Enhancing students’ mathematical creative problem solving

Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.4, No.11, 2014
44
Enhancing Students’ Mathematical Creative Problem Solving
Ability Through Situation-Based Learning
Isrok’atun1*
Tiurlina2
1. Indonesia University of Education, Jl. Dr Setiabudi No. 229, Bandung, 40154, Indonesia
2. Indonesia University of Education, Jl. Dr Setiabudi No. 229, Bandung, 40154, Indonesia
* E-mail of the corresponding author: isrokatun@gmail.com
Abstract
Learning activities which emphasize more on answering questions than presenting questions have caused
students’ lack awareness to encounter some problems. The situation of the students’ weak problem finding
competence leads to their weak idea finding and problem solving. As a result, Creative Problem Solving (CPS)
ability necessarily has to be developed in learning mathematics. There are six aspects of CPS competence as
parts of thinking process stages, namely: objective finding, fact finding, problem finding, idea finding, solution
finding, and acceptance finding. In this case, to learn mathematics is about to explore the ability to present and to
solve the problems emerged by the students themselves, applying Situation-Based Learning (SBL). This research
used quasi-experimental design with experimented and controlled groups. The experimented group was
examined using SBL learning while the controlled one using conventional learning. Based on the research result,
it can be concluded that the enhancement of students’ mathematical CPS ability who were taught under SBL
learning is higher than those who were taught under conventional learning. Fact finding is the highest aspect of
the students’ mathematical CPS ability, and the lowest aspect is acceptance finding.
Keywords: Mathematical situation, Mathematical problems, Mathematical creative problem solving,
Situation-based learning
1. Introduction
Thinking has become a part of humans’ mental activities whether they face problem or certain situation which
needs to be solved. However, not all people possess similar point of view to encounter some problems in that
certain situation. The cause is that someone’s knowledge background may really influence his/her point of
view on particular situations. One situation could be crucial for him/her, but not for other people who do not
realize that it may become big problem for them. In the other words, one situation may become someone’s
complicated problem or not.
One situation will be identified as a problem for someone if he/she realizes the existence of the situation, admits
that the situation needs action and then immediately figures out that the situation is unsolved (Newell and Simon,
1972); (Yee, 2002); (Hamzah, 2003); (Dindyal, 2009); (Kaur and Yeap, 2009). Problem is thing that needs action,
but difficult or confusing (Schoenfeld, 1992). Hayes supports the previous opinion by stating that problem has
created gap between recent condition and goal to achieve when we do not know exactly what should be done to
reach the goal (Hamzah, 2003). In this case, problem can be defined as question that must be answered exactly
at that time while we do not have any fixed solution plans.
Treffinger, Isaksen, and Dorval state that problem is ‘… any important, open ended, and ambiguous situation for
which one wants and needs new options and a plan for carrying a solution successfully’ (Steiner, 2009). A
problem is known as open ended since it gives so many various options, or in the other words, the answer is not
figured out in singular option or one solution only, but also in many ways. Therefore, it does not rely on true
answers but on how the process to answer the problem goes. And, all answers may be possibly true. While one
situation is stated here as ambiguous, it can be interpreted that the situation is not meant singular but consists of
much understanding. So, it needs various solutions to solve the problem in order to interpret the situation
significantly.
Someone will be able to solve a problem if he/she has adequate ability to do so. According to Utari-Sumarno, the
importance of students’ mathematical problem solving competence becomes objective of teaching Mathematics,
even becomes the heart of Mathematics (Soekisno, 2002). In Education-Unit-Based Curriculum (a.k.a.
Kurikulum Tingkat Satuan Pendidikan or KTSP for short) (Depdiknas, 2007), it states that objective of learning
mathematics is to develop problem solving competence.
During teaching-learning activities in the classroom, however, teacher frequently asks his/her students too many

Vol.4, No.11, 2014
45
questions with low level. Learning method used commonly emphasizes on answering instead of presenting
problems. So, the method is not proper to develop the students’ awareness on problem and competence on
problem solving. Therefore, Creative Problem Solving (CPS) competence needs to be developed in learning
mathematics. In this case, mathematical CPS ability consists of: 1) objective finding; 2) fact finding; 3) problem
finding; 4) idea finding; 5) solution finding; and 6) acceptance finding. For every aspect of competence,
students start their learning by divergent thinking activities and end by convergent ones (Ellyn, 1995); (Mitchel
and Kowalik, 1999); (Proctor, 2007); (Isrok’atun, 2012a).
In order to develop the competence, learning mathematics has to explore the students’ competence on presenting
and solving the problems creatively proposed by the students themselves. One of learning methods used to
overcome the problems is Situation-Based Learning (SBL). SBL learning process can be applied through a set of
designing materials based on situation-based learning so that the students are able to develop their creativity and
thinking productivity further. Teacher’s roles here are merely as motivator and facilitator.
1.1. Research Question
The problem proposed in this research: Is the enhancement of students’ mathematical CPS ability who were
taught under SBL learning is higher than those who were taught under conventional learning?
1.2 Situation-Based Learning
Situation-Based Learning is a strong, flexible and new learning approach intended to develop constructive
learning paradigm (Tarek, Thomas, Hermann, and Maja, 2000). Lave; Lave and Wenger; Greeno, Smith, and
Moore assume that there are many things student learns from a situation, like where he/she studies (Anderson,
Reder, and Simon, 1996). The objective of SBL is to develop students’ ability on problem posing, problem
understanding, and problem solving through mathematics point of view.
Situation-Based Learning consists of four learning process stages, namely: 1) creating mathematical situations; 2)
posing mathematical problem; 3) solving mathematical problem, and 4) applying mathematics, being described
as follows (Xia, LÜ, Wang, and Song, 2007); (Xia, LÜ, and Wang, 2008); (Isrok’atun, 2012b); (Isrok’atun,
2012c).
Figure 1. Situation-Based Learning
Creative mathematical situations are prerequisite. Posing mathematical problem is core. Solving mathematical
problem is goal. Meanwhile, applying mathematics is the application of learning process to new situation.
There are four SBL learning strategies, such as (Isrok’atun, 2012d):
(1) Teacher creates situation
Teacher creates mathematical situation. It is expected that there are some mathematical questions asked by
students through activities of observing and analyzing. Here, the situation starts from firstly simple one to
more complex one.
(2) Students pose mathematical problems
By investigating and guessing, students implement mathematical problem posing. It is intended to increase
their awareness on problems of situation they have faced. Teacher’s role here is to place problems proposed
by students at certain levels based on difficulty grades.
(3) Students practice mathematical problem solving
At the second learning step, teacher and students sort existing problem levels, whether the problems need to
be followed up or not. Solved problems start from simple ones to complex ones. As learning materials, the
main objective here is to emerge problems that require problem solving with mathematical CPS competence.
In this strategy, teacher’s roles are to guide, to direct, and to stimulate students by implementing scaffolding
techniques.
(4) Applying mathematics

Vol.4, No.11, 2014
46
The strategy of applying mathematics is hoped to become students’ positive habit so that they can find out
the way to solve every mathematical problem. After students conduct SBL strategies in the classroom, it does
not mean the end of everything. In daily life, every student is obliged to continue applying the strategies as
part of his/her character whatever, wherever and/or whenever he/she faces certain situation or problems. The
students become more critical to view a problem which exists in every situation.
1.3 Conventional Learning
In this research, conventional learning is teacher’s learning model which limits students’ roles during the process
of teaching-learning activities. Teaching method is teacher-centered and learning process emphasizes more on
expository method.
1.4 Mathematical CPS Ability
The ability of mathematical CPS has six aspects, each of aspect begins from divergent activity and ends by
convergent activity. The aspect of mathematical CPS ability such as (Ellyn, 1995); (Mitchell and Kowalik,
1999) ; (Proctor, 2007); (Isrok’atun, 2012a). Osborn-Parnes creative problem solving process:
(1) Objective finding
Effort to identifying the situations to become more challenging form.
(2) Fact finding
Effort to identifying all the data which is still related to the situations context, finding and identifying an
important information that didn’t contain in the situation, but it is important.
(3) Problem finding
Effort to identifying of all possible problems, and then sorting which are important.
(4) Idea finding
Effort to identifying several solutions which is possible for the statement problem.
(5) Solution finding
Using a list of solutions that have been on the stage of idea finding, and selecting the best solution to
resolve the problem.
(6) Acceptance finding
Effort to increase the capacity, planning an action, and implementing the solutions.
For further explanation about CPS thinking process, see on picture below (Isaksen and Treffinger, 1985):
Figure 2. The Flow of CPS Thinking Process

Vol.4, No.11, 2014
47
2. Experiment
2.1 Purpose
The research aims to figure out whether students’ mathematical CPS ability using SBL learning is more
improving than those ones’ using conventional learning.
2.2 Sample and Population
Research population was all SD (elementary school) students in the Province of Banten, Indonesia with
medium-leveled elementary school category. Based on the category, SD Negeri 9 Kota Serang was chosen as the
research subject. The sample were grade 5 because grade 5 can be deemed to have been invited to think more
highly (high-order mathematical thinking skills, is the mathematical CPS ability) than previous classes, and are
not preoccupied with preparations for the National Examination (UN).
Two classes were randomly selected among all classes of Class 5. One class was treated as experimented group
(Class 5A, with 47 students were examined using SBL learning) and the other one as controlled group (Class 5B,
with 47 students were examined using conventional learning).
2.3 Research Design
The research was quasi-experiment using experimented and controlled groups recognized as pretest-post test
control group design (Fraenkel and Wallen, 1990); (Ruseffendi, 1998); (Sugiyono, 2011). The experimented
group was treated using SBL learning and controlled group was treated using conventional learning. The
research design is described as follows:
O X O
O O
Note:
O = pretest = post test on mathematical CPS ability
X = SBL learning
3. Research and Discussion
After two classes had been treated differently, one group using SBL learning and the other one using
conventional learning, the research result of students’ mathematical CPS ability was performed as follows.
Table 1. Mathematical CPS Ability
Learning n
Pretest Post test Gain Gain
CategoryAverage S.D Average S.D Average S.D
SBL 47 16.32 11.58 32.91 14.38 0.24 0,16 low
Conventional 47 16.21 7.82 24.66 9.56 0.12 0,12 low
S.D = standart deviation
Based on pretest result, two groups started from significantly same mathematical CPS ability (after examined
statistically). The students’ mathematical CPS ability average treated with conventional learning (16.21) and
than ones’ with SBL ability (16.32). Though post test was later conducted, the student group’s average of
mathematical CPS ability treated with SBL learning was highly achieved, 32.91.
Both groups experienced improvement (gain) of significant mathematical CPS ability. The student group’s
average of mathematical CPS ability treated with SBL learning (0.24) was more improving than one’s with
conventional learning (0.12). So, the group with SBL and conventional learning was determined as
low-categorized.
3.1 Hypothesis Testing and Statistical Significance
To prove which group is better, whether the student group with SBL learning or the other group with
conventional learning, statistical test is urgently required. The statistical test result is as follows:

Vol.4, No.11, 2014
48
Table 2. Statistical Test Summary on Mathematical CPS Ability Gain
Learning n
Gain Statistical test Mean Difference Test
(Mann-Whitney)Average S.D Normality Homogenity
SBL 47 0.24 0.16 Normal Varians not
same
Both means were
differentConventional 47 0.12 0.12 Not normal
Note:
The table above explained that the student group with SBL learning was more significantly improving than the
other one with conventional learning.
Therefore, it can be concluded that the student group examined using SBL learning got more exceeding result
than the controlled group though the experimented group had got lower result at the beginning. It clarifies that
students’ mathematical CPS ability with SBL learning is better than ones’ with conventional learning.
The explanation acquisition of student’s score in experimental class if viewed each aspect, which one is strongest
or weakest of student’s mathematical CPS ability, describe as:
Table 3. The Students’ Mathematical Ability CPS in Experimental Class
Viewed each individual aspects
Aspect of mathematical CPS O F P I S A
Frequency 5 5 3 5 4 2
The maximum score 3 3 4 4 4 4
The score for item: - - - - - -
1 51 49 - 51 42 36
2 36 20 23 23 - -
3 56 56 66 59 54 -
4 41 38 - 38 24 22
5 10 73 6 45 45 -
Sum 194 236 95 216 165 58
% for CPS aspect 28 33 17 23 22 15
Information:
The strongest aspect : Fact finding
The weakest aspect : Acceptance finding
The table above explained that the percentage gain scores on students’ mathematical CPS ability viewed per
aspect. The strongest aspect is the fact finding aspect (33%). Fact finding is an effort to collection of the data
which related the problems and to exploring facts of situations, it’s indicates an to be able to relating; to
connecting about the problems and to exploring; to organizing; to caring the hiden information of situation. The
weakest aspect of mathematical CPS mathematical CPS ability is the acceptance finding aspect (15%). It’s an
effort to increase the capacity of the answers obtained, planning an action to solve it, and implementing a
solutions. It indicates the ability to acting the completion, considering the support acquisition the previous
answers, and expressing the plan of the support answers.
4. Conclusion
SBL learning is a kind of learning consisting of four learning process stages, namely: 1) creating mathematical
situations (prerequisite); 2) posing mathematical problem (core); 3) solving mathematical problem (goal), and 4)
applying mathematics (application).
This SBL learning can be one of learning alternatives in order to improve students’ mathematical CPS ability.
Deriving from problems proposed by students, teacher plays role to guide them solving problems by applying
mathematical problem solving techniques. Therefore, students’ problem posing and problem solving are well put
in balance.

Vol.4, No.11, 2014
49
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