ASSIGNMENT 2 HMEF5103

Task I: Research Topic, Site and Group.

Mathematics Problem in Fraction among Year 5 Students

at Sekolah Kebangsaan Karai, 33600 Enggor, Perak.

Abstract

Students' difficulties in learning fractions have been mentioned in many previous

mathematics educations’ literature. The purpose of this study is to identify the problems in

fraction in Mathematics among Year 5 students. The way mathematics is taught in schools

has not changed much for the past many years. Previously, teachers might recognize that

technology such as calculator; geometrical sketchpad and spreadsheet provide just an

instructional tool for their mathematics classes and at the same time perceived that

technology potentially interferes with learning key mathematical ideas. This study however

proved that, adopting technology into classrooms may help students to improve their

understanding of mathematical concepts and ideas while having a meaningful learning

experience. 

1.0 INTRODUCTION

Research in mathematics education has repeatedly shown that too few children have adequate

mathematics skills with understanding (National Research Council [NRC], 2001). To help

students understand mathematics conceptually, mathematics teachers need to develop various

strategies to make mathematics concepts visual, live, connected, and meaningful (An, Wu, &

Kulm, 2004). In recent years, researcher started paying attention to the effects of integrating

technology to enhance student learning (Thompson & Thompson, 1987; Groves, 1994). The

National Council of Teachers of Mathematics (NCTM, 1998), the first professional

organization to create national standards for appropriate uses of technology in mathematics

areas, recommends that in mathematics classrooms:

• A computer must be available in every classroom for demonstration purposes.

• Every student has access to a computer for individual and group work.

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• Students learn to use the computer as a tool for processing information and performing

calculations to investigate and solve problems.

It is believed that using information technology in teaching and learning will enable students

to have access to learning materials that they may have difficulty obtaining or could not

obtain in other ways. Teachers must prepare materials well and this means an improved

presentation of materials. Students have an increased opportunity to understand what is being

presented in class.

Fraction in Kurikulum Bersepadu Sekolah Rendah (KBSR)

One of the main topics in elementary mathematics is fraction. In Malaysian school context,

fraction was first introduced to Year 3 students as stipulated in KBSR Curriculum. Some

fractional terminologies were introduced to students at this year such as one quarter, one half,

three quarter and one whole and the symbols and diagrams that represent them. At Year 4 the

content of fractions is more specific to proper fraction, equivalent fraction, addition and

subtraction of fractions. In Year 5 the content of fraction is extended to improper fraction,

mixed number, addition and subtraction of improper fraction with like and unlike

denominator, multiplication and division of fractions, improper fractions and mixed numbers

as well as problem solving. At Year 6, the focus more on addition, subtraction,

multiplication and divisions of fractions with bigger numbers.

Students in primary schools should be able to be good in fraction as KBSR provides

comprehensive curriculum for the topic. Unfortunately the scenario is that fraction has

always been the topic that students most dislike. Many parents and teachers are aware that

many students do not perform in this topic. Since it’s a hierarchical, many students in year 5

unable to do fractions due to their poor understanding of fractions at lower levels. As

educators we should focus more on this issue by trying to find ways and strategies to remedy

the situation.

Why are fractions so difficult to learn?

According to Maria (2009), it's not the concept of fraction that is difficult; it is the addition,

multiplication, subtraction, simplifying various operations that you do with fractions. She

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added that the simple reason why learning the various fraction operations proves difficult for

children is the way they are typically taught in school books. They need to memorize the

amount of rules to learn about fractions.

If children simply try to memorize these without knowing where they came from, they will

probably seem like a jungle of seemingly meaningless rules. Maria (2009) also reminded that

fraction math can then become a blind following of the rules, tossing the numbers here and

there, calculating this and that and getting answers, of which the kids have no idea if they are

reasonable or not. And of course, it is quite easy to forget these rules, or remember them

wrong especially after 5-10 years. Frances (2004) listed several educational literatures on

problems involving learning fractions.

1. Most students have difficulty with fractions. (Tourniaire & Pulos, 1985)

2. Students apply whole number concepts to fractions. (Mack, 1995)

3. Students do not successfully transfer informal knowledge to abstract setting. (Mack, 1990)

Researcher also found that students who are in transition from concrete to formal thinking

often interpret fractional representations in unintended ways. When children possess a solid

understanding of fractional concepts, they can use this knowledge to describe real world

phenomena. Therefore educators and researcher in Malaysia need to take a proactive action

in understanding issues.

2.0 STATEMENT OF PROBLEMS

The Mathematics Curriculum at the primary level (KBSR) emphasizes the acquisition of

basic concepts and skills. The content is categorized into four interrelated areas, namely,

Numbers, Measurement, Shape and Space and Statistics. The topic of fractions is first

introduced in Year 3 which requires the students to understand and use the vocabulary related

to fractions. The Malaysian primary school syllabus covers several learning areas in the topic

of fractions such as proper fractions, improper fractions and equivalent fractions. Fraction, in

the primary school, is defined as a part of a whole, where all parts are of equal size. It is also

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defined as equal shares of a whole set. Fractions are recognised to be a difficult topic in

school-mathematics due to the written form of the fractions being comparatively complicated.

Fractions are used less in daily life and are less easily described than natural numbers. A

research in New Zealand shows that children’s mathematical performance has improved over

the years via the Numeracy Development Project (NDP) but the improvement in performance

on proportion and ratio was lower than expected. Proportion and ratios are topics related to

fractions. However, fractions, ratios, and proportions are essential concepts in the secondary

school curriculum, which take root and grow from the fundamental curriculum in primary

school.

Many researchers have been conducted on students understanding of fractions but

most of the researches investigate the understanding of fractions as part of a whole. The study

proposed in this paper aims to investigate the problem in fraction among year 5 students. In

Malaysia, the topic of fraction is one of the topics which bring challenge to both teachers and

students alike. Children have difficulties in understanding fractions because fractions involve

relations between quantities that are represented by natural numbers. They frequently make

procedural mistakes in answering the questions and research has shown that many of the

errors made when working with fractions are consequences of children’s failure to understand

that natural and rational numbers involve different concepts.

The Year 3 text book has included the concept of fractions as part of a set of objects

in the topic on fractions. In fact, it is one of the fundamental concepts of fractions which form

the foundation for children to learn fractions. The Malaysia syllabus is the main guideline to

prepare all teaching and learning activity. The textbook examples and activities are also based

on the demands of the syllabus. However, there was an only fruit (same size and shape) used

as examples in our text books for the development of the concept of fractions as part of a set

may impede students understanding that items other than fruits can form set. The question

that arises is, are students able to transfer the knowledge of fractions that they have learnt

based on the primary school textbook to situations that are dissimilar to the examples they

have been exposed to.

3.0 AIMS OF THE STUDY

This study aims to identify the problems in fraction in Mathematics among Year 5 students.

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4.0 THE OBJECTIVES OF THE STUDY

Specifically, the objectives of the study are to: 

1. Identify the problems in fraction among Year 5 students.

2. Identify the causes of the problems in fraction among Year 5 students.

5.0 RESEARCH QUESTION

1. What are the problems in fraction among Year 5 students?

2. What are the causes of the problems in fraction among Year 5 students?

6.0 LIMITATIONS

The study is only done in the single school which at Sekolah Kebangsaan Karai, 33600

Enggor, Perak and the findings can’t generate to another school.

7.0 RESPONDENT

Subject consists of 30 students of Year 5 Bestari in Sekolah Kebangsaan Karai, 33600

Enggor, Perak.

Task II: Research Method and Fieldwork Write-ups.

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1) OBSERVATIONS

1.1 LEARNER'S ANALYSIS

Students' background

SK Karai is situated in Karai district which is about 19 km from the heart of Kuala Kangsar.

Although it is located in the urban city, most of the students live in the squatter areas near the

school. The subject of study is students from class 5 Bestari. Majority of the students come

from lower class social economic family.

Academic achievement

Based on UPSR 2010 result, only 6% managed to get A, 15% (B), 27% (C), 42% (D) and

10% (E). During 2011 Mid Year Exam, only 40% of the students passed the exam with none

got A. Only 7% got B, 33% (C), 58% (D) and 2% (E). The overall performance of these

students in Mathematics is relatively very poor.

Students' Attitude

According to their mathematics teacher, students in class 5 Bestari are fairly attentive during

mathematics lesson and also do their work as instructed. Regularly about half of the class will

complete their homework on time. The students also seem too aware the importance of

mathematics in their education. This can be seen through their interest shown in trying hard

to solve math problems and understand the lesson. They are also participative in class such as

do not hesitate to try to answer teacher's question and also actively having group discussion

to solve math question.

It is also noted that these students do not have any communication problem with their

teacher as they will normally ask their teacher anything that they do not understand during

the lesson.

Prior knowledge

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In order to know their level of understanding of fraction and their prior knowledge on

fractions, the students in this class were given a short test on basic fractions which they have

learned since Year 3. The test consists of 15 basic questions on fractions such as naming

fraction from diagrams (one whole, one half, one quarter, three quarter), comparing fractions,

simple addition and subtraction (like and equal denominator). Apart from that, students were

also given a few problems on mixed number which they have learned in Year 4. Based on the

test, the following problems have been identified:

Many unable to compare fractions.

Many unable to perform addition and subtraction of fractions with unlike

denominators.

Majority gave wrong answer for the questions that involve mixed number and

improper fraction.

1.2 CONTEXT ANALYSIS

School background

SK Karai is a one session school where standard 1 until 6 are in morning session. There are 6

classes for each level, where more or less 30 student in each class. The total number of

students approximately is 168. The majority of students are Malays where it contributes 99%

of total students. The number of students in Class 5 Bestari is 30 and all of them are Malay.

School facilities

There are one computer laboratories in SK Karai. Each laboratory consists of 30 personal

computers. SK Karai does not have a special room for learning Mathematics as there is

inadequate of rooms. However each lab has LCD projector with internet facilities. Teachers

will bring the students to the lab for teaching and learning Mathematics whenever required.

SK Karai also has one access room with internet facilities. The room consists of 10

computers where students can surf internet at their leisure time.

Support from administration and teachers

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Successful operation of a school requires competent administrators. The school

administrators develop academic programs, monitor students’ educational progress, train and

motivate teachers. In order to increase Mathematics teacher’s literacy in Information and

Communication Technology (ICT), they have to attend courses handled by Jabatan Pelajaran

Perak. Some of the courses attended by Mathematics teachers are PowerPoint, Geometer’s

Sketchpad, Handling Notebook, Using Graphic Calculator and a few more. There are also

courses that are not related to ICT such as Marking Techniques and Developing Mathematics

Question based on UPSR Standard. Hopefully this will increase competency and efficiency

among Mathematics teachers.

Meeting is held in Mathematics Panel to discuss the activities that need to be done in order to

increase students’ achievement. Some of the activities are Motivation Camp, extra classes in

Mathematics, Mentor / Mentee, Educational Trip and Mathematics Week. The activities are

planned, not only to increase the achievement, but also to develop students’ interest and

likeness in Mathematics, and eliminate the Mathematics phobia among students.

Support from parents

Parents have a vital role in their child's education. Parents can help children enjoy school

more; improve their studying and homework skills. Based on the survey, 69% of the students

feel that they need help with their homework. 61% said that they like learning Mathematics

with their friends. 62% said that their parents help them with their homework and 36% went

to tuition class to increase their knowledge. We can say that even though the parents are not

highly educated (based on annual income), they realize the importance of Mathematics in

their children’s life. They tried to help as much as they can, although some totally rely on

teachers to educate their children.

2.3 IDENTIFY PROBLEM

For my case study, I choose a problem faced by Year 5 students from SK Karai in Fractions,

a topic taught in Mathematics subject. Teaching fractions has been a complex and largely

unsuccessful aspect of mathematics instruction in the elementary grades for many years.

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Students' understanding of fraction concepts is a big stumbling block in their mathematical

development. Some researchers have pointed to children's whole-number knowledge as

interfering with, or creating a barrier to, their understanding of fractions (Behr et al. 1984;

Streetland 1993; Lamon 1999).

From observation and experience, we noticed that students have difficulties to understand the

concept of fraction. I noticed that when the students set their mind that fraction is the difficult

topic in mathematics and they feel it’s difficult to learn. They always forget what they have

learned, and teacher always has to remind them and sometimes re-teach the topic. Sometimes

teacher felt that the students lack of motivation and always wait for teacher to give them

input. They don’t go for themselves to find out what they don’t understand.

Root Cause:

1. Students do not remember the multiplication table

Students were weak in memorization. They cannot memorize multiplication table between 6

till 12. That's why they were having problem to solve addition and subtraction fractions

involving different denominator.

2. Students do not have strong foundation of fractions.

Students do not understand the basic concept of fractions. Students can understand when

teacher uses concrete object in explaining the problem. But when the problem is displayed as

a mathematical sentence, this is where the problem arises. They have difficulties to analyze

the problem. Due to this, they were having problem to solve problem solving type of

questions.

3. Students cannot relate fraction with its uses in their daily life.

Students cannot make connection between the fractions concept with their daily activity. This

makes it difficult for them to grasp the meaning of fractions.

1.3 PARTICIPANT OBSERVATION

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DAY 1: SUBTOPIC - PROPER AND IMPROPER FRACTION (2 hours)

Activity 1:

- Students are shown a video on how to do multiplication using fingers. After that teacher

explained further on the concept. Teacher then asked two students to challenge on each other.

Teacher gave one question and whoever the faster in answering the question correctly may sit

down. The other one left was asked to challenge another friend. Again teacher asked another

question. This went on for 5 minutes. Students enjoyed it very much, where some volunteer

to answer any question. Surprisingly students who had difficulties in multiply before, can

answer the question given by teacher quite fast. It was a good start of a lesson that day.

Activity 2:

- Using a website http://www.coolmath4kids.com/fractions/index.html, teacher explained the

concept of Proper and Improper Fraction. To enhance students understanding, teacher asked

the students in pairs to draw shapes that represent proper and improper fraction using window

paint. Students showed interest in the activity as they are able to color the shape. Majority got

it correctly.

Activity 3:

- Teacher later introduced online educational games with multiple players at

http://www.iknowthat.com/com/L3?Area=FractionGame. Before the class, teacher has

already registered for the whole class. To enable teacher to monitor, all students' sign up

name began with SKK. Still worked in pairs, teacher asked the students to use either one of

the pair to sign up and chose level improper fractions. Students were so excited as that was

the first time they learned to play mathematics games online. Furthermore they enjoyed

competing with one another. Some of them showed great achievement. And when teacher

asked the students to stop playing, some of them cant seem to stop. That was the challenge

for teacher when she wants to bring the students away from the excitement and back to the

real world.

Activity 4:

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- Teacher distributed handout on Proper and Improper Fractions. Students are asked to do it

in class. 33% of them manage to get Grade A and B.

Evaluation:

Students really show great interest when teacher taught them how to do multiplication using

finger. They were also interested with fraction game. Since the internet connection was not

quite strong that day, teacher informed that they could continue that game at home (if they

had internet connection) or using the access room. After the school ended, some of the

students continued playing at home, at access room in school and even at the cyber cafe. This

activity can really engage students in active learning.

DAY 2 : SUBTOPIC - ADDITION OF FRACTION (2 hours)

Activity 1:

- For set induction, teacher still asked the students with multiplication table. This time around

teacher asked everyone to stand up. Teacher asked more difficult questions than before.

Those who answered correctly may sit down. Most of the questions are answered correctly by

students.

Activity 2:

-Teacher explained the concept of Addition

Using http://www.coolmath4kids.com/fractions/index.html and demonstrated it using the

white board. Teacher gave examples of Addition with like and unlike denominators.

Activity 3:

- Teacher continued the lesson by showing web site http://www.ixl.com/math/grade/sixth.

Teacher chose word problems questions (U2 and U4) This exercise introduced on scenario-

based question where questions were given in sentences. This exercise promoted the students

on how to relate and use fractions with their daily life. This activity was quite difficult for

weaker students. They were not only have to understand the sentence in English, but also to

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solve the problem. Teacher showed the students on how to chunk the question and identify

the main term in the question.

Activity 4:

- Teacher formed the students into groups of 5. A group consists of good and weak students.

Each student was given worksheet on Addition. They were asked to work together

cooperatively to answer the questions. Good students would help weak students. All groups

gave the answer correctly. Peer-tutoring really helped weak students to understand better, as

they learned from their friend.

Activity 5:

- Teacher distributed handout on Addition of Fractions as homework. Students are asked to

submit the answer on the next lesson.

Evaluation

Students gave full cooperation and commitment with all the activities. They can add fraction

with like denominators easily. Some of the students were still having problem to add unlike

denominators but with helped from their friends and teacher, they managed to solve it.

DAY 3 : SUBTOPIC - SUBTRACTION OF FRACTION (2 hours)

Activity 1:

- For set induction, teacher still asked the students with multiplication table (1-10) with more

big numbers. This time, teacher chose a student by throwing a ball to him. After he asked

correctly, the student would throw the ball to someone else, and teacher would pose other

questions until 6 students answered correctly.

Activity 2:

-Teacher explained the concept of subtraction

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using a website http://www.coolmath4kids.com/fractions/index.html. Using examples from

the website, teacher teaches students how to do subtraction with like and unlike

denominators.

Activity 3:

- Teacher started a Quiz activity by dividing the students into 2 groups. Each group consists

of good and weak students. Teacher started the online games on subtracting fractions at

http://www.funbrain.com/fractop/index.html. Group 1 members would take turn to answer

the question. When they answered correctly, mark would be added for them. Then the next

question would go to another group. At the end of the Quiz, teacher praised Group 2 for

scoring higher mark thus wins the Quiz activity. It was very fun to see how the students

competing among themselves in order to win the game. In directly, that activity became a

drilling practice for the students as there were approximately 30 questions was answered on

that day.

Activity 4:

- Teacher distributed handout on Subtraction of Fractions as homework. Students are asked to

submit the answer on the next lesson.

Evaluation

Students were improved in multiplication. They were able to master the multiplication

method using finger. During mathematics lesson, they were very enthusiastic and they will

ask their teacher to question them with multiplication. This skill really helped students to

solve questions on subtraction of fraction with different denominators.

DAY 4 : SUBTOPIC - EVALUATION ON FRACTIONS (2 hours)

Activity 1:

- Teacher gave students a short test questions that consists of 20 questions. The objective of

the activity was to evaluate the students' achievement after teacher has completed teaching

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fractions. Later, teacher checked the answer with the students. The findings from the test

showed that pupils have improved in understanding the basic of fraction. They can name and

write the fraction correctly. They also know how to convert from mixed number to improper

fractions and vice-versa by themselves.

Now, most of them have confident to do fraction. Even some of them still slow in

understanding the basic concept of fraction, but they have improved it. They show their

interest in mathematics and always try to get the answer.

From this test, 75% have achieved the objectives and can understand the basic concept. The

rest still need guide especially for fractions that involve basic operation. But, they have

increase their mark and understanding in mathematics especially in fractions.

Activity 2:

- Teacher requested students to fill in the Post Evaluation Form. The objective was to

evaluate students' perspective towards fractions and mathematics after they have been

introduced with a few technology-based teaching and learning strategies. It was found that

students have changed their mindset on mathematics and fractions in particular.

- For post evaluation, teacher distributed again the same short test and survey form during

pretest to students.

2) INTERVIEW

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Basis for doing the interview: On the previous day, a revision class was observed on

fractions in Year 5 of this school. The focus of the entire class was superficial understanding

of terms (proper, improper and mixed fractions, equivalent fractions etc.). On raising this

point in the interactive session later on, the teachers voiced that the students would be able to

answer conceptual questions related to fractions also, if they were asked. The interview was

planned to try and find out whether this really was the case.

The mode of selection of the questions: Though the original plan was to use only those

questions where the students of that particular school had demonstrated a misconception later

it was decided to use at least one question from a past round. This turned out to be a good

idea, as the class seemed to have been tutored on the questions from their own paper.

Methodology: A question was projected on the computer monitors around the class and

written on the board. Students were given time to put down the correct option and think of the

justification. Then the one by one the options were read out and students who had chosen that

asked to raise their hand to enable a head count. In 2 of the questions, the answers were read

out in scrambled order for the head count, keeping the correct option for the last. After giving

a few kids the opportunity to justify their answer to the class, students were again asked for

the answer (noting to see if some had changed their answer).

Discussions:

Question 1:

11/4 is a number between

A. 1 and 2

B. 2 and 3

C. 3 and 4

D. 11 and 12

Initial responses:

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A. 2,

B. 11,

C. 6,

D. 14

When one of the children who chose D was asked why, he said “I took the numerator and

chose D.” The other children choosing this option agreed – no one had a different reason for

choosing D. The children who chose C had a similar reason (“took the denominator 4 and

option C says between 3 and 4”) for choosing D. The group choosing correct answer B was

asked for the reasoning last, thinking that that might give away the answer to the class. What

followed was truly surprising.

Child 1 (The very first child who was questioned among those who chose B as the

answer): “When we convert 11/4 into a mixed fraction, it becomes 2 ¾. So they are the

same.”

[At this point the class was asked if the students agree that 11/4 can be written as 2 ¾. Most

students agreed. However,  on being asked if they also agree that that they have the same

value, only a few students said yes.]

Child 1 (continuing): “So, if we cut off the 4 from the denominator (of 2 ¾), we have 2 and 3

left. So 11/4 is between 2 and 3.” At this point, one girl was very keen to say something.

When called upon, she said: Child 2: “We can cut off the 2 (of 2 ¾), and then 3 and 4

remain and so we can say that it is between 3 and 4.”

[The interviewer was not sure whether she was trying to prove that ‘cutting off’ is wrong or

now believed this to be the actual reason for selecting option C – on being asked it turned out

to be the latter!]

On being asked if anyone had a different reason for selecting B, some kids were raising their

hands. One boy responded. Child 3: “Till 2 ¾ it is correct, but when you cut off 4 it is wrong,

2 ¾ means it is between 2 and 3, cutting off 4 is not proper.”

Interviewer: He has taken 11/4 as 2 ¾, does 11/4 mean the same as 2 ¾? All students agreed

to this now. At this point, the class was asked to think about what quantity 2 ¾ represents –

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that is if they have 2 ¾ apples, how much is that. On taking a head count again on responses

it was found that now:

A. 2,

B. 15,

C. 6,

D. 11.

So, the whole discussion had only convinced 4 students that 2 ¾ was between 2 and 3.

[At the end of the class, the discussion led once again to this (while discussing whether a

fraction represents one quantity or 2). By having a student’s show ‘2 ¾ doses’ pictorially on

the board and than being prompted to think about whether 2 ¾ means ‘2 and a little more’,

‘3 and a little more’ or ’11 and a little more’, many students finally said it is 2 and little more

and therefore the answer is B.]

Question 2:

What fraction of the children in the following group are GIRLS?

(Above figure was not used in the interview; it was drawn with 2 boys in top row, and 2 girls

and 1 boy in bottom row)

A. 2/3

B. 2/5

C. 3/5

D. ½

(Actually, the old version of this question, which had 2 boys in the top row and 2 girls

and 1 boy in the bottom row got used accidentally. Interestingly, hardly any child

overlooked the fact that the second row had a boy among the girls, and counted

correctly).

Not much came out of this question – with only 5 students going for option A and no one for C

or D. It looked like this question or similar ones had been discussed in class, but there was

some interesting words from the few children who initially went for option A - 2/3.

Child 4: “I saw 2 (children) in the numerator column of the picture and 3 (children) in the

denominator column and wrote 2/3.” Child 4: “I saw 2 (children) in the numerator column of

the picture and 3 (children) in the denominator column and wrote 2/3.” Another child

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explained the reason for choosing A as counting 2 girls and 3 boys and hence picking 2/3 as

the answer.

Question 3:

Arjun had 6 pencils.

(picture of 6 pencils)

He gave one third of the pencils he had to his sister. How many pencils did he give?

A. 1

B. 2

C. 3

D. 4

Again, this was a question from the paper they had taken and the responses reflected it, but

the few children who answered incorrectly opened up a whole new interesting discussion

which exposed some glaring gaps in learning.

Child 5 (responding to why he thought the answer is C, 3): “When he (Arjun) shares with his

sister, they must share equally. He has 6, so he has to give 3.”

[This child stuck to this answer even after he was made to read the question again and check

whether it mentions sharing equally or some other way.]

Child 6 (also responding to why he thought the answer is C, 3): “one third means 3.” Child 7

(responding to why he thought the answer is A, 1): “I read the full question – it says ‘He gave

one third of the pencils he had to his sister’ – since one third has 1 as the first number, I feel it

will be A. Based on the above two responses, a discussion was started on what ‘one third

‘really means.

Interviewer: “Is ‘one third’ one number or two different numbers – that is, does it mean one

quantity or two different quantities? Only 4 students said it is one quantity, 22 said “2

quantities” and the others were not sure. One of the children from the second group explained

why he thought one third was two different quantities. Child 8: “One third means 1 out of 3.

So 1 is one quantity out of 3. 3 is a different quantity.’

[At this point there was a short discussion on this at the end of which all kids seemed to agree

that one third is one quantity. But the understanding was very shaky.] In an attempt to relate

this to the first question (11/4 is between…) the class was then asked whether 11/4 represents

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one quantity or two – again students were not sure, and in case of 2 ¾, many felt it

represented 3 different quantities].

The ensuing discussion showed up huge gaps in the very basic understanding of fractions.

The interviewer tried to get the students to arrive at the fact that the quantity 2 ¾ means ‘2

and a little more’. When asked to represent 2 ¾ doses on the board, the first child who came

to the board just chopped off a part of the third circle.

3) CONSENT FORM

SEKOLAH KEBANGSAAN KARAI

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QUALITATIVE STUDY INTERVIEW CONSENT FORM

Purpose of Study

The Sekolah Kebangsaan Karai is conducting a small-scale study title “Mathematics Problem

in Fraction among Year 5 Students at Sekolah Kebangsaan Karai, 33600 Enggor, Perak”.

You have been asked to be in this study because you fit on these categories.

Study Procedures

Your participation in this study is totally voluntary. If you decide to participate, you will be

interviewed by Norihan Bt Kamal. You may be asked to participate in interviews or focus

groups more than once. You will be asked questions about your problem in fraction.

If you decide to participate in the study, you may choose not to answer any question that

makes you uncomfortable and you can stop the interview at any time. The interview will take

between 20 - 30 minutes. The discussion will be audio-taped so that the information obtained

from the interview can be transcribed, analyzed and summarized. Audio-taping of the

interview is a requirement for participation in the study. You may, at any time following an

interview, see a copy of the interview transcript.

Benefits and Risks

You understand that you may not personally get any direct benefits from being in this study.

However, the answers you give will be used to identify the needs of other students as well as

lecturers/supervisors, OUM management, policy makers and other relevant stakeholders. To

protect your confidentiality, no identifying information about you will appear in tape

transcripts except by your request. Research records will be kept in a secure location and will

be available only to Norihan Bt Kamal. Your answers will remain confidential; answers will

not be shared directly at any time. You understand that this study has been designed to keep

information confidential, but there is a small risk that the information you provide may

inadvertently become known to other people.

Compensation

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ASSIGNMENT 2 HMEF5103

There is no compensation for informants to participate in the study.

Questions

If you have any questions about this study, you can call Norihan Bt Kamal, Teacher, Sekolah

Kebangsaan Karai, 33600 Enggor, Perak at 05 7576237.

Refusal or Withdrawal of Participation

You agree to participate in this study. You understand that your participation is totally

voluntary. You can choose not to be in the study, and can refuse to answer a particular

question or withdraw your consent at any time. You understand that anything said in the

interview is confidential.

Consent to Participate in the Study

You hereby agree to participate in the qualitative interview and to the aforementioned terms.

____________________________ __________________________

Signature of Participant Date

Name:

____________________________

Signature of Researcher

Name:

Task III: Representation of Data and Discussion.

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ASSIGNMENT 2 HMEF5103

DESIGN PHASE

1. Using fingers in learning multiplication

Method of teaching like memorization was not suitable for weak students. Teacher will

introduce new method in teaching multiplication table. Students are not going to rote the

multiplication table but they will use their finger to find answer on multiplication.

2. Using Web based in teaching basic concept of fractions

With recent advances in computer technology, it is no surprise that the manipulation of

objects in mathematics classrooms now includes the manipulation of objects on the computer

screen. These objects, referred to as virtual manipulative, are essentially replicas of physical

manipulative placed on the World Wide Web. Teacher is going to use mathematics sites

available on the internet to teach basic concept in fraction. Teacher will show and teach

fraction using concrete examples. Colorful graphics and pictures will be used in order to

capture students’ attention and interest.

3. Engage the students in active learning

Let students learn actively. Engage students in exploring, conjecturing and thinking rather

than on rote learning of rules and procedures. Teacher will present mathematics in positive

and light way. Online mathematics games will be used in order to create fun learning.

Teacher can organize quiz to encourage student to compete among each other in answering

fractions questions.

4. Develop Cooperative learning among students

Student can improve mathematics achievement and encourage higher level thinking when

students are involved with other students (Marzano, 2007; Stigler & Hiebert, 1999; Tobin,

1986). Cooperative learning is a successful teaching strategy in which small teams, each with

students of different levels of ability, use a variety of learning activities to improve their

understanding of a subject. Each member of a team is responsible not only for learning what

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ASSIGNMENT 2 HMEF5103

is taught but also for helping teammates learn, thus creating an atmosphere of achievement.

Students work through the assignment until all group members successfully understand and

complete it. To encourage cooperating learning, students will be divided into 5 groups. Each

group will be given problem on fractions. Good students will help the weaker students. The

students will discuss cooperatively to come out with the solution.

5. Relates fraction in students’ daily lives

In order to make fractions more meaningful for the students, teacher will have to relate the

usage of fraction in everyday lives. Tzur (1999) explains how students' learning of fractions

can be prompted with realistic situations that lead the students to use their informal

knowledge to construct meaning for them. Using authentic problems with students can be

useful to demonstrate how the mathematical concept may be interpreted and applied in real-

life situations. Manipulative combined with real-life problems can interest students in solving

problems, which, in turn, helps them construct meaning. This process contributes to students'

mathematical knowledge base

6. Drill and practice

Students will improve their mathematics achievement with drill and practice. Frequent

practice is necessary to attain strong mental arithmetic skills and reflexes. There are 2 types

of drill and practice that will help students in building fact and operations skills.

The first way is by using worksheet, workbook or textbook. Teacher will distribute

worksheets that may consist of 10 to 20 questions. The number of questions will vary from

easy to intermediate. Teacher may give the question after each class, and discuss the answer

during next class.

Secondly, there are drill and practice online games. This exercises aim primarily at building

fact and operations skills. Using games to practice number skills also greatly reduces the need

for worksheets. Because the numbers in most games are generated randomly, the games can

be played over and over without repeating the same problems. The games can also reinforce

other skills including calculator skills, money exchange and shopping skills, logic, geometric

intuition, and intuition about probability and chance.

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ASSIGNMENT 2 HMEF5103

LESSON PLAN

Lesson plan for the whole fraction topic was designed according to Curriculum Specifications

for Primary Schools – Mathematics.

FORMATIVE EVALUATION

Engagement strategies:

One area of improvement could focus on how teachers engage students. Students can be

shown how fractions apply to their personal lives. This makes the lesson more motivating and

successful for the students. Many teachers did not make connections from the content to real-

life applications. Many of the fraction lessons were not engaging nor did they actively

involve the students. Instead, they consisted of the teacher providing examples and the

students practicing.

DEVELOPMENT PHASE

INTERNET

1. Using fingers in learning multiplication

I have downloaded a video from YouTube. This video teaches us how to learn multiplication

table from 6 till 9 by using fingers. In case the video cannot be watched, I used free Picasa

software from Google to snapshoot the video into photos and transformed it into PowerPoint

presentation.

2. Teaching basic concept of fractions

http://www.coolmath4kids.com

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ASSIGNMENT 2 HMEF5103

3. Engage the students in active learning

Fraction multiplayer online games:

http://www.iknowthat.com/com/L3?Area=FractionGame

4. Relates fraction in students’ daily lives

http://www.gamequarium.com/fractions.html

5. Drill and practice

Examples Online fraction games :

http://www.visualfractions.com

http://www.quia.com/cb/62195.html - adding and subtracting fraction games)

http://jamit.com.au/fraction-games.htm - all games according each fractions subtopic)

http://www.learn-with-math-games.com/

http://www.primarygames.com/fractions/start.htm

WORKSHEET

The worksheets are used to test students' understanding and knowledge.

FORMATIVE EVALUATION

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ASSIGNMENT 2 HMEF5103

Internet really helps teacher in their teaching and helps students in their learning. Students

can understand fraction more easily because the examples used to teach the concept of

fraction I related to their daily life. All pictures are colorful and attractive. It helps to motivate

students to learn fraction especially they are still young. Normally children like to play

games. Fraction games will help students to do drill and practice. I found that I have to think

a few strategies to motivate or to engage students with the fraction website. I took quite a

long time to choose the most suitable materials for fractions as there are so many available on

site.

SUMMATIVE EVALUATION PHASE

The implementation phase has been done quite successfully. Teacher managed to attract

students’ attention to learn fraction. The activities have created excitement not only to the

students but also to the teacher herself as learning fraction using technology has never been

done before in that class. The students are participative and engaged themselves in the

learning part throughout the session. The teacher is quite excited to see the improvement in

terms of student understanding of fraction.

CHALLENGES/PROBLEMS FACED BY TEACHER

1. Teacher had to do the drilling activities for Year 6 students in preparing them for the UPSR

exam in September. So it would be quite difficult for teacher to do the fractions activities in

order to test the effectiveness in applying technology in teaching.

2. The internet connection at school is not stable.

3. Difficult to remove students' attention from the games and continue with next lesson.

Students are always excited to computer games.

4. Students find it difficult to understand word problems or scenario problem as most of them

are not really good in English.

5. The teacher also finds it difficult to encourage students to play outside the classroom.

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ASSIGNMENT 2 HMEF5103

Teacher hopes that students, who are lazy in doing their homework, can use this type of

games to increase their knowledge and understanding. Unfortunately for those who do not

have internet access at home, that will slightly create a hindrance to their learning process.

HOW TEACHER OVERCOME THE PROBLEMS

1. Teacher changed the subject of study from Year 6 students to Year 5 students.

2. Teacher will use her broadband modem in case the internet connection is slow and only

teacher will control the computer. Teacher need to change the strategy for the activity.

3. Change the time for games activities towards the end of the lesson, instead of in the

middle. This way, the students have to stop playing so that they may return to their class to

continue with next subject.

4. Teacher introduced on how to do the chunking and to identify the key words in the

sentence. Teacher listed key words that provide the same meaning. For example, taken out,

remove from, out of, represent the subtraction operation. Students have to remember the key

words.

5. Encourage the students to use access room after school for further understanding of the

lesson in order for them to participate in multiple player games.

SUGGESTIONS

1. Teachers need to think of ways and strategies that will ensure students to continue learning

and exploring about technologies within mathematics subject on their own when they are

outside classroom.

2. Teacher needs to focus more on the scenario problem as we found that students still having

problem in that area.

3 For group discussion, we should diversify the way we portray the questions. During

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ASSIGNMENT 2 HMEF5103

previous activity, we distributed worksheet like we normally used as exercise or homework.

Last week, we have been introduced with Hot Potatoes. With this program, we can create

quite interesting type of questions like crossword/numbers, matching and a few more.

Hopefully students will be more interested to learn mathematics, and answer questions in

mathematics.

ANALYSIS OF THE POST TEST AND POST EVALUATION

I used the same short test during pretest and post test. From the result, there was improvement

on students' performance. Most of the students can answered the fractions questions

correctly. From the pretest, the average mark was 38%, whereas in the post test, the average

mark was 64%.

Based on the post evaluation, it shows that students have positive perception towards

mathematics, they were able to memorize multiplication table and interested in learning

fractions.

CONCLUSION

This study investigated on the how to overcome the problem faced by Year 5 students in

learning fractions in Mathematics subject. The findings from this study indicate that students

have difficulties in multiplication. Thus it will affect their understanding in addition and

subtraction. They also did not have strong foundation of fractions and did not understand the

true meaning of fractions to enable them to relate it in their daily life. I introduced a few

different strategies than we normally did in classroom. Colorful fraction diagrams and

exciting games from several websites managed to attract their attention and hence create fun

learning environment. The integration of technology in teaching fractions to those students

also has result the awareness among them of how technology can really assist them in

understanding many concepts in mathematics. They were just made to realize that there are

infinitely many fun and educational sites for them to explore.

After all the activities introduced to the students, I cannot 100% sure that the students

understand all the lesson taught and being able to answer well in the exam. But I am sure that

students showed more interested in mathematics than before. They are fewer phobias in

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ASSIGNMENT 2 HMEF5103

learning mathematics. They realized that learning mathematics can be fun too. I think that a

good start as I feel that they students need to feel comfortable with the classroom and teacher

before they can absorb with what I teach them.

Integrating technology is not about technology itself. It is primarily about content and

effective instructional practices. Technology involves the tools with which we can deliver

content and implement practices in better ways. Its focus must be on curriculum and learning.

Integration is defined not by the amount or type of technology used, but by how and why it is

used (Earle, 2002).

Reference

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1. Dick, W., & Carey, L. (1996). The Systematic Design of Instruction (6th Ed.). New

York: Haper Collins College Publishers

2. Frances M. Butler.(2004), Using Research-based Methods to Teach Fraction

Concepts: What Really Works

3. http://edtech.kennesaw.edu/intech/cooperativelearning.htm

4. http://en.wikipedia.org/wiki/ADDIE_Model

5. http://math-and-reading-help-for-kids.org/article_directory/

A_Parent's_Role_in_Education.html

6. http://www.bls.gov/oco/ocos007.htm

7. http://www.coolmath4kids.com/fractions/index.html

8. http://www.funbrain.com/fractop/index.html

9. http://www.iknowthat.com/com/L3?Area=FractionGame

10. http://www.ixl.com/math/grade/sixth

11. http://www.k8accesscenter.org/training_resources/mathpeertutoring.asp

12. http://www.tpck.org/tpck/index.php?title=Main_Page

13. http://www.visualfractions.com/Investigate/Rename/renamedremo.htm

14. Integrated Curriculum for Primary Schools - Curriculum Specifications. Mathematics,

Curriculum Development Centre, Ministry of Education Malaysia, 2006

15. Kelly Reimer, & Patricia S Moyer. (2005). Third-Graders Learn About Fractions

Using Virtual Manipulatives: A Classroom Study.

16. Kervin, K. (2007). Exploring the Use of Slow Motion Animation (Slowmation) as a

Teaching Strategy to Develop Year 4 Students' Understandings of Equivalent

Fractions.. Contemporary Issues in Technology and Teacher Education. 7 (2), pp.

100-106. AACE. Retrieved from http://www.editlib.org/p/26213.

17. Mack, N. K. (1990). Learning fractions with understanding: Building on informal

knowledge. Journal for Research in Mathematics Education, 21, 16-32.

18. Mack, N. K. (1995). Confounding whole-number and fraction concepts when building

on informal knowledge. Journal for Research in Mathematics Education, 26 (5), 422-

441.

19. Merrilyn Goos, Anne Bennison. Technology-Enriched Teaching of Secondary

Mathematics: Factors Influencing Innovative Practice

20. Smith O'Regan, M. & Dehler, C. (2005). Interactive Multimedia Mathematics:

Streamlining 6th Grade Content for Better Teaching, Practice, Remediation and

Enrichment. In C. Crawford et al. (Eds.),Proceedings of Society for Information

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Technology and Teacher Education International Conference 2005 (pp. 3528-3533).

Chesapeake, VA: AACE. Retrieved from http://www.editlib.org/p/19685.

21. Tatsuoko, Kikumi K, Ed. Analysis of Errors in Fraction Addition and Subtraction

Problems Final Report.

22. The Journal of Computers in Mathematics and Science Teaching, 24

(1), 5-25. Retrieved August 30, 2009, from ProQuest Education Journals. (Document

ID: 785060121).

23. Tourniaire, F, & Pulos, S. (1985). Proportional reasoning. Educational Studies in

Mathematics, 16, 181-204.

24. Wilson, M. (1999). Student-Generated Multimedia Presentations: Tools to Help Build

and Communicate Mathematical Understanding. Journal of Computers in

Mathematics and Science Teaching. 18 (2), pp. 145-156. Charlottesville, VA: AACE.

Retrieved from http://www.editlib.org/p/18888

25. Zhonghe Wu, Shuhua An. Comparison Study of Integrating Technology in

Mathematics Teachers' Knowledge and Confidence between U.S. and Chinese

Teachers.

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APPENDIX

APPENDIX 1

Coded Transcript

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ASSIGNMENT 2 HMEF5103

This appendix comprises the coded transcript of the interview conducted with Clodagh (AC).

This was the twenty-first interview conducted in the overall process. The column to the right

of the transcript lists the initial codes assigned to the text. Reference to the codes listed

demonstrates the style of coding used in the initial data analysis. That is, line-by-line coding

using gerunds. In the transcript certain changes have been made in an effort to protect the

anonymity of the interviewee.

Transcript: Interview with Clodagh

Course: AC2

Gender: Female

Age: 20

CD: When I say ‘culture’ to you, what

comes into your head?

Clodagh: Eh, it kind of defines a person’s

country, where they are from. Like myself

personally, I would kind of distinguish Europe

and America as having different cultures. For

instance in America, although I haven’t been

there, from reading, it doesn’t really have

much of a culture about it. Whereas, in

Europe, especially somewhere like France

where I have been a good few times, there is a

distinct culture about it. Whether it’s the food

or the way people socialise or just generally

how people get on with themselves. It has a

distinct culture about it.

CD: But you wouldn’t think the States do?

Clodagh: No, the States, I think they kind

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