The Effects of Media based on Open Ended Problem to Enhanced

Creative Thinking Ability

Sri Hastuti Noer

and Pentatito Gunowibowo

Faculty of Teacher Training and Education, University of Lampung

Keywords: Creative Thinking, Open-Ended, Problem based Learning.

Abstract: A quasi-experimental study with the pre-test post-test control group design was conducted to determine the

effect of media based on open-ended problem in Problem Based Learning (PBL). The population of the study

was students of grade VIII of Junior High School in Bandar Lampung city. Sampling was done by stratified

purposive random sampling technique, to select one high-rank school and one low-rank school randomly from

31 schools in Bandar Lampung City. Furthermore, from each of the selected school, two classes were taken

randomly. One class was the experiment group and one class was the control group. The experimental class

obtained a PBL facilitated by media based on open-ended problem; meanwhile the control class obtained

conventional learning. The research data were obtained through the test of mathematical creative thinking

ability. The results showed that students' creative thinking ability in PBL facilitated by media based on open-

ended problem at high-rank school and low-rank school had averaged 73.78 and 76.71 respectively. Students'

creative thinking abilities in conventional learning had averaged 65.43 and 63.96, respectively. Hypothesis

testing showed that there are significant differences in creative thinking ability between students in two group.

So that the media based on open-ended problem in PBL has a positive influence on students' mathematical

creative thinking ability

1 INTRODUCTION

Reformation in mathematics learning implies that

students must be a self-directed learner.

Independence in learning is an integrated learning

process, containing a set of constructive behaviors

that affect learning. Students can build a deep

understanding of the content of mathematics to build

their high-order thinking skills, if they can control the

learning process. It can be obtained when the learning

experience gives them the opportunity to do so.

Students’ learning experience is largely

determined by the learning activities designed by

teachers and media used by the teacher. Therefore,

the teacher should design the activity and choose the

right model for the students. Selection of learning

models and appropriate media will affect students'

understanding of the subject matter. In mathematics,

students 'understanding of the material being studied

will affect students' understanding of the next

material.

One of the abilities that is expected to be appeared

on students after learning of mathematics is the ability

to think creatively. This ability is very important

about the student's ability to solve problems.

Therefore, the development of these capabilities

needs special attention in the study of mathematics,

especially in junior high school. But in general, the

ability to think creatively of junior high school

students is still low. This is reflected in the low

percentage of correct answers of students in the

international studies Trends in International

Mathematics and Science Study (TIMSS) and the

Program for International Students Assessment

(PISA). In the TIMSS study, the student is weak in

solving non-routine problem related to justification or

evidence, solving problems that require mathematical

reasoning, finding generalizations or conjectures, and

find relationships between data or facts provided. In

the PISA study the student is weak in using

mathematics to solve problems in everyday life. The

development of creative thinking abilities needs

serious attention, because several studies, for

example (Henningsen,1997; Mullis et al, 2000)

showed that the learning of mathematics in general

are still focused on the development of lower stage of

thinking skills. In addition, research (Noer, 2010a;

Noer, 2010b; Noer, 2011; Noer, 2007a, Noer, 2007b)

448

Noer, S. and Gunowibowo, P.

The Effects of Media based on Open Ended Problem to Enhanced Creative Thinking Ability.

DOI: 10.5220/0008523504480454

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 448-454

ISBN: 978-989-758-407-7

suggests that problem-based learning and open-

endedlearning can be used to improve a wide range of

mathematical skills, particularly in increasing

mathematics high order thinking skills.

Addressing problems that arise in mathematics

and hopes to achieve in mathematics, innovative

efforts are needed to mitigate them. Students must be

accustomed to construct knowledge and is able to

transform the knowledge to other situations are more

complex. In this way, the knowledge will be their

own. One of the learning models that was chosen to

address the problem above is problem-based learning

(PBL). Hmelo-Silver (2004) said that PBL is a

learning method that facilitates student learning

through solving the problem at the center of learning.

Issue raised in the PBL is complex and does not only

have one correct answer (open-ended).Students work

in collaborative groups to identify what they need to

resolve the issue, involving students in independent

learning, applying the knowledge they have on the

issue, and reflecting on what they learned and how

effective the strategy used. Based on the developed

the model of learning media base on open-ended

problem and learning tools to improve students'

mathematical creative thinking ability.

2 METHODS

The population in this experimental research was all

Junior High School students in Bandar Lampung city.

Samples were determined using stratified purposive

random sampling to select one high-rank school and

one low-rank school. From a group of high-rank

schools, subject sample was students of SMPN 19

Bandar Lampung. From a group of low-rank schools,

subjects’ sample was students of SMPN 22 Bandar

Lampung. Furthermore, from these two schools, two

classes are chosen; one class as an experiment class

and one class as a control class. The two selected

classes, previously tested, have the same initial ability

using two similarity tests on average with the t test.

Experiment class receives a PBL facilitated by media

based on open-ended problems and control class

receives a conventional learning. The media used is

the student worksheet, which contains the activities

of students to achieve the concept of mathematics

through the PBL stage, which begins with the giving

of problems that are open-ended both in the process

of finding the concept and in the exercise. The

subjects of this study were 106 students from two

selected schools where selected randomly (51 student

from experiment class; n1= 24, n2= 27; and 55

students from control class, n1= 24, n2= 27). Data

were obtained through an essay test of mathematical

creative thinking ability. This test is given to students

before and after learning, either in the experiment

class or control class. As an illustration, here is an

example of the creative thinking problem used in this

study.

“In a school, the road to the cafeteria is parallel to the

road to the library, and the road to the teacher room is

perpendicular to the road to the library. if the school

plan has been made in the Kartesius-plane and the

road to the cafeteria satisfies the equation: 2x - y - 10

= 0.

a. Determine the slope of the line that represents the

path to the library?

b. If the teacher's room is in coordinates (7, 3),

determine the equation of the line that represents

the path to the teacher's room”.

The student's answer score is based on indicator of

creative thinking ability, i.e.: sensitivity, fluency,

originality, flexibility, and elaboration. Before the test

is used, instrument is tested first to find out the

validity, reliability, distinguishing power, and

difficulty level. Furthermore, to know the influence

of media based on open-ended problem in PBL to

creative thinking ability, then tested the hypothesis,

that is test of difference of two mean using t-test. The

results of statistical tests are interpreted and analyzed

for conclusion.

3 RESULTS AND DISCUSSION

3.1 Result

Based on the data processing from the creative

thinking ability test, obtained score of creative

thinking ability of students as presented in Table 1.

Table 1 show that the mean average score of students'

mathematical creative thinking ability on high-rank

or low-rank school that used PBL facilitated by media

base on open-ended problem, higher than

mathematical creative thinking abilities of students

who received conventional learning.

Table 1: Creative Thinking Ability Score.

Research

Group

MIS

Exp -1

112

108

76.71

22.66

Cont-1

112

63.96

12.02

Exp-2

100

73.78

18.85

Cont-2

100

65.30

17.38

Note: Exp-1: experiment class on low-rank school

Exp-2: experiment class on high-rank school

MIS : Maximum Ideal Score

The Effects of Media based on Open Ended Problem to Enhanced Creative Thinking Ability

449

From the data that has been described in Table 1,

then several hypotheses related to improving Creative

Thinking Ability. For this purpose, the normality test

and variance homogeneity test are first carried out.

The test results show that the data on students'

Creative Thinking Ability in the experimental class

and control class for high-rank and low-rank schools

are from the population not normally distributed.

Next, to test the average difference in creative

thinking ability were used t-test. The hypotheses

tested are:

: μ

= μ

(There is no difference in the average

of the two sample groups)

H1: μ

≠ μ

. (There are differences in the average

of the two sample groups)

Test criteria: Reject H

if with a significance level

of 0.05, the value of t-

count

is greater or equal to the

value of t-

table

. Summary of test results is presented in

Table 2.

Table 2: t-Test Results Summary.

Rank

School

Average of

Creative

Thinking

Ability

value

Sig.

Conclusio

PBL

Conv.

Low

76.71

63.9

2.47

0.02

Rejected

High

73.78

65.3

1.69

0.02

Rejected

Based on data presented in Table 2, the value of

the probability (sig.) at low-rank school and high-

rank school for both the learning model is smaller

than 0.05. This means that the null hypothesis is

rejected. This means that, there are significant

differences between the scores of mathematical

creative thinking abilities of students between the

experimental group and the control group at both low-

rank school and high-rank school. Given that the

average value of creative thinking abilities of students

in the experimental group was higher than the average

value of creative thinking abilities of students in

control group, it can be concluded that the average of

creative thinking ability of students in PBL with

media base on open-ended problem is higher than the

average of creative thinking abilities of students in

conventional learning.

3.2 Discussion

The results showed that student mathematical

creative thinking ability in PBL higher than student

mathematical creative thinking ability in

conventional learning. This is in accordance with the

characteristics of PBL. PBL describe learning

environment which encourages learning problems.

Learning begins with a problem to be solved. The

problem posed is a means for students to gain new

knowledge before they can solve the problem. In

PBL, students interpret the problem; collect the

information needed, identify possible solutions,

evaluate options, and provide conclusions. Some

experts in mathematical problem solving said that

students would be a good problem solver by studying

the mathematical knowledge heuristically. The

successful experiences of students in managing their

own knowledge also help them to solve math

problems correctly (Schoenfeld,1985; Boaler, 1998).

This is because the experience of students in

managing their knowledge to solve problems will

provide confidence to solve other problems, either

relatively similar problems or more complex.

Problem-based learning is the strategy classes that

contain problem-solving activities and enable

students to think critically, think creatively, and

communicate with their colleagues mathematically

(Krulik& Rudnick,1999; Lewellen& Mikusa,1999;

Erickson, 1999; Carpenter et al, 1993; Hiebert&

Carpenter, 1996;Hiebert et al,1997).

Another thing is the reason why students in PBL

have better learning outcomes is the use of media-

based on open-ended problems. Open-ended problem

is a problem that has few or many answers correct.

Through solving the problem, students are expected

to understand the concept learned. Students are not

only required to show the results of their work but are

often asked to explain how they got the answer. When

they use the open-ended based media, they discuss

with their friends. This activity makes students more

actively learn and dare to express their ideas, to solve

the problem. An important goal in PBL is for students

to be responsible for their own learning process. The

PBL literature suggests that the development of self-

directed learning can be used to improve content

knowledge and encourage problem solving,

communication and critical thinking skills (Hmelo-

Silver, 2004). Schmidt et al (2011), also refers to

studies that show that students in PBL become more

self-reliant during the study compared to students

who do not study with PBL.

Several studies have shown that PBL is effective

in improving student learning, compared with the

traditional teaching (Schmidt et al, 2012). In a study

involving 47 students are enrolled in vocational

nursing program (Mathews, 2011), found that

problem-based learning increases students'

knowledge and ability to apply that knowledge.

ICMIs 2018 - International Conference on Mathematics and Islam

450

Kennedy (2007), found similar results in a study of

the pathophysiology of students in advanced courses.

Both of study compared PBL with traditional

teaching methods and concluded that problem-based

learning in order to improve the learning and

application of learning it in other contexts.

Research shows that students' mathematical

creative thinking ability in PBL facilitated by media

base on open-ended problem is significantly better

than conventional learning; both of high and low-rank

school. This means that the learning approach and the

school ranking influence the students' mathematical

creative thinking ability. Students at high and low-

rank schools are more successful in enhancing

mathematical creative thinking ability in PBL that

facilitated by media base on open-ended problem than

students in conventional learning.

Some research on the application of PBL that

strengthen and complement previous research on

PBL, among others, research conducted by Abdullah

et al (2010), that the study indicated that PBL is just

as efficient as the conventional teaching strategy in

enhancing the Form Four students' mathematics

performance. Even though both groups of students

have positive perceptions towards group work,

interest in mathematics and perception towards the

learning experience they went through, the PBL

group used the Polya’s problem solving procedures

more effectively, presented better mathematical

communication skills and showed stronger teamwork

than to the conventional teaching group. Tarmizi and

Bayat (2012), state that there are significant positive

effects on the students' meta-cognitive awareness and

on students’ motivation level after undergoing PBL

intervention. Malan et al (2014), state that

Introducing PBL into a foundation program can

develop self-directed learning skills in students and

set in motion a process of growth towards lifelong

learning. Padmavathy&Mareesh (2103), states that

PBL should be adopted as an alternative instructional

strategy to the Traditional Method in enhancing

meaningful learning in PBL into the pre-service

teachers' curriculum at the teacher-preparation

institutions in Nigeria.

Based on the characteristics of PBL and

conventional learning, it is fairness if there is a

difference in the ability of students after following the

lesson. PBL initiated its activities by presenting the

contextual problems to the students. Then through

group discussions, students organize their ideas and

knowledge related to the problem, the students ask

questions or issues around the problem. Students are

given the opportunity to state what they understand

and do not understand. The teacher looks at the course

of the discussion and if necessary, the teacher can

provide clues. In class discussions, these issues are

discussed together, and students integrate new

knowledge into the context of the problem. Teachers

also remind students to reflect on what they have

achieved. When time permits, presentations from

several groups are accompanied by frequently asked

questions.

The most dominant thing that causes the

increasing of students' mathematical creative thinking

ability is the use of media base on open-ended

problem. The media in this study has given students

the opportunity to hone their thinking skills. This

ability is honed when students are faced with issues

that are open and have a variety of ways or answers.

Such problems make students try to find, recognize

and answer the problem. This is in line with

Hashimoto's opinion, (Silver, 1997) says that open-

ended issues provide flexibility for students to come

up with answers. In this way, students can acquire

knowledge or experience of discovering, recognizing,

and solving problems with several techniques. In

addition to the use of a wide range of open-ended

issues, it can improve students 'flexible in math

capacities related to students' creative thinking

abilities.

The media used in this study is an activity sheet

which contains open-ended mathematical problems.

This open-ended problem is done by students both in

groups and individually. Through solving this open-

ended problem, students' creative thinking activities

can be facilitated. because the questions that are open

ended, require students to be responsive to the

problem, able to think in a variety of different ways,

bring up new ideas and apply various knowledge they

already have in solving problems, able to describe

answers in detail, and be able to provide an

explanation for the answer. This can be seen in

observations during the study.

The success of students in PBL is in line with some

research on the effectiveness of PBL and its benefits

for students. From several studies on PBL, it has been

concluded that there are two benefits to be gained: 1)

related to student reflection and learning

independence, and 2) positive affective results of

PBL. Regarding student reflection and learning

independence, PBL has shown cognitive and

metacognitive advantages for students in the

classroom. Downing et al (2009), concluded that PBL

activities have been positively associated with

metacognition development, directing students to

self-study (Blumberg, 2000a; Blumberg, 2000b).

Meta-analysis of the use of PBL in the classroom has

shown that PBL is consistently positive for improving

The Effects of Media based on Open Ended Problem to Enhanced Creative Thinking Ability

451

student skills (knowledge application) and long-term

knowledge acquisition (Dochyet al, 2003; Strobel &

van Barneveld, 2009), better learning strategies and

critical thinking (Sungur&Tekkaya, 2006; Stefanou

et al, 2013), flexible knowledge and problem-solving

(Hmelo-Silver, 2004). Related to the positive

affective results of PBL; including increased student

involvement in learning activities

(Ahlfeldt&Sellnow. 2005); better learning effort,

including time management, concentration and self-

examination (Wijnia et al, 2011). Furthermore, PBL

has also improved the value of secondary school

students' tasks and intrinsic goal orientation

compared with traditional instruction

(Sungur&Tekkaya, 2006), higher social and

academic integration, and satisfaction of their

relationship with faculty and peers (Severiens&

Schmidt, 2009). Hays & Vincent (2004) found that

students in undergraduate psychology courses, rated

that PBLs are good for promoting interaction between

students and faculty. In addition, PBL is inspired by

Piaget's different theoretical approaches as Piaget,

Lewin, Negt, Vygotsky, Kolb, Lave & Wenger,

Illeris(Kolmos et al, 2004). We have described how

PBL holds some very interesting educational

potential. Among others can be mentioned how

students get motivated by working with real-life

problems

Meanwhile, in the conventional learning the

teacher explains the subject matter in detail, giving

examples of ways to solve the problem. Students pay

attention to the teacher's explanation, and then record

what the teacher explained. Before the students take

notes, the teacher usually gives the students time to

ask questions about things that have not been

understood. If any student asks, the teacher

immediately explains the classical. Furthermore, the

teacher gives students the exercise questions done

individually. Meanwhile, teachers’ pay attention to

the way the students do the exercises and help guide

the students who are experiencing difficulties. After

completing the exercise, all students collect their

work to the teacher for grading. For the discussion,

some students are asked to work on the board.

In general, the implementation of learning with

PBL at high-rank school and low-rank school has

been running well. Based on the PBL format, the

steps taken in the classroom learning are appropriate.

This is reflected in group discussion activities, class

discussions, questioning and responding activities,

and presentation activities. All components in this

lesson can be well executed. PBL is a new learning

model for students and teachers in schools where the

research is conducted. Therefore, in the first and

second meetings, students are still confused and rigid

in carrying out the activities of each phase contained

in this lesson. But at the next meeting, the students are

already accustomed, without being asked they have

joined their respective groups to discuss the Student

Worksheet (SW).

In the first phase of orienting students on the issue,

the teacher asked several issues and activities that

should be done by the students and the students try to

understand the material by means of discussion. In the

second phase, which is organizing the students to

learn, teachers divide the students into groups

consisting of 4 or 5 people are heterogeneous. In this

activity, teachers distribute SW to each group and

said that if students have difficulty, the students are

given the opportunity to ask questions. Teachers

emphasize the student to put his own group ideas on

how to solve the problem. In the third phase of the

investigation that lead individuals and groups, the

teacher asks each group to resolve the issue in SW.

During the discussion, teachers monitor to each group

and directing students who have difficulty with

Scaffolding techniques. It appears that each group

actively discusses SW with discussion. This can be

seen in Figure 1. In the fourth phase of developing

and presenting the work, representatives from the

group present the results of the group discussion,

while the other group asks questions or responds if

there are different answers. Figure 2 shows one of the

group representatives presenting the results of the

group discussion. In the fifth phase of analyzing and

evaluating problem-solving processes, the teacher

help students reflect on or analyze and evaluate their

thinking processes and problem-solving results from

phase 1 to phase 4. The use of open-ended media

problems in this study provides an opportunity for

students to practice their creative thinking skills. This

can happen because open-ended problems require

students to be sensitive to issues that give and think

openly, be able to look at a problem from a different

point of view, able to elaborate their understanding of

the problem so as to obtain the correct answer (in

phase 1 to phase 3), able to express its own original

answer without hesitation (in phase 4 and phase 5).

This experience gives students the opportunity to

solve problems creatively.

ICMIs 2018 - International Conference on Mathematics and Islam

452

Figure 1: Focus group discussions in the PBL.

Figure 2: Presentation of the group in PBL.

4 CONCLUSIONS

Based on the results of data processing on research

conducted and discussion, it can be concluded that

the use of media based on open-ended problem will

facilitate the improvement of students' creative

thinking ability. Therefore, the construction of open-

ended problems is an important thing to be

considered in learning. Problems are created with the

aim of enabling students to look at things from

different perspectives, to be more flexible to a

thought or opinion. Media based open-ended

problems need to be developed in a planned manner,

such that through the open-ended problem students

can understand the concept of mathematics well.

Based on these conclusions, the following

suggestions can be put forward: (1) to the teacher, to

improve mathematics creative thinking ability, it is

advisable to use problem-based learning model in

learning mathematics. Teachers could develop

lessons plan and media base on open-ended problem

to other materials, at the school and other grades; (2)

to other researchers who want to develop advanced

research on the application of problem-based

learning model to improve students' mathematical

creative thinking ability, should pay attention to the

division of time in learning in order to obtain optimal

results.

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