The Increasing Students’ Mathematical Creative Thinking Ability

using Treffinger Model of Indonesian Lower Secondary Students

M. Duskri

, Khairatul Ulya

, Rauzatul Munawarah

Mathematics Education Department, UIN Ar-Raniry, Banda Aceh, Indonesia

Mathematics Education Department, IAIN Langsa, Langsa, Indonesia

MTs Oemar Diyan Aceh Besar, Aceh Besar, Indonesia

Keywords: Treffinger Model, Creative Thinking

Abstract: One of mathematics teaching goals is to improve students’ mathematical creative thinking ability as they are

able to solve problems in variety ways. The purpose of this study was to analyze the increasing of students’

mathematical creative thinking ability by using Treffinger at student lower secondary school. Treffinger

Model is a collaborative learning using divergent and convergent thinking processes. The research method

used in this study was a quasi-experimental research design using pre-test and post-test design. As a sample,

there were two groups of students grade VII SMPN 2 Unggul Mesjid Raya Aceh Besar that was chosen

randomly. The study results showed that students’ mathematical creative thinking ability taught by using

Treffinger model is better than students’ mathematical creative thinking ability taught by conventional

model. There was an increasing of each students’ mathematical creative thinking ability indicator in

experimental group, namely, flexible increased significantly from 0.00% to 70.69%, fluency raised from

50.00% to 89.66%, and elaboration grew from 20.69% to 77.59%.

1 INTRODUCTION

Thinking skills consist of recall thinking, basic

thinking, critical thinking, and creative thinking (S.

Krulik and Rudnick, 1999). Recall thinking and

basic thinking are categorized to lower order

thinking, while critical thinking and creative

thinking are categorized to higher order thinking.

Mathematical creative thinking is a reflective

pure thinking that produces a complex product

(Alimuddin, 2009). Prasetiyo et al. (2014) stated that

a creative thinking is a usual thinking related to

intuition that encourage imagination and give a

novel possibility which produce great ideas that is

not expected. As a result, a creative thinking is a

thinking process that produces variety ideas to solve

a problem.

A creative thinking skill is an integral part in

education. Permendikbud (2016) stated that

authentic learning in mathematics focuses on (1)

process and product oriented in solving problem (2)

a reasoning to improve logic, critical, analytic and

creative. A creative thinking is added as

instructional strategy and lesson plan as well.

Mathematics is able to train the thinking to

improve reasoning. As the result, logical, critical,

analytic and creative thinking will improve as well.

However, in practices, students’ activity and

achievement is not quite good yet. Based on

preliminary study on SMPN 2 Unggul Mesjid Raya

Aceh Besar, it was found that a mean score of each

indicator of students’ creative thinking ability is low

namely flexible indicator 8%, fluency indicator

reached 64% which no one can produce an original

idea in solving problem, and elaboration indicator

39%. The problem faced is needed to solve by using

instructional model that is able to explore students’

creative thinking. One of model used is Trefingger

Model. Trefingger model is a model that combines

two domains of learning namely cognitive and

affective domain. Moreover, the model describes

level of learning start from basic level to complex

level

There are 3 levels of Treffinger Model namely

basic tools, practice with process, and working with

158

Duskri, M., Ulya, K. and Munawarah, R.

The Increasing Students’ Mathematical Creative Thinking Ability using Trefﬁnger Model of Indonesian Lower Secondary Students.

DOI: 10.5220/0008518701580161

In Proceedings of the International Conference on Mathematics and Islam (ICMIs 2018), pages 158-161

ISBN: 978-989-758-407-7

real problems. Level 1 (basic tool) consist of

divergent thinking skills and creative technique. As

introduction, divergent function consists of the

improving of fluency, flexibility, originality,

elaboration. Level 2 (practice with process) is a

chance given for students to practice the skills that

have been learnt in level I. Level 3 (working with

real problem) is applying skills learnt in two level

toward a challenge in real world (Nisa, 2011)

Study of model Treffinger showed that students’

mathematical creative thinking ability taught by

using Treffinger model is better than students’

mathematical creative thinking ability taught by

conventional model. In addition, there is a positive

response of students toward applying Treffinger

model in mathematics learning (Rohaeti, 2016).

From the background, it is a need to study about

“The influences of Treffinger Model towards

students’ mathematical creative thinking in lower

secondary school”. There are some research

questions (1) How is students’ mathematical creative

thinking in lower secondary school after applying

Treffinger Model? and (2) How is students’

mathematical creative thinking in lower secondary

school after applying Treffinger Model and

conventional model.

2 METHOD

Quasi Experimental design using pre-test and post-

test with qualitative approach was used in this study.

The Sample is students grade VII SMP Negeri 2

Unggul Mesjid Raya Aceh Besar year 2017/2018.

Grade VII-1 was chosen as experiment group and

grade VII-2 as control group. The primary

Instrument is creative thinking ability item with its

rubric. While supporting instrument is lesson plan

and students’ worksheet.

3 RESULT STUDY

Students’ Mathematical Creative

Thinking Ability

This analysis was used to determine the influences

of students’ mathematical creative thinking before

and after applying Treffinger Model. The picture

below showed that students’ mathematical creative

thinking before applying Treffinger model. It is clear

that students’ mathematical creative thinking is low

level.

Based on the answer on Figure 1, it is seemed

that the indicator flexible, CS got score 2. It means

that she is able to give one-way answer with correct

computation. The answer that she gave is correct. In

the case of the fluency indicator, she got score 4. It

means that she is able to give relevant ideas and

correct answer without doing a mistake. In addition,

the elaboration indicator, CS got score 3 because she

is only able to give a correct answer, but the answer

given is not detail. Moreover, the original indicator,

she got score 0 because the answer given is similar

to other friends in his class.

Figure 1: Students’ pre-test of students’ mathematical

creative thinking.

Based on the answer given on Figure 2, it is

found that RN got score 1 on the flexible indicator.

It means that he is able to give one-way answer even

though there are some mistakes given. However, R

got score 2 on fluency indicator because he is only

able to give a relevant idea, but the answer given is

not fully correct. In the case of elaboration indicator,

RN got score 1 because he did some mistakes on

answering and the answer, he gave is not detail.

Moreover, original indicator, he got score 0 because

the answer given is similar with other students in is

classroom.

Figure 2: A student (RN) pre-test answer of creative

thinking.

From the answer given on Figure 3, it is found

that RN got score 4 on flexible indicators. It means

that he is able to give more than one answer with

correct computation. Like flexible indicator, RN got

score 4 on fluency indicator. It means that he is able

The Increasing Students’ Mathematical Creative Thinking Ability using Trefﬁnger Model of Indonesian Lower Secondary Students

159

to give a relevant idea with a correct solution.

However, CS got score 3 on elaboration indicator, it

means that she is able to give a correct answer

without detail. Like the answer before, the original

indicator could not reach by the student, and he got

score 0 because the answer give is similar to other

students in her classroom.

Figure 3: A Student (RN) pre-test answer of creative

thinking.

Treffinger model enables students to develop

their creative thinking ability since in the first level,

it uses open-ended questions to encourage students

to think flexibly, originally and fluently. In addition,

in the second level, both students are encouraged to

have a role in working groups. In this level, they will

be given complex questions. The purposes of these

activities are to encourage students to think

creatively with working-learning activity.

Moreover, the third level, the model used is

creative thinking technique. In this level, student

was asked to answer non-routine question relate to

their real world. The students were asked to get

solution of the problem given to encourage them to

think creatively.

The data analysis in Table 1 showed that the

creative thinking indicator is increasing in each

indicator except original indicator. As the result, it is

concluded that Treffinger Model has a positive

impact towards students’ mathematical creative

thinking.

4 DISCUSSION

Students’ Mathematical Creative Thinking

After applying Treffinger Model on learning

process, there is an increasing of students’

mathematical creative thinking of each indicator

except original indicator. In original indicator, both

pre-test and post-test, the student’s achievement is

categorized as low ability. It is caused by some

reasons: (1) the topic of learning is less effective to

develop original indicator (2) original indicator is

one of the difficult indicators to improve because

students need to find the solution that is not similar

with other students. Moreover, the original indicator

needs more time to develop. However, the

researcher conducts 3 meeting classes, for the

reason, it is predicted that the original indicator did

not increase.

Table 1: Students pre-test and post-test achievement on

creative thinking ability.

Experiment Group Post-Test

Observing Aspect

Low

Good/

Excellent

Originality

100%

0.00%

Flexibility

29.31%

70.69%

Fluency

10.34%

89.66%

Elaboration

22.41%

77.59%

Control Group Post-Test

Observing Aspect

Low

Good/

Excellent

Originality

100%

0,00%

Flexibility

75%

25,00%

Fluency

30%

70,00%

Elaboration

50,85%

49,15%

It was predicted that the original indicator would

not increase in this research. There are three reasons

why the indicator did not increase. Firstly, the

Acehnese students do not have a habit to think

dependently. it means that students are still thinking

as their habitual thinking. For this case, further

research needs to conduct in order to focus on

encouraging students to think “out of the box”.

Secondly, the students feel afraid or not feel

confidently in asking or answering the question from

the teacher. The culture of “ a shame” is affected in

creating original ideas because the students choose

ICMIs 2018 - International Conference on Mathematics and Islam

160

being silent rather that asking or answering the

question.

In other hand, the different thing happens to 3

other indicators. The flexible indicator increases

from low level with 100% to 29.31%, while good or

excellent categorized increase 0% to 70.69%. For

fluency indicator fluency, the number of students

with low categorized decrease from 50.00% to

10.34%, on the other hand, students reached good

and excellent categorized increase from 50.00 %

89.66%. The last indicator, elaboration, the number

of low achievement student decrease from 79.31%

to 2.41%, while students who reach good/excellent

categorized increase from 20.69 % to 77.59%.

Treffinger Model is one of learning models that

is reliable, visible and applicable model in teaching

and learning (Supriyono, 2011). In addition, the

model has success in order to teach learners in

achieving divergen thinking (Wirahayu, Purwito,

Juarti, 2018). Morever, there are stated that

Treffinger model is able to improve students’

creativity (Pomalato, 2006; Siswati, 2011; Haryono,

2009).

5 CONCLUSION

This study showed that Treffinger model has a good

impact on students’ creative thinking ability.

Moreover, it is claimed that students’ creative

thinking ability taught by Treffinger model is better

than students’ creative thinking ability taught by

conventional model.

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