Proposal defence

1. Creative Problem Solving in Mathematics
Among the Engineering Undergraduates
Lim Keng Keh
Mathematics Education
Universiti Teknologi Malayisa
PP133001
Supervisor: Dr. Zaleha Ismail

2. ABSTRACT
Engineering students nowadays facing the problem of applying whatever they have
learnt in the university to their future real world. This study is used to promote
engineering students to use their creative and critical thinking skills to solve open-
ended mathematical problem based on creative problem solving Therefore, we have to
understand how engineering students using their creativity and strategies to solve
mathematical problems. The aim of the research is to show that creative problem
solving can be applied in solving open-ended mathematical problems. This research
employed an exploratory design. Qualitative educational research method was chosen
as a methodology to explore and understand how the students can use solve open-
ended mathematical problems by applying all the procedures in creative problem
solving. First, a literature review is carried out in order to understand the methodology
and instruments used in the previous study of creative problem solving. The qualitative
data of the instruments can be triangulated to provide evidence of the validity of the
research.

4. Introduction : Nature of Open-Ended Mathematical Problems
1. Open-ended problems are ill-structured and there are many missing data and therefore
there is no fixed procedure to guarantee to get a correct answer. Foong (2002)
2. There are more than one solution for these types of problems and students can use
multiple approaches to solve the problems with little constraints on their methods
using.  Hancock (1995)
3. Open-ended problems can be considered as ill-structured problems and they lack of
sufficient data and standard procedures to find a correct answer for the problems.
Yee (2002)
4. This requires students to foster their higher order thinking skills to create solutions for
their open-ended mathematical problems.  Dyer and Moynihan (2000)

6. Introduction : Advantages of Open-Ended Mathematical Problems
1. It can encourage students to use multiple approaches to find a solution for their problem base
on their own scope and mathematical abilities.  Kwon and Park (2006).
2. It can also help students to engage in their active learning and construct their own
mathematical knowledge.  Sullivan (2006).
3. It can allow students to use different strategies to obtain their solutions and this gives them the
opportunity of developing their mathematical understandings and skills.  Capraro and
Cifarelli (2007)
4. It can help students to deepen their mathematical understandings and develop their
mathematical thinking by learning how to use different strategies to solve open-ended
mathematical problems.  Klavir and Hershkovitz (2008)
5. In the process of problem solving, students can discuss their solutions with diverse inferences
and this will also cultivate their mathematical communication skills.  Kwon and Park
(2006).

8. Introduction : Applying of CPS to solve Open-ended Mathematical Problems
Creative problem solving skills can be applied in solving open-ended mathematical problems.
This is because divergent and convergent thinking skills are demanded in the task of creative
problem solving (Basadur, 1995; Chang & Weng, 2002).

9. Divergent thinking
Divergent thinking can be evaluated with quality and quantity such as
fluency (How many ideas can be produced), flexibility (How much different
are the ideas produced), originality (How unique are the ideas produced) and
elaboration (How detailed are the ideas produced) (Sak & Maker, 2005).
According to Sak and Maker (2005), divergent thinking can use open-ended
problem to stimulate a variety of creative ideas by exploring many possible
solution. Therefore, divergent thinking can produce a variety of solutions.
The application of creativity can combine different ideas and generate more
than one possible solutions (Hudson, 1966,1968; Guilford, 1959, 1978).
Gibson, Folley and Park (2009) pointed out that divergent thinking can
produce a variety of responses with open-ended problems. They also told us
that divergent thinking can work best with poorly defined or unstructured
open-ended problems. According to Guilford (1959), divergent thinking is
determined by fluency, flexibility and originality and required to search for
ideas in all directions and boundaries.

10. Divergent thinking

12. Convergent thinking
According to Gomez (2007), Convergent thinking is characterized by
reproducing of known concepts or existing data and adopt old response to new
situation in a more or less logical manner. Convergent thinking can narrow the
possible responses to come up with a correct solution (Gibson, Folley & Park,
2009). Puccio (1998) pointed out that convergent thinking can be used to derive
the single best or correct solution form the given or stored information. Cropley
(1999) also told us that convergent thinking can produce only a single best solution
Convergent thinking can work best with well-defined problems with clearly
defined responses (Gibson, Folley & Park, 2009). Akbari Chermahini (2011)
claimed that convergent thinking is emphasized by its logic, accuracy and speed
with the application of set techniques, recognition of familiarity, recalling stored
information and decision-making strategies.

13. Convergent thinking

18. Background of the Research
Tong (2003) stated that most employers in Malaysia would employ engineering graduates
with not only technical skills but also non-technical skills such as communication skills,
planning and scheduling, people management skills, problem-solving skills, team
management and cost control. According to Kamsah (2004) engineering graduates in
Malaysia lack of generic skills to help them to apply their technical skills effectively.
Mohamed (2004) pointed out that engineering graduates nowadays not only have to possess
excellent academic degree but also generic skills in order to get employed as more
companies look for engineering graduates who can use their employability skills to help
them to apply their technical and knowledge effectively. Hassan (2007) also developed a
framework for employability skills and listed out the most important generic skills for
engineering graduates which is based on the criteria required for professional engineers
from the Accreditation of Engineering Program (EAC) manual as to indicate the most
important skills required by employers in Malaysia.

20. Employability skills as required by EAC

22. Statement of the problem
Mathematical problems with only one correct answer is very hard to develop
mathematical creativity (Shimada, 1997) and mathematical creativity is the essence
of mathematics which requires students to think creatively in mathematics and not
just to come out with correct answer (Dreyfus & Eisenberg, 1966; Ginsburg, 1996.
Problem solving can be used to foster creativity. According to Guilford (1987),
problem solving and creative thinking are closely related. He stated that creative
thinking can produce novel ideas while problem solving can produce a new income
in a new situation.
Vass and others (2002) provided a theoretical basis to develop problem solving
environments in order to support creativity. They also extend the concept of
usability to include creativity in the process of problem solving.

24. Concept Mind of Problem Solving

26. Purpose of the Study
The aim of the research is to show that creative problem solving can be applied in
solving open-ended mathematical problems. Open-ended mathematical problems are
not well-defined and there is no fixed procedure in solving the problems. Therefore,
students have to use multiple approaches and ideas with divergent and convergent
thinking skills to solve open-ended mathematical problems. Students are given the
opportunities to have freedom to find their own solutions based on their creative
problem solving skills.
According to Kwon and Park (2006), 398 seventh grade students were carried out
in the study of their divergent thinking skills by using open-ended mathematical
problems. The result shows that divergent thinking in mathematics can be cultivated
by using open-ended problems Therefore, creative problem solving in mathematics
can be used to solve open-ended mathematical problems since the problem solvers
have to alternate using not only their convergent but also divergent thinking skills
(Giangreco et. al., 1994).

28. Objectives of the study
This study is based on the use of strategies in creative problem solving in
mathematics and mathematical creativity and it is attempted to achieve the
following objectives:
To determine the mathematical creativity of the engineering undergraduates used to
solve open-ended mathematical problem.
To determine the mathematical strategies of the engineering undergraduates used to
solve open-ended mathematical problem.
To formulate a framework for solving open-ended mathematical problem by using
CPS.

30. Research Questions
The following research questions were formulated based on the objectives of the study:
What are the mathematical strategies used by engineering students to solve open-ended
mathematical problems?
What is the mathematical creativity used by engineering students to solve open-ended
mathematical problems?
How can a framework for solving open-ended mathematical problem by using CPS skills
be developed ?

32. Scope of the Study
This research study involves using creative problem solving to
solve open-ended mathematical problems. From this study, students
have to use their convergent and divergent thinking to develop their
solutions in a creative way. Engineering students from a local
university will participate in this research.

34. Significance of the Study
This study is significant in such a way that it is used to help us to
construct and design a framework for using strategies to solve creative
mathematical problems in mathematics.
This study can promote students to use their mathematical creativity and
strategies of creative problem solving to solve open-ended mathematical
problems. It is also help the students to develop their soft skills such as
problem-solving and creative thinking skills to enable them to succeed in
their future work place.
Malaysia Ministry of Education encourages students to develop their
creative and critical thinking skills in the 21st Century as stated in the
Preliminary Report of Malaysia Education Blue Print 2013-2025. This
study can help students to use their creative problem solving skills to
develop their critical thinking as well as their creative thinking.

36. The conceptual framework for the research.
was based on solving open-ended
mathematical problems with strategies in
creative problem solving and mathematical
creativity. Their relationships were
illustrated as shown in the Figure.
Finally, a framework for assessing creative
problem solving in mathematics is
generated. CPS was developed by
Treffinger et al. (1994). This conceptual
framework is also based on Lumsdaine’s
processes of creative problem solving by
using different mind sets with
superimposing on the Herrmann model of
thinking preference (Lumsdaine, 2007).
Conceptual Framework

38. Vygotsky recognized that learner as active learner
based on previous experience in a social and
cultural environment (Cobb, Wood & Yackel,
1990). He wrote that learner can develop new
understanding of mathematical knowledge with the
help of capable peers in the zone of proximal
development ZPD. As shown in the following
diagram, student can develop a new understanding
of a mathematical knowledge with the help of
capable peers by using CPS skills in the zone of
proximal development. According to Valsiner
(1987), there are two other zones added to
Vygotsky’s ZPD such as ZPA (Zone of Promoted
Action) and ZFM (Zone of Free Movement). ZPD
is the student’s skills and knowledge using CPS for
solving problem, ZPA is the student’s effort to
work collaboratively with capable peers and ZFM
is the student’s attitude and ability.
Theoretical Framework

40. Creativity
There are many definitions regarding creativity. Newell & Shaw (1972) defined
Creativity as generation of new ideas. Higgins (1999) suggest creativity must has
value either in new solution or recombined with other ideas. Haylock (1987)
defined creativity as the ability to associate the unrelated ideas with applications. He
believed that creative ideas can be generated by overcoming the fixation barriers.
Krutetskill (1976) characterized creativity with problem finding, originality and
invention. Runco (1993a) stated that creativity involves divergent and convergent
thinking, problem finding and problem solving. Boden (2004) mentioned that
combining familiar ideas in unfamiliar ways is known as creativity. According to
Boden, there are three types of creativity to generate new ideas. The first type is
combinational creativity which can use familiar ideas to generate new idea. The
second type is the exploratory creativity which can generate new idea by exploring
structured concepts. The third is the transformational creativity which transform
some dimensions of the structures to come out with new structure. Therefore, the
process of exploring and transforming a conceptual space can be used to generate
creativity.

41. All the definitions are actually can be combined
into three main categories. These are known as
creative person, products and processes. Creative
person is based on the intellectual, motivation,
personality and other characteristics. The creative
products are outcome or result based on its
usefulness and novelty. The creative processes are
focused on the cognitive processes to come out
with creative products. Creative context is the last
theme and it enables us to understand the place,
climate, culture or environment where creativity
can flourish (Isaksen, Dorval & Treffinger, 2011).
Creativity can be described with four overlapping
themes such as the characteristics of creative
people, the process, product of creativity and the
context of creativity (Isaksen, Dorval & Treffinger,
2011.
Four Overlapping Themes of Creativity
Isaken (1989) represented these
four themes with a Venn diagram
as shown in the diagram. Its show
their interactions in order to get a
whole picture of creativity

42. Assessment of creativity in terms of creative
products or creative outcomes had been developed by
Besemer and her colleagues. (Besemer, 1997; Besemer
& O’Quin, 1987, 1993, 1999; Besemer & Treffinger,
1981). Creative products can be evaluated based on
three dimensions as shown in the following diagram
Figure 2.2 (Isaksen, Dorval & Treffinger, 2011). The
first dimension is novelty which shows the originality
and newness of the products. The second dimension is
resolution which shows the effectiveness of using the
products to solve a problem. The third dimension is
style which shows how attractive and elegant the
product is. It is the extension or elaboration of the
product and extend beyond the basic requirement of
the product (Isaksen, Dorval & Treffinger, 2011).
Besemer’s Characteristics of Creative Products

44. Guilford started his research by
developing intelligence tests to select
pilots during World War II (Barlow,
2000). He developed a model to guide
his research of finding the creativity
among the people. In his book “The
Nature of Human Intelligence”,
Guilford (1967) proposed a model of
intelligence and represented it with a
cube of 150 factors as shown in the
following diagram Figure 2.3. He also
found that a person can be high in certain
ability and low in others, he wrote a book
in the year of 1977, “Way beyond the IQ”
to show that a person’s creativity can’t be
determined by his or her IQ.
Model of Intelligence
Convergent production (ability to look
for single solution for a problem).
Divergent production (ability to look for
many solutions for a problem).

46. Definition of Mathematical Creativity
Torrance (1984) applied the concepts of fluency, flexibility and originality to creativity in
mathematics.
Hamard (1945) identified the ability to solve mathematical problems as the indicators of
mathematical creativity.
Henri Poincare (1948) defined mathematical creativity as forming, recognizing and
choosing important and useful combinations of ideas.
Erynck (1991) considered mathematical creativity as to create new mathematical concepts
by combining previous concepts or discovering new and unknown relationships between
mathematical facts.
According to Chamberlin and Moon (2005), mathematical creativity is based on divergent
thinking to generate nonstandard solution for a problem which can be solved by using
standard procedures.
Laycock (1970) claimed that mathematical creativity is the ability to look at the
mathematical problems from different perspectives and generate many ideas and then select
the best method to deal with them in different situations. Balka (1974) outlined six criteria to
describe mathematical creativity. They are used to check mathematical ability.

48. Assessment of mathematical creativity
According to Idris (2006), creativity-enriched mathematical problems rather than
routine problems can be used to assess mathematical creativity. Evans (1964) found
out three parameters used to assess mathematical creativity such as fluency,
flexibility and originality. Fluency is determined by the number of relevant
responses generated, flexibility is the number of relevant responses in different
categories of ideas generated and originality is the number of unusual ideas
generated. Prouse (1967) used students’ responses to assess their creativity based on
the parameters of fluency, and originality. Fluency is determined by the number of
responses given and originality is determined by the percentage of each relevant
response within the range of total responses given by the students.

49. Development and Foster of Mathematical Creativity
Torrance (1987) claimed that the tasks with the use of generating
many possible solutions can be used to stimulate mathematical
creativity compared to the tasks that can only generate one solution
Craft (2001) pointed out that problem which can be used to
generate more than one conjecture can be used to develop
mathematical creativity.
Hutchison (1990) also told us that two ancient mathematical
problems can be used to stimulate mathematical creativity. The first
problem is to trisect an angle into three equal parts and the second
problem is to divide a circle into any number of equal parts.
Tanner and Jones (2013) suggested that practical tasks and real
life mathematical problems which based on the procedure and rather
than the product can be used to help students to foster their
mathematical creativity.

53. The creative problem solving process uses different mind
sets by superimposing on the Herrmann model of thinking
preference (Lumsdaine, 2007). The explorer and
detective’s mind sets are used in the stage of problem
definition. Explorer uses divergent thinking to look for
more information to understand the problem whether the
detective uses convergent thinking to identify the problem.
Artist can come out with many unusual ideas based on
divergent thinking and judge only uses the best idea based
on convergent thinking. This is because artist’s mind set is
to generate many ideas in the stage of ideas generation
whether judge’s mind set’s is used in the stage of decision
making to select the best idea to be used. Producer’s mind
set is used to coordinate with others to carry out the plan in
the stage of solution implementation and engineer’s mind
set is used to create, evaluate and make practical use of the
solution in the stage of ideas evaluation. Both of them use
convergent and divergent thinking (Lumsdaine, 2007).
Mind Sets Superimposed on Herrmann Model

55. Creative and Critical thinking in CPS
CPS use both creative and critical thinking skills (Isaksen, Dorval & Treffinger, 2011). There
are two kinds of thinking in the process of CPS. Creative thinking can be used to generate many
types of unusual ideas while critical thinking can focus on the best ideas. We have to use critical
and creative thinking to help us to solve a problem. Generating many wild and unusual ideas can
help us to expand and stretch our thinking to search for ideas from many different directions;
however, we have to contract and focus our thinking by screening, filtering and selecting the best
ideas. The dynamic balance generating and focusing work hand in hand. In order to make full use
of CPS skills (Isaksen, Dorval & Treffinger, 2011). Diverging and converging are actually
replaced by generating and focusing in the third edition of the book. Critical thinking involves the
process of analysing, evaluating, refining, developing and selecting while creative thinking
involves the process of brainstorming, making new connections, developing novel ideas (Isaksen,
Dorval & Treffinger, 2011). Brainstorming and ALUo (Advantages, Limitations, Unique
Qualities and overcoming limitations) are the two basic tools to be used for generating and
focusing in CPS (Isaksen, Dorval & Treffinger, 2011).

63. Creative Thinking
Creative thinking is a thinking process to explore many possible solution to generate many
creative ideas. As determined by its fluency, originality and flexibility, it can be used to generate
many responses from open-ended problem (Gibson, Folley & Park, 2009).
According to Gomez (2007) creative thinking is characterized by searching for many
alternatives and set aside for later evaluation. The generation of various ways of solving a
problem with defer judgement is to loosen up fixed patterns of thinking and come up with many
different ways of solution (Gomez, 2007). Problem can be solved in many different ways but
there is no guarantee of the best solution in every approach. Therefore, the judgement and
evaluation is done later to select the best solution (Gomez, 2007).
Kneller (2005) also pointed out that the process of creative thinking can be used to see
beyond the given situation and bring a new insight to the given situation by producing many
unusual and relevant ideas which can redefine some or all aspect of the problem.
Kirby (1999) claimed that we can superimpose one concept into another to modify and come
up with new ideas. He also told us that we can practice creative thinking by using brainstorming
(Kirby, 1999).
Creative thinking is actually a process of lateral and wide-ranging with suspended judgement

65. Barriers to Creative Thinking
In the book “Strategies for Creative Problem Solving”, Fogler (1995) also pointed out
that there are some barriers to generate creative ideas. He told us that if we define the
problem too narrowly, ambiguously, too anxious to finish the problem, look for the
solution that does not work or get too attached to the first solution that coming first to our
minds can become obstacles in generating our creative idea (Fogler, LeBlanc & Rizzo,
1995). Sometime, we assume that there is only one right answer and we do not look for
alternative solutions to the problem or we do not attack the real problem and get
distracted by irrelevant information (Fogler, LeBlanc & Rizzo, 1995). We will get
discouraged by our failure can this can make us losing our confidence and not willing to
take risk to solve the problem in the future because of our failure.
Fogler (1995) also pointed out that paying attention to negative aspect of the
problem, following the rules, depending too much on logic, not willing to take risk
because of failure and believing that one’s is not creative can cause barriers to generate
creative solution to the problems

67. Overcome barriers to creative thinking
There are some barriers to overcome in the process of creative thinking. Adair (1990)
pointed out that we can’t make our judgment too quickly and too early to come up with
many new ideas. We should suspend our judgment to allow our creative ideas to go
through the thresholds of our creative minds. If we lower our thresholds to let many of our
creative ideas to get through, we can prevent our creative ideas from killing. According to
Adair (1990), criticism can also kill seeds of creative ideas. If we stop criticizing our own
ideas, and help them to escape from premature criticism, the seeds of our creative thinking
may grow up to become trees of inspirations. According to Fogler (1995), we have to be
open to new ideas and develop the new ideas until at least it is completed. Learning new
things in other fields of study can bring new ideas to our creative minds and therefore we
have to keep us ahead of the field of study that we are now in can avoid using yesterday’s
technology to solve today’s problem. We also need to keep track of creative ideas that
coming to our minds at all time. Keeping sense of humour can also be used to relieve our
tensions and thus we will become more creative when we are relaxed. Engaging ourselves
in a creative hobbies can foster our creativity and promote creative thinking (Fogler,
LeBlanc & Rizzo, 1995).

69. Strategies Used in Creative Problem Solving
The book “Strategies for Creative Problem Solving” which was written by H. Scott Fogler and
Steven E. LeBlanc showed that there are strategies to solve problems with creativity. However,
there are altogether five main steps in the process of problem-solving such as Defining the
Problem, Generating Ideas, Deciding the Course of Action, Implementing the Solution and
Evaluation (Fogler & LeBlanc, 1995).
1. Define the Problem – Find the real problem, understand the main problem, collect data and
explore more details about it.
2. Generate Ideas – Generate as many ideas as possible to solve problem by using
brainstorming. Using Osborn’s Checklist SCAMER (Substitute, Combine, Adapt, Modify,
Magnify, Minify, Put to other uses, Eliminate and Rearrange) to generate ideas.
3. Deciding the course of action – Make a good decision by comparing all the approaches
based on their efficiency, effect and flexibility.
4. Implement the Solution – Get approval from all the members and plan to use their man
power, budget and resources to solve the problem.
5. Evaluation – Find out whether the solution meets all the criteria and logically solve the
problem. Check whether the solution chosen has significant impact on the problem.

71. Impact of Creative problem Solving Training
Therefore, two major effects after Creative Problem Solving CPS
training were found. They are the effects towards attitudes and the
effects towards behaviors. The development of creative attitudes can
also foster creative behaviors. Therefore, two types of researches are
carried out to understand the effect of Creative Problem Solving CPS
training.
In one hand, some researchers investigated attitudes towards
openness to divergent thinking, preference for ideation; in the other
hand, other researchers examined behaviors towards production of
creative ideas, ideational fluency and evaluation skills. However,
there were very little literature regarding the effects of Creative
Problem Solving CPS on mathematics.

73. Creative problem Solving and Mathematics
In the year of 1988, Baer researched the long term effects of creative problem solving training in
mathematics. The experimental group which was given a training on how to solve problems
based on Osborn Parnes CPS model and the control group was given a pre-tests just like the
experimental group before the training. The control group wasn’t given any training at all. The
post-tests were made up of divergent and convergent ideas. The results showed that the
experimental group outscored the control group even after 6 months later. Kandemir and Gür
(2009) stated that the study of creative problem solving had been carried out in mathematics
education. It was based on the views from the prospective mathematics teachers by
investigating what they had learned during and after their participation in the creative problem
solving training. The prospective mathematics teachers explored the questions used in the
creative problem solving scenario and thus helped them to develop their students’ creative
problem solving thinking skills. As a result, the training helped the prospective mathematics
teachers understood creativity and how to apply it in their teaching in mathematics (Kandemir &
Gür, 2009). Kashefi, Ismail, Yusof and Rahman (2011) also investigated the effects of using
creative problem solving skills to learn engineering mathematics in a blended learning
environment. First year undergraduates students participated in this study with 59 of them in the
treatment group and 57 in the control group. The result showed that the students in treatment
group abled to use CPS skills to help them to learn engineering mathematics

75. Qualitative educational research method was chosen as a methodology to
explore and understand how the students can use solve mathematics problems
by applying all the procedures in creative problem solving. This research can
also be used to study how students can solve problem collaboratively together
with the help of their peers The instrument of the research is based on the
literature review of CPS and problem solving in mathematics. A qualitative
research design for in CPS is drafted and generated. It is used to design a
framework for the implementation of the research. The instruments are tried
to uncover the procedures in the creative problem solving based on theoretical
framework to ensure that they all fit the purpose of the study. The qualitative
data will be collected and analyzed later.
Research methodology

77. Research Design
This research study employs a qualitative design. First, we would
like to know the results of students who use creative problem solving to
collaboratively solve mathematical problem with the support of their
peers. The quantitative data of the research study will be used to support
the qualitative data of the research. The quantitative data will be
collected from the analysis of the coding of qualitative data collected
from interviews, observation and documents analysis.

79. Population and Sample
This research study employs purposeful sampling as to help us to identify information-rich
cases (Suri, 2011). According to Patton (2005), purposeful sampling can help us to learn a great
deal of the information by focusing in depth on the carefully and purposely selected sample.
This is used to help us to understand how students using their strategies and creativity to solve
open-ended mathematical problems. There will be an intervention of creative problem solving in
mathematics after the students have solved the first problem in the process of mathematical
problem solving. The students will have to use all the stages of creative problem solving to solve
their second mathematical problem. Therefore a CPS training program is used to help the
students to get familiar with all the processes of CPS. A lesson plan is provided as a guide for
the instructor as well as the students. At last, their results will be assessed by using a rubric for
assessing CPS in mathematics. The students will be selected based on their willingness to
participate in the research. According to Olcay Sert (2005), pair work can contribute in students’
learning as they can check each other mistakes in their work and thus they can come out with a
good quality of work. Think-aloud strategy is also used in this study as Van Someren and others
(1994) stated that think-aloud method is very useful as it is a very direct way to understand
people in their problem solving. The method can also help other people to understand his or her
cognitive process of problem solving (Van Someren, et. al, 1994).

81. Instruments
The first instrument is used to find out the students’ creativity in solving the
mathematical problem. This instrument is based on the Lumsdaine’s Creative
Problem Solving. Students in a group of two are required to work out the
mathematical problem collaboratively. The students can use different strategies
to solve the open-ended mathematical problem and they are also required to
provide their solutions with their own explanations and sketches to be used for
further document analysis. They will be interviewed after they have solved the
open-ended mathematical problem to find out their opinions and ideas to use
their strategies and creativity to solve the mathematical problem. The second
instrument is interview questions are created in order to understand in depth the
students using their strategies and creativity to solve open-ended mathematical
problems.

83. Data Collection
Survey questionnaire is
used to collect quantitative data
as to understand how students
using their strategies to solve
mathematical problems. This
can be used to find out what
will they do before, during and
after solving the mathematical
problems. There are also three
qualitative data collection
methods used in this research
such as semi-structured
interviews, observations and
document analysis.

85. Open-ended mathematical problem is used to
determine the mathematical creativity of the
engineering students and their works will be
collected as documents for document analysis.
Document analysis, interview and observation are
used to determine whether the mathematical
creativity of engineering undergraduates is improved
after they have employed creative problem solving
strategies to solve open-ended mathematical
problems. All the three different instruments are
also used to help to triangulate the data. The
qualitative data will also be analysed from the semi-
structured interviews, observation and document.
These are thick and rich descriptions of personal
perceptions and point of views which are very useful
in understanding how the students solve the problem
creatively and critically.
Triangulation Of Data

87. An interview is conducted to understand the students’ opinions regarding their uses of
different strategies in solving mathematical problems. It is the best way to look into their
mathematical thinking and ideas to carry out the process of problem solving. Semi-structured
questions are used in the interview to investigate students’ ideas and planning in the process of
problem solving, so that we can get deep understanding in the investigation.
Observation is used to get deeper understanding than interview, this is because we can use
observation to capture moment, gesture and expression that participants themselves are not
aware of during their interactions in the group discussion. Participants are required to use
their creativity and strategies to solve the mathematical problems .
Document is another source of data that can help us to get even deeper understanding of
students’ interactions. These documents are students’ works, drawing, sketch or projects
which can provide evidence used for analysis. In the pilot study, the students work out the
problem in the whiteboard as recorded in the observation. .
Qualitative Research Study

89. Data Analysis
All these qualitative data are then combined at the end of data collection to verify the
results by means of triangulation in order to study the use of creative problem solving in
mathematics. With the help of these different methods, it can provide a richer and more
authentic description of the fields to investigate. In order to find out how the students are
going to use creative problem solving in their mathematical problem solving, we have to get
some understandings of the students’ interactions and discussions by using these methods to
get significant insight into their discussions, solving problems and building of knowledge
through mathematical thinking. Therefore, at the end of data analysis, we can get deeper
understanding of their thinking skills in using creative problem solving in mathematics. All
the qualitative data will be collected can therefore help us to uncover and to understand the
findings.
During the analysis procedure, all the significant quotations and patterns from the
conversation will be retained and the rest of them will be filtered out. The results will reveal if
there is a relationship among these qualitative data. Then, a conclusion will be drawn after
interpreting and analysing the findings.

91. Limitation of the Study
A study of group learning such as creative problem solving has been researched
interdisciplinary and internationally to find out the impact of learning among the
students in various fields of studies such as business, science, accounting and art.
However, the impact of the using creative problem solving to enhance learning in
mathematics among the students remains a challenge for the researchers to find out.
There is very little prior research has been studied creative problem solving in
mathematics and therefore, this research is carried out based on exploratory research
design to understand the effects of the using CPS in mathematics. Another limitation is
the small sample size with only one class of 25 students, the researcher can only use
qualitative research to understand how the students using creative problem solving skills
to solve open-ended mathematical problems collaboratively and there is a need and
great opportunity for future research.

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98. Comparison between PBL and CPS

103. Creativity Problem
Solving CPS was
developed over the years.
It started with Alex
Osborn who was the
founder of Creative
Education Foundation.
He outlined the seven
stage process of CPS
such as orientation,
preparation, analysis,
hypothesis, incubation,
synthesis and verification
in the first version of 1.0
of CPS in the year of
1952
CPS (Creative Problem Solving) Version 1.0

104. In the latest version of 6.1 of CPS, it
was developed into a system for carrying
out decision in the process of generating
outcomes and results. It also allows the
integration of other frameworks and tools in
the process of CPS. The appraising task and
designing process were also integrated in
the system. There were four elements in the
appraising task such as understanding the
people involved, understanding the desired
result, understanding the situation and
understanding the process option. The
designing process included the need
(components, stages and tools), scale
(session, project and initiative) and level
(individual, group and organization)
(Isaksen & Treffinger, 2004).
CPS (Creative Problem Solving) Version 6.1

105. In his book “Creative Thinking and Brainstorming”, Rawlinson (1981) pointed out that
creative thinking can be used to relate previously unrelated things or ideas which were already
existed. New ideas can be generated by making a connection of two or more existing
concepts or unrelated things. According to Rawlinson (1981), we don’t create new thing out
of nothing but just to change the old into new. Creative thinking can help us to find a
solution. This is because creative thinking is divergent, lateral and required to use imagination
to generate as many possible creative solutions with wild, unusual and even crazy ideas
(Rawlinson, 1981).
In his book “The Art of Creative Thinking”, Adair (1990) told us that creative thinking
require us to think in an opposite direction. He also mentioned that the process of making the
familiar strange can help us to develop creative thinking. Thus, we can aware of the new idea
in an old situation. We have to think outside the box and not allow our minds to be
constrained by our own preconceptions. Creative thinking can add wings to our imaginations
and break away from our own preconceptions. Creative thinking is a way of finding out
something new in our familiar situation (Adair, 1990). We get used to think in one way
direction and reverse thinking can help us to increase the ability to generate more new ideas.
We can also assimilate the strange with our familiar understanding is the process of making
strange familiar (Adair, 1990).

106. Meta Analysis of Creative Problem Solving
A meta-analysis is used to find out the effects of using creative problem solving.
These can be used as dependent variables in further study and thus independent
variable can be found after carefully examining their relationship. IEEE Xplore
Digital Library, UTM database library, Web of Science, Science Direct and
ProQuest were used as search enginee. Keywords such as creative problem solving,
creative thinking, creativity and problem solving were used to find out the relevant
materials.
The results showed that there is very little literature regarding creative problem
solving in mathematics. However, the effects of using creative problem solving in
other fields of study can be used as reference to support the findings. A meta-
analysis table is drawn based on the literature review of creative problem solving
and shows that creative problem solving can be applied in many fields of study
such as science, technology, art, design, engineering and accounting. The results
also shows that creative problem solving can be effectively applied in different
fields.

136. A framework would be a structure which will guide what you are going
to do, what concepts you will deal with. However, a model may seem to
be similar yet it contains variables which have been tested and are
supported by theories
a framework indicates the perspective you are using to approach
educational research. For example, your investigative framework might
suggest whether a quantitative or a qualitative approach is best for
addressing your research question. A model, though, is developed
within a framework. Your model is a descriptive tool that might, for
example, help you impose some order on how variables are potentially
interrelated so you can begin to formulate questions aligned with your
chosen framework. Theories are different. They can emerge from
models but they are prescriptive, not merely descriptive; therefore,
they can be tested.