Where Exactly for Enhance Critical and Creative Thinking: The

Use of Problem Posing or Contextual Learning

Toheri

and Widodo Winarso

nstitut Agama Islam Negeri Syekh Nurjati Cirebon, Indonesia

Keywords: Critical Thinking, Creative Thinking, problem posing, contextual learning.

Abstract: Critical and creative thinking are the two essential competencies of the four competencies required in the

21st century. However, both are still difficult to achieve well by students due to lack of training during the

course of mathematics learning. This study was conducted to determine what model of learning is

appropriate to develop students' critical and creative thinking skills. The study used three class samples from

class VIII. First class is given problem posing lesson, second class is given contextual learning and third

class as control class. The results of the study indicate that improving students' critical and creative thinking

skills are included in the moderate category for classes using contextual and contextual classroom posing

problems. In addition, it is also found that contextual learning is more effective for improving critical

thinking skills when compared with learning posing and exposure problems. Meanwhile, learning problem

posing is more effective to improve creative thinking skills compared with contextual and expository

learning.

1 INTRODUCTION

Critical and creative thinking is very important for

students in school and life going forward. Thinking

of this is necessary to face the 21st century (Center.

Pacific Policy Research, 2010; Koetzsch, 1997), as

the objective of mathematics learning (Mahmuzah,

2015), analyzing problems and synthesizing

(McCormick, Clark and Raines, 2015), make

decisions and make judgments (Paul and Linda,

2006). Both are essential for solving everyday

problems (Apino and Retnawati, 2017).

Results of the 2015 TIMSS Review show

Indonesian students are still weak in the content and

cognitive domains of mathematics. In line with the

findings of Indah Nurul Faizah and Budi Murtiyasa

which states that UN questions are still minimal in

the domain of cognitive reasoning such as generalize

and justify (Faizah, Budi and M., 2017). Lack of

linkage between creativity in the curriculum and

creativity taught by teachers (Aizikovitsh-Udi and

Diana, 2015), Feeling less ready to teach creativity

(Mullet et al., 2016).

The various notions of critical thinking are

presented by experts and researchers. Trend and

skills to engage in activities with reflective

skepticism (McPeck, 2016). A rational-reflective

thinking to decide what to believe or do (Ennis,

2015), a metacognitive process involving analysis,

evaluation, and inference (Dwyer, Hogan and

Stewart, 2014).

In this study, the critical thinking that we use is

adopting from Ennis with 4 indicators: 1)

formulating the main issues, 2) analyzing arguments,

3) determining the strategy, and 4) concluding.

Creative thinking refers to Torrance containing 4

cognitive processes, fluency, flexibility, authenticity,

and elaboration (Almeida et al., 2008), stated

creative thinking contained innovative creativity

(fluency, originality), and adaptive creativity

(flexibility, the abstractness of titles, and Resistance

to Premature Closure).

In this study, the creative thinking that we use is

adopted from Torrance with 4 aspects: 1) fluency, 2)

flexibility, 3) originality, and 4) elaboration.

Various efforts were made by teachers and

researchers to develop students' critical and creative

thinking in mathematics learning. Problem posing is

central to the nature of mathematical thinking (Silver

and Cai, 1996). Strategies for questions asked by

teachers in discussions and play roles in real-life

problem solving very well for developing critical

thinking (Abrami et al., 2015). Problem-based

learning affects the students' mathematical thinking

698

Toheri, . and Winarso, W.

Where Exactly for Enhance Critical and Creative Thinking: The Use of Problem Posing or Contextual Learning.

DOI: 10.5220/0009914806980705

In Proceedings of the 1st International Conference on Recent Innovations (ICRI 2018), pages 698-705

ISBN: 978-989-758-458-9

skills (Widyatiningtyas et al., 2015). At the same

time, Rifaatul Mahmuzah suggests Problem Posing

as an alternative to improving critical thinking

(Mahmuzah, 2015). State the importance of effective

learning so students become critical thinkers and

how students learn effectively, the role of students,

teachers and the context in teaching critical thinking,

In line with the traditional paradigm shift and the

transfer of information toward constructivism of

student activities for more meaningful learning

(Bonney and Sternberg, 2016). If the teacher

consistently and systematically encourages critical

thinking in their class by applying mathematics to

real-life problems, encouraging debate, and planning

investigative lessons, students tend to practice

critical thinking skills and develop critical thinking

languages (Aizikovitsh-Udi and Diana, 2015).

Creative thinking can be developed through

problem posing and problem-solving (Suastika and

Wahyuningtyas, 2017), MEAs with realistic

problems (Wessels, 2014).

According to Ranak Lince revealed that NHT is

more suitable to enhance students' creative thinking

mathematically (Lince, 2016). Apino and Retnawati

suggest the importance of providing a variety of

non-routine issues that enable students to practice

asking "why and How” (Apino and Retnawati,

2017). Huang, Ricci, and Mamikon Mnatsakanian

suggested that Students be taught how to: identify

the steps; evaluate; choose a troubleshooting

strategy; identify possible conclusions; choosing

logical conclusions; explains how solutions are

obtained; and shows how the solution can be applied

to wider mathematical problems (Huang, Ricci and

Mnatsakanian, 2016). The importance of student and

context analysis, the setting of learning objectives,

differences in strategy development or assessment

techniques in designing learning steps on problem-

based learning approaches to develop students'

critical and creative thinking (Birgili, 2015).

Another approach that teachers can use as an

effort to optimize students' critical and creative

thinking skills is a contextual approach called

Contextual Teaching Learning (CTL). Contextual

Teaching and Learning (CTL) is a learning strategy

that emphasizes the full process of student

involvement in order to find the material learned and

relate it to real life situations that encourage students

to apply it in their lives(Sanjaya, 2006). Johnson that

in Contextual Teaching and Learning (CTL) requires

a more empowering approach to students in the hope

that students are able to construct knowledge in their

minds rather than memorizing facts (Johnson, 2002).

This study uses learning posing and contextual

problems given to students with the aim of

developing critical thinking (analyzing arguments,

being able to ask, able, answering questions, solving

problems, determining strategies and making

conclusions) and thinking creatively (thinking

fluently, thinking flexible, thinking original, and

detailed thinking) students.

2 METHODS

The quantitative approach is done by quasi-

experimental method (Campbell and Stanley, 2015)

with Nonequivalent Control Group Design (Bryk

and Weisberg, 1977) in sample 3 class VIII MTs N 1

Cirebon-Indonesia. This research was conducted to

see the learning of the mathematical problem of

posing and contextual in improving critical and

creative thinking skill.

2.1 Procedure

The research procedure is done through the

determination of 3 class samples, where 2 classes

are given treatment and 1 class as a control. Class 1

is treated by learning problem posing, second class

is given contextual learning treatment, and third

class is controlled by traditional learning. Prior

learning was given preliminary tests with students'

critical and creative thinking skills for the three

groups.

Implementation of learning problem posing for

experiment class 1 refers to pre-positioning posing

activity (Leonard, 2017) with the learning stages

adopting Mathematical education research. While

contextual learning for experimental class 2 refers

to Elaine B Johnson which describes the stages of

Contextual Teaching Learning with student activity

and teacher activity (Johnson, 2002). while the

control class is given expository learning.

After the implementation of the learning, each

group is given a final test related to students'

critical and creative thinking skills related to the

topic of the circle in accordance with the

competencies contained in the 2013 curriculum at

the topic of the circle and their parts.

2.2 Data Collection

The technique of data collecting using description

test which amounted to 9 item, where 5 items about

which to measure a student's critical thinking ability

and 4 remaining matter to measure student's creative

thinking ability. The test will be done before

Where Exactly for Enhance Critical and Creative Thinking: The Use of Problem Posing or Contextual Learning

699

(pretest) and after learning (postest) in experiment

and control class. both of tests have similar

indicators, but are different in the question The

scoring to calculate the results of the description test

is by using Holistic Scoring Rubrics criteria

(Mertler, 2001).

Critical thinking tests using instruments with

indicators cover four aspects (Ennis, 2013), details

of this including at the table below;

Table 1: Instrument of critical thinking

Aspects Indicator

analyzing

arguments

Determining a problem and

identify reasons that match the

question

formulating

problems

Digging information by asking

and answering through various

alternative answers to solve a

problem

determining

strategies

Determining an alternative

action that is possible to solve

the problem

concluding the giving a meaningful idea

Examples of pretest and post for determining

strategies can be seen in the following figure 1 and 2

below;

Figure 1: Sample Pre-test of critical thinking

Figure 2: Sample Post-test of critical thinking.

The creative thinking test uses instruments with

indicators, including: 1) fluency, 2) flexibility, 3)

originality, and 4) elaboration (Torrance, 1972),

details of this including at the table bellow;

Table 2: Instrument of creative thinking

Aspects Indicator

Fluency Students can provide relevant

ideas to solve problems

Flexibility Students can express various

ways or approaches to a

problem

Originality Students can provide unique

answers to solve problems

Elaboration Students Able to develop ideas

or ideas and explain in detail

the problems resolved so that

they are more interesting

Examples of pretest and post for elaboration can

be seen in the following figure 1 and 2 below;

Figure 3: Sample Pre-test of Creative thinking

Figure 4: Sample Post-test of Creative thinking

This instrument is analysed in advance to see the

validity, reliability, indices of difficulty (easy and

middle) and distinguishing power (good and very

good) previously tested by experts.

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2.3 Data Analysis Technique

Data analysis techniques used to describe the

learning approach (problem posing, contextual, and

expository approach) in terms of students' critical

and creative thinking ability include normality test

by using Kolmogorov Smirnov test, homogeneity

test, and N-gain calculation for both thinking

variables (Creswell and Creswell, 2017). To test the

hypothesis done through One Way ANOVA (Kim

and Kohout, 1975). which compares the N-gain of

critical and creative thinking to the three groups.

Data analysis is continued by using the Scheffe Test

to determine which variable is better. All data

analysis is done by using SPPS software version 20.

3 RESULTS AND DISCUSSION

Overall, the critical and creative thinking for the

three groups can be presented in the following table;

Table 3 : Mean value of creative and critical Thinking

Critical Thinking Creative Thinking

Pretes Postest Pretes Postest

Eks. 1 38,82 77,37 35,36 79,44

Eks. 2 37,57 77,30 35,47 75,17

Control 36,25 65,14 33,85 63,19

The data in table 3 shows all groups have an

average increase from pretest to posttest. This

increase occurs in students' critical and creative

thinking skills in mathematics, especially with

regard to the topic of circle and theirs parts.

To achieve the intended objectives in this study, the

research findings will be presented in 3 sections,

namely: the difference in the increase of critical and

creative thinking, the best improvement of critical

thinking, and the best improvement of students'

creative thinking.

3.1 Differences in Improving the

Critical and Creative Thinking

Skills of Students

The students' critical and creative thinking skills

improved in the medium category as measured by

N-gain. This increase is experienced by all students

in experimental 1 (Problem Posing), experiment 2

(Contextual Problem), and the control group.

However, the N-gain value varies for both

capabilities and the three groups as shown in table 2

below.

Table 4: N-gain value of students' critical and creative

thinking skills

Class N-Gain Interpretation

Critical Creativ

Critical Creative

Exp. 1

0,63 0,68

Moderat

Exp. 2

0,64 0,61

Moderat

Control

0,45 0,44

Moderat

The data in Table 4 shows that the N-gain of

experimental group 1 (who studied with probing

problem) and experiment 2 (who studied

contextually) were greater than the control group

either critical thinking or creative thinking in

mathematics.

 For critical thinking, the n-gain value

of the posing's problem group is greater than the

contextual group. Conversely, n-gain creative

thinking posing problem groups are lower than

contextual groups. Although, all of treatment give as

same as criteria about n-gain.

The involvement of students in learning posing

and contextual problems is the cause of the

development of critical thinking (Abrami et al.,

2015; Widyatiningtyas et al., 2015) and creative

students

(Ayllón, Gómez and Ballesta-Claver, 2015).

The existence of mathematical problems presented

in learning posing and contextual problems make

learning more meaningful (Yen and Halili, 2015).

3.2 The Differences in Increasing

Critical Thinking

To answer the second question, first analysis used by

anova. The differences in critical thinking between

groups can be seen in Table 5 below;

Table 5: Anova the ability of creative thinking

Sum of

Squares

df Mean

Square

F Sig

Betwe

Group

1,127 2 ,564

22,12

,000

Within

Group

2,751 108 ,025

Total 3,879 110

Furthermore, we founded significant differences

in students' critical thinking skills between classes in

the learning process using problem posing,

contextual problem and expository approaches. The

Where Exactly for Enhance Critical and Creative Thinking: The Use of Problem Posing or Contextual Learning

701

analysis used Scheffe test which is 95% significant

level to know the difference of significance at

treatment. The output results of this analysis can be

seen as follows:

Table 6: Scheffe test of critical thinking skill

Multiple Comparisons

Dependent Variable: Learning approaches

Scheffe

(I)

Learn

. App.

(J)

Learn.

App.

Mean

Diff. (I-

Std.

Error

Sig.

95% Confidence

Interval

Lower

Bound

Upper

Bound

Exp.

Exp. 2 -,00753 ,0335 ,975 -,090 ,0756

Exp. 3 ,15240

,0338 ,000 ,0686 ,2362

Exp.

Exp. 1 ,00753 ,0335 ,975 -,075 ,0907

Exp. 3 ,15994

,0340 ,000 ,0756 ,2442

Exp,

Exp. 1 -,15240

,0338 ,000 -,236 -,068

Exp. 2 -,15994

,0340 ,000 -,244 -,076

Table 6 shows significant differences in students'

critical thinking skills between classes using

problem posing approaches (Experiments 1) and

those using a contextual approach (Experiment 2)

with a class using an expository learning approach.

However, there is no significant difference in

students' critical thinking skills between classes

using the problem-posing approach (Experiment 1)

with those using the contextual approach

(Experiment 2). Nonetheless, classes that acquire a

contextual learning approach are better than classes

using problem posing approaches the inability of

critical thinking.

Real issues related to the student's daily life in

contextual learning trigger student activities to

identify and analyze information logically, find

solutions and present them argumentatively.

Discussions of small groups and large groups trigger

them to argue with each other and reasoning that

train them to be more critical. As Sanjaya and

Hassoubah argue that Contextual Teaching and

Learning (CTL) is a learning strategy that

emphasizes the full process of student involvement

in order to find the material learned and relate it to

real life situations that encourage students to be able

to apply it in their lives, to empower students with

the hope that students are able to construct

knowledge in their minds, rather than memorizing

facts (Sanjaya, 2006; Paul and Linda, 2006).

This is in line with what suggests, Bonney and

Sternberg state the importance of effective learning

so that students become critical thinkers and how

students learn effectively, the roles of students,

teachers and the context in critical thinking teaching

(Bonney and Sternberg, 2016). Contextual learning

is a constructivism approach to student activity for

more meaningful learning (Yen and Halili, 2015).

The students who learn through contextual have

excellent abilities in identifying, formulating things

that are known and asked correctly and the results of

calculations are correct. However, the aspect of

determining the strategy for problem-solving is less

systematically and logically even though the results

are correct.

The aspects of critical thinking to analyze and

conclude are good. They can identify 5 to 6 elements

contained in a circle. They were able to provide a

good explanation of the results from the right

calculations, although in concluding there were still

a few mistakes.

3.3 Differences in Enhancing Creative

Thinking

Differences in creative thinking between groups can

be seen in table 5 below.

Tabel 7: Anova the ability of creative thinking

Sum of

Squares

Mean

Square

f Sig.

Between

Groups

1,127 2 ,564 22,128 ,000

Within Groups 2,751 108 ,025

Total 3,879 110

Table 7 shows that there is a significant

difference in students' creative thinking ability

between classes which in their learning process use

posing, contextual and expository approaches.

The next analysis used Scheffe test which is 95%

significant level to know the difference of

significance at treatment.

Table 8, shows significant differences in

students' creative thinking ability between classes

using problem posing approach (Experiment 1) and

using contextual approach (Experiment 2) with a

class using an expository learning approach.

However, there is no significant difference in

students' creative thinking ability between classes

using the problem-posing approach (Experiment 1)

with those using the contextual approach

(Experiment 2). Nonetheless, the class that acquired

the problem-posing learning approach is better than

the class using the contextual approach in ability of

creative thinking.

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702

Tabel 8: Scheffe test-the ability of creative thinking

Multiple Comparisons

Dependent Variable: Learning approaches

Scheffe

(I)

Learn.

appr.

(J)

Learn.a

ppr.s

Mean

Differen

ce (I-J)

Std.

Erro

Sig.

95%

Confidence

Interval

Lowe

Boun

Uppe

Boun

Exp. 1

Exp. 2 ,068 ,0369 ,189

,0237 ,1593

Exp. 3 ,240

,0371 ,000 ,1482 ,3325

Exp. 2

Exp. 1 -,068 ,0369 ,189

,1593 ,0237

Exp. 3 ,173

,0374 ,000 ,0798 ,2653

Exp. 3

Exp. 1 -,240

,0371 ,000

,3325

,1482

Exp. 2 -,173

,0374 ,000

,2653

,0798

*. The mean difference is significant at the 0.05 level.

This findings reinforce the results of Ayllón's,

Gómez and Ballesta-Claver research, who argue that

posing problems can develop students' creative

thinking (Ayllón, Gómez and Ballesta-Claver,

2015), supporting also the results of Silver and Cai's

research that posing problems are at the core of

mathematical thinking, a problem that implies

students train to ask " why and how "through a

variety of problems, so students have various ways,

arguments, alternatives in identifying ways to solve

problems at hand (Silver and Cai, 1996).

The exercises to make sub-questions from the

main problem make them accustomed to finding

ideas, ideas in finding alternative solutions. Students

are also trained to complete their ideas so that they

are triggered to find new ideas or strategies for

finding more effective solutions. Sharing ideas in

posing problems is an important medium in finding

new ideas and revised old ideas.

Students who learn through problem posing have

excellent abilities in aspects of flexibility and

elaboration. This is characterized by the ability to

provide answers in more than one way, the

calculation process and the results are correct, and

resolve problems accompanied by reasons or

explanations in detail correctly and the results are

correct.

4 CONCLUSION

Based on the results and discussions conducted in

this study can be concluded that learning posing and

contextual problems more effectively used to

improve the ability of critical thinking and creative

thinking of students compared with expository

learning. Problem posing learning enables the

development of creative thinking better than

contextual learning. In line with the findings that

learning problem posing and problem-solving can

develop creative thinking (Ayllón, Gómez and

Ballesta-Claver, 2015). Conversely, contextual

learning is more instrumental in developing students'

critical thinking than learning problem posing. In

parallel with the traditional paradigm shift and the

transfer of information toward constructivism from

student activities for more meaningful learning (Yen

and Halili, 2015).

Critical and creative thinking can be improved

through thinking exercises during the learning

process (Bostic, Pape and Jacobbe, 2016). This

practice of thinking will be formed through the

context of problems that are close to their lives,

questions that have many ways to be solved.

To provide opportunities for them to share ideas

or opinion, give one or two trigger questions by the

teacher when they are deadlocked. Teachers should

make instruction how to talk or use talk to ask

questions, to explain their thinking, to analyze and

solve problems, explore and evaluate ideas, argue,

reason and justify (Gillies, 2016).

5 RECOMENDATIONS

Furthermore, the study needs to be done to see

which aspects of critical thinking and creative

thinking can be developed through learning of

posing and contextual problems. In addition, the

study also needs to be done through a mix method

approach to obtain more complete data again.

Innovations in learning posing and contextual

problems by utilizing technology and collaboration

with other subjects need to be done in order to

comprehensively the students can develop specially

to face the century 21 ahead. Teachers can

implement this method for any topic in mathematics.

Further studies can be conducted to identify 21st-

century character quality through contextual learning

and problem posing.

ACKNOWLEDGEMENTS

The authors wish to thank Faculty of Tarbiyah and

Teacher Science (FITK) IAIN Syekh Nurjati

Cirebon-Indonesia.

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