
nuance and elements, staging students understanding and hence build confidence.
Asking questions and promoting discussion are integral parts of the best
mathematics classroom. Teachers should allows students to ask questions and
does not feel threatened by these and will answers the question that were asked
rather than avoiding it. At the end of a class would allow students to ask
questions and ask teachers for explaining if and only if they still don’t
understand the lesson that had been taught. Effective questioning can scaffold
learning and probe understanding. It creates teachable moments for teachers to
correct a misconception, reinforce a point or expand on an idea. The questions
can be open-ended to encourage students to consider alternative approaches.
Question would be used when you are
working with a student who understands the problem and who may well have a
correct solution. The questions is directed to challenge the students methods
and them consider if the methods would work with similar problems or not. The
questions will be directly to get students to check the accuracy of their
solutions.
2.10
Ensuring Good Behavior
Teachers who always ensuring the good behavior is one of
a good mathematics teacher. Student behavior will always be linked to the
engagement and motivation in the mathematics classroom. The teacher who promote
positive behavior toward learning and teaching mathematics such as patient,
give motivation, support and respect to the students are one of a good
mathematics teacher.
These are the things that effective
teachers do, without thinking.
Effective
Teachers Stands
i)
When
talking, teachers stand still to allow students to clearly hear what is being
said.
ii)
Waits
until the class is silent before speaking and is confident enough to do this,
standing in front of the class.
iii)
Moves
around while speaking but always pauses to speak.
iv)
May
deliver parts of the lesson from the back of the room, expecting students to
look at the board and yet listen to what the teacher is saying.
Use
Of the Body Language
i)
Smiles,
frown and stares as necessary
ii)
Uses
commanding gestures and clear arm movements, points for clarity and gestures
for emphasis.
Use
Eye Contact
i)
Use
glance to stop someone from losing concentration
ii)
Looks
student in the eye, but not in staring or creepy way
iii)
Avoids
from having papers or books as a barrier when talking, if reading a text,
teachers should brings the head up frequently and makes continued, regular eye
contact with the class.
Use
of Voice
i)
Waits
before speaking
ii)
Has
a good volume for normal class delivery that is neither too loud nor too quiet
iii)
Uses
and increase or decrease in volume for affect to grab attention or to create a
moment at atmosphere in the class
iv)
Uses
students’ name a lot
v)
Has
alternatives to asking questions
If and only if some of the students
are misbehavior, teacher have a hard time to dealing with it. A good teachers
would try to identify why students are misbehaving and address the causes where
possible and try to respond decisively and appropriately.
2.11 Care and Concern
Being concern and care about the
students are also part of a good mathematics teacher. Teachers should
recognizes if students are having a bad day or needs some encouragement and
addresses the problem to help the student refocus on the material. While
teachers holds students a high expectations, they recognizes that occasionally
life gets in the way of homework and that studying sometimes take a back seat
to family obligations. Therefore, the teachers should offers students a second
chances when warranted and takes time out of their own schedule to help the
students to catch up back.
2.12
Respecting Students’ Differences
The fact that students come from the
variety of backgrounds creates challenges for teachers. There are some differences
between students in term of their background, ability and mathematics
achievement. The teacher who respect and concern about these differences are a good
mathematical teacher. They should be able to design questions with various
difficulty levels according to students’ learning ability, frame a reasonable
knowledge structure and present teaching content gradually which is from easy
to difficult. When involve grouping activities teachers should mixed the students
groups with difference abilities so that it would be fair and the students
could share and change findings with one another.
2.13
Summarizing
The teachers who always summarize the lesson at the end
of the class also one of the good mathematics teachers. The teachers summarizes
the group findings and in particular emphasizes the important points addressed
in the lesson. Teachers will challenge the students with similar or
developmental problem for homework. Through practices, students will develop
habits and strategies that will help them be better and more independent
learners. Students often write down what
they have in their class.
2.14
Teaching Approach
There are many teaching approach that a good mathematics
teacher can use to gain an effective teaching and learning process. Which is :
2.14.1
Direct Instruction
This approach is about explicit teaching which is
teachers introduce, explain and demonstrate new concepts and skills. Students
are told what they will be learning and what they are expected to be able to
do. This will help them focus on the learning goals. Teacher will draw connections,
pose questions, emphasize key concepts, and role-model thinking.
2.14.2
Directed Inquiry Teaching Approach
One of the conceptual of a good
mathematics teacher are the teacher who are using the directed inquiry as a
teaching approach. This approach is about learning through the guided inquiry. Teachers
as a facilitator of learning, lead students to explore, and investigate by providing
students with the knowledge and tools instead of giving the answers to find the
answers on their own. Student learn to focus on specific questions and ideas
and also engaged in communicating,
explaining and reflecting on their answers. By doing this approach, students
will be enjoying doing mathematics as a result, it can help students learn to
enjoy and sense personel reward in the process of thinking, searching for
patterns and solving problems. They also learned to pose questions, process
information and data and seek appropriate methods and solutions. This enhances
the development of mathematical processes and 21st century competencies.
2.14.3
Mastery Approach
The final phase of teaching where
teachers helps student consolidate and extend their learning are by using the
mastery approaches which is motivated practice, reflective review and extended
learning. Student need practice to achieve mastery. Practice can be motivating
and fun. The practice must be include repetition and variation to achieve
proficiency and flexibility. For example, structuring practice in the form of
games in one of a good strategy to make practice motivating and fun. There
should be a range of activities, from simple recall of facts to application of
concepts. Then reflective review which is also important so that students can
consolidate and deepen their learning through tasks that allow them to reflect
on their learning. It can be done by summarizing their learning using concepts maps.
Next is extended learning. Student who are mathematically inclined should have
opportunities to extend their learning. Therefore teachers would give exercises
in the form of more challenging tasks that will stretch students thinking and
deepen their understanding.
3.0 Conclusion
An
understanding of teachers’ views about what constitutes good mathematics
teaching will not only help illustrate teachers’ assumption about what should
be accomplished during mathematics teaching, and what is the ideal goal of
mathematics teaching, but also help them to understand good mathematics practice
in certain context. It would be interesting to see how well students meets the
good mathematics teacher in the future. Those who train future mathematics
teachers have an important job to do. They have to figure out how they can best
helps students to become a good mathematics teachers. Being taught by a great
teacher is one of the genuine privileges of life. Successful mathematics
teachers can come from many different backgrounds, using many different routes.
4.0 Reference
Upton, J.
(2015) Teach Now! Mathematics. New York, NY : Routledge
Posamentier,
A. S., Hartman H. J. & Kaiser, C. (1998) Tips for the Mathematics Teacher,
London: Corwin Press, INC.
Tanner, H.
& Jones, S. Becoming a Successful Teacher of Mathematics, New York, NY :
RoutledgeFalmer
Yang, X.
(2012). Journal of Mathematics Education. What
Constitutes Good Mathematics Teaching in Mainland China : Perspectives from
Nine Junior Middle School Teachers. 5, 76 – 96
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