1.0 PREFACE
Mathematics education plays an important role in enhancing the development
of our nation and country. It is one of the main contributors that produce young
generation with creative and critical thinking. The creative and critical thinking
enable youngsters to make wise and rational decisions in their daily lives. Therefore,
it is important to equip our young generations with the mathematical knowledge and
increase their interest in learning mathematics since their elementary schools.
The mathematics performance shown by the pupils through examinations or
tests in school is one of the methods used to evaluate pupils’ mastery of mathematical
concepts and skills. In this research, one of the cooperative models, Student Teams
Achievement Divisions (STAD) was applied to enhance the pupils’ academic
performance as well as their attitude towards mathematics. In addition, the common
errors made by the pupils in the mathematics tests are analysed and the effectiveness
of STAD model in helping the pupils to make less common errors were also
evaluated.
1.1 Introduction
Mathematical thinking benefits us as members of this modern society not just
because of its application in workplaces but also in businesses and finance. Most
important of all, it is very useful in facilitating personal decision making process.
Mathematics itself is a powerful tool in providing means in understanding
engineering, science, technology and etc.
In education field, mathematics equips pupils with essential mathematical
knowledge to solve problems in their daily lives. Normally, pupils who excel in
mathematics have good financial management. Furthermore, they are able to think
independently and wisely in practical and abstract ways in solving problems or
challenges faced inside or outside of the classroom.
In the olden days or even nowadays, most of the mathematics teachers let their
pupils sit by themselves with papers, workbooks and pencils to struggle
independently to understand lessons or solve the problems assigned to them. This
learning process can be boring, lonely and frustrating. Therefore, it is not surprising
that most of the pupils lost interest in learning mathematics. Subsequently, this leads
to poor performance in the class for mathematics subject.
Cooperative learning is one of the effective methods used in enhancing
pupils’ performance in mathematics. According to Gillies and Ashman (2003),
cooperative learning is able to promote higher achievement and liking among
students which include the promotion of high-quality cognitive strategies, the
constructive management of controversy and debate, time on task, elaborate sharing
and processing information, peer encouragement of effort, active peer group
involvement in learning, interaction between students of different achievement levels,
perceptions of psychological support, positive attitude towards subject areas and
perceptions of fairness in grading.
Student Teams Achievement Divisions, namely STAD model is one of the
cooperative models. According to Davidson (1990), the main idea behind STAD is to
motivate students to encourage and help each other in mastering skills presented by
the teachers. If pupils want their teams to succeed, they must help and encourage each
other to learn the materials. The application of STAD requires the pupils to work in
pairs and compare answers, discuss any discrepancies, and help each other with any
roadblocks faced during teaching and learning in mathematics. The word “team” is
the most important element in STAD. The team provides peer support for academic
performance that is significant for positive effect on learning mathematics.
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1.2 Teaching and Learning Reflection
Based on researcher’s observation, it was discovered that most of the pupils’
performance in mathematics subject of the researched school were weak or could be
said as poor. Their academic performance in most of the subject especially
mathematics was below expectation. Most of the pupils either failed the mathematics
examination or just flied above the passing marks. If this problem was not well
tackled from the early learning stage, it was believed that the pupils would not be able
to proceed further to achieve higher achievement in mathematics subject now or in
the future.
After observing the normal teaching and learning process in the mathematics
class, it was discovered that pupils were seldom exposed to team or group works.
They were often asked to do work individually. This had caused the weaker pupils to
lose interest in learning mathematics as they could not catch up with the learning
progress in the teaching and learning during the class. When the pupils themselves
felt unable to cope with the lesson taught, they would choose to give up their learning
in mathematics. This circumstance would cause the pupils’ low academic
performance in mathematics and also brought negative effect on pupils’ attitude
towards mathematics. Moreover, researcher also discovered that the common errors
made by the pupils when solving the mathematics questions or problems was one of
the contributors that caused the pupils to lose marks in the mathematics tests and thus
affected their academic performance in the mathematics tests. Due to the above
scenario, a suitable strategy or technique should be created or designed in order
enhance pupils’ performance in mathematics.
During the previous teaching and learning experiences, researcher had tried to
expose the pupils to cooperative learning during her mathematics lesson in the class.
Researcher let the pupils do their work in group or team. It was delighted to see the
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pupils were showing their interest in learning mathematics in cooperative manners
with their team members and improving from time to time. They tended to make less
common errors in the mathematics tests and able master most of the previous
mathematical knowledge and skills learnt in the class. This was proven that the
strategy had successfully increased most of the pupils’ academic performance in
mathematics as well as reinforced their learning attitudes in mathematics. Hence, it
was hopeful that the STAD, one of the cooperative learning models, was able to help
the pupils in increasing their performance in mathematics.
According to Orlich et al. (2007), cooperative learning fosters the pupils’
positive interdependence by teaching pupils to work and learn together in a small-
group setting. It is an approach that organises classroom activities into academic and
social learning experiences where pupils are encouraged to learn in a group or as a
team. Cooperative learning is an approach to group work that minimises the
occurrence of those unpleasant situations and maximises the learning experience and
satisfaction that are the results of working on a high-performance team (Felderl and
Brent2, 2008).
Through cooperative learning, pupils’ learning time is able to be increased
while reduces teacher’s workload by teaching pupils to assist each other with
learning, completing a task and also monitoring one another’s learning progress
during the teaching and learning of mathematics in the class. As stated by Huang
(2008) which extracted from Kagan and Olsen (1992),
“Cooperative learning is group learning activity organized so that
learning is dependent on socially structured exchange of information
between learners in groups and in which each learner is held
accountable for his or her own learning and is motivated to increase
the learning of others.”
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The STAD strategy in cooperative learning is aimed at enhancing pupils’
learning as a team or group to achieve the goal. It is considered as the simplest of the
Student Team Learning (STL) methods. By implementing the STAD strategy in
mathematics subject, pupils need to help each other in their learning and work
together as a team to resolve obstacles faced in solving a mathematical problem. The
team members at last will share their team achievement together. The cooperative
learning model requires student cooperation and interdependence in its task, goal and
reward structures (Miller and Peterson, n.d).
1.3 Educational Values Reflection
Education is an act or process of imparting, or acquiring general knowledge,
developing the powers of reasoning and judgment, and generally of preparing oneself
or others intellectually for mature life. It could be a certain degree, level or kind of
schooling (Jackson, 2010). With the reference to Macdude (2006), GATE's chairman
and CEO, Mr. Glenn Jones, has said that "Education is the great hope for the survival
of humankind and for the forward progress of civilization."
Education makes man a right thinker. It tells man how to think and how to
make decision. Beside that, through the attainment of education, man is able to
receive information from the external world; to acquaint himself with past history and
receive all necessary information regarding the present (Maulana Wahiduddin Khan,
n.d)
Values are the ideals or standards that people use to direct their behavior;
values are what people strive to realize in their lives (Lombardo, 2008). Values are
very important for us as they are the standards that we have to use in making
judgments or decisions about what is important in our life and what is right or wrong
in human behaviour.
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There are many values connected with education. For example, learning,
thinking, integrity, honesty, growth, and excellence. These values mirror the general
goals and principles of behaviour among educators and schools. These values define
the elements that are important in the educational process. Educators need to try to
encourage their students to pursue these values through the teaching and learning
process in the schools not only in mathematics subject but also all the other subjects.
These values are able to help the students to embrace and practice them in their daily
lives, enhance their academic performance and also serve as the foundation for the
students to acquire factual knowledge and also intellectual skills that they require in
their learning process. For example, the value of the love of learning and thinking.
This value enhances students not just in academic performance but also aids the
students to explore and achieve knowledge and skills which are beneficial to
themselves, others and also the society.
The educational values are able to help an individual to become a life-long
learner. According to Jones (2009), making lifelong learning part of one's life also
fosters a sense of personal empowerment and increased self-esteem. In other words,
life-long learning ensures individuals which include the students, to have continued
growth and intellectual stimulation, leading to a more fulfilling, enjoyable, and
enriched lifestyle in their education.
2.0 RESEARCH FOCUS
The challenge in education today is to effectively teach pupils of diverse
ability and differing rates of learning (Effandi Zakaria and Zanaton Iksan, 2006).
Therefore, teachers are expected to teach in a way that enables the pupils in acquiring
process skills, positive attitudes and values and problem solving skills besides
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learning the mathematical knowledge. Various types of strategies have been
advocated for the use of teaching and learning of mathematics. Cooperative learning
is one of the effective strategies.
Focus of this research is to apply STAD model during teaching and learning
of mathematics subject in the class to improve year 5 pupils’ performance in
mathematics from the aspect of their academic performance. Besides, the changes of
their attitudes towards mathematics after the implementation of STAD model in the
teaching and learning of mathematics are also observed. This research also examines
and analyses the common errors made by the pupils in the mathematics test that bring
negative effect towards the pupils’ performance in mathematics.
2.1 Research Issue
Mathematical thinking is important for all of the members in our society as it
is used widely in the workplace, business and finance as well as for personal
decision-making in daily life. Mathematics is fundamental to national richness in
providing tools for understanding science, engineering, technology and economics
and also in public decision-making. In the education field, mathematics equips pupils
with exclusive powerful ways to describe, analyse and change the development of
world. It can motivate moments of pleasure for all pupils when they solve a problem
for the first time, discover a more elegant solution, or notice hidden connections.
Pupils who are functional in mathematics are those who able to think independently
in applied and abstract ways. They can reason, solve problems and evaluate risk.
Therefore, it is important for pupils to master the subject of Mathematics.
In the Section 1.2, the previous teaching and learning reflection had been
discussed. It was discovered that the year 5 pupils’ academic performance in
mathematics was weak and the pupils were showing low interest and confident in
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learning mathematics. The social interaction in the class during the teaching and
learning of mathematics in the class was low as well. Moreover, it was discovered
that most of the pupils often made some common errors that caused them to lose
marks in the mathematics tests due to their inappropriate attitude and low mastery in
mathematical concepts. It was also realised that pupils were bored with the teaching
and learning strategy applied by the teacher in the class in which the pupils were
asked to do their study and work individually. However, pupils showed a high interest
in learning when they were asked to work as a team and do their work cooperatively
with their team members.
Therefore, it is important for us as mathematics teachers to use and apply the
cooperative learning strategy especially the STAD model during the teaching and
learning in the mathematics class so that our pupils can learn mathematics effectively.
2.2 Literature Review of the Research Issue
Based on Huang (2008) which adapted from Chong (1994), cooperative
learning is formed based on three main theories. The theories are social
interdependence theory, cognitive developmental theory and behavioral learning
theory. According to INTIME (2008), interaction with other people is essential for
human survival. In an education setting, social interdependence refers to students’
efforts to achieve, develop positive relationships, adjust psychologically, and show
social competence.
There are two main theorists that play important roles for the cognitive
development theory. They are Jean Piaget and Lev Vygotsky. Piagetian perspectives
suggest that when individuals work together, socio-cognitive conflict occurs and
creates cognitive disequilibrium that stimulates perspective-taking ability and
reasoning (INTIME, 2008). This means that different views from peers can put a
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child in disequilibrium, prompting them to accommodate this and make sense of
different ideas and perspectives. Vygotsky presented the theory that children learn
through their interaction with others, thus the people in their world hold great
influence on their learning (Driscoll and Nagel, 2002). "What the child can do in co-
operation today he can do alone tomorrow." (Myers, 2001 adapted from Vygotsky,
1986, p. 188). It is believed that children learn through their peers. When they are
working together with their peers on a task or learning together with them, they are
learning at the same time. After they have learnt the knowledge or skill needed from
their peers, they can perform the same task again by themselves.
For behavioral learning theory, the contributors are Watson, Skinner, Pavlov
and Thorndike. The behavioral-social perspective presupposes that cooperative
efforts are fueled by extrinsic motivation to achieve group rewards (INTIME, 2008).
The extrinsic motivation can be in the form of praises, presents and also formal
recognitions. With the help of extrinsic motivation, children tend to be more
motivated to work with other group members in settling a task or achieving a goal.
The various features of cooperative learning, particularly positive interdependence,
are highly motivating because they encourage achievement-oriented behaviours such
as trying hard, praising the efforts of others, and receiving help from the group
members.
It is understood that children are learning in numerous ways. They learn from
reading, observing, listening, and also teaching others. As stated by Putnam (1997)
which excerpted from Acorn et al. (1970) about what people learn:
“ 10% of what they READ
20% of what they READ and HEAR
30% of what they SEE
50% of what they SEE and HEAR
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70% of what they SAY*
90% of what they SAY and APPLY in life*
95% of what they TEACH others*”
It is clearly shown that we learn the most when we teach others so as for the pupils.
When the pupils are discussing ideas with the other, they are learning most at the
time.
Lourenco (1998) claimed that the more time that the pupils invest in their own
learning process, the more they will learn. This has shown that pupils learn more
when they spend more time and effort in doing their own learning. This approach is
believed to enhance students’ performance and achievement in various subjects and
aspects of the language and producing positive social outcomes (Syafini Bt. Ismail
and Tengku Nur Rizan Bt Tengku Mohamad Maasum, n.d.). According to Slavin
(1989) in Gillies and Ashman (2003), cooperative learning may be an effective mean
of increasing students’ achievement, opportunities for learning can be maximised
only if group goals and individual accountability are embedded in the cooperative
method used. Armstrong et al. (1998) mentioned that pupils commented that using
STAD made learning fun and the content easier to understand.
According to Snyder and Shickley (2006), the National Council of Teachers
of Mathematics (NCTM) expresses that learning with understanding is essential to
enable students to solve new kinds of problems that they will inevitably face in the
future. This is because not all pupils are participating regularly in the whole class
discussions; teachers need to monitor their participation to ensure that some are not
left entirely out of the discussion for long periods. The use of small groups will
permit the pupils to have the chance to share important thoughts and ideas with their
group members, thus improving confidence in sharing of ideas and communicating
about mathematical ideas.
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Besides, cooperative learning groups set the stage for students to learn social
skills. These skills help to build stronger cooperation among group members.
Leadership, decision-making, trust-building, and communication are different skills
that are developed in cooperative learning (Dahley, 1994). In addition, cooperative
learning has been shown to improve relationships among students from different
backgrounds (Lyman et al., 1988). Effandi Zakaria et al. (2010) mentions that
cooperative learning emphasises on social interaction and relationships among groups
of students in particular and among classmates in general.
STAD is one of the simplest and most flexible of the cooperative learning
methods, having been used in grades 2 through 12 and in such diverse subject areas
as math, language arts, social studies, and science (Mifflin, n.d. excerpted from
Biehler/Snowman, 1997). Slavin (1980) claims that STAD has shown positive
improvement towards pupils’ academic achievement as well as encouraging pupils to
have higher cognitive thinking skill. Teaching and learning in mathematics through
STAD model in cooperative learning brings positive effects towards the academic
performance and also their achievement in mathematics (Wong, 2007).
Cooperative learning experiences promote more positive attitudes toward the
instructional experience than competitive or individualistic methodologies. In
addition, cooperative learning should result in positive effects on pupils’ achievement
and retention of information (Rosini B. Abu, 1998 excerpted from Dishon & O'Leary,
1984; Johnson & Johnson, 1990; Slavin, 1991). According to Wong (1998) adapted
from Gan and Wong (1995), cooperative learning has positively improved the
attitudes of their participants towards learning mathematics.
All cooperative learning structures are designed to increase pupils’
participation in learning. The more opportunities pupils have to participate, the
greater likelihood that they will become empowered to do mathematics in
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knowledgeable and meaningful way (Kennedy and Tipps, 1999). According Effandi
Zakaria and Zanaton Iksan (2006), cooperative learning is grounded based on the
belief that learning is most effective when pupils are actively involved in sharing
ideas and work cooperatively to complete academic tasks. Johnson and Johnson
(1998) claims that promotive interaction occurs as individuals encourage and
facilitate each other's efforts to reach the group's goals (such as maximizing each
member's learning). Besides, a pupil doesn't always catch his own mistakes, though,
no matter how skilled he may be. Group correction is an alternative, with peers in
small groups pointing out mistakes (Cotter, n.d.).
3.0 RESEARCH AIM
This action research is carried out to apply one of the cooperative models -
STAD in enhancing the year 5 pupils’ academic performance in mathematics subject.
This research is also aimed to evaluate the pupils’ attitude in learning mathematics
before and after implementation of the STAD model during the teaching and learning
of mathematics in the classroom at one of the primary school which is located at the
outskirt of the Miri City.
3.1 Research Objectives
Based on the research aim stated above, researcher has decided on four
research objectives that are to be achieved. The objectives are:
(a) To evaluate the effectiveness of the implementation of STAD model in
increasing year 5 pupils’ academic performance in mathematics subject.
(b) To determine whether the application of cooperative learning model – STAD
model is able to change the pupils’ attitude towards mathematics.
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(c) To analyse the common errors made by the pupils when answering the
questions in the mathematics tests.
3.2 Research Questions
The research questions are stated as below:
(a) Does the implementation of STAD model bring improvement towards year 5
pupils’ academic performance in mathematics subject? What are the
improvements shown by the pupils in their academic performance in
mathematics after implementing the STAD model?
(b) Does STAD model change the pupils’ attitude towards mathematics subject?
What are the changes?
(c) What are the common errors made by the pupils when answering the
questions in the mathematics tests? Can STAD model help the pupils to make
less common errors in the mathematics tests?
4.0 PARTICIPANTS
There were 4 participants in this research. The personal information of each
participant was collected based on the Participant Information Form (Appendix 1).
Based on the information collected, the gender of the participants was male. The
participants were the year 5 pupils from one of the primary schools at the outskirt of
the Miri City. They were all eleven years old. The participants, namely P1, P2, P3
and P4 had different economic background but same cultural background. All of them
were from Kedayan cultural background. Their academic performance in
mathematics subject was at the range of weak to moderate. This could be seen
through their average scores for their mathematics tests in the year 2009. Participants
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had sat for mathematics tests for five times in the year 2009. The average score of the
five tests taken by each of the participants was obtained as their pretest results. The
results were stated in the Table 1.
Table 1: Participants’ Average Score in Mathematics in the Year of 2009
Participant Test
1
Test
2
Test
3
Test
4
Test
5
Average Mathematics
score in 2009 (%)
P1 49 65 54 58 60 286/5 ≈ 57
P2 22 44 48 50 54 218/5 ≈ 44
P3 27 38 47 45 29 186/5 ≈ 37
P4 27 43 34 38 40 182/5 ≈ 37
5.0 ACTION PROCEDURE
The date of implementation for STAD model during the teaching and learning
in mathematics classroom was from 8th February 2010 until 26th March 2010. The
duration for the planned research is 6 weeks (2 hours per week). In this session, the
action plan for this research was clearly planned. The researcher focused on
discussing about the steps of action which included the steps of diagnosing, action
planning, taking action, evaluating and specifying learning which contributed to the
next cycle and so on.
According to O’Brien (1998) which is adapted from Susman (1983), there are
five phases to be conducted within each research cycle (Figure 1).
14DiagnosingNext Cycle
(Modified from O’Brien (1998); adapted from Susman (1983))
Figure 1: Research Model
Firstly, the problem was diagnosed and defined. Diagnosing corresponds to
the identification of the primary problems that were the underlying causes of the
organisation’s desire for change (Baskerville, 1999). Therefore, it was important to
choose a suitable problem or issue to be researched. To define a suitable issue or
problem to be researched and solved, observation was made at the researched
classroom. After that, the main issue which was the year 5 pupils’ low performance in
mathematics was defined as the main issue that needs to be solved.
Researcher and participants were then collaborate in the next activity, action
planning. This activity specifies organisational actions that should relieve or improve
the primary problem. The discovery of the planned actions must be guided by the
theoretical framework. The plan establishes the target for change and the approach to
change. After referring to the different resources, STAD model was chosen as the
main concept for the planned action. A schedule of work for the implementation of
the STAD model was prepared at the stage of action planning. Action planning was
important to make sure that the action research for the issue identified could be
carried out smoothly according to the work schedule planned. At the stage of action
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Action Planning
Taking ActionEvaluating
Specifying Learning
planning, researcher also needed to seek for the literature reviews from the other
resources about STAD model as well as the previous researches done about the
implementation of the STAD model in the teaching and learning.
Action taking was then implemented. Before interpreting the STAD model,
the number of participants for this action research was decided and their background
from socio-economic and culture were examined. Once the number of participants
had been decided, the participants’ previous tests score in the year 2009 were
collected. This was done to take the mean scores (base score) of the participants for
the mathematics subject. The 5 tests previously taken by the participants were
considered as the pre test while the mean scores calculated would be taken as the
participants’ pre test data.
Referring to the STAD model, participants were assigned into teams of two,
with each team mirroring the make-up of the class in terms of ability. Members for
each team were decided by the researcher. Each team must have a participant with
better academic performance in mathematics. After referring to the participants’
previous academic performance in mathematics, researcher decided to put participant
P1 and P3 in team 1 while participant P2 and P4 in team 2. Once these assignments
were made, a four-step cycle which refers to teach, team study, test, and recognition
would begin.
For the first stage of STAD model, class presentation, lesson and materials
was presented to the class through direct instruction, discussion format and etc. In
the team work phase, pupils were asked to complete worksheet or a task as a group.
They were required to work together and help each other in completing the tasks
assigned to them. The team members were also responsible for making sure their
partners in the group was able to understand and master the skills and knowledge
delivered in the class.
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After 2 weeks of teaching, a post-test was given to each of the participants
individually to check their understanding on the materials learned. The team members
were not allowed to help each other for the individual test given. The achievement
test was then graded by the researcher. The individual achievement scores for every
member in each team were then calculated and summed up as the team scores. If the
participant’s score was higher than the base score, then the participant would
contribute positively to the team score. The scoring methods were used to reward the
participants for their effort in making improvement. The use of improvement scores
had been shown to increase participants’ academic performance even without teams
and it is an important component of student team learning. Team recognition would
be given based on their improvement scores.
Last stage of the STAD model was team recognition. The team recognition
was given based on the group improvement scores. The team which collected the
most points was declared as the best team. Rewards were given to the winning team.
The rewards could vary but they had to be informal. Here, researcher put up the name
of the best team on the class bulletin boards. In addition, rewards in the form of prizes
were also given. After that, questionnaire was given to the participants to identify and
evaluate participants’ learning attitudes after implementing the STAD learning model.
After the first cycle of the action research was completed, the outcomes of the
planned action were evaluated. The evaluation includes determining whether the
theoretical effects of the action were realized, and whether these effects relieved the
problems.
After collecting, analyzing and evaluating the data, the activity of specifying
learning was formally undertaken last. General findings were identified at this stage.
The action research cycle could continue, whether the action was proved successful
or not. This was to develop further knowledge about the validity of relevant
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theoretical frameworks. The second cycle of this action research was carried out after
modifying the first action plan. The action research would go for one or more cycles
until the problems were overcame and the outcomes and findings fulfilled the
objectives of this research.
6.0 DATA COLLECTION PROCEDURE
The instruments used in this research were achievement test, questionnaire
and observation. The details of these instruments were discussed in this section.
6.1 Achievement Test
Testing is extremely important however, because without it no teacher can
really know how much the pupils have learnt (Sachs, 2010). In the other meaning, test
is a tool that used to evaluate the pupils’ performance in a specific task or subject.
This instrument was mainly used to evaluate the effectiveness of the
implementation of the STAD model in increasing the participants’ academic
performance for mathematics subject. Through this instrument, researcher aware of
and noticed the common errors made by the participants when solving the
mathematical problems.
The previous five tests that were taken by the participants in the year 2009
were considered as their pretest. The average scores for the tests were calculated as
their pretest scores before the implementation of the STAD model in the teaching and
learning of mathematics.
The post-test was carried out to examine the participants’ academic
performance after implementing the STAD model. The post-test items were modified
based on the Curriculum Development Centre (2006).
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6.2 Questionnaire
Questionnaire is used to allow feedbacks from pupils. It also allows each
pupil to have the opportunity to provide anonymous feedback on their experience. It
can be used to collect data and allow all participants the opportunity to provide
feedback. According to University of Sheffield (2010), the feedback is generally
anonymous, which encourages openness and honesty.
In this research, 4-point Likert Scale Questionnaire was used. The Likert
Scale is a popular format of questionnaire that is used in educational research
(Markusic, 2009). The questionnaire was given to the participants to answer after the
implementation of STAD model for the last cycle in action plan. The main purpose of
this questionnaire was to evaluate the participants’ respond towards STAD model
from the aspect of mastery in mathematics, interest towards mathematics and also
social interaction in the class. The questions given to the participants to answer in the
questionnaire were not arranged according to its groups but were shuffled.
18 questions (Appendix 5) were prepared for this questionnaire. The
questionnaire was modified based on the questionnaire in Huang (2008). 8 questions
were prepared to survey the participants’ interest in learning mathematics. Besides
that, 6 questions and 4 questions were designed to survey the participants’ mastery in
mathematics and participants’ social interaction in the class respectively.
6.3 Observation
Observation is a term that describes several methodological techniques, and
can be used to collect qualitative or quantitative data. Non-verbal behaviour and
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tactile skills are particularly amenable to observation. The presence of an observer
may affect the behaviour of subjects. Data collection may be influenced by the
observers' expectations and motives (Lynes, 1999).
Besides observing the participants’ learning behaviours and participation
informally in the class, parts of the observation were also written in the form of
journal to identify and examine the problem faced when carrying out the STAD
model during the teaching and learning of Mathematics in the class so that
improvement can be done to overcome the problems faced. A journal was written
after two weeks of teaching.
7.0 DATA ANALYSIS PROCEDURE
In this section, the methods used to analyse the data collected were discussed.
The researcher had carried out the teaching lesson plan for mathematics subject in the
researched school for the chosen participants for 6 weeks times (2 hours of teaching
per week). The data were collected and analysed based on the three instruments
(achievement test, questionnaire, and observation). The data analysis was made
based on quantitative and qualitative approaches.
7.1 Achievement Test
The post-test was built from 10 objective questions and 20 subjective
questions (Appendix 2, Appendix 3 and Appendix 4). The total score allocated for the
10 objective questions was 20% whereas 2% for each correct answer. For the
subjective questions, the total score of 80% was given. The score for each of the
subjective question was different. Score of 1% until 3% was given based on the level
of difficulty of each question.
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After marking the participants’ post-test 1, the score of the post-test 1 was
obtained for each of the participants and recorded down. The comparison of the
pretest and post-test 1 scores was done and visualised by using the spreadsheet.
Researcher firstly recorded down the scores in Table 2.
Table 2: Form Used in Recording Participants’ Scores
Participant Score (%)
Pretest Post-Test 1
P1
P2
P3
P4
Researcher compared the pretest and post-test 1 scores as well as measured
the effectiveness of STAD model in enhancing participants’ academic performance in
mathematics. The scores collected in post-test 2 and post-test 3 were analysed in the
form of percentage (%). Each of the post-tests was compared with the test taken in the
previous cycle. Researcher also analysed the common errors done by the participants
that have caused the participants inability to score well in their achievement tests.
The scores achieved by the participants in the pretest and post-tests were compared to
evaluate the effectiveness of STAD model in helping the participants to make less
common errors in mathematics tests.
7.2 Questionnaire
After participants had done the questionnaire, researcher grouped and
reorganised the items based on its type. The numbers of participants’ that chose
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“Strongly disagree”, “Disagree”, “Agree” and “ Strongly agree” for each of the items
in the questionnaire were recorded down.
7.3 Observation
Three aspects were observed. The aspects were participants’ behaviours,
social interaction, and the participants’ participation during the implementation of
STAD model in the teaching and learning of mathematics in the classroom. Through
observation, the participants’ learning progress and their attitude shown in
mathematics subject are examined. Researcher observed the interaction between the
participants as a group or team when the STAD model was implemented. Besides, the
engagement of the participants with the class and group activities designed in
accordance to the STAD model was also observed.
8.0 RESEARCH FINDINGS
In this section, the findings that obtained from the each cycle were discussed
based on the participants’ scores in the pretest and post-tests. Besides, the findings of
the questionnaire and observation on participants’ attitude towards mathematics were
made. By examining the achievement tests taken by the participants, the common
errors made by the participants were analysed.
8.1 Findings of the First Cycle
In this research, the improvement of the year 5 participants’ academic
performance in mathematics was measured by pretest and the post-tests. The
22
comparisons of the pre-test and post-test of the four participants were analysed and
interpreted in this section. The pretest and post-test were meant to evaluate the
effectiveness of STAD model in increasing the participants’ academic performance in
mathematics subject.
For the first cycle of this action research, the participants’ scores in the post-
test 1 (Appendix 2) after the implementation of the STAD model for the first time are
collected and compared with their scores achieved in the pretest. The participants’
scores in pretest and post-test 1 are displayed in Figure 2.
P1 P2 P3 P40
10
20
30
40
50
60
70
80
90
Pretest
Post-test 1
Participant
Sco
re (
%)
Figure 2: Participants’ Scores in Pretest and Post-test 1
With reference to the data observed in Figure 2, the post-test 1 score of
participant P1 if comparing with the pretest score was improving from 57% to 79%
while participant P2 was improving from 44% to 70%. Besides that, it was also
discovered that the test score of participant P3 was improving from 37% to 46%. In
addition, participant P4 was also showing improvement in his post-test 1 score when
comparing to his pre test score with his test score improved from 37% to 52%.
23
It was discovered that there were 2 participants’ mathematics test scores were
improving for more than 20% if compared to the test scores they obtained in pre test.
The participant was participant P1 and P2. The improvement score shown by
participant P1 was 22% while the improvement score of participant P2 was 26%. As
for participant P3, he obtained the improvement score that more than 5% and that was
9%. On the other hand, participant P4 achieved improvement score of 5%.
Based on the pretest scores achieved by the participants, it was discovered that
the participants’ academic performance in mathematics were in the range of weak and
average. Most of the participants were only able to solve simple mathematical
questions with the application of simple mathematical skills. The main important
factor that led to their inability to achieve good results in mathematics was because
they unable to perform the correct steps in solving the mathematics questions given in
the tests as well as the correct answers for the mathematics questions. This happened
because of their weak mastery of the 4 basic operations. Besides, they were not able
to fully understand the previous lessons taught in the class due to the ineffective
teaching and learning strategy in the class.
By referring to the participants’ scores in the post-test 1, it was discovered
that, the participants’ academic performance in mathematics subject had increased
after implementation of STAD model in the teaching and learning of mathematics
subject for 2 weeks. They were able to solve the mathematics questions in the test
better.
Through the observation made during the teaching and learning of
mathematics in the classroom, it was noticed that instead of only learning from the
teacher, participants learnt better when they were asked to study in the form of group.
They enjoyed studying with their team members; correcting their team members’
24
mistakes in solving mathematics questions or problems as well as sharing knowledge
with each other in the group.
Not just with the members in their own team, but they also like to share their
knowledge with the other team through the group activity that requires interaction
among groups, for instance, checking the steps of solving and answers of the
mathematics questions given by the opposite teams. Based on the examination, it was
proven by participants that learning could be enhanced when participants or the pupils
had positive interaction with their peers. Through the implementation of STAD
model, the participants were motivated to give support and assist each other
especially their team partners.
8.1.1 Constraint and Suggestion
Although all of the participants’ results in the mathematics tests improved
after the implementation of STAD in the first cycle, some constraints were faced.
Unable to master the basic concept of multiplication especially in memorizing the
multiplication tables was the main constraint faced by the participants that had caused
them to lose most of the marks when solving and answering the mathematics
questions. Most of the participants were unable to memorise the multiplication tables
well. When the participants were unable to memorise the multiplication tables well,
this would influence their test scores as they were unable to perform the correct steps
of solving the multiplication and also division questions thus giving the wrong
answer.
Lack of drilling or practices was also one of the constraints that faced during
the application of STAD model in the first cycle. Most of the activities or tasks given
to the participants required the participants to solve or do in group in the class. Not
many worksheets or practices were given to them to be done as homework during
25
their leisure time whether in group or individually to enhance their learning of the
mathematical concepts taught in the class.
To overcome the first constraint, participants were taught to build and write
multiplication table that was required to solve each of the multiplication and division
questions or problems. They were taught to use repeated addition to build the
multiplication tables. By referring to the multiplication table, participants could easily
solve the questions involving multiplication and division without memorising the
multiplication tables. In order to overcome the second constraint mentioned above,
more worksheets and exercises were given to the participants as homework to do and
solve during their leisure time. It was believed that through drilling, participants are
able to foster the mathematical knowledge and skills taught by the researcher in the
class. Second cycle of this action research was carried out to overcome the constraints
faced in the first cycle. It was done to spur the participants to achieve better academic
performance for the next mathematics test.
8.2 Findings of the Second Cycle
After carrying out the second cycle for another 2 weeks, participants were
asked to sit for the post-test 2 (Appendix 3). The test scores obtained from the
participants in the post-test 2 were compared with their test scores in the post- test 1.
The comparison could be seen in Figure 3 below:
26
P1 P2 P3 P40
10
20
30
40
50
60
70
80
90
100
Post-test 1 Post-test 2
Participant
Sco
re (
%)
Figure 3: Participants’ Scores in Post-test 1 and Post-test 2
Based on Figure 3, participant P1 was showing improvement in his post-test 2
score if compared to post-test 1. He improved from 79% to 87%. Participant P2 was
showing improvement in his test score by gaining 77% in the post-test 2 if compared
to his previous test score, 70% in post-test 1. For participant P3, his test score was
improving from 46% to 57%. In the other hand, participant P4’s test score was
increasing from 52% to 64%.
It was realised that the academic performance of the participants after the
implementation of the modified plan in the second cycle was enhanced. All of the
participants were doing better in post-test 2 if compared to post-test 1. Among the
four participants, participant P3 and P4 achieved the improvement score which more
than 10%. The improvement score for participant P4 was 12% while participant P3
was 11%. As for participant P1 and P2, they both received more than 5% for
improvement score and that was 8% and 7% respectively.
Through the observation made, it was discovered that the participants
increased their academic performance in mathematics after carrying out the modified
27
action plan in the second cycle. By asking the participants to build out the
multiplication tables based on the requirements of the multiplication questions by
using repeated addition was shown as an effective method to help the participants to
solve the mathematics questions involving multiplication. In addition, by building
and writing out the multiplication tables, the participants were able to refer to the
multiplication tables built formerly when solving another similar multiplication or
division questions. This method proved to benefit the participants with short-term
memory or facing difficulties in memorizing the multiplication tables from 1 to 9.
Moreover, the drilling method applied together with STAD model succeeded
in helping the participants to improve their learning in mathematical concepts and
skills. Through practices given to the participants to be done and completed in the
group or individually during their leisure time, participants were able to practice and
recall the mathematics skills and concepts learnt repetitively.
8.2.1 Constraint and Suggestion
When carrying out the modified action plan in the second cycle, it was found
that some of the participants did not finish or complete the tasks or worksheets given
to each of the groups. The main reason that caused this situation was due to problem
with their learning attitude. Pupils’ learning attitude in mathematics was one of the
main reasons that drove the pupils’ low academic performance in the mathematics
subject. Pupils usually lack of motivation to complete the homework or practices
given to them when there was nobody beside them to guide or motivate them. The
learning attitude shown by the participants in this research would be the one of the
main factors that stopping them from achieving higher academic performance if there
was no action taken to overcome this problem.
28
To solve the issue above, researcher integrated “Token System” together with
STAD model to motivate participants learning attitude in mathematics as well as to
aid the participants to maximise their academic performance in mathematics. To
implement the “Token System”, a reward card was given to each of the participants.
When a participant performed well in their learning or completed the tasks or
homework given by the researcher, a “smiley face” would be stamped on the reward
card. The participants could claim their rewards from the researchers when they had
collected 8 smiley faces. This modified action plan was carried out in the third cycle.
8.3 Findings of the Third Cycle
After carrying out the action plan modified from the second cycle, post-test 3
(Appendix 4) was given to the participants to obtain the outcomes of the action plan
implemented for the third cycle. After calculating the participants’ scores in post-test
3, comparison of their scores in post-test 2 and post-test 3 was made. Figure 4 showed
clearly the scores achieved by the participants in post-test 2 and post-test 3, the
comparison of scores of the participants obtained from the two tests.
P1 P2 P3 P40
10
20
30
40
50
60
70
80
90
100
Post-test 2 Post-test 3
Participant
Sco
re (
%)
Figure 4: Participants’ Scores in Post-test 2 and Post-test 3
29
Based on the graph above, participant P1 showed improvement in his test
score in post-test 3 if compared to post-test 2. His test score was increasing from 87%
to 92%. For participant P2, his test score was increasing from 77% to 84% while
participant P3 improved his test score from 57% to 70%. In addition, participant P4
also showed improvement in his test score in post-test 3 if compared to post-test 2 by
increasing of test score from 64% to70%.
It was discovered that, participant P3 achieved improvement score of 13%
then followed by participant P2 with improvement score of 7%. Participant P4 and
participant P1 respectively obtained 6% and 5% for their improvement scores.
The “Token System” applied together with STAD model reinforced the
participants’ learning and enhanced their learning attitude in mathematics was proven
to be effective. Participants who completed the homework or practices were given by
researcher in time without reminding from the researcher were qualified to collect
enough “smiley face” stamps to exchange with mystery rewards. The “Token
System” was meant to be a tool to motivate and reinforce participants’ learning in
mathematics as well as to improve their learning attitude. The application of the
“Token System” enabled the participant to take learning more seriously for
mathematics subject.
8.3.1 Constraint and Suggestion
Although “Token System” had proven its effectiveness, it brought
disadvantages at the same time to the participants. One of them was that participants
tend to ask for rewards for their completed work or tasks. They were becoming more
materialistic. The participants would not work hard to complete the tasks or practices
given if no rewards or extrinsic motivation given. Such attitude would also affect
their attitude in treating the people around them. For example, they would not lend
30
their hands to the ones who needed it if there was no reward for their sacrifices. To
investigate more detail about the “Token System” as well as their advantages and
disadvantages, further research should be made to analyse the “Token System” in
influencing pupils’ learning in mathematics.
8.4 Participants’ Attitude towards Mathematics
A set of questionnaire (Appendix 5) was designed to be used as the instrument
to measure participants’ attitude towards mathematics after the application of STAD
model. The four participants in this action research had taken the questionnaire after
the implementation of STAD model for mathematics subject respectively. The
questionnaire was meant to evaluate the effectiveness of STAD model in enhancing
participants’ interest, mastery in mathematics and also their social interaction in the
class.
8.4.1 Participants’ Interest in Learning Mathematics
The Table 3 displayed the participants’ responses towards the implementation
of STAD model in the teaching and learning mathematics in the aspect of their
interest in learning mathematics based on the eight questions from the questionnaire.
From the Table 3, all of the participants strongly disagreed that learning in
group was not suitable for them in learning mathematics. Besides that, they were also
strongly agreed that they would like to share their knowledge with their team
members in learning mathematics. There were 2 participants who respectively agreed
and strongly agreed that the group activities increased their interest in learning
mathematics and they would like to have group activities most of the time for the
mathematics subject.
31
In addition, 2 participants respectively agreed and strongly agreed that the
teaching and learning of mathematics was more interesting after the implementation
of group activities. There was 1 participant who agreed and 3 participants who
strongly agreed that they enjoyed learning in group, looking forward for the
mathematics lessons because they could study together with their friends, and
continued learning mathematics in groups with their friends.
Table 3: Analysis of Participants’ Interest in Learning Mathematics
No.
Item Question
Number of Participant
Strongly Disagree
Disagree Agree StronglyAgree
1. I enjoy learning in group 1 3
4. The group activities increase my
interest in learning mathematics. 2 2
5. The teaching and learning of
mathematics is much more
interesting with the
implementation of group
activities.
2 2
8. I am looking forward for
mathematics lesson because I
can study together with my
friends.
1 3
13. I love to share my knowledge
with my group members in
learning mathematics. 4
15. I would like to have group
32
activities most of the time. 2 2
16. I would like to continue learning
mathematics in group with my
friends.
1 3
18. Learning in group is not suitable
for me in learning mathematics. 4
8.4.2 Participants’ Mastery in Mathematics
The Table 4 below showed the participants’ response towards the mastery in
mathematical concepts and skills after the implementation of STAD. Six questions
were answered by the participants for this session to survey participants’ opinions
towards the implementation of STAD in helping them to master the mathematical
knowledge and skills.
According to the data arranged in the table 4, it could be seen that there were 3
participants who strongly disagreed that group activities did not help them a lot in
learning mathematics. Four of them all agreed that it was easy for them to learn
mathematics by working together with their friends and their academic performance
in mathematics had improved after learning together with their friends in groups.
Moreover, all of them were also able to solve most of the mathematical problems
after learning mathematics in groups. 3 participants strongly disagreed while 1
participant disagreed that group activities did not help them a lot in learning
mathematics and they were still facing troubles in learning mathematics after the
group works were carried out. 3 participants and 1 participant strongly agreed and
disagreed respectively that learning in groups made them easier to understand
mathematics.
33
Table 4: Analysis of Participants’ Mastery in the Mathematics
No.Item Question
Number of ParticipantStrongly Disagree
Disagree Agree StronglyAgree
3. It is easy for me to learn
mathematics by working
together with my friends.
4
6. Group activities do not help me a
lot in learning mathematics. 3 1
7. Learning in group makes me
easy to understand mathematics. 1 3
10. I am still facing difficulties in
learning mathematics after the
group works are carried out.
3 1
14. My academic performance in
mathematics is improved after
learning together with my
friends together as a group.
4
17. I able solve most of the
mathematics problems after
learning mathematics in group.
4
8.4.3 Participants’ Social Interaction in the Class
The set of questions extracted from the questionnaire below was meant to
evaluate the participants’ social interaction with their own team member as well as
their friends from the other groups in the class after the implementation of STAD
34
model in the teaching of learning in mathematics. 4 questions were prepared in this
session.
From the response given by the participants in Table 5, it was discovered
that there were 4 participants strongly agreed that they liked to learn with friends and
believed that group activities gave them chances to participate activity in the
mathematics subject. Respectively, there were 3 participants strongly agreed and 1
participant disagreed that they were able to communicate better with their friends in
the class after learning in the groups for mathematics subject and learning in groups
enabled them to have positive relationship with their friends.
Table 5: Analysis of Participants’ Social Interaction in the Class.
No.Item
Question Number of ParticipantStrongly Disagree
Disagree Agree StronglyAgree
2. I like to learn with friends. 4
9. I able communicate better with
friends after learning in group
for mathematics subject 1 3
11. Group activities give me chances
to participate actively in the
mathematics subject.
4
12. Group learning enables me to
have positive relationship with
my friends.
1 3
35
8.5 Participants’ Common Errors
There were some errors made by the participants in the mathematics tests
throughout the three cycles of the action research. These errors were the mistakes
that caused them to lose marks in the examination and influenced their academic
performance in mathematics negatively. STAD model had shown its effectiveness in
helping the participants to make less common errors in the mathematics tests through
the improvement of scores in their achievement tests (Figure 2, Figure 3 and Figure
4) after STAD model was implemented in the teaching and learning of mathematics
in the classroom.
It was also discovered that the common errors made by the participants were
normally due to the reason of comprehension error, careless error, procedural error
and encoding error. In the next sessions, the four common types of errors made the
participants were analysed and discussed.
8.5.1 Comprehension Error
Comprehension error was made by the participants when they did not
understand the requirement of the questions or the specific terms within the problems.
When the participants could not understand the requirement of the questions, they
would surely unable perform the correct solutions for the questions. Some examples
of the comprehension error made by the participants were analysed and interpreted in
Table 6.
36
Table 6: Analysis of Comprehension Errors
No. Question and Solution Error and Explanation
1. Arrange the numbers in ascending
order.
123 540, 120 234, 123 430,
123 411
Solution:
120 234, 123 411,124 430, 123 540
Error:
123 540, 120 234, 123 430, 123 411
Explanation:
Participant did not understand the key
word “ascending” in the question. They
misunderstood the meaning of
“ascending” with “descending”.
2. Find the differences between 221
871 and 120 121.
Solution:
221 871- 120 121 101 750
Error:
221 871+ 120 121 341 992
Explanation:
Participant did not understand the key
word “differences” in the question. They
misunderstood the meaning of
“differences” with “total”.
3. Write 22 345 in extended notation.
Solution:
20 000 + 2 000 + 300 + 40 + 5
Error:
2 + 2 + 3 + 4 + 5
Explanation:
Participant did not understand the
concept of “extended notation”. He
thought that “extended notation” was just
about separate the 5 digit numbers in “22
345” and connected them with “+”.
37
8.5.2 Careless Error
Participants often made careless errors in the mathematics tests. Careless error
was made due to the participants learning attitude. They tended to rush to solve all the
questions in the tests in the shortest time. They did not want to recheck their solutions
for the second time although enough time was left for them to do so. Their laziness
shown in their learning attitude caused them to make careless error in the
mathematics tests. Some examples of the careless errors made by the participants
were listed in Table 7.
Table 7: Analysis of Careless Errors
No
.
Question and Solution Error and Explanation
1. 574 239 can be written in extended
notation as ___________.
Solution:
500 000 + 70 000 + 4 000 + 200 +
30 + 9
Error:
500 000 + 70 000 + 200 + 30 + 9
Error
Explanation:
The participant overlooked the digit
“4” in the numbers “574 239”
2. 700 005 – 37 287 = _______
Solution:
700 005- 37 287 662 718
Error:
700 005- 37 28 5 662 710 Explanation:
The participant carelessly copied
down the wrong number to be
subtracted from 700 005. Instead of
37 287(correct number), the number
38
Error
37 285 was copied down.
3. 451 062 + 142 337- 361 781 =
Solution:
451 062 593 399- 142 337 - 361 781 593 399 231 618
Error:
451 062 593 399- 142 337 - 361 1 81 Error 593 399 232 218
Explanation:
The participant able performed the
procedural steps of solving this
question correctly. However, the
participant carelessly copied the
wrong number to be subtracted.
Instead the number “361 781”, he
copied “361 181”. He carelessly
copied the digit “7” with “1”.
8.5.3 Procedural Error
Procedural error meant the error occurred during the process of solving the
questions. These errors made caused the participants unable to get the correct answer
for the questions. The participants who made such errors were mostly due to the
problem of incorrect steps or missing steps. Some examples of the procedural errors
done by the participants were displayed in Table 8.
39
Table 8: Analysis of Procedural Errors
No
.
Question and Solution Error and Explanation
1. 234 871 × 4 =________
Solution:
234 871 × 4 939 484
Error:
234 871 × 4 939 704
Explanation:
The participant firstly built the times-
table of 4. The participant used
repeated addition to form the times-
table of 4. Mistake occurred at
“4 × 7”. He counted “24 + 4”
wrongly. Instead of the correct
answer “28”, he wrote “30”.
2. 456 989 + 334 567 – 165 213 = ___
Solution:
456 989 791 556+ 334 567 -165 213 791 556 626 343
Error:
456 989 791 555 Error+ 334 567 - 165 213 791 55 5 626 342
Explanation:
The participants miscalculated and
wrote down the “5” at the ones for the
answer “791 556”. This caused the
participants unable to proceed to get
the correct answer for this question. 40
4
× 1 = 4
× 2 = 8
× 3 = 12
× 4 = 16
× 5 = 20
Error
3. 628011 – 233 192 – 123 762 =____
Solutin:
628 011 394 819-233 192 - 123 762 394 819 271 057
Error:
628 011 - 233 192 394 819
Explanation:
Firstly, participant only solved first
half of the mathematical sentence and
did not solve the second half of the
question. The second step of solving
the question and that was subtracting
“123 762” from the answer obtained
from the first step was missing.
8.5.4 Encoding Error
Encoding error occurred when the participants solved the problems but did not
write the solution in appropriate and acceptable forms. Encoding the answers for the
mathematics questions was the last part of solving the questions. However, some
participants unable performed this step well and made such kind of error and thus
caused them to lost marks in the mathematics tests. The analysis and interpretation of
the participants’ encoding errors were shown in Table 9.
41
Participant did not
do the second step
Table 9: Analysis of Encoding Errors
No
.
Question and Solution Error and Explanation
1. What is the mixed number for
136
?
Solution:
62
|13 12 1
Answer: 2 16
Error:
62
|13 12 1
Answer: ?
Explanation:
The participant worked out the correct
solution to the problem, but unable wrote
the correct answer that required by the
problem and that was “mixed number for
136
” .
2. Jaafar earns RM 345 901. He
spent RM 290 000. How much
money does Jaafar have now?
Solution:
RM 345 901+ RM 290 000 RM 635 901
Error:
345 901 +290 000 635 901
Explanation:
The answer written was not together with
its unit. Although the calculation of this
question was correct, participants lost
marks because no unit “RM” was added
together with the answer obtained.
42
Error
Error
9.0 RESEARCH FINDINGS REFLECTION
This research was carried out to apply and evaluate the effectiveness of STAD
model to enhance Year 5 pupils’ performance in mathematics especially their
academic performance in mathematics. Besides, this research also aimed to help the
year 5 pupils to have positive attitude towards mathematics and analyse the common
errors made in mathematics tests.
The instruments in this research were achievement test, observation and
questionnaire. Each of the instruments was respectively used to evaluate the
effectiveness of STAD model in enhancing the participants’ academic performance in
mathematics, analysing participants’ common errors in the mathematics tests,
observing and determining the constraints faced in each of the cycles when carrying
out this action research, and evaluating participants’ attitude towards mathematics.
This action research was carried out in total of 3 cycles. 5 previous tests’
scores of the participants were collected and counted to get the participants’ base
scores. A post-test was carried out every after 2 weeks of the implementation of
STAD model to obtain the data needed to compare the participants’ test’s scores
before and after the implementation of STAD model. Action plan was modified for 2
times based on the constraints faced in the previous cycles. The post-tests were meant
to identify participants’ improvement shown in academic performance and also the
common errors made by the participants in mathematics. Questionnaire was the
instrument used to evaluate participants’ attitude towards mathematics from the
aspects of interest in learning mathematics, mastery in mathematics and also their
social interaction in the class. Observation was done through informal observation in
the class, journal and reflection in the daily lesson plan. The aspects observed were
based on participants behaviours, social interaction and participants’ participation in
STAD model.
43
9.1 Effectiveness of STAD in Enhancing Participants’ Academic
Performance
According to the analysis and interpretation of the data presented in Figure 2,
Figure 3 and Figure 4, the effectiveness of the STAD model in enhancing
participants’ academic performance was proven. The participants’ academic
performance was improving from the post-test 1, post-test 2 and post-test 3.
Participants gained better scores in the mathematics tests after implementing the
STAD in the teaching and learning of mathematics in the classroom. It was proven
that implementation of STAD model was effective in increasing participants’
academic performance in mathematics. The improvement scores obtained in their
post-tests were the best evidences.
These positive results gained verified that when participants were
participating actively in the teaching and learning of mathematics through STAD
model with the same group goals, the participants could easily understand the
mathematical knowledge taught to them and hence enhanced their academic
performance in mathematics. The positive results gained from this research was also
supported by Slavin (1980) in Wong (2007), Syafini Bt. Ismail and Tengku Nur
Rizan Bt Tengku Mohamad Maasum (n.d) and Slavin (1989) in Gillies and Ashman
(2003). Based on the analysis and interpretation of data done, the researcher
confidently concluded that the implementation of STAD model is effective in
enhancing year 5 pupils’ performance in mathematics.
9.2 Participants’ Attitude towards Mathematics
Based on the analysis of the questionnaire shown in Table 2, participants’
attitude towards mathematics were analysed from three aspects (interest, mastery in
mathematics, and social interaction). After analysis of the questionnaires was done, it
44
was discovered that the participants’ interest in mathematics had increased after the
implementation of the STAD model if compared to before. They found that learning
mathematics was fun and enjoyable when cooperative learning was applied. They
participated actively in the teaching and learning in mathematics with their own group
members through group activities. Through group activities, the participants initiated
to finish the tasks given to them. Researchers or teachers only played the role of the
guide most of the time when cooperative learning were applied. The findings agreed
with Armstrong et al. (1998).
The participants’ mastery in mathematics was also improved. This statement
could be proven through the analysis of the post-tests (Figure 2, Figure 3 and Figure
4) and also through the questionnaires taken by the participants (Table 4). Participants
agreed that the STAD model enabled them to understand better the mathematical
knowledge and skills taught to them in the class easily. The participants’ critical
thinking and problem solving skills were also enhanced throughout the group
discussion. These findings were similar with the findings of Effandi Zakaria and
Zanaton Iksan (2006).
Moreover, participants’ social interaction in the class was also enhanced after
the implementation of STAD model. Participants prefer to work together with their
peers or group members more when solving the tasks given in mathematics instead of
working alone. They loved to share ideas with their peers or group members and thus
maximized their learning. Through the discussion among their own group or with
other groups, positive interaction was occurred, hence fostered their relationship.
These findings were proven the findings Effandi Zakaria et al. (2010). Therefore,
based on these findings, researcher can confidently claim that STAD model is able to
enhance participants’ attitude towards mathematics.
45
9. 3 Participants’ Common Errors
The most common errors made by the participants in the mathematics tests
were also analysed in this research. These errors disabled the participants to obtain
good scores in mathematics tests. There were four main common errors made by the
participants in the tests. The errors were comprehension error, careless error,
procedural errors and encoding error. These errors occurred were mainly due to the
reasons of did not understand the requirement of the mathematics questions,
participants’ impatience in doing the mathematics tests, and their laziness in
rechecking their answers. However, most of these errors were pointed out and
improved through group learning. Participants taught each other through STAD
model and help in correcting the mistakes made by their peers or team members.
Hence, the participants would be more aware of the common errors made by them
and made less common errors when solving the mathematics questions in the tests.
The findings above were supported by the findings of Huang (2008).
10.0 FURTHER RESEARCH
Based on the research carried out, it is suggested that the time given to carry
out the research can be extended. The motive to do is so that the researcher can carry
out the research for longer time to collect more data to evaluate the effectiveness of
STAD in enhancing participants’ performance in mathematics. It is believed that the
data collected for this research can be more precise and accurate if more time is
given.
In addition, it is also recommended that further research can be carried out to
evaluate the effectiveness of STAD model in enhancing participants’ performance in
other subjects such as Science and English.
46
Thirdly, researcher also proposes that further research can be carried out to
overcome the constraints faced in the third cycle after the application of “System
Token” with STAD model. Further research should be carried out to analyse the
“System Token” in influencing the participants’ learning attitude in mathematics.
Lastly, it is suggested that similar research can be carried out in the other
primary schools especially the town schools. This is because the teaching and
learning styles of the pupils from the town schools might be different with the pupils
from the outskirt of the town.
47
REFERENCES
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Curriculum Development Centre. (2006). Curriculum Specifications Mathematics Year 5. Putrajaya: Ministry of Education Malaysia.
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Davidson, N. (1990). Cooperative Learning in Mathematics. United States of America: Addison-Wesley.
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Effandi Zakaria, Lu Chung Chin, and Mohd. Yusoff Daud. (2010). The Effect of Cooperative Learning on Students’ Mathematics Achievement and Attitude towards Mathematics. Journal of Social Science, 6(2), 275. [Online]. Available: http://www.scipub.org/fulltext/jss/jss62272-275.pdf. [2010, August 2].
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48
Gillies R.M. and Ashman A.F. (2003). Co-operative Learning: The Social and Intellectual outcomes of Learning in Groups. London and New York: RoutledgeFalmer.
Huang, Lieu Sang. (2008). Keberkesanan Kaedah Pembelajaran Koperatif Model STAD ke atas Prestasi Matematik Tingkatan Satu Bagi Topik Algebra. Open University Malaysia.: Thesis of Undergraduate.
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Kennedy, L.M. and Tipps, S. (1999). Guiding Children’s Learning of Mathematics (9th edition). Belmont: Wadworth / Thomson Learning.
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Lynes D. (1999). Using Observation for Data Collection. [Online]. Available: http://www.ncbi.nlm.nih.gov/pubmed/10205546 . [2010, February 24].
Macdude. (2006). The Importance of Education for Development. [Online]. Available: http://www.echeat.com/essay.php?t=32168 . [2010, July 18].
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49
Mifflin, H. (n.d.) Cooperative Learning. [Online]. Available: http://college.cengage . com/education/pbl/tc/coop.html#1 . [2010, February 3].
Miller, C.K.and Peterson, R.L. (n.d.). Creating A Positive Climate: Cooperative Learning. [Online]. Available: http://www.indiana.edu/~safeschl/ cooperative_learning.pdf . [2010, February 26].
Myers, E. (2001). Enhancing Education through Cooperative Learning. [Online]. Available: http://www.nade.net/documents/Mono96/mono96.3.pdf . [2010, February 5].
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Orlich, D.C. et al. (2007). Teaching Strategies: A Guide to Effective Instruction (8th
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Putnam, J. (1997). Cooperative Learning in Diverse Classroom. New Jersey: Prentice-Hall.
Rosini B. Abu. (1998). The Effects of Cooperative Learning Methods on Achievement, Retention, and Attitudes of Home Aconomics Students in North Carlina. [Online]. Available: http://scholar.lib.vt.edu/ejournals/ JVTE/v13n2/Abu.html . [2010, August 10].
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Snyder, S.S. and Shickley, N.E. (2006). Cooperative Learning Groups in the Middle School Mathematics Classroom. [Online]. Available: http://scimath.unl.edu/MIM/files/research/SnyderS.pdf . [ 2010, February 25].
Syafini Bt Ismail and Tengku Nur Rizan Bt Tengku Mohamad Maasum. (n.d.). The Effect of Cooperative Learning in Enhancing Writing Performance. [Online]. Available: http://pkukmweb.ukm.my/~solls09/Proceeding/PDF/Shafini.pdf.[2010, August 10].
University of Sheffield. (2010). Data Collection Method. [Online]. Available: http://www.shef.ac.uk/lets-evaluate/general/methods-collection/questionnaire. html. [2010, February 25].
Wong, Ai Chu. (2007). Keberkesanan Kaedah Pembelajaran Kooperatif Model STAD ke atas Prestasi Matematik Bagi Topik Integer. Open University Malaysia: Thesis of Undergraduate.
Wong, Siew Ming. (1998). The Effectiveness of Cooperative Learning on Mathematics Achievement and Change in Attitudes Towards Mathematics Among Preservice Teachers of Heterogeneous Ability Majoring in Mathematics in Sarawak Teacher Training College. Jurnal Pendidikan MPS. 1(1): 82-89.
50
APPENDIX 1
PARTICIPANT INFORMATION FORM
Please fill your information in the blanks provided for each of the questions. Tick (√)
your option.
Participant’s Information
Name : ……………………………………
Class :……………………………………
Gender:……………………………………
Race :……………………………………
1. Previous test score in mathematics subject:
0 – 30%
31 – 50%
51 – 70%
71 – 80%
81 – 100%
2. Interest in mathematics subject:
High Medium Low
51
APPENDIX 2
Post-test 1
MATHEMATICS YEAR 5
Name:_____________________ Date:______________Score:_________________
Section A:Circle the correct answer:
1) 54 143 is read as
A. fifty-four thousand one hundred and forty-three
B. fifty-three thousand one hundred and forty-three
C. fifty-four thousand one hundred and forty-four
D. fifty-four thousand two hundred and forty-four
Answer: A
2) What the place value of the numerals 7 in the number 327 610?
A. tens
B. hundreds
C. thousands
D. ten thousand
Answer: C
3) Round off 537 927 to the nearest ten thousand
A. 540 000
B. 530 000
C. 520 000
D. 500 000
Answer: A
52
4) 123 458 + 213 654 =
A. 333 112
B. 327 112
C. 337 112
D. 338 112
Answer: C
5) 446 819 – 210 456 – 100 000 =
A. 134 363
B. 135 363
C. 146 363
D. 136 363
Answer: D
6) - 15 421 = 54 214. Find the answer in blank.
A. 89 635
B. 69 645
C. 89 635
D. 69 635
Answer: D
7) 31 203 × 2 =
A. 62 406
B. 61 406
C. 62 306
D. 61 306
Answer: A
53
8) 6 456 × 100 =
A. 64 560
B. 64 500
C. 645 600
D. 656 000
Answer: C
9) 2 435 × 52 =
A. 106 620
B. 116 620
C. 126 620
D. 136 620
Answer: C
10) 7 404 ÷ 6 =
A 1 034
B. 1 134
C. 1 234
D. 1 334
Answer: C
54
Section B: Answer all the questions below.
55
1) Write 234 879 in words
Answer: two hundreds thirty-four thousands eight hundreds and seventy-nine
2) Write 22 345 in extended notation.
Answer: 20 000 +2 000 +300 + 40 + 5
3) Write sixty-five thousand seven hundred and twenty-one in numeral.
Answer: 65 721
4) Arrange the numbers in ascending order.
123 540 , 120 234, 123 430, 123 411
Answer: 120 234, 123 411, 123 430, 123 540
6) State the value of the digit 7 in the number 876 234.
Answer: 70 000
5) Round off 871 253 to the nearest ten thousand.
Answer: 870 000
7) 286 274 + 345 761 =
286 274 + 345 761 632 035
Answer: 632 035
8) 671 921 – 521 813 =
671 921 - 521 813 150 108
Answer: 150 108
56
9) 234 871 × 4 =
234 871 × 4 939 484
Answer: 939 484
10) 628 011 – 233 192 – 123 762 =
628 011 394 819 - 233 192 - 123 762 394 819 271 057
Answer: 271 057
11) Calculate the sum of 234 871 and 123 456
234 871 + 123 456 358 327
Answer: 358 327
12) 267 180 × 3 =
267 180 × 3 801 540
Answer: 801 540
13) 672 234 + 112 234 = ____________
672 234 + 112 234 784 468
Answer: 784 468
14) Mary had 345 568 sweets. Rafiq took 76 123 sweets from Mary. Rafiq left how many sweets left?
345 568 - 76 123 269 445
Answer: 269 445 sweets
57
15) + 123 728 = 872 234. Find the answer in
872 234 - 123 728 748 506
Answer: 748 506
16) Find the differences between 221 871 and 120 121.
221 187 - 120 121 101 750
Answer: 101 750
17) Halim has 8 561 crates of oranges. There are 24 oranges in each crate. How many oranges are there altogether?
8 561 × 24 34 244 17 122_ 205 464
Answer: 205 464 oranges.
18) Erricson bought 124 980 apples while Rafiq bought 293 345 apples. How many apples altogether?
124 980 + 293 345 418 325
Answer: 418 325 apples.
19) Jaafar earns RM 345 901. He spends RM 290 000. How much money does Jaafar have now?
RM 345 901 -RM 290 000 RM 55 901
Answer: RM 55 901
58
20) There are 80 123 match boxes. Each box has 5 matchsticks. How many matchsticks are there altogether?
80 123 × 5 400 615
Answer: 400 615 matchsticks.
APPENDIX 3
Post-test 2
MATHEMATICS YEAR 5
Name:___________________Date:_________________Score:________________
Section A: Circle the correct answer.
1) Six hundred fifty-eight thousand six hundred and five written in numerals is
A. 658 006
B. 658 055
C. 658 605
D. 658 650
Answer: C
2) Which of the following number has digit 4 with a value of 40 000?
A. 842 397
B. 794 316
C. 572 142
D. 390 164
Answer: A
3) 256 641+ 45 723 – 23 454 =
A. 275 910
B. 276 910
C. 277 810
D. 278 910
Answer: D
59
4) 2 345 × 32 =
A. 75 030
B. 75 040
C. 75 050
D. 75 060
Answe: B
5) Find quotient of 19 314 × 6
A. 114 880
B. 114 894
C. 115 884
D. 116 884
Answer: C
6) 1 632 ×5 ÷ 10
A. 716
B. 816
C. 916
D. 1 016
Answer: B
7) 700 005 – 37 287 – 1 000 =
A. 614 719
B. 648 719
C. 661 718
D. 671 718
Answer: C
60
8) Which of the following is not an improper fraction?
A. 73
B. 76
C. 74
D. 78
Answer: D
9)
The shaded part in the diagram above represents
A.103
B.104
C.93
D.94
Answer: D
10) 2 550 ÷ 3 × 8 =
A. 7 040
B. 6 840
C. 6 940
D. 6 800
Answer: D
61
Section B: Answer all the questions below.
62
1) Write 356 760 in words
Answer: three hundred fifty-six thousand seven hundred and sixty
2) 451 062 + 142 337 + 361 781 =
451 062 593 399 + 142 337 + 361 781 593 399 955 180
Answer: 955 180
3) What is the differences between 776 158 and 43 116?
776 158 - 43 116 733 042 Answer: 733 042
4) 4 761 × 23 =
4 761 × 23 14 283 95 22_ 109 503_
Answer: 109 503
5) 130 100 ÷ 10 × 4 =
1013 010
|130 100 - 10 30 -30 1 -0 10 - 10 0 -0
Answer: 52040
63
13 010× 4 52 040
6) Find the total of 600 165, 45 783 and 2 546
600 165 554 382 + 45 783 + 2 546 645 948 648 494
Answer: 648 494
7) 466 954 ÷ 8 =
858 369
|466 954 -40 66 -64 2 9 -2 4 55 - 48 74 -72 2
(r)
11) Calculate 123 450 × 3 ÷ 10 =
1037 035
|370 350 -30 70 -70 3 -0 35 -30 50 -50
Answer: 37 035
12) 2 134 + = 321 210
321 210 - 2 134 319 076
Answer: 319 076
13) What is the mixed number for 127
?
71
|12 - 7 5 =
157
Answer:157
14) Mary has 123 456 sweets. Rafiq takes 34 123 sweets from Mary. Rafiq has how many sweets left?
123 456 - 34 123 89 333
Answer: 89 333 sweets
15) - 123 728 = 872 234. Find the answer in
872 234 + 123 728 995 962
Answer: 995 962
64
123 450
× 3
370 350
6) Find the total of 600 165, 45 783 and 2 546
600 165 554 382 + 45 783 + 2 546 645 948 648 494
Answer: 648 494
7) 466 954 ÷ 8 =
858 369
|466 954 -40 66 -64 2 9 -2 4 55 - 48 74 -72 2
(r)
16) 872 234 + 123 728 – 165 213 =
872 234 995 962 + 123 728 -165 213 995 962 830 749
Answer: 830 749
17) Azrin has 2 345 crates of oranges. There are 12 oranges in each crate. How many oranges are there altogether?
2 345 × 12 4 690 23 45_ 28 140
Answer: 28 140 oranges
18) Mr. Lim puts 15 072 marbles into 12 boxes. How many marbles are there in 7 boxes?
121 256
|15 072 -12 3 0 -2 4 67 -60 72 -72
Answer: 8 792 marbles.
19) The population of the three towns are 234 897, 120 970 and 87 123. Calculate the total population of the three towns.
234 897 355 867 + 120 970 + 87 123 355 867 442 990
Answer: 442 990 population
20) A supermarket ordered 5 875 boxes of oranges for Chinese New Year. There are 80 oranges in each box. Find the total number of oranges ordered.
5 875 × 80 0 000
65
1 256
× 7
8 792
470 00 470 000
Answer: 470 000 oranges.
APPENDIX 4
Post-test 3
66
MATHEMATICS YEAR 5
Name:___________________Date:_________________Score:________________
Section A: Circle the correct answer.
1) Six hundred sixty-eight thousand six hundred and five written in numerals is
A. 658 006
B. 658 055
C. 668 605
D. 668 650
Answer: C
2) Which of the following number has digit 4 with a value of 400?
A. 842 397
B. 794 316
C. 572 402
D. 390 164
Answer: C
3) 256 641+ 45 723 – 23 453 =
A. 278 911
B. 279 910
C. 278 811
D. 279 910
Answer: A
4) 2 345 × 31 =
A. 72 695
B. 72 694
67
C. 72 705
D. 72 704
Answer: A
5) 45 661÷ 7
A. 6 423
B. 6 523
C. 6 623
D. 6 723
Answer: B
6) 1 632 × 5 ÷ 10
A. 716
B. 816
C. 916
D. 1 016
Answer: B
7) 25 789 + 37 287 – 1 000 =
A. 61 176
B. 61 176
C. 62 076
D. 62 176
Answer: C
8) Which of the following is an improper fraction?
A. 13
68
B. 76
C. 34
D. 78
Answer: B
9)
The shaded part in the diagram above represents
A.103
B. 104
C. 93
D. 114
Answer: D
10) 338 460 ÷ 6 × 4 =
A. 222 640
B. 223 640
C. 224 640
D. 225 640
Answer: D
69
Section B: Answer all the questions below.
70
1) Write 151 760 in words
Answer: one hundred and fifty-one thousands seven hundred and sixty
2) 451 062 + 142 337 - 361 781=
451 062 593 399 + 142 337 - 361 781 593 399 231 618
Answer: 231 618 3) What is the difference between 76 159 and 43 816
76 159 - 43 816 32 343
Answer: 32 343
4) 4 761 × 45 =
4 761 × 45 23 805 190 44 214 245
Answer: 214 245
5) 113 010 ÷ 10 × 6 =
1011301
|113010 -10 13 - 10 3 0 - 3 0 1 - 0 10 - 1 0
Answer: 67 806
11 301× 6 67 806
71
6 ) Find the total of 600 165, 45 783 and 12 546
600 165 645 948 + 45 783 + 12 546 645 948 658 494
Answer: 658 494
9) 994 229 can be written in extended notation as _________________
Answer: 900 000 + 90 000 + 4 000 + 200 + 20 +9
7) 234
+ 124
= 2 +1 + 34 +
24
= 3 + 54
= 3 + 44 +
14
= 3 + 1 + 14
= 4 14
Answer: 4 148) 168 352 ÷ 32 =
325 261
|168 352 -160 8 3 -6 4 1 95 -1 92 32 -32
Answer: 5 261
10) Write 74
in words.
Answer: seven quarters
72
11) Calculate 123 450 × 6
123 450 × 6 740 700
Answer: 740 700
12) 12 134 + = 321 210. Find the answer in
.
321 210 - 12 134 309 076
Answer: 309 076
13) What is the mixed number for 136 ?
62
|13 -12 1
Answer: 2 16
14) Azrin had 145 456 sweets. Alif took 54 023 sweets from Azrin. Azrin left how many sweets?
145 456 - 54 023 91 433
Answer: 91 433 sweets.
15)
- 423 788 = 972 134. Find the answer in
.
972 134 - 423 788 1 395 922
Answer: 1 395 922
16) 456 989 + 334 567 – 165 213 =
456 989 791 556 + 334 567 - 165 213 791 556 626 343
Answer: 626 343
73
17) Zul has 12 345 crates of oranges. There are 12 oranges in each crate. How many oranges are there altogether?
12 345 × 12 24 690 123 45 148 140
Answer: 148 140 oranges
18) Ali put 469 278 marbles into 9 boxes. How many marbles in 8 boxes?
952 142
|469 278 -45 19 -18 1 2 - 9 37 -36 18 -18
Answer: 417 136 marbles
19) The population of three towns are 214 897, 121 970 and 187 123. Calculate the total population of the three towns.
214 897 336 867 + 121 970 + 187 123 336 867 523 990
Answer: 523 990 population
20) A supermarket ordered 115 875 boxes of oranges for Chinese New Year. There are 8 oranges in each box. Find the total number of oranges ordered.
115 875 × 8 927 000
Answer: 927 000 oranges.
52 142× 8417 136
APPENDIX 5
Questionnaire
Recently, your mathematics teacher has applied cooperative learning during the
teaching and learning of mathematics subject in the classroom. Your opinion and
view about this cooperative learning strategy is need. Please give your respond based
on the questions posed below on how much you agree with the application of
cooperative learning strategy for mathematics subject by using four-point scale which
stated as below:
1 – Strongly disagree
2 – Disagree
3 – Agree
4 – Strongly Agree
Instruction:
Please (√) at the columns which match with your answer.
For example,
No. Question
Scale
1 2 3 4
1. I enjoy learning mathematics with my team
member.
√
74
No. Question
Scale
1 2 3 4
1. I enjoy learning mathematics in group.
2. I love to learn with friends
3. It is easy for me to learn mathematics by
working together with the others.
4. The group activities increase my interest in
learning mathematics.
5. The teaching and learning of mathematics is
much more interesting with the
implementation of group activities.
6. Group activities do not help me a lot in the
learning of mathematics subject.
7. Learning in group makes me easy to
understand mathematics.
8. I am looking forward for the mathematics
lessons because I can learn together with my
friends.
9. I able communicate better with my friends
after learning in group for mathematics
subject.
Scale
75
No. Question 1 2 3 4
10. I am still difficulties in learning mathematics
after the group works was carried out.
11. Group activities give me chances to
participate actively in the mathematics
lessons.
12. Learning in group enables me to have
positive relationship with my friends.
13. I love to share my knowledge with my group
members in learning mathematics.
14. My academic performance in mathematics is
increased after learning together with my
friends.
15. I would like to have group activities for the
mathematics lesson most of the time.
16. I would like to continue learning
mathematics in group with my friends.
17. I able solve most of the mathematics
problems after learning mathematics in
group.
18. Learning in group is not suitable for me in
learning mathematics.
76