Analisis Topik Circles Form 2
Transcript of Analisis Topik Circles Form 2
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1.0 INTRODUCTION TOPIC CIRCLE
Mathematics is the machinery or driving to the development of and developments in science
and technology. As such, Ministry Malaysian Education through Curriculum Development
Centre (PPK) made the Integrated Curriculum for Secondary School (ICSS) syllabus Form 2
for Mathematics subject effort to realize Philosophy National Education objective and
Malaysian government desire to making our country as a those countries industrial based on
K-Ekonomi.
In the Integrated Curriculum for Secondary School (ICSS) syllabus Form 2 for
Mathematics, Circles chapter is one of the topics which need learned and dominated by
student. Knowledge of circles chapter would be further developed positively in themselves
and skill achieved would make inside basis produce skilled work force in cater to industrial
sector's needs year 2020. Previous theory and new discovery in Circles chapter would enable
school pupils implemented in their daily life and further produce something useful and
innovative for goodness society and country. Based on Rukunegara, this topic can develope
student to become a citicen whose belief in god, loyalty to king and country, upholding the
constitution, rule of law and good behaviour and morality. From what students have learn,
they will know that all the concept and properties of the circle will bring them that the unique
thing that God made in our life. Futhermore, application the concept of circle in their life will
made them become the citicen which is good behaviour and morality.
2.0 AIM OF THE TOPIC
The Circles chapter of the Mathematics curriculum aims are :-
To develop individuals who are able to think briefly about concept of circle include its
properties, application of part of a circle by using drawing and calculating.
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Apply all knowledge about circles effectively and responsibly in solving problems and
making decision.
Enable the individual to face challenges in everyday life that arise due to the
advancement of science and technology.
3.0 OBJECTIVES OF THE TOPIC
Based on Integrated Curriculum for Secondary School (ICSS) Mathematics syllabus for Form
2, five learning objectives which need achieved and dominated by pupils in this chapter are:-
The mathematics curriculum of the Form 2 in Circles chapter enables students to:-
1) Understand definition, concept and properties of circle.
2) Widen the use of basic operations of addition, subtraction, multiplication and division
related to circle.
3) Acquire basic mathematical skills such as:
Making estimation about the value of π
Measuring the area, chord and length of arc and constructing center and
radius of a given circle.
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Collecting and handling data about circle.
Representing and intrepreting data by derived the formula.
Recognizing and representing relationship mathematically.
Using relationship to solve the problem.
Solving problems involving circle
Making decisions
4) Student will communicate mathematically about the circle.
5) Apply knowledge and skills of mathematics in solving problems and making
decisions.
6) Relate the knowledge of circle with other areas of knowledge.
7) Use suitable technologies in concept building, acquiring skills, solving problems and
exploring the field of mathematics.
8) Acquire mathematical knowledge and develop skills effectively and use them
responsibly.
9) Inculcate a positive attitude towards circle.
10) Appreciate the importance and beauty of circle.
4.0 ORGANIZATION OF CONTENT
The organization of the content usually start with learning outcomes that must be achieve
after teaching and learning process. In Learning Objective, it defines what should be taught. It
cover all aspects of the mathematics curriculum programmed and are presented to support
students’ understanding of the concepts and skill of mathematics. For example, “Student must
understand and use the concept of circumference to solve problems.”
In column Suggest Teaching and Learning Activities, it list some examples of teaching
and learning activities including methods, techniques, strategies and resources pertaining to
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the specific concepts for skills. These are, however, teacher are encouraged to look another
examples, determining teaching and learning strategies most suitable for students and provide
appropriate teaching and learning materials such as the textbooks and the internet. For
example, “use dynamic geometry software to explore parts of a circle or use advanced
calculator that already has π as one of the buttons. This will allow less typing for you and a
more accurate answer because the π button produces an approximation to π that is much more
accurate than 3.14.”
The Learning Outcomes define specifically what students should be able to do. They
prescribe the knowledge, skills or mathematical process and values and this are measurable in
all aspects. For example, “student will be able to do identify parts of circle such as center,
circumference, radius, diameter, chord, arc, sector, and segment.”
In the Point To Note column, attention is drawn to the more significant aspects of
mathematical concepts and skills to ensure that they are taught and learning effectively as
intended. For example, Emphasize п = 3.142 or 22/7.”
5.0 EMPHASES IN TEACHING AND LEARNING
The teaching and learning process of circles emphasize concept building and skills acquisition
as well as the inculcation of good and positive values. There are other elements that have to
be taken into account and carefully planned and infused into the teaching and learning of the
circle. This is arranged in such a way to give flexibility to teacher to implement an enjoyable,
meaningful, useful, and challenging teaching and learning environment. At the same time, it is
important to ensure that student show progression in acquiring the mathematical concepts and
skill. There are five main elements focused in teaching and learning of circles. That is
problem solving in mathematics, communication in mathematics, reasoning in mathematics,
mathematical connection and application of technology.
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The problem solving in circles teach and train student to be taught how to solve
problem given and problems related in our daily life. It is important because it is
comprehensive and covers the whole curriculum. The development of problem solving skills
needs to be emphasized so that the students are able to solve various problems effectively by
using ‘Polya Model’ and the more specific problem solving strategies.
The communication in circles is useful to helps students to reinforce and strengthen
their knowledge and understanding of circles to a deeper level. Through effective
communication students will become efficient in problem solving and be able to explain their
conceptual understanding and mathematical skill to their peers and teachers. There are three
processes in communication of circles. There are communication through listening, reading
and visualization.
Communication through the listening process encourages students to think using their
mathematical knowledge in circle in making decisions. Communication through the reading
process need students to collect data and rearranges the relationship idea and concepts. Lastly,
communication through the visualization encourages students to make an observation,
analyses, interprets and synthesizes data. In addition, an oral communication is an interactive
process involves psychomotor activities.
The development of mathematical reasoning is closely related to intellectual and
communicative development of students. It also encouraged students to estimate, predict, and
make intelligent guesses in the process of seeking solutions. Therefore logical and rational
thinking has to be absorbed in students thinking.
Opportunities for making connections must be created so the students can link the
conceptual to procedural knowledge and see circles as integrated whole rather than jumble of
unconnected ideas. Circles ideas can be related with two other topics that are loci in two
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dimension and lines and angles. In these two chapters students know ideas about radius and
angles. Than circles topic will be continue with circles II and circles III in next year.
Applications of technology in circles help students to understand circles concept in
depth, meaningfully and precisely and enable them to explore circles idea. The technology
that circles topic will be used is the geometry software. This software can help to explore
parts of a circle such as center, circumference, radius, diameter, chord, arc, sector and
segment, to explore the value of pi, to explore the relationship between the length of arc and
angle at the center of a circles, to explore the relationship between the radius and the area of
circles and to explore the relationship between the area of a sector and the angle at the center
of the circles.
6.0 APPROACHES IN TEACHING AND LEARNING
Teaching and learning approaches refer to specific techniques that the teacher or facilitator
will use during a particular lesson, course, activity, etc. Any kind of learning approach used
must take into account that means giving information is not enough. Thus, learning
approaches should provide the knowledge, skills and attitudes that the learner needs rather
than the specific content or knowledge of the curriculum in order to develop and improve a
permanent, healthy, sustainable, citizenship orientated lifestyle.
Suitable choice of teaching and learning approaches will provide stimulating learning
environment that enhance effectiveness of learning mathematics. In other words, it is better to
know how the learners study than what they study. Over the years, students’ approaches to
learning have been a focus of study for many researchers. There are some researchers mention
that there is a general agreement that there are two fundamental approaches to learning : deep
and surface. Some features of student approaches to learning include the following :
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Deep approach Surface approach
Intention to understanding
Vigorous interaction with content
Relate new ideas to previous knowledge
Relate concepts to everyday practice
Relate evidence to conclusions
Examine the logic of the argument
Intention to reproduce
Memories information needed for assessments
Failures to distinguish principles from examples
Treat task as an external imposition
Focus on discrete elements without integration
Unreflective about purpose or strategies
A few theory of teaching and learning with regard to circle chapter can apply by
teachers such as Mathematical Concept (Zoltan P Dienes), The Principles or Theorems of
Learning Mathematics (Jeromer Bruner), The Phases of Learning Sequence (Robert Gagne')
and Ausubel Meaningful Learning Model (David P.Ausubel): Teaching Mathematics In
Secondary Schools: Theories and Practices by Noor Shah Saan & Sazelli Abdul Ghani.
In chapter ‘Circles’ Mathematics form 2, there are many suitable approaches in
teaching and learning that teacher can apply in the classroom in order for students to get an
effective learning. For example, teacher can apply cooperative learning to students to achieve
learning objectives where students will be taught to understand and use the concept of
circumference. Besides that teacher also can use the same approaches in teaching subtopic
concept of area of circle. Teacher also can teach this chapter by using constructivism where
students will be able to derive the formula of the circumference of a circle. Teacher also can
use this approach so that student can estimate the value of Pi.
Problem solving also can be one of approaches in teaching and learning that teacher
can apply to teach chapter ‘Circles’. This approach can be used to teach students to
understand and use the concept of area of sector of a circle to solve problem. Besides, teacher
also can use the same approach so students can solve problems by understanding and using
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the concept of arc of a circle. There are many other approaches that teacher can use in
teaching and learning of this chapter. It depends on the teacher to use the most appropriate
and suitable approach that he/she thinks in order to produce an effective learning for students.
7.0 TEACHING METHODS
A method can be regarded as the teacher’s systematic and well-planned series of action in
order to achieve the short-term instructional objectives. Inductive method, deductive method,
expository method and practical work are the examples of method that can be used of teacher
in the classroom. A would-be teacher might feel inadequate in many areas such as experience,
mathematical background or creativity that are required to generate an effective method for a
certain topic or skill. An effective and successful teacher needs to know a multitude of ways
on how to deliver and explain any mathematical ideas based on their suitability and whether
the learning situations warrant them to be used.
For chapter ‘Circle’ Mathematics form 2, there are many methods that can be used of
teacher in teaching and learning. For example, teacher can use expository method. This
method is the most frequently employed method in mathematical instruction. It involves the
delivery of the lesson’s content through explaination, story-telling or demonstration with the
sole purpose of teaching a certain concept. For this chapter, teacher can use this method to
explain the concept of circle and parts of a circle. Teacher can explain the concept with the
aid of the teaching materials for example circular object such as a globe. With this method,
students listen to the teacher’s explaination, remember and record important point.
Besides that, teacher also can use inductive method to teach this chapter. This method
can be used to obtain the formula, fact or the general property from studying or investigating
several specific examples from specificity to generalization. In chapter ‘Circle’, teacher can
use this method so that students can derive the formula of the circumference of a circle.
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Besides, students also will be able to derive the formula of the length of an arc by using this
method. Students also can derive the formula of the area of a circle and formula of the area of
a sector with inductive method. One more thing that students can obtain by using this method
is the value of Pi.
Practical work method is one more method that teacher can apply in the classroom to
teach chapter ‘Circle’. This method can be used to train students in the application of the
teaching aids to help them learn mathematical facts and concepts. For this chapter, teacher can
use this method for example to obtain the value of Pi. Students are required to draw circles of
different diameters on the manila card and they are required to measure the circumference of
each circle. Then students are required to fill a table and generalise the value of Pi obtained.
Besides that, teacher also can apply this method so students can recognize parts of a circle by
drawing a circle.
Teacher must apply the most appropriate and suitable method so that the process of
teaching and learning will be a meaningful one to teacher and especially to students in order
to get an effective learning.
8.0 TEACHING STRATEGIES
As a teacher, we must use some kind of teaching strategies to help students understand better
in Mathematics. In topic of circle, there are several teaching strategies that can be applied.
The most commonly used strategy by the teacher in any mathematics instruction is the
question and answer strategy. Bloom (1977) proposes the following six levels of thinking
which are known collectively as Bloom’s Taxonomy. Taxonomy level bloom can be divided
into two parts namely low level and high level while information that want to be conveyed by
teachers to his pupil could be categorized on facts, concept, skill and principle. For examples,
students need to understand the concept and skill on how to draw a circle if given a diameter.
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Another strategy that can be applied is called thinking skill strategy. As an example,
the “find my rule” strategy could help in generating inductive thinking. The teacher would
provide several items or articles that follow a certain rule. The students would then be
required to identify the rule associated with these items. For example teacher requires students
to identify parts of a circle such as center point, chord, arc, and etc.
Case method strategy providing opportunity for students to apply what they learn in
the classroom to real life experience has proven to be an effective way of both disseminating
and integrating knowledge. For example, teachers can tell the students circles are used for
making products such as wheels of a bicycle or a car.
There are also a variety of ways to stimulate discussion. For example, some faculty
begins a lesson with a whole group discussion to refresh students’ memories about the
assigned reading. Other faculty fined it helpful to have student’s list critical points or
emerging issues, or generate a set of questions stemming from the assigned reading. These
strategies can also be used to help focus large and small group discussions. Obviously, a
successful class discussion involves planning on the part of the instructor and preparation on
the part of the students. Instructors should communicate this commitment to the students on
the first day of class by clearly articulating course expectations. Just as the instructor carefully
plans the learning experience, the students must comprehend the assigned reading and show
up for class on time, ready to learn.
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9.0 TEACHING SCHEME
Week Chapter Learning Objective Topic/ Subtopic Activity T&L Duration20-22(3 weeks)
Chapter 10 : Circles Recognize and draw parts of a circle
Understand and use the concept of
circumference to solve problems
Understand and use the
concept of arc of a circle to solver problems
Understand and
use the concept of area of a circle to solve problems
Understand and use the concept of area of sector of a circle to solveProblems
10.1 Part of a circle Identify circle as
a set of points equidistant from a fixed point.
Identifying part of a circle
Draw a circle Determine the
center and radius
Introduce the concept of circle as a locus.
Use dynamic geometry software to explore parts of a circle
Class work in pair Exercise
(minutes)
10.2 Concept of circumference
Value of Formula of the
circumference of a circle
Diameter and radius of the circumference of the circle
Solving problems
Measure diameter and circumference
of circular objects Explore the history of
Explore the value of using dynamic
geometry software Class work
individually Class work in pair Exercise
(minutes)
10.3 Concept of arc of a Explore the (minutes)
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circle Formula of the
length of an arc Solving problems
relationship between the length of arc and angle at the centre of a circle using dynamic geometry software
Class work in pair Exercise
10.4 Concept of area of a circle
Formula of the area of a circle
Radius and diameter of a circle
Solving problems
Explore the relationship between the radius and the area of a circle:a) using dynamic
geometry software
b) through activities such as cutting the circle into equal sectors and rearranging them
into rectangular form
Class work in pair Exercise
(minutes)
10.5 Concept of area of sector of a circle
formula of the area of a sector
solving problems
Explore the relationship between the area of a sector and the angle at the centre of the circle using dynamic geometry software.
Exercise Quiz
(minutes)
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Closure : Summary Check
understanding
The teacher summarizes the circle
Students make reflection on what they have learned
10 (minutes)
Circles topic will be continue with circles II and circles III such below :
Form 2 : Circles
Form 3 : Circles II
Form 4 : Circles III
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10.0 EVALUATION PROCESS
In this syllabus, there are no different between mathematics of lower form and upper form. In
form of assignment, oral questioning and answering, observation and interview it is the part of
the teaching and learning process to ascertain the strengths and weakness of the students.
In this chapter of circle I from form 2, the students will use the knowledge in circle I
to learn another chapter in form 3, 4 and 5. Based on form 2 learning about the circle, students
can understand the concepts of circle.
To know the students understand or not this chapter, the teacher must do some
evaluation to their students. The suitable evaluation the teacher can do for this chapter is do
some activities out of class such as apply the concepts of circle in daily life. So this activity
can give more happening to students and changes their mood to student is have more
interesting to study.
The other evaluation can do during teaching and learning is the teacher need spend 5
minutes before end of the class lesson. This is because, the teacher can do summarize about
the lesson for that day already teaches. It is also important to know the students understand
about the learning of the circle. After that, the teachers also can do another activity to use the
5 minutes before end of the class. The activities are, the teacher can give the exercise to
students and students should do it as homework. For the next class, teacher and students need
discuss the answer for the exercise. Based on the exercises, the teachers also can know how
far the student understands about the topic of the circle. Then, it can know the objective of
the teaching and learning process achieve for this topic.