INSTITUT PENDIDIKAN PERGURUAN KAMPUS SULTAN ABDUL HALIM

08600 SUNGAI PETANI,KEDAH

PROGRAM DIPLOMA PENDIDIKAN LEPASAN IJAZAH

MATEMATIK-SR

AMBILAN KHAS DISEMBER 2011

PROJEK KERJA KURSUS(INDIVIDU)

NAMA PELAJAR : MEYYAMMAI @ SUMATHI A/P

M.JAYARAM

NO.KAD PENGENALAN : 851122-08-6208

NO.MATRIKS : 2011252050018

KUMPULAN UNIT : DPLI-SR

KOD MATA PELAJARAN : MTM2103-Pendekatan Pedagogi Matematik 1

NAMA PENSYARAH : DR.NG KOK FU

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CONTENT

NO TOPIC PAGE

1 Project Introduction 3

2 Conceptual and Procedural Knowledge 4 - 8

3Conceptual and Procedure Teaching Steps Based on

CPA Approach 9 - 11

4 Misconception on Numbers 11 - 12

5 Daily Lesson Plan 13 - 20

6 Script of Teaching Numbers 1 to 10. 21 - 22

7 Feedback 23

8 Suggestions to Improve in Teaching 23 - 24

9 Conclusion and Reflection 25 - 26

10 Attachment 27 - 30

11 Bibliography 30 - 31

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Project Introduction

Children need to develop a good understanding of numbers in order to build a

good foundation for computational skills. Therefore, Whole Numbers is a major topic in

KSSR Mathematics. As a primary school mathematics teacher, it is important for me to

have an overview of the major mathematical skills that our students will need to acquire

after attending six years of primary education. In order to guide our pupils to learn the

concepts of whole numbers effectively, students must know the meaning of number,

numeral and digit. When teaching the concept of whole numbers, students need to

know the difference in meanings for the term “number” and “numeral”.

Number is an abstract idea related to quantity of objects. In other words, a

number is an abstraction of a quantity. Symbol that is used to represent a number is

called a numeral. In this project, I would like to introduce digit which is an individual

numeral. There are ten digits in the Hindu-Arabic Numeration System such as

1,2,3,4,5,6,7,8,9 and 0.Hence ,digits are the basic symbols used to form numerals.

Children will concentrate on learning numbers 1 to 10 and zero. Students’ learning will

be focused on reading, writing and ordering numbers represented in the forms of

concrete objects, pictures and symbols or numerals. Besides counting on numbers 0 to

10,in addition students also need to be able to explain the meaning of zero as the

number to represent the quantity of “empty”.

In summary, number sense consists of a complex and interrelated set of

conceptions. Number sense is an awareness and understanding of the meaning and

magnitude of number, the relationships among numbers, and the relative effect of

number operations, including the use of mental computation and estimation. According

to Berch , processing number sense allows a child to achieve problem-solving from

understanding the meaning of numbers to developing strategies from making number

comparison to creating procedures for operating numbers and integrating her or his

knowledge to interpret information.

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Conceptual and Procedural Knowledge

It is believed by neuropsychologists that humans are born with “number sense”,

or an innate ability to perceive, process, and manipulate numbers. It is an intuitive ability

to attach meaning to numbers and number relationships, to understand the magnitude

of numbers as well as the relativity of measurement of numbers, and to use logical

reasoning for estimation.

While some ability to understand numbers may be intuitive, this ability is also one

which uses many visual referents. The child is able to compare groups of objects and

immediately analyze differences and likenesses in amount, size, and other

characteristics. There are many incidental opportunities for the young child to use this

number sense in their daily life. Teacher need to direct and guide through these

opportunities for exploring, comparing, ordering and problem-solving in the real world to

allow students for a natural development of number sense. Such opportunities will also

cultivate a positive attitude toward mathematics and facilitate the child’s achievement

and confidence. Following are some suggestions such as they are encourage children

to explore groups of objects which can be perceived with one or two hands .For

example coins, candy, beads, buttons, pretzels, Cheerios to compare the relative size of

groups of things, provide extensive opportunities to match number of objects to number

of fingers ,talk about numbers on how many, how many more or less, how many more

are needed. Lastly, assign number names to groups of objects which are dissimilar in

size or shape, for experience with the concept of quantity and comparison of quantity.

Number sense is difficult to define but easy to recognize. Students with good

number sense can move seamlessly between the real world of quantities and the

mathematical world of numbers and numerical expressions. They can invent their own

procedures for conducting numerical operations. They can represent the same number

in multiple ways depending on the context and purpose of this representation. They can

recognize benchmark numbers and number patterns especially ones that derive from

the deep structure of the number system. They have a good sense of numerical

magnitude and can recognize gross numerical errors that is, errors that are off by an 4

order of magnitude. Finally, they can think or talk in a sensible way about the general

properties of a numerical problem or expression without doing any precise computation.

Most children acquire this conceptual structure informally through interactions

with parents and siblings before they enter kindergarten. Other children who have not

acquired it require formal instruction to do so. For example, one child may enter school

knowing that 8 is 3 bigger than 5, whereas a peer with less well-developed number

sense may know only that 8 is bigger than 5. Other children may have very well-

developed number sense and may have a strategy for figuring out how much bigger 8 is

than 5 using fingers or blocks.

This number sense not only leads to automatic use of math information, but also

is a key ingredient in the ability to solve basic arithmetic computations. Griffin, Case,

and Ziegler suggested that number sense is often informally acquired prior to formal

school and is a necessary condition for learning formal arithmetic in the early

elementary grades. Bruer detailed bow research since the late 1970 has provided

evidence of a preverbal component to number sense. By age 3 or 4 years, most

children can compare two small numbers for size and determine which is larger and

which is smaller.

Number sense is facilitated by environmental circumstances. As with phonemic

awareness, the environmental conditions that promote number sense are, to some

extent, mediated by informal teaching by parents, siblings, and other adults. For

example, Griffin found that entering kindergartners differed on questions such as "which

number is bigger, 5 or 4?" even when they controlled for student abilities in counting

and working simple addition problems in the context of visual materials. It is even

common to hear educators comment that some students are "just good with numbers"

or generalize about the mathematics prowess of certain groups of students. We contend

that number sense is more than a common parlance notion. There is increasing

empirical support for its relationship to underlying deficits and some support that

instruction including number sense activities leads to significant reductions in failure in

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early mathematics. Moreover, we submit that simultaneously integrating number sense

activities with increased number fact automaticity rather than teaching these skills

sequentially. It is also likely that some students who are drilled on number facts and

then taught various algorithms for computations will develop much number sense

despite some phonics instruction and work on repeated fluency and accuracy able to

develop good phonemic awareness or any sense of the purpose or pleasure of reading.

There are numerous differences between the development of an understanding

of and proficiency in mathematics and the development of the ability to read with

understanding. For example, beginning reading clearly involves a heavy auditory

component, whereas number sense is much less dependent on auditory processing.

Nonetheless, we believe this analogy can be helpful in conceptualizing directions for

improvement of math instruction for students. In particular, we believe that if beginning

math instruction were focused in part on building number sense, many students would

benefit.

Education researchers attempted to increase automaticity with math facts by

systematic drill and practice because of the correlation between automaticity and

mathematics competence. But this "brute force" approach made mathematics

unpleasant, perhaps even punitive, for many. In addition, it had the effect of

disassociating mathematics facts from mathematical reasoning, just as some earlier

approaches toward phonics instruction separated practice with sounds from the actual

blending of sounds into words or needlessly separated reading instruction from the

experience of reading. Early interventions focusing on pre numeracy skills attempt to

expose children to experiences lacking in their home or in preschool. For example,

parents can help children develop early number sense by asking them to ascend and

count four steps and then count and descend two steps. Similarly, parents might ask

their children to set the table and count the correct number of place settings. This

requires children to map the number of forks, knives, and spoons with the number of

people eating the meal. Griffin referred to such experiences as "mini-lessons" in

mathematical concepts that parents provide to their children. These early pre numeracy

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experiences form an analogy to emergent literacy experiences described by Teale and

Sulzby.

Adams noted that children develop awareness that letters determine sounds in

words. However, many children need explicit, consistent help in understanding the

specifics of the system. In other words, they possess very crude levels of phonemic

awareness and need help developing the sophisticated awareness necessary for fluent,

non-stressful reading. Part of phonemic awareness is awareness that words are

composed of sounds. This awareness, coupled with an understanding that the alphabet

represents sounds, helps children know that reading involves putting sounds together to

create words. After all, we understand that phonemic awareness is necessary for fluent

reading and ultimately for reading comprehension to say numbers in words.

It is important to note at this point that strategies such as the "min" strategy are

not easy to teach. To recall quickly that 8 is bigger than 3, a child must have some

factual automaticity. Also, a child needs a sense of numbers to assist in access or

automaticity. Children need to master all three components which are problem-solving

strategies, verbal comprehension, and automaticity with relevant facts. In a sense, our

current knowledge base consists of our understanding that children differ in their sense

of numbers, their representation of problems, and their application of strategies that

integrate an the previous components to solve even basic arithmetic problems.

Examples of these differences have been identified in research. For example,

Woodward and Howard reviewed computational performance among more than 100

middle school students. Careful analysis of these tests revealed that more than half the

students showed systematic error patterns, many of which revealed limited conceptual

understanding of the algorithms and strategies taught to them. This finding is

particularly troubling considering that many of these students were in the eighth grade

and had been receiving mathematics instruction since first grade. One interpretation of

the problems students have with subtraction that requires regrouping is that this is the

first math skill for which the child needs number sense to solve problems and, without

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such a sense, performance breaks down. The development of conceptual and

procedural knowledge about counting was explored for children in kindergarten.

Conceptual knowledge was assessed by asking children to make judgments about

three types of counts modeled by an animated frog: standard left-to-right counts,

incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-

object correspondence principle. On unusual counts, the frog violated a conventional

but inessential feature of counting, for example, starting in the middle of the array of

objects. Procedural knowledge was assessed using speed and accuracy in counting

objects. The patterns of change for procedural knowledge and conceptual knowledge

were different. Counting speed and accuracy improved with grade. In contrast, there

was a curvilinear relation between conceptual knowledge and grade that was further

moderated by children's numeration skills as measured by a standardized test where

the most skilled children gradually increased their acceptance of unusual counts over

grade, whereas the least skilled children decreased their acceptance of these counts.

These results have implications for studying conceptual and procedural knowledge

about mathematics.

In summary, to provide the best learning environment for children to develop

number sense, a teacher should understand a child’s current number sense, and

existing knowledge, then address teaching to make sure that the child understands

mathematical concepts and procedures is a crucial foundation. To achieve this,

teachers must balance their teaching between conceptual and procedural knowledge of

mathematics. In addition, teachers can have discussions with their children concerning

methods of problem solving. From the interactions with teacher and peers, teachers will

understand the level of number sense each child has and can provide children with new

insights on problem solving. On the other hand, from listening and sharing during

interaction with peers, children will see and learn how other peers solve problems. They

may adopt these skills to help them approach new problems in the future.

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Conceptual and Procedure Teaching Steps Based on CPA Approach

Firstly, I introduce the topic which the students are going to learn by showing a

short video of dropping 3-dimensional numbers and numbers countdown. I call out

student to count number of sweets in the packet. I use sweets as a concrete object. I

would like to encourage children to explore groups of objects which can be perceived

with one or two hands and I use many visual referents to grab students’ attention.

Secondly, I display numbers 1 to 10 using power point presentation. I guide

students to recognize numbers and read the numbers in words. I demonstrate the

numbers by using cards and pictures. I explains the concept of more than, less than and

as many as by comparing two quantities by using the pictures of chickens, ladybird,

sharks and balls. All these pictures were used as a pictorial approach. These possess

very crude levels of phonemic awareness and need help developing the sophisticated

awareness necessary for fluent reading. This awareness, coupled with an

understanding that the alphabet represents sounds, helps children know that reading

involves putting sounds together in the PowerPoint to create words and ultimately help

students to say numbers in words.

Thirdly, I give 8 animals’ cards to 4 students. Each student gets 2 animals cards.

I ask the students to come forward and paste the animal card on the white board while

counting the numbers orderly. Students come out simultaneously and stick the animals’

card until the last student configure the number of animals’ cards altogether. In this

step, I use pictorial approach and abstract where student need to think in this activity. I

use approach where teacher need to direct and guide through opportunities for

exploring and ordering to allow students for a natural development of number sense and

cultivate a positive attitude toward mathematics and facilitate the student achievement

and confidence.

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After that, I stick 2 manila cards consisting of fishes which are label as ‘Aquarium

A’ and ‘Aquarium B’. Two students come forward and count number of fishes in

‘Aquarium A’ and ‘Aquarium B’. I explain which AQUARIUM has more fishes and less

fishes. Again for this step, I used pictorial approach and abstract approach where

students need to figure out the answer by themselves. In this step, I want to determine

types of counts model used by students because there are three types of counting

which are standard left-to-right counts, incorrect counts, and unusual counts.

Next, I calls few students to come forward to paint numbers 1 to 10 to identify the

image.10 colours are displayed on the screen from 1- 10. Students need to colour

according to the numbers. A 2-dimensional bird picture was displayed .So, I use

pictorial approach. Students do not use abstract approach because the numbers are

already displayed on the screen where they just have to colour without thinking. This will

indirectly increase automaticity with math facts by systematic drill and practice because

numbers are difficult to define but easy to recognize.

After that, I conducted a caterpillar’s game where students work in a group of 5

and stick the number of flowers according to the number written on the caterpillar’s

body. In this activity, I use pictorial and abstract approach where student need to count

the quantity of flowers and stick on the corresponding number. In this step, I want to

provide extensive opportunities for students to match quantity of objects to

corresponding numerals and for experience for the students with the concept of quantity

of object.

In addition, I give worksheet consist of 6 questions with pictures to evaluate

students’ understanding. In this step, I again use pictorial and abstract approach where

students need to think and choose the answer. I assess students using speed and

accuracy in counting objects. Counting speed and accuracy improved with exercises. I

want to measure children numeration skills by standardized exercises.

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Finally, I wrap up the lesson by encouraging students to always careful in

counting to avoid mistakes. I explain that numbers are the fundamental to build a good

foundation for computational skills. I explain there are many incidental opportunities for

the young child to use this number sense in their daily life. Students with good number

sense can move seamlessly between the real world of quantities and the mathematical

world of numbers and numerical expressions. They can invent their own procedures for

conducting numerical operations. They can represent the same number in multiple ways

depending on the context and purpose of this representation.

Misconception on Numbers

1. Conservation of numbers ( More or less )

In his experiment on conservation of number, Piaget presented children of less than six

years of age two rows of checkers:

The children were then asked if there are more in the one or the other row or if there is

the same number in both rows.

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Many participants answered that there are more of the red checkers. This situation

shows that the student recognize the two equal quantities are the same amount even

though both appears the same.

2. Counting numbers

A student is asked by his teacher to count the number of pencils on his table. He clearly

counts out loud,” One, two , three.” When asked by the teacher,” So, how many pencils

on the table? ”He immediately starts to count loud again,” One, two, three.”

Students’ does not understand the cardinality of numbers. Counting is so much more

than reciting the words and writing the numerals for the counting sequence: 1, 2, 3, 4,

When successfully counting a group of objects, children give a unique number name to

each object (one-to-one correspondence).They should recognize that the last number

represents the quantity of objects in the group according to the concept of cardinality to

how- many questions. This is a key development in children’s understanding of number

because it allows children to integrate their counting knowledge with an understanding

of group.

3. Misconception in understanding the questions

When asked by teacher “How many pictures are there?”. The student answered 10

frogs. Students’ does not understand the question asked. Misconception occurs about

understanding of the question. Actually there are 2 pictures and not the number of frogs.

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DAILY LESSON PLAN

Subject : Mathematics

Class/ Year : 1 Neptune

Date: 18 May 2012

Time: 10.15 a.m – 11.15 a.m (1 hour)

Class size: 30 students

Topic: Whole numbers

Learning area: Numbers 1-10

Learning objectives: Students will be taught to recognize, count and arrange numbers according to orders.

Learning outcomes: By the end of the lesson, the students will be able to i. to recognize numbers 1 to 10.ii. to name numbers 1 to 10.iii. to count, read and write numbers 1 to 10.iv. to compare the values of whole numbers.

Previous knowledge: i. Classifying objects by their physical attributes. ii. Comparing the quantities of two sets of objects by one-to-one matching. iii. Conserving the quantitative relation between two sets: as-many –as relation;more than relation; and less than relation.

Integration of knowledge: i. English Language – Answering questions .

ii. Reading and interpreting daily life count in numbers.

Integration of thinking skills: i. To compare two quantities and identify the different numbers displayed. ii. Explain the meaning of zero as the number to represent the quantity “empty” .

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Integration of Moral values: i. To strive for conscientiousness and accuracy.

ii. To share and cooperate in group work.

Teaching Resources: i. short video clip ii. power point presentation iii. flash cards

v. worksheets

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Daily Lesson Plan

Steps(duration)

Content Teaching and Learning Activities Remarks/ Notes

Set induction

(5 minutes)

The idea of :a) Counting

numbers 1 to 10

Teacher calls out student to count number of sweets in the packet.

Teacher shows a short video of dropping 3-dimensional numbers and numbers countdown.

Teacher asks the students about the above information.

Teacher introduces the topic which the students are going to learn today ,e.g:vi. To recognize numbers 1 to 10.vii. To name numbers 1 to 10.viii. To count, read and write numbers 1 to 10.ix. To compare the values of two quantities.

Laptop LCD projectorA short video clip Select few students to answer

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Lesson Development

Step 1 (15 minutes)

To recognize numbers by symbol and numbers by words.

To count , read number 1 to 10 according to quantities.

Teacher displays numbers 1 to 10 using power point presentation.

Teacher guides students to recognize numbers and read the numbers in words.

Teacher demonstrates the numbers by using cards and pictures.

Power – point presentation

Flash cardManila card

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Step 2(15 minutes)

To compare two quantities

To count numbers 1 to 10 correctly.

Teacher explains the concept of more than , less than and as many as by comparing two quantities.For example:

Less More

As many as

Teacher gives 8 animals’ cards to 4 students. Each get 2 animals cards. Teacher asks the students to come forward and paste the animal card on the white board while counting the numbers orderly. Students come out simultaneously and stick the animals’ card until the last student configure the number of animals’ cards altogether.

Power – point presentation

Manila cardSelect few students to answer.Students are encouraged to count on their own.

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To compare two quantities.

Teacher sticks 2 manila cards consisting of fishes which are label as AQUARIUM A and AQUARIUM B. Two students come forward and count number of fishes in AQUARIUM A and AQUARIUM B. Teacher explains which AQUARIUM has more fishes.

Manila cardSelect few students to answer.Students are encouraged to count on their own.

Step 3(10 minutes)

To recognize numbers with colours.

Teacher calls few students to come forward to paint numbers 1 to 10 to identify the image.

10 colours is displayed on the screen from 1- 10. Students need to colour according to the numbers.

Laptop LCD projector

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Step 4(10 minutes)

Practice for students through a game in a cooperative group work environment.

Evaluationexercises(individual).To evaluate the students’ individual performance and understanding.

Teacher gives instruction:1. GAME PLAY. Count the flowers on each circle. Match the circle to the section on the

caterpillar with the corresponding number.

Teacher gives instructions:1. Each student is provided with a worksheet and

they are required to complete the 6 questions in the time allotted.

2. Students submit their worksheet at the end of 5 minutes.

Manila card

Worksheet Integrate the value of being conscientious and being accurate in your calculation.

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Closure(5 minutes)

To summarize the main ideas of the lesson.1. To calculate accurately number of an objects.2. To estimate

number of certain objects.

Teacher wrap up the lesson by encouraging students to always careful in counting to avoid mistakes.

Teacher explains that numbers are the fundamental to build a good foundation for computational skills.

Integrate the value of being conscientious.

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Script of Teaching Numbers 1 to 10.

I’m using ‘activity skill’ to teach numbers 1 to 10. Students’ already understood recognize and count numbers 1 to 10. I prepared few activities to enhance their skills. For example,

Teacher : Good morning ,students. How are you, today? Can anyone tell me what we

learnt yesterday.

Student : Teacher , we learnt about numbers 1 to 10 .

Teacher : Yes ,very good . I’m happy you still can remember what teacher taught you

yesterday. I want to test whether you can count 1 to 10. Ok, now I want one

student to come forward and count for me number of sweets in this packet.

Student : Teacher , I want to try.1,2,3,4,5,6,7,8,9,10.There are 10 sweets.

Teacher : I’m happy you still remember counting 1 to 10. Let’s start with few activities

now. All these activities are related to numbers 1 to 10. I want to evaluate

students’ understanding on numbers.

Student ; Ok ,teacher. Yeah!!!

Teacher : Now , we are going to colour according numbers.

Student : Yes , teacher. We like to colour.

Teacher : I want one student to come forward and colour the picture according to the

numbers. If you see the slide, you can see different type of colours which are

labeled by numbers. Teacher will show you demo. I start first, pay

attention and look carefully. Ok, now I want you to colour acoording numbers .

Student : Ok , teacher. I understand.

Teacher : I belief student can recognize numbers 1 to 10 by now. Let’s go for counting

numbers 1 to 10. Now we are going to count from pictures. I’m going to stick

two aquariums which are labeled as A and B. So I want student to count

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number of fishes in both aquariums.

Student : Teacher, I want to try. Aquarium A consists of 10 fishes.

Teacher : Who wants to count number of fishes in Aquarium B?

Student : Teacher , I want to try.

Teacher : Ok , very good. Come in front and count the number of fishes in Aquarium B.

Student : There are 8 number of fishes in Aquarium B.

Teacher : Clever you are correct. Ok, just now I showed a picture, you count from the

picture. Now, I will say a number and you have to stick number of different

type of animals according to the number mentioned. Can you do it for me?

Student : Yes, teacher. We can do it.

Teacher : I will show you one picture .This insect will soon developed into a butterfly.

What is this insect? Can you guess?

Student : Yes teacher. The insect is caterpillar.

Teacher : Yes, you are rite. Very good. We are going to play caterpillar game. I will

paste few cards with flower pictures on the board. If you see the long body of

the caterpillar. What you can see here?

Student : Teacher , I can see numbers 1 to 10 arranged orderly.

Teacher : Ok, very good. Now, I want student to stick corresponding number of flowers

on caterpillar’s body according to the numbers.

Student : Ok teacher.

Teacher : That’s all for today. I hope you really enjoyed the lesson. See you next class .

Student : Thank you , teacher.

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Feedback

One of the weaknesses is too many activities were done in a short period of time.

It is too draggy for micro teaching. Students feel that the painting activity is fun because

it involve different types of colours and sound where attract their attention. They really

enjoyed the colouring activity. Small magnet cannot support the big manila card and it

was kept on dropping. This situation interrupted the lesson. Finally, each student in a

group work was not assigned a task.

Suggestions to Improve in Teaching

I have to build my creativity in making material and learning activities, speak loud

and give clear instruction, use interesting media in learning activities. But the most

important thing is that i have to build my confidence to teach in front of the class. I found

that most of my weakness was lack mastery of vocabulary and as a teacher did not

encourage my students to answer it by themselves but they directly gave the answer.

My time management was still uncontrolled. I spent much time in one activity so that

there was no time left for the rest of activities. And at the closing, they became hurry in

making a review of the lesson and giving time to students to reflect what they have

learnt then to check indicator attainment. All of these weaknesses and strength time by

time I learn to build my understanding about what a good teacher is. By taking

microteaching class, helped me a lot to build my teaching competences.

At the first time before taken this class, I have limited knowledge and skills of

teaching. I also learn how to be creative in making material and the teaching learning

activities. Being observer of my peers’ performances and pretending as student of

different level gave me real perspective of what must I do as teacher and what should I

avoid. It gave me foreshadowing of teacher world. Limited activity must be prepared in a

given period of time and manage the time well during the lesson. I should to prepare

well with suitable material such as blue tack before start the lesson or may be do some

trial with the materials.

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Furthermore, when doing activity in a group, teacher must assign a task to each

student so that no one will be left out doing nothing or become the sleeping partner in

the group. By assigning task to each student, they will play their role actively in the

group. I should provide more opportunities for pupils to work collaboratively and ensure

an appropriate level of challenge for all pupils. Improved approaches to learning and

teaching in primary schools including interactive teaching by using variety teaching

materials. Finally in the end, I hope that what I have learnt in this micro teaching will be

guidance for me when I become a teacher. There is nothing that I cannot do to become

a successful teacher.

CONCLUSION AND REFLECTION

When I want to begin my assignment, I was a bit confuse about my topic which I

want to choose as my preparation for micro teaching. After searching from internet and

books, I got few ideas in teaching numbers 1 to 10. So I started my research on

numeracy to teach primary students. I borrowed few books from library as my reference

and browse from internet about the topic that I have been chosen. I taught it would be

easy to teach basic number but later after the research only I discovered that my

assumption was wrong. My passion is in mathematics, particularly the 'more complex'

ideas in secondary school and I am in some ways disappointed that I will be teaching

'the simpler stuff' to younger pupils. By knowing the topic, I taught it is easy to make

someone else especially a young mind coming across an idea for the first time to

understand. It seems simple to count 1 to 10, but I realize that it is hard to teach

children who have never experienced that before.

All the steps given from the project course work sheet was very useful and

beneficial to prepare daily lesson planning. All the guidelines are inter-related and

helped me a lot to do the following steps. In the process of completing this task, I have

done a lot of research and I discovered that there are actually many ways of teaching

numbers 1 to 10. By doing conceptual and procedural knowledge, I understand the topic

which I have been chosen in further detail. Other than that, I learnt to plan teaching

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concept and procedural knowledge based on CPA approach. I did analysis on the

misconception may done by students from reference book and notes given. During my

teaching experience, I never done or does not think about student misconception may

occur. By doing this assignment, I realize student can view the knowledge that we

delivered in different angle which is actually wrong. This phenomenon helped me to be

careful and give clear explanation in my teaching to avoid misconception among

students in this topic.

In addition, I did few mistakes during my micro teaching. I learnt to improve

myself in teaching from the feedback given by Dr. and friends. So, if it is not just about

subject knowledge, how does make an effective teacher of mathematics to primary

children. If we think counting to 10 is easy, think about what we need to understand to

do it.. There is a lot of room for error, even in that most basic of concepts. Children will

miss numbers out, not order them correctly or confuse the digits. A good teacher can

recognize where these errors could be made, breaking down the teaching into the

individual small steps and teaching children to avoid specific mistakes even in skills we

take for granted.

In my opinion, Mathematics should be fun, practical and inspiring too. I would not

deny that subject knowledge is vital, without it we cannot teach successfully at all. A

good teacher has good subject knowledge, but someone with good subject knowledge

would not always be a good teacher; it takes a balance of the two elements. It would

take a great teacher to get me to understand complex calculus and I think we need to

remember that it takes the same to teach a child to count for the first time and be proud

of it.

Finally, I would like to thank Dr.Ng Kok Fu for his dedication and support in

completing this assignment. He has helped me in many ways. Whenever I have doubt,

he was not hesitating to teach me and not forgettable my dear friends for giving me

room for improvement by giving their comment and ideas on how to improve teaching

from the observation of my micro teaching on numbers.

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ATTACHMENT

TEACHING MATERIALS

PICTURES

1.

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2.

Less More

27

As many as

3.

28

4.

29

5.

6.

30

7.

31

BIBLIOGRAPHY

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1. Baroody, A. J. (2004). The development bases for early childhood number and operations standards. In Clements, D. H., Sarama, J., & DiBias, A. H. (Eds.). Engaging children in mathematics: Standards for preschool and kindergarten mathematics education, pp.173-219. Hillsdale, NJ: Lawrence Erlbaum Association.

2. Baroody, A. J., & White, M. S. (1983). The development of counting skills and number conservation. Child Study Journal, 13, 95-105.

3. Baroody, A. J., & Wilkins, J. L. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48-65). Washington, DC: National Association for the Education of Young Children.

4. Baroody, A. J. (1993). The relationship between the order-irrelevance principle and counting skill. Journal for Research in Mathematics Education, 24, 415-427.

5. Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.

6. Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11. Cambridge, MA: Harvard University Press.

7. Marzita Puteh, Wan Yusof Wan Ngah dan Chan Yook Lean. (2010). Matematik Tahun 1(KSSR). Buku Teks -Jilid 1.: Dewan Bahasa dan Pustaka:Kuala Lumpur.

8. Marzita Puteh, Wan Yusof Wan Ngah dan Chan Yook Lean. (2010). Matematik Tahun 1(KSSR). Buku Aktiviti- Jilid 1. Dewan Bahasa dan Pustaka: Kuala Lumpur.

9. Robert J. Jensen, (1993). Research Ideas For The Classroom Early Childhood Mathematics: National Council of Teachers of Mathematics Research Interpretation Project.

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10. Pn.Wan Ilyani Yusrina Binti Wan Mustama, (2011). Rancangan Pengajaran Tahunan Matematik Tahun 1 (KSSR). Derived from: http://skkayang.edu.my/rancanganpengajarantahunankssrmatematiktahun1-101219233339-phpapp02.pdf

11. Number Theory.Derived from:http://www.math.niu.edu/~rusin/known-math/index/11-XX.html\

12. Number Systems.Derived from:http://www.jamesbrennan.org/algebra/numbers/real_number_system.htm

13. Maths is Fun.Derive from:http://www.mathsisfun.com/whole-numbers.html

14. Knowing Numbers.Derived from:http://611mte.mycikgu.net/Semester%201/Nota%20Portal/MTE3101%20Knowing%20Numbers/resources/372.html

15. The teaching Principle of Developing Young Children through Number Sense.Derived from:http://wik.ed.uiuc.edu/index.php/Number_Sense#The_Teaching_Principle_of_Developing_Young_Children.E2.80.99s_Number_Sense

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