The Level of Creative Thinking Skill in Graph Theory Application

Course

Sapti Wahyuningsih, Darmawan Satyananda

Universitas Negeri Malang, Malang Indonesia

Keywords: Application of Graph Theory, Problem Posing, Problem Solving, TTCT

Abstract: Graph theory can be applied to solve various life problems such as optimization of distribution cost, minimum

time routing, and project scheduling. In the Graph Theory Application course, one of the student’s project

tasks was a field survey to the industry / institution / company. From problems found, they identified and

solved problems, modelled problems in graph, and developed the solution design. The purpose of this study

was to identify the students’ level of creative thinking in posing the problem and designing for the problem

solving. To measure the level of creativity, Terrace Test of Creativity Thinking (TTCT) was adapted. Data of

the students' creativity dimensions (fluency, flexibility and novelty) in solving the problem of graph theory

were used to analyse the creative thinking level of students (very creative, creative, creative enough, less

creative, and not creative). From the data analysis, the students' creative thinking level in the Graph Theory

Application was dominant in level of creative thinking 3 i.e. the student was able to show fluency and novelty

or fluency and flexibility in problem posing and problem solving. For the creative thinking level 4 (very

creative) and level 1 (less creative) were in small percentage, and no student with creative level 0 (not

creative).

1 INTRODUCTION

In facing the era of globalization and the challenges

of 21st century education, it is necessary to have a

learning pattern that makes students have high skills

that involve critical, systematic, logical, and creative

thinking. Similarly to the challenges of the working

world that job seekers need to have are the ability to

work together in teams, master the technology, able

to communicate effectively and the most important is

to have problem-solving ability. Learning innovation

is needed to develop those abilities and meet the

demands of skills needed in the 21st century.

Graph theory is one of course in Mathematics

study program, State University of Malang, which has

wide application field in real life. The learning

achievement of graph theory application is a) able to

understand the problem and develop problem solving

algorithm, b) able to design mathematical model,

complete the model, and interpret the obtained

solution, c) able to plan and control the optimization

process in industry, decision making, and business.

(Catalogue of FMIPA UM, 2017). Characteristic of

the content of Graph Theory Application course is the

content can be used to solve a number of real-world

problems, hence the problem solving ability can be

incorporated into this course.

According to (Pehkonen, 1997) problem solving

is one way to encourage creativity as a product of

creative thinking because problem solving is useful in

developing cognitive skills, motivating learning math

applications, and encouraging creativity of thinking.

Some researchers linked the effects of problem

solving to creative thinking, such as (Kandemir, M

and Gür, 2009; Nozari and Siamian, 2014; Dostal,

2015; Kirmizi, Saygi and Yurdakal, 2015; Rodzalan

and Saat, 2015). Problem solving skills are also

needed to face the challenges of 21st century

education (Greiff et al., 2014).

In addition to problem solving, some researchers

suggest that assigning problem posing tasks can be

used to measure creativity of thinking (Leung, no

date; Stoyana and Ellerton, 1996; Silver, 1997).

Problem posing activity is also needed in

mathematics learning, as stated by (Akay and Boz,

2009; Cildir and Sezen, 2011; Şengül and Katranci,

2012; Kunimune and Niimura, 2014).

Creative thinking ability can be measured by

several criteria. According (Silver, 1997) to assess

creative thinking ability in adults can be done with

Wahyuningsih, S. and Satyananda, D.

The Level of Creative Thinking Skill in Graph Theory Application Course.

DOI: 10.5220/0008411403030307

In Proceedings of the 2nd International Conference on Learning Innovation (ICLI 2018), pages 303-307

ISBN: 978-989-758-391-9

303

The Torrance Test of Creative Thinking (TTCT). The

creativity dimension consisting of the three main

components considered in TTCT is fluency,

flexibility and novelty. Fluency refers to the number

of ideas created in response to a command. Flexibility

appears in the approach changes when responding to

commands. Novelty is the originality of an idea

created in response to a command. Some researchers

are adapting TTCT to identify the level of creative

thinking that is (Rababah et al., 2013; Turkey, 2018).

(Siswono, 2011) develops students' creative thinking

level in the mathematics classroom.

This article discusses about how to identify the

students' level of creative thinking in graph theory

application course. The method used adapted

(Siswono, 2011; Rababah et al., 2013; Turkey, 2018).

2 METHOD

The type of this research was descriptive qualitative.

The research data source was 25 students who

followed the lectures of the Graph Theory

Application in even semester of 2017-2018 academic

years. To identify student's creativity level, the

following methods were used. 1). Formation of field

survey groups and selection of applied graph

materials, 2). Preparation of survey proposals to

industry / institution, 3). Acquisition of field data, 4).

Formulation / modelling problems, 5). Create

problem-solving designs with various appropriate

algorithms.

The creativity level of students was identified

based on the creativity dimension (fluency, flexibility

and novelty). This level of student creativity was

observed from the problem posing and problem

solving they made based on the results of field

surveys. The level of creativity of students is

described as very creative, creative, creative enough,

less creative, and not creative.

3 RESULT AND DISCUSSION

3.1 Field Survey in Graph Theory

Application Course

Field survey conducted by students related to material

of graph theory application course. The main subjects

include are (1) Algorithm in the Traveling Salesman

Problem (TSP) variant and its application, (2)

Matching, matching in bipartition network, matching

in no bipartition network, and its application; (3)

Maximum flow, maximum flow algorithms and its

application, (4) Minimum cost flow, minimum cost

flow algorithms and their application, (5) Vehicle

Routing Problem (VRPPD), Vehicle Routing

Problem with Time Windows (VRPTW), Vehicle

Routing Problems with Simultaneous Deliveries and

Pick-ups (VRPSDP), Multiple Trip Vehicle Routing

Problems (MTVRP) and their implementation, and

(6) Network implementation for project scheduling

(FMIPA UM catalogue, 2017).

Some field surveys conducted by students in even

semester of 2017-2018 are: Optimizing the

Distribution of Newspapers Using Dynamic

Traveling Salesman Problem in Radar Malang,

Optimization of Employee Assignment in “Adi

Bungsu” Cigarette Factory using Bipartition

Matching Graph, Maximum Flow Implementation for

Distributing Product in PT Gatra Mapan Malang,

optimization route of newspaper distribution in radar

malang by using Vehicle Routing Problem With Time

Window (VRPTW), Implementation of Network

Analysis for Solving Project Scheduling Problem in

PT. Kharisma Menara Abadi Malang, Distribution of

Sosro Products Using Minimum Cost Flow Method

at PT Sinar Sosro Malang, Optimization of “Walls”

Ice Cream Distribution Using Capacitated Vehicle

Routing Problem at PT Lukindari Permata Malang.

An example of a graph model of a problem and

the result of a solution on a student assignment is

shown in Figure 1, 2, and 3.

Figure 1: Example of graph model of goods distribution.

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Figure 2: Solving TSP in software.

Figure 3: Example of TSP solution.

The Figure 1, 2, and 3 shows the model of the

route of newspapers distribution to a number of

agents in several areas in Malang. Searching of

minimum length route which passed all agents is

examined with Nearest Neighbor Heuristic

Algorithm, Nearest Insertion Heuristic Algorithm and

Cheapest Link Algorithm. In the modeled case, the

Cheapest Link algorithm provides better results than

the other two algorithms.

3.2 Creativity Dimension in Problem

Posing of Survey Result

Problem posing of survey results is a task for students

to create or formulate problems obtained from real

survey results, which then modeled and solved. The

steps taken are the students doing field survey,

finding problems, formulating the problem, and

making the draft solution. Problem posing and

problem solving can be used to measure the ability of

creative thinking (Silver, 1994, 1997) .The dimension

of creativity can be measured from three components

of creativity products, i.e. fluency, flexibility and

novelty.

3.3 Description of Students Creativity

Level

Instruments to determine the level of students’

creative thinking were adapted from Torrence Test of

Creative Thinking (TTCT) (Silver, 1997), the level of

creative thinking (Turkey, 2018), and level student's

creative thinking in classroom mathematics

(Siswono, 2011). Description of indicator of creative

thinking ability used in this research is

 Fluency (able to model and solve problems

with various problem interpretations or

answers).

 Flexibility (able to solve problem and to

discuss in various methods or algorithms), and

The Level of Creative Thinking Skill in Graph Theory Application Course

305

 Novelty (able to check or analyze a number of

methods or algorithms, and to implement new

algorithm or methods)

Of the indicator components above, the creative

thinking level can be described as follow.

 Creative thinking level 4 (very creative)

 Students are able to demonstrate fluency,

flexibility and novelty, or novelty and

flexibility, in problem posing and problem

solving.

 Creative thinking level 3 (creative)

 Students are able to show fluency and novelty,

or fluency and flexibility, in problem posing

and problem solving.

 Creative thinking level 2 (fairly creative)

 Students are able to demonstrate flexibility or

novelty in problem posing and problem

solving.

 Creative thinking level 1 (less creative)

 Students are able to show their fluency in

problem posing and problem solving.

 Creative thinking level 0 (not creative)

 Students are unable to show the three aspects

of the creative thinking indicators in problem

posing and problem solving.

From the analysis result of students’ creative

thinking level in graph theory application course, the

dominant percentage is the creative thinking level 3

(creative) ie the student is able to show fluency and

novelty, or fluency and flexibility in problem posing

and problem solving. As for the percentage of

creative thinking level 4 (very creative) and the

creative thinking level 1 (less creative) is very small.

No student with creative level 0 (not creative).

The result of student creative thinking level

analysis can be seen in Table 1 and Figure 4. In detail,

components of students’ creativity indicator shown in

Table 2.

Table 1: Distribution of students’ creative thinking level.

Creative thinking

level

Number of

students

Percentage

4 (very creative)

12 %

3 (creative)

56 %

2 (fairly creative)

24 %

1 (less creative)

8 %

0 (not creative)

0 %

Total

100 %

Figure 4: Proportion of students’ creative thinking level.

Figure 5: Proportion of students’ creative thinking level

based on its components.

Table 2: Distribution of students’ creative thinking level based on its components.

Creative thinking level

Iindicator components

Number of students

Percentage

4 (very creative)

fluency, flexibility and novelty

8 %

novelty and flexibility

4 %

3 (creative)

fluency and novelty

32 %

fluency and flexibility

24 %

2 (fairly creative)

fflexibility

12 %

nnovelty

12 %

1 (less creative)

ffluency

8 %

0 (not creative)

0 %

Total

100 %

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Of three students in creative thinking level 4, only

two students could show fluency, flexibility and

novelty, and only a student could have novelty and

flexibility in posing and solving problems.

Figure 5 showed depict distribution of creative

thinking level, based on its indicator components.

4 CONCLUSION

In this research, most students of graph theory

application course were in creative thinking level 3

(56%). They could present fluenct and novelty, or

fluency and flexibility in posing problem as well as

solving problems. The rest in descending order are in

level 2 (24%), level 4 (12%), and level 1 (8%). This

showed that students were enthusiastic in the course

that involved problem posing and problem solving,

and they could have creative thinking skill which is

really needed in work field afterthat.

ACKNOWLEDGEMENTS

This article is part of PNBP Research year 2018

entitled “Peningkatan Kreatifitas Mahasiswa Pada

Matakuliah Penerapan Teori Graph Melalui

Pembelajaran Blended Learning”

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