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The Interaction of Problem-Based Learning with “Murder” Strategy,

Educational Background, and Mathematical Prior Knowledge toward

Mathematical Creative Thinking Ability and Disposition of Preservice

Elementary School Teacher

Maulana*

Didi Suryadi****

Utari Sumarmo******

Jarnawi Afgani Dahlan********

Abstract

Similar to creative thinking ability, the development of high order mathematical ability is demanded in the mathematics learning activity in preservice elementary school teacher study program (called PGSD). For that purpose, the selection of appropriate approach and strategy will make the objective of learning activity be achieved. However, only few people who try to recognize the other factor beside the learning approach/strategy which is possible in giving contribution in the development of the creative thinking ability, for example the students’ educational background factor (science and non-science) and mathematical prior knowledge that is acquired before. In addition, affective aspect, which accompanies creative thinking ability (creative disposition), is a study that is rarely found. This paper is made to give a brief description about the selection of learning approach and strategy type that is the problem based learning “MURDER” strategy and the interaction with the educational background and mathematical prior knowledge toward the enhancement of thinking ability and PGSD students’ mathematical creative disposition. The research subject consist of three treatment groups, those are the classes which is given : (1) problem based learning with “MURDER” strategy, with the learning material that is made from the result of didactical design research, (2) problem based learning with “MURDER” strategy, and (3) conventional learning.

Keywords: Problem-based learning, “MURDER” strategy, educational background, mathematical prior knowledge, mathematical creative thinking ability, mathematical creative thinking disposition.

1 Introduction

* Student of Mathematics Education Doctoral Program, Indonesia University of Education. Postal address: PGSD UPI Kampus Sumedang, Jalan Mayor Abdurrahman No. 211 Sumedang, West Java, Indonesia. Postal Code: 45322. Email: [email protected] **** Professor of Indonesia University of Education, Department of Mathematics Education. Postal Address: Jalan Dr. Setiabudhi No. 229 Bandung, West Java, Indonesia. Postal Code: 40154. Email: [email protected] ****** Emerita Professor of Indonesia University of Education, Department of Mathematics Education. Jl. Dr. Setiabudhi No. 229 Bandung, West Java, Indonesia. Postal Code: 40154. Email: [email protected] ******** Doctor in Mathematics Education, Indonesia University of Education, Department of Mathematics Education. Postal Address: Jl. Dr. Setiabudhi No. 229 Bandung, West Java, Indonesia. Postal Code: 40154. Email: [email protected]

mailto:[email protected]

2

How to develop high order thinking ability and to make it into significant objective

that must be achieved in learning mathematics is an actual issue in learning mathematics

nowadays. The mathematical high order thinking ability which is non-algorithmic, complex,

involving the autonomy of thinking, often involving uncertainty that needs consideration and

interpretation, involving the various criteria and occasionally trigger the conflict emergence,

and creating open solution, also need the considerable effort in performance (RESNICK,

1987; ARENDS, 2004).

One of the thinking ability that include in high order thinking ability is creative

thinking ability. There are four exhortations about the need of critical thinking ability

development, those are: (1) demand of the era which desires the citizens to be able to find,

select, and use information for the social and state life, (2) every citizen always deals with

various problems and choices so that he/she is demanded to be able to think critically and

creatively, (3) the ability to see anything with different ways in solving the problem, and (4)

critical thinking is an aspect in solving the problem creatively in order that students are able to

compete fairly and able to cooperate with the other nation (WAHAB, 1996; MAULANA,

2007).

Creative thinking is a process of thinking various ideas in dealing the issue or

problem, playing with the ideas or the elements in mind, finding the new relationship or

relevance to see the subject from the new perspective, and creating the new combination from

two or more concepts in mind (EVANS, 1991).

This creative thinking ability is definitely able to develop through mathematics

learning at school or college, which emphasizes the system, structure, concept, principal, and

the tight relevancy among one element and the others. The essence of mathematics as a

structured and systematic science, as a human activity through active, dynamic, and

generative process, and as a science that develops the critical, objective and open thinking,

becomes very important to be mastered by the student in facing the rapid change of science

and technology.

In fact, as stated by Maier (1985) and Dahrim (2004), it cannot be denied that the

belief of some students which develops nowadays is about mathematics as a subject that is

hard and dislike. Even according to Çatlioğlu, Gürbüz, and Birgin (2014), the preservice

elementary school teachers sill feel greatly mathematics anxiety. Only a few students who are

able to dip into and comprehend the mathematics as a science that can drill the higher order

thinking ability, especially the creative thinking. Whereas, they know that mathematics is

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important for their life. Other than the students’ bad judgment about mathematics, Slettenhaar

(2000) stated that in the present learning model, generally students’ activity is only listening

and watching the teacher in doing mathematical activity, and then the teacher solves the

problem with one solution, and it ends by giving the exercise to students to be finished by

themselves. That learning activity, as stated by Rif’at (2001) is called as rote learning, which

is learning activity that only makes the students tend to memorize without comprehend or

understand what is taught, while the teacher often does not realize it. In line with the

statement, Abdi (2004) stated that some of students feel the difficulty in absorbing and

comprehending mathematics, but the difficulty in comprehending mathematics is probably

related to the way of the teacher teaching in the classroom that does not make students feel

enjoy and sympathy to mathematics, and the approach that the teacher used is generally less

varied.

Jenning and Dunne (1998) stated that most of students have difficulty to apply

mathematics in daily life because in mathematics learning, real world is just a place for

applying the concept. The other thing that creates the difficulty in mathematics for students is

because mathematics seems to be less meaningful. Teacher in the lesson does not relate

students’ prior knowledge that they are already acquired and they are given less opportunity

to reinvention and self-construct mathematics ideas. Wahyudin (1999) stated that one of the

cause of students are poor in mathematics is they have less ability to comprehend the

knowledge, to identify the basic concept of mathematics that relates to the subject under

discussion.

Based on those reasons, it is clear that students’ creative thinking ability is very

important to be developed. Therefore, teacher or lecturer should investigate and improve

teaching practices that have been implemented, which might just mere routine.

It is true that at this time mathematics learning are quite emphasize on change-

oriented approach and introduce the importance of the involvement of students in the use of

mathematics through an active process. In the process of mathematics learning, there are

enough teachers/ lecturers who create condition that allows the students to develop the

mathematical creative thinking ability. Siswoyo (2004), Pomalato (2005), and Wardani

(2009), carry out a study of creative mathematical thinking abilitys to high school students,

both junior and senior high school. Aspects of creative thinking that they are reviewed are

originality, fluency, flexibility, and sensitivity, either on some aspects of five as well as the

whole. Meanwhile, the research on mathematical creative thinking disposition is still very

rare.

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Apart from that problem, all studies on thinking ability and creative disposition that

have been carried out at the level of secondary school and college, has yet show how

successful the creative thinking ability and disposition to students, the preservice elementary

school teachers (students of PGSD). If the creative thinking ability and investigative students,

prospective elementary teachers, are not developed during undergraduate education, it is not

impossible that after they graduate and become primary school teachers, they are also difficult

to develop students’ thinking abilitys and critical disposition. In fact, students of preservice

elementary school teachers study program (PGSD) are students who are prepared to become

professional homeroom teacher in primary school, who should be able to develop thinking

abilitys and creative disposition of students as mandated by the curriculum in Indonesia.

The situation is ironic because in one side of the creative thinking ability of students

is very important to be owned and developed, but on the other hand the creative thinking

ability of students is still lack. It can be seen from the results of preliminary study conducted

by Maulana (2011) against PGSD students who have diverse latest educational background.

The students come from senior high school (SMA), vocational school (SMK), and special

class dual modes (SPG). For the courses taken are Natural Science, English, Social Studies,

Management, and Engineering. If the students were grouped into large groups, then there are

two major groups that are students with science and non-science background. In preliminary

studies that have been carried out, critical thinking ability test is given and the result is the

average score is less than 50% of the maximum score for both groups (Maulana, 2011).

All the information found in the field-on the low of mathematical creative thinking

ability of students, the prospective teachers, especially PGSD-should not be left. However, it

needs an effort to follow in order to improve; one alternative is to implement a strategy and a

more innovative learning approach.

Along with creative thinking abilitys that must be developed, it could not be

separated from the ability; there is mathematical disposition that should be trained

simultaneously. In mathematics, the guidance of affective component sort of mathematical

disposition will form the desire, awareness, dedication and a strong tendency to students to

think and act mathematically in a positive way and based on faith, piety and good values

(SUMARMO, 2011). The meaning of mathematical disposition as above is basically in line

with the meaning contained in the culture education and nation’s character. Thus the

development of culture and character, mathematical disposition and thinking abilitys basically

can be grown themselves together. Mathematical disposition related to creative thinking

ability, in this case is termed as creative disposition.

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The research’s result of Sumarmo, et al. (HULUKATI, 2005) suggests that

mathematics instruction today, among others, has the following characteristics: learning is

more centered on the teacher, the approach is more expository, teacher dominates the

classroom activities process more, routine exercises are given more. While the curriculum

requires a learning process which is student-centered, developing students' creativity, creating

a fun but challenging conditions, developing value ability, providing a diverse learning

experience and learning by doing. Therefore, it needs extra hard efforts of all parties

concerned with the educational process to jointly strive to improve the learning process that

occurs at this time.

Realizing the importance of a strategy and learning approach to develop the thinking

abilitys of students, it is absolutely necessary for mathematics learning involve students more

actively in the learning process itself. This can be realized through an alternative form of

learning that is designed in such way that reflects the involvement of students actively and

constructively. Students as learners need to get used to be able to construct their own

knowledge and able to transform them into more complex situations so that that knowledge

will become the learner's own belongings that inherent forever. The process of constructing

knowledge can be carried out by the students themselves based on the experience that has

been owned previously, or it can also be a result of the discovery that involves environmental

factors.

Based on the view of constructivism, a learning strategy must have characteristics are

as follows: using more time to develop an understanding that can improve the ability of

learners to converting knowledge, involving the students in the learning process so that the

abstract concept can be presented more concrete, implementation of discussion in small

groups, and the presentation of the problems are not routine.

One of the mathematics learning approaches which based on the view of

constructivism is problem-based learning (PBL). In the process, this learning presents a

learning environment with the problem as a base. The problem is raised so that the students

need to interpret the problem, gather the needed information, assess alternative solution, select

and present the solution that have been chosen. When students try to develop a procedure to

resolve the problem, then in fact they are integrating conceptual knowledge with their own

ability. Therefore, overall in this case the students who build their knowledge, and be

supported by the presence of teacher who plays a major role as a facilitator of learning.

Problem-based learning provides a learning environment that gives many

opportunities for students to develop their mathematical thinking ability. By a problem-based

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learning, they try to explore, adapt, change the resolution procedures, and also verify the

appropriate solution to the new situation of the obtained problem. Problem-based learning is

also have the metacognitive atmosphere, which focuses on learning activities, helps and

guides students who face difficulties, and helps to develop their metacognitive awareness,

both in terms of selecting, remembering, recognizing, organizing the faced information, up to

how to resolve problem (SUZANA, 2003). Problem-based learning that is based on the view

of constructivism can trigger the growth of students’ metacognitive ability, because the

learning process begins with cognitive conflict and it resolves by the students themselves

through self-regulation which is finally in the learning process the students construct their

own knowledge through the experience of the result of interaction with the environment.

One of the strategies used in implementing problem-based learning is by using the

"MURDER" strategy. The "MURDER" strategy emphasizes that the interaction and

collaboration with others is an important part of learning (SANTYASA, 2008). The term

"MURDER" is an acronym of the words Mood-Understand-Recall-Detect-Elaborate-Review.

In the Mood phase, the learning is more directed to set the mood appropriately by relaxation

and focusing on learning tasks. The second phase, Understand, students are invited to

understand the particular material of the script without memorizing it. In Recall phase, one

member of the group gives the oral performance by repeating the material being read. Then

Detect phase, the members examine and criticize the emergence of errors, the omission of

notes, or the different views. The fifth phase, a fellow mate Elaborate the 2nd, 3rd, 4th, and 5th

step, and it is repeated for the next material. Finally, in the Review phase, the students review

the results of their work and transmit it to another couple in their group. Through problem-

based learning "MURDER" strategy, students are expected to (students of PGSD) develop

thinking ability and mathematical disposition.

Based on the description that has been stated above, a study of mathematics learning

alternatives that can develop thinking ability and mathematical creative dispositions is

necessary to be carried out. In this case, the research that implements problem-based learning

with "MURDER" strategy to improve creative mathematical thinking ability and disposition

of PGSD students that are estimated in accordance with the needs of students in developing

thinking ability and creative disposition of the different backgrounds (in this case the level of

prior knowledge, as well as the origin of schools/educational background).

2 Method

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2.1 Design and research procedure

This study was conducted in two stages: 1) the preparation stage, and 2) the

implementation stage. At the preparation stage, the developmental research of problem-based

learning teaching materials with "MURDER" strategy by using didactical design research

(DDR) is conducted. As stated by Suryadi (2010), DDR is a research methodology that was

developed from the tacit didactical and pedagogical knowledge.

Suryadi (2010) explains that DDR has three stages, those are:

a) Didactical Situation Analysis (DSA) is carried out by the lecturer in the development of

teaching materials before it is tested in a learning event. DSA is a synthesis of the

lecturer’s ideas on students’ various possible responses that are predicted to appear on

learning events and the anticipated steps.

b) Metapedadidactical Analysis (MA) is carried out by lecturer before, during, and after the

trials of teaching materials. MA is the ability of the lecturer to be able to view at learning

events comprehensively, identifying and analyzing the important things that happened, as

well as do a prompt action (scaffolding) to overcome learning obstacles so that the stages

of learning can be run smoothly and students’ learning outcomes become optimal.

c) Retrospective Analysis (RA), is carried out by the lecturer after performing a trial

teaching materials. RA of teaching materials that have been previously developed that will

produce an ideal teaching materials is revised, i.e. teaching materials that suit the needs of

students, can predict and anticipate any learning barriers that arise, so that the stages of

learning can be run smoothly and student learning outcomes can be optimal.

The end of this preparatory stage is by obtaining: (1) teaching materials for problem-

based learning with "MURDER" strategy with DDR, problem-based learning "MURDER"

strategy without DDR, and conventional learning; (2) a set of mathematical prior knowledge

test, mathematical creative thinking ability test that have met the requirements: validity,

reliability, level of difficulty, and discrimination index; and (3) the mathematical creative

thinking disposition scale.

If the preparation stage has been completed, then proceed with the implementation

stage of research using quasi-experimental method with non-equivalent control group design.

The use of quasi-experimental method is because it is not possible to perform full control of

the research sample, so that the subject is not grouped randomly, and the condition of the

subject is accepted as it is (RUSEFFENDI, 2003).

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Based on the mathematical prior knowledge test result, students in each grade are

grouped into three categories: high, middle, and low achiever. Grouping of students’

mathematical prior knowledge is determined based on the categorization with grouping

criteria based on the average combined score of all students and the standard deviation. Thus,

quasi-experimental research with the non-equivalent control group design briefly described as

follows (FRAENKEL; WALLEN, 1993; RUSEFFENDI, 2003).

0 X1 00 X2 00 0

Description:X1 : Problem-based learning with "MURDER" strategy by the results

of didactical design research teaching materials (PBMM-DDR).X1 : Problem-based learning with "MURDER" strategy (PBMM)0 : The distribution of test and non-test at the beginning and end of

the learning.

2.2 Population and sample

The population of the study is students of preservice elementary school teacher study

program (PGSD) at the State University who sign Mathematics Education II up in the scope

of the province of West Java and Banten. Of the population, a number of samples in this study

is taken, 119 of people were distributed into 3 classes. Of the three classes, two classes are

selected as an experimental class and the other class as the control class. In the experimental

class, the lecture with problem-based learning approach "MURDER" strategy is conducted,

while students in the control class obtain conventional learning activities.

2.3 Variables and operational definitions

a) The independent variable is denoted by X. The independent variables in this study are

problem-based learning with "MURDER" strategy with teaching materials based on

the results of DDR (X1), and the regular problem-based learning with "MURDER"

strategy (X2).

b) The control variables in this study are the educational background (science and non-

science), as well as the students’ initial level of mathematical ability, which consists of

three categories: high, middle, and low.

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c) The dependent variable is denoted by Y. The dependent variables in this study are

creative thinking ability and mathematical creative disposition.

d) Problem-based learning (PBL) is a learning that begins with preparation for the

orientation of the real problems or issues that are simulated to gain an understanding

of concepts, relationships between concepts, application of concepts, communication

of the concept, as well as to find, define, evaluate and present the solution of the

problem according to the invention itself. In general, problem-based learning consists

of five kinds of activities: (1) orientation or preparation, (2) organization, (3)

exploration, (4) negotiation, and (5) integration (developed from Barret, 2005 and

Karlimah, 2010).

e) "MURDER" strategy is an acronym of Mood, Understand, Recall, Detect, Elaborate,

and Review (adopted from Santyasa, 2008).

f) The mathematical creative thinking ability is the ability of high level mathematical

thinking which covers the aspects: (a) sensitivity, (b) fluency, (c) flexibility, (d)

elaboration, and (e) originality.

(1) Sensitivity is the ability to capture and locate the problem in response to a

situation, or ignore the facts that were not appropriate (misleading fact).

(2) Fluency is the ability to build ideas to resolve the problems relevantly or to

provide answers in the form of examples related to specific mathematical concept.

(3) Flexibility is the ability to use a variety of completion strategies, or the ability to

try different approaches in solving the problem, or the ability to switch from one

approach to the other approaches in solving problems.

(4) Elaboration is the ability to explain in detail, in order and coherent to a procedure,

an answer; or specific mathematical situation. These explanations use the concept,

representation, term, or the appropriate mathematical symbol.

(5) Originality is the ability to use strategies that are new, unique, or unusual to solve

the problem; or give examples that are new, unique, or unusual.

g) Mathematical creative thinking disposition is a tendency to think and act in a creative

way to mathematics, which include: (a) Feeling of problems and opportunities, as well

as willing to take risks. (b) Sensitive to the environmental situation, and appreciate the

creativity of others. c) Be more oriented to the present and the future than the past. (d)

Have self-confidence and autonomy. (e) Have a great curiosity. (f) Declare and

respond to the feelings and organize emotions. (g) Creating a various considerations.

(h) Respect fantasy, rich in initiatives, has the original idea. (i) Persistent and not

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easily being bored; be not desperate to solve the problem (adopted from Sumarmo,

2011).

All data that is netted from the device of mathematical prior knowledge test,

mathematical creative thinking ability test, and mathematical creative disposition scale of the

students and then are analyzed quantitatively, or quantified in the hope to answer the problem

of research related to the interaction of independent, control, and dependent variables in this

research.

The data analysis is carried out in stages, starting from the assumptions of normality

and homogeneity test, t-test (Student) to test the difference of mean of two independent or

dependent samples and One-Way Anova to test the difference of mean of more than two

independent samples. If the assumptions of normality and homogeneity are unfulfilled, then

the U-test (Mann-Whitney) for two independent samples and Kruskal Wallis for more than

two independent samples is conducted. Meanwhile, in testing the interaction, the Two-Way

Anova is used.

3 Results and discussion

3.1 Mathematical prior knowledge analysis

The whole sample group was divided into three groups of mathematical prior

knowledge (MPK), the categories of MPK are high achiever (x≥ 70, middle achiever (

50 ≤ x<70), and low achiever (x<50). The assessment is based on an agreement of the

mathematics lecturers of Campus Sumedang PGSD relates to the method of determining the

minimum completeness score of Mathematics Education II subject. In the first experimental

group, of 40 students were known as 9 high achiever, 22 middle achiever and 9 low achiever.

In the second experiment class, of 40 students, there were 9 high achiever, 22 middle achiever

and 9 low achiever. Then in the control class, there were 7 high achiever, 23 middle achiever

and 9 low achiever.

Shapiro-Wilk test provided information that PBMM-DDR and PBMM class showed

normal distribution (the value of its each opportunity are 0.707 and 0.509), whereas the

conventional class did not show normal distribution (opportunity value 0.004). Since one of

them is did not normally distribute, then Kruskal-Wallis test was used to test the mean score

difference among the three groups.

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Table 1 – Ranks of mathematical prior knowledge score

Research Class N Mean Rank

Score_MPK PBMM-DDR 40 59.12

PBMM 40 59.34

Conventional 39 61.58

Total 119

Source: developed by the authors

Table 2 – Test statisticsb,c

Score_MPK

Chi-Square .122Df 2Asymp. Sig. .941Monte Carlo Sig. Sig. .939a

95% Confidence Interval Lower Bound .935

Upper Bound .944

a. Based on 10000 sampled tables with starting seed 2000000.b. Kruskal Wallis Testc. Grouping Variable: Research Class


From the Kruskal Wallis test, Asymp.Sig value was known at 0.941. This showed that

at the 5% significance level, there was no difference among the students’ mathematical prior

knowledge at the 1st experiment class, 2nd experiment class, and control class, so prior to the

treatment of PBL-MURDER was carried out, the three groups’ mathematical prior knowledge

were significantly same.

3.2 Mathematical creative thinking ability based on the class

Based on the results of Kruskal Wallis test on the pretest data, it was found that the

value Asymp.Sig = 0.802 > 0.05. This showed that there was not any difference of PGSD

students’ initial creative thinking ability. Or in other words, students in the third grade PGSD

before PBMM-DDR, PBMM, and PK learning was implemented have the same initial

creative thinking ability.

Judging from the posttest result through the One-Way Anova, it was found that there

were mean score differences in the final creative thinking ability (after learning) of all three

groups (PBMM-DDR, PBMM, and conventional learning). The advanced Scheffe test

showed that these differences occurred to the three groups, which was the final creative

thinking ability of PGSD students who acquired PBMM-DDR learning was significantly

better than who acquired PBMM and the students’ final creative thinking achievement that

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followed PBMM learning was significantly better than students who acquired conventional

learning.

Similarly, the creative thinking ability data gain processing, based on the results of

One-Line Anova, p-value = 0.000 was obtained. Thus it can be explained that there were

mean score differences increase of creative thinking ability in those three grades (PBMM-

DDR, PBMM, and conventional learning). The Scheffe follow-up test showed that these

differences occurred to the three groups, which was an increase in the PGSD students’

mathematical creative thinking ability who acquired PBMM-DDR learning that significantly

better than who acquired PBMM. Then the increase of students’ creative thinking ability that

followed PBMM learning was also significantly better than students who acquired the

conventional learning. The complete computation is in the table below.

Table 3 – Anova

Sum of Squares df Mean Square F Sig.

Posttest_creative Between Groups 5454.617 2 2727.308 25.482 .000

Within Groups 12415.562 116 107.031

Total 17870.179 118

Gain_creative Between Groups .821 2 .410 34.019 .000

Within Groups 1.399 116 .012

Total 2.220 118


Table 4 – Multiple comparisonsScheffe

Dependent Variable (I) Research Class (J) Research ClassMean

Difference (I-J) Std. Error Sig.

95% Confidence Interval

Lower Bound

Upper Bound

Posttest_Creative PBMM-DDR PBMM 5.93750* 2.31334 .041 .2011 11.6739

Conventional 16.42803* 2.32812 .000 10.6550 22.2011

PBMM PBMM-DDR -5.93750* 2.31334 .041 -11.6739 -.2011

Conventional 10.49053* 2.32812 .000 4.7175 16.2636

Conventional PBMM-DDR -16.42803* 2.32812 .000 -22.2011 -10.6550

PBMM -10.49053* 2.32812 .000 -16.2636 -4.7175

Gain_Creative PBMM-DDR PBMM .06832* .02456 .024 .0074 .1292

Conventional .20072* .02472 .000 .1394 .2620

PBMM PBMM-DDR -.06832* .02456 .024 -.1292 -.0074

Conventional .13241* .02472 .000 .0711 .1937

Conventional PBMM-DDR -.20072* .02472 .000 -.2620 -.1394

PBMM -.13241* .02472 .000 -.1937 -.0711

*. The mean difference is significant at the 0.05 level.Source: developed by the authors

Table 5 – Scheffe test (homogenous subsets) for creative thinking ability

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Research Class N

Subset for alpha = 0.05

1 2 3

Conventional 39 44.9787PBMM 40 55.4693PBMM-DDR 40 61.4068Sig. 1.000 1.000 1.000

Means for groups in homogeneous subsets are displayed.Source: developed by the authors

Table 6 – Scheffe test (homogenous subsets) for normalized gain of creative thinking ability

Research Class N


1 2 3

Conventional 39 .3427PBMM 40 .4751PBMM-DDR 40 .5434Sig. 1.000 1.000 1.000


3.3 Creative thinking ability of science and non-science educational background

From the pretest data through the Mann-Whitney test, the value of Asymp.Sig. =

0.335 > 0.005 was obtained. This showed that the hypothesis which stated that there was no

mean score difference of initial creative thinking ability was accepted. That means the

students’ initial mathematical creative thinking ability between the science and non-science

group was not significantly different.

From the posttest data, the normality assumption was filled through the Shapiro-Wilk

test. From Levene test computation, with p-value = 0.329, the information was obtained that

both of data group was homogeneous. Then based on two independent sample t-test, p-value

= 0.002 < 0.005 was obtained. This indicates that the null hypothesis (H0) was rejected. That

is, the student's final mathematical creative thinking ability between the science and non-

science group were significantly different. In this case, the mean score of science group with

57.45 was better than mean score of non-science group with 50.43.

Then Levene test computation on the data gain gave p-value = 0.278. Thus, the

homogeneity of variance of the two groups was fulfilled. Then based on two-sample of

independent t-test p-value = 0.002 <0.005 was obtained. This indicates that the null

hypothesis (H0) was rejected. This means that the increase in the mathematical creative

thinking ability between the science and non-science group were significantly different. In

this case, the average increase in the science (0.4919) was better than the non-science group

(0.4155).

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Table 7 – Mann-Whitney test for creative thinking ability pretest

Educational Background N Mean Rank Sum of Ranks

Pretest_Creative IPA 61 62.95 3840.00

Non-IPA 58 56.90 3300.00

Total 119


Table 8 – Test Statisticsa

Pretest_Creative

Mann-Whitney U 1589.000Wilcoxon W 3300.000Z -.964Asymp. Sig. (2-tailed) .335

a. Grouping Variable: Education BackgroundSource: developed by the authors

Table 9 – Independent Samples Test

Levene's Test for Equality of Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed)

Mean Diff.

Std. Error Diff.

95% Confidence Interval of the

Difference

Lower Upper

Pretest_ Creative Equal variances assumed .042 .838 1.109 117 .270 1.187 1.069 -.93 3.30

Equal variances not assumed 1.109 116.702 .270 1.186 1.069 -.93 3.30

Postes_ Creative Equal variances assumed .961 .329 3.230 117 .002 7.014 2.172 2.71 11.32

Equal variances not assumed 3.240 116.419 .002 7.014 2.165 2.73 11.30

Gain_Creative Equal variances assumed 1.187 .278 3.152 117 .002 .076 .024 .028 .124

Equal variances not assumed 3.166 115.106 .002 .076 .024 .029 .124


3.4 Creative thinking ability based on mathematical prior knowledge (high, middle, and

low achiever)

After fulfilling the assumptions of normality and homogeneity, based on the pretest

data processing, it was found that p-value = 0.000. Since the value was less than 0.005, it

means that H0 was rejected; so that there were mean score differences of students’ initial

creative thinking ability with high, middle, and low achiever groups. To see where the

difference was laid, then post hoc test which use Scheffe test was conducted. Based on

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Scheffe test result, the information was obtained that initial creative thinking ability of high

achiever students was better than middle and low achiever students. Thus, the ability of high

achiever students in creative thinking before learning was already better than middle and low

achiever students.

Based on the pretest data processing result, it was found that p-value = 0.001. This

probability value indicates that the final ability as the students’ achievement after learning

was different. To see the difference, Scheffe test was conducted, and the information were

obtained that the final creative thinking ability of high achiever students better than middle

and low achiever students. Or, as when before learning, high achiever students' ability in

creative thinking after learning was still better than middle and low achiever students.

Based on the results of gain data processing, it was found that p-value = 0.015 which

less than 0.05. Thus the decision was made that H0 was rejected, which means that there was a

difference among high, middle, and low achiever students in terms of improving the

mathematical creative thinking ability. To see the difference, Scheffe test was conducted. The

results of this further tests showed that there were significant difference between the increases

of high and low achiever students’ creative thinking ability, where the increase of high

achiever group was much better. While the difference of creative thinking ability increase

between students of high and middle achiever, and between students of middle and low

achiever, was not significant. The complete calculation is shows in the tables below.

Table10 – Anova

Sum of Squares df Mean Square F Sig.

Pretest_Creative Between Groups 764.512 2 382.256 13.626 .000

Within Groups 3254.141 116 28.053

Total 4018.653 118

Posttest_ Creative Between Groups 2113.920 2 1056.960 7.782 .001

Within Groups 15756.259 116 135.830

Total 17870.179 118

Gain_ Creative Between Groups .156 2 .078 4.384 .015

Within Groups 2.064 116 .018

Total 2.220 118


Table 11 – Multiple comparisonsScheffe

Dependent Variable (I) MPK (J) MPK

Mean Difference (I-

J) Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

Pretest_ Creative High Middle 5.32781* 1.24130 .000 2.2498 8.4059

Low 7.32487* 1.47007 .000 3.6795 10.9702

16

Middle High -5.32781* 1.24130 .000 -8.4059 -2.2498

Low 1.99706 1.20735 .259 -.9968 4.9909

Low High -7.32487* 1.47007 .000 -10.9702 -3.6795

Middle -1.99706 1.20735 .259 -4.9909 .9968

Posttest_ Creative High Middle 7.73637* 2.73139 .021 .9633 14.5094

Low 12.63892* 3.23480 .001 4.6176 20.6602

Middle High -7.73637* 2.73139 .021 -14.5094 -.9633

Low 4.90255 2.65670 .187 -1.6853 11.4904

Low High -12.63892* 3.23480 .001 -20.6602 -4.6176

Middle -4.90255 2.65670 .187 -11.4904 1.6853

Gain_ Creative High Middle .06294 .03126 .136 -.0146 .1405

Low .10923* .03702 .015 .0174 .2010

Middle High -.06294 .03126 .136 -.1405 .0146

Low .04629 .03041 .317 -.0291 .1217

Low High -.10923* .03702 .015 -.2010 -.0174

Middle -.04629 .03041 .317 -.1217 .0291

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


Table 12 – Scheffe test for creative thinking ability pretest based on MPK

MPK N


1 2

Low 27 13.4259Middle 67 15.4230High 25 20.7508Sig. .317 1.000


Table 13 – Scheffe test for creative thinking ability posttest based on MPK

MPK N


1 2

Low 27 48.6115Middle 67 53.5140High 25 61.2504Sig. .240 1.000


Table 14 – Scheffe test for normalized gain of creative thinking ability pretest based on MPK

17

KAM N


1 2

Low 27 .4057Middle 67 .4519 .4519High 25 .5149Sig. .378 .167


3.5 Three Approaches is Significant in Enhancing Mathematical Creative Thinking

Ability

Based on the two-sample paired t-test, in the experimental class-1 which used PBMM-

DDR, the result of calculation p-value = 0.000 was obtained. Therefore, it is clear that

learning by using PBMM-DDR was significantly able to improve PGSD students’ creative

thinking ability.

Then for experimental class-2 that was given PBMM, based on two-sample paired t-

test, the result of calculation p-value = 0.000 was obtained. Thus, it is clear that learning by

using PBL was significantly able to improve PGSD students’ creative thinking ability.

Similarly, in the control group with conventional approach, through a two-sample

paired t-test, the calculation results p-value = 0.000 was obtained. Therefore, it is clear that

learning by using any conventional approach can significantly improve the PGSD students’

creative thinking ability.

3.6 Mathematical Creative Thinking Ability Increase of Science and Non-Science Group

in Each Classroom

In the experimental class-1, which used PBMM-DDR, since both of data group were

not normally distributed, then U-test (Mann-Whitney) was administered, in order to obtain p-

value = 0.010 that indicates that there was a difference in the increase of students’

mathematical creative thinking ability in the science and non-science group in the PBMM-

DDR class, where the science group (0.5779) increased better than the non-science group

(0.5012).

Table 15 – Mann-Whitney test for normalized gain of creative thinking ability in PBMM-

DDR class

18

Educational Background N Mean Rank Sum of Ranks

Gain_Creative_PBMMDDR Science 22 24.80 545.50

Non Science 18 15.25 274.50

Total 40


Table 16 – Test Statisticsb

Gain_Creative_PBMMDDR

Mann-Whitney U 103.500Wilcoxon W 274.500Z -2.570Asymp. Sig. (2-tailed) .010Exact Sig. [2*(1-tailed Sig.)] .009a

a. Not corrected for ties.b. Grouping Variable: LatBel_PBMM_DDR


Meanwhile for the experimental class-2 (PBMM), after the normality and

homogeneity assumption were fulfilled, based on the results of independent samples t-test, the

p-value = 0.000 was obtained which indicates that there was a difference in the increase of

mathematical creative thinking ability of students in the science and non-science group in

PBMM class, where science group (0.5325) increased better than non-science group (0.4117).

Then in the control class that used the conventional approach, after the assumption of

normality and homogeneity were fulfilled, based on the results of the t-test for two

independent samples, p-value = 0.875 was obtained which indicates that there was no increase

difference in students’ mathematical creative thinking ability in the science group (0, 3395)

and the non-science group (0.3454) in the conventional class.

Table 17 – Independent samples test for normalized gain of creative thinking ability in

PBMM and conventional class

19

Levene's Test for Equality of

Variances t-test for Equality of Means

F Sig. t dfSig. (2-tailed)

Mean Diff.

Std. Error Diff.

95% Confidence Interval of the

Difference

Lower Upper

Gain_Creative_PBMM-DDR

Equal variances assumed

.758 .390 2.614 38 .013 .07671 .02934 .01731 .13611

Equal variances not assumed

2.633 37.312 .012 .07671 .02913 .01770 .13571

Gain_Creative_PBMM


.029 .866 3.873 38 .000 .12078 .03118 .05765 .18390


3.881 37.841 .000 .12078 .03112 .05777 .18379

Gain_Creative_PK


.178 .675 -.158 37 .875 -.00591 .03744 -.08178 .06996


-.158 36.365 .875 -.00591 .03737 -.08167 .06984


In addition, there were other findings, that was the increase in the creative thinking

ability of non-science group in PBMM-DDR (0.5012) and PBMM class (0.4117) which was

better than science group in the conventional class (0.3395), although it was not significant.

3.7 Students’ Mathematical Creative Thinking Ability in Each Class Based on the Inter-

Same Mathematical Prior Knowledge Level

Based on the One-Way Anova, p-value = 0.001 was obtained. This indicates that there

was a difference in the increase of creative thinking ability on PBMM-DDR, PBMM, and

conventional class, based on high mathematical initial ability. Then, Scheffe test showed that

the increase of creative thinking ability of high achiever students in PBMM-DDR (0.6125)

and PBMM class (0.5537) was equally good, and the increase in both classes was

significantly better than high achiever students in conventional class (0.3395).

Based on the One-Way Anova (p-value = 0.000) the information that there was an

difference of creative thinking ability increase in PBMM-DDR, PBMM, and conventional

class, based on students’ mathematical prior knowledge who are at middle levels. Then

Scheffe test showed that the increase of creative thinking ability of students was significantly

different at the three classes. The increase of creative thinking ability of middle achiever

students who were being in PBMM-DDR class (0.5385) was significantly better than who

20

were being in PBMM class (0.4648), and the increase in PBMM class was decisively better

than middle achiever students in conventional class (0.3568).

Based on One-Way Anova (p-value = 0.004) the information that there was a

difference in the increase of creative thinking ability of lower achiever students in PBMM-

DDR, PBMM, and conventional class.. Then further tests showed that an increase of creative

thinking ability of low achiever students at PBMM-DDR class was significantly better than at

the conventional class. The difference of creative thinking ability increase of low achiever

students between PBMM-DDR and PBMM class, also between PBMM and conventional

class, was not significant.

3.8 Increase Differences of Mathematical Creative Thinking Ability in Each Class in

Each Category of Mathematical Prior Knowledge

In PBMM-DDR class, based on Levene test, it was found that the variance of high,

middle, and low achiever group on PBMM-DDR class was homogeneous (p-value = 0.282).

Based on the One-Way Anova (p-value = 0.020) the information that there were differences

in the increase in the creative thinking ability of student groups with high, middle, and low

achievement at PBMM-DDR class. Then Scheffe test showed that in PBMM-DDR class, the

increase of creative thinking ability of high achiever students was significantly better than the

students with lower one. Meanwhile, the difference of creative thinking ability increase

between the group of high and middle achiever students, also between students with middle

and low ones, the difference was not significant.

Then in the PBMM class, based on the Levene’s test, it was found that the variance of

high, middle, and low achiever groups at PBMM class was homogeneous (p-value = 0.484).

Based on the One-Way Anova (p-value = 0.037) the information that there were the increase

differences of creative thinking ability of high, middle, and low achiever students at PBMM

class. Then Scheffe test showed that in PBMM class, the increase of creative thinking ability

of high achiever students was significantly better than the students with low ones. Meanwhile,

the difference of creative thinking ability increase between the groups of high and middle

achiever students, also between middle and low achiever students, was not significant.

As in a conventional class, based on the Levene’s test, it was found that the variance

of high, middle, and low groups on PBMM class was homogeneous (p-value = 0.104). Based

on One-Way Anova (p-value = 0.584) the information that there was no difference of creative

thinking ability increase of group of students with high, middle, and low mathematical prior

21

knowledge achievement at conventional class. In other words, conventional learning was

equally good in increasing PGSD students’ mathematical creative thinking ability.

3.9 PGSD Students’ Mathematical Creative Thinking Disposition

Based on the initial scale, it was found that in the PBMM-DDR, BPM, and

conventional class, the mean score of initial creative disposition of PGSD students

respectively were 62.62; 62.46; and 63.60. For the mean score scale of the final creative

disposition was found at 68.43; 67.70; and 65.19. While the gain for the three classes were

0.151; 0,139; and 0.043.

For initial and final creative disposition, it was found that all of them distributed

normally, while for creative disposition gain of all three classes did not normally distributed.

Based on the Kruskal-Wallis test, the result was found that there was a significant difference

in mathematical creative disposition increase of PGSD students at the three classes.

Table 18 – Kruskal-Wallis test for normalized gain of creative thinking disposition

Research Class N Mean Rank

Gain_SD_Kf PBMM-DDR 40 72.65

PBMM 40 70.75

Conventional 39 36.00

Total 119


Table 19 – Test statisticsa,b

Gain_SD_Kf

Chi-Square 28.147Df 2Asymp. Sig. .000

a. Kruskal Wallis Testb. Grouping Variable: Research Class


To find out where the difference it was, the further test using the Multiple

Comparisons Between Treatments (SIEGEL; CASTELLAN, 1988) was administered by

testing the couple of PBMM-DDR, PBMM, and conventional class. The null hypothesis will

be rejected at the 0.05 significance level if the calculated value is more than the critical value.

From the calculation, it was found that there was no difference between PBMM-DDR and

PBMM class, while between PBMM-DDR and conventional, and PBMM and conventional,

there was significant differences. Thus, an increase in creative disposition between PBMM-

22

DDR and PBMM group were same, and it turned decisively better than the conventional

class.

3.10 Interaction between PBL-MURDER, Educational Background, and Mathematical

Prior Knowledge toward PGSD Students’ Mathematical Creative Thinking Ability and

Disposition

By using the Two-Way Anova at a significance level of 5%, some interesting findings

were found related to the interaction between problem-based learning approach (PBL) with

"MURDER" strategy, the educational background, and students’ mathematical prior

knowledge. The summary of the results of Two-Way Anova test are presented in the

following table.

Table 20 – PBL-MURDER interaction, educational background (EB), and mathematical prior

knowledge (MPK), toward final achievement of PGSD students’ mathematical creative

thinking ability (MCA) and disposition (MCD)

Source Dependent VariableType III Sum of

Squares dfMean Square F Sig.

Partial Eta Squared

Corrected Model MCA Gain 1.279a 17 .075 8.074 .000 .576

MCD Gain .417b 17 .025 2.198 .008 .425

Intercept MCA Gain 17.876 1 17.876 1.918E3 .000 .950

MCD Gain 1.053 1 1.053 94.316 .000 .616

Class MCA Gain .624 2 .312 33.464 .000 .399

MCD Gain .198 2 .099 8.861 .000 .308

MPK MCA Gain .055 2 .028 2.975 .056 .056

MCD Gain .024 2 .012 1.089 .340 .009

EB MCA Gain .108 1 .108 11.543 .001 .103

MCD Gain .000 1 .000 .009 .923 .002

Class * MPK MCA Gain .059 4 .015 1.571 .188 .059

MCD Gain .016 4 .004 .353 .841 .001

Class * EB MCA Gain .141 2 .070 7.564 .001 .130

MCD Gain .008 2 .004 .356 .702 .009

Error MCA Gain .941 101 .009

MCD Gain 1.128 101 .011

Total MCA Gain 26.820 119

MCD Gain 3.022 119

Corrected Total MCA Gain 2.220 118

MCD Gain 1.545 118

a. R Squared = .576 (Adjusted R Squared = .505)b. R Squared = .270 (Adjusted R Squared = .147)


Table 20 above indicates several findings as follows.

23

a) The learning approach had a significant influence to the increase of thinking abilitys and

creative dispositions of PGSD students.

b) Meanwhile, mathematical prior knowledge was not too affecting to the increase of

mathematical creative thinking ability and disposition of PGSD students. From the partial

eta squared value, it can be known that the influence of this mathematical prior knowledge

differences is just 5,6% for mathematical creative thinking ability, and 0,9% for

mathematical creative thinking disposition. In other words, each approach which was

conducted increased thinking abilitys and creative dispositions in the relative same range.

c) Educational background gave significant influence on the increase of PGSD students’

mathematical creative thinking ability asa much as partial eta squared = 10,3%. But the

educational background will not give effect to the increase of the mathematical creative

thinking disposition (the influence is just 0,2%). It means that students who are interested

in science will have a tendency to achieve the increase of mathematical creative thinking

ability than non-science group. Meanwhile, the attitude pattern to tend to be creative

between science and non-science group increased equally at the same range.

d) There was no signficant interaction (combined effects) between the approaches and

mathematical prior knowledge toward thinking ability and mathematical creative

disposition mathematical of PGSD students. The influence is 5,9% and 0,1%. It means

that an increase of thinking ability and mathematical creative disposition of the students

had a similar increase at each level in both variables (approaches and mathematical prior

knowledge).

e) Although there was no interaction between the learning approaches and educational

background toward the increase of mathematical creative thinking disposition (it’s

influence is 0,9%), but the interaction was significantly visible toward the increase of

mathematical creative thinking ability (it gave influence as much as 13%).

24

Graph 1 – The interaction between the approaches and educational background toward the increase of PGSD students’ mathematical creative thinking ability

Through a series of hypothesis testing, it was found that the raw input of PGSD

students who become research subjects had initial ability or mathematical prior knowledge

which is relatively same. In other words, it is understandable that all new students who passed

the PGSD admission in the place of study passed through the same steps so the generic

ability, especially mathematical prior knowledge was not different. Similarly, after the

distribution of higher, middle, and lower subgroups, the proportion of three subgroups of the

study in those three classes relatively even.

The mathematical creative thinking ability of PGSD students at the end of the study

showed a difference, from the point of view of learning activities were used. From the results

of data analysis and statistics hypothesis testing, a valuable information was obtained that

PBL-MURDER learning that using teaching materials which is the DDR study result was

better than learning regular PBL-MURDER and conventional, and the regular PBL-

MURDER learning was better than conventional learning in achieving mathematical creative

thinking of PGSD students. This can be seen clearly that students’ learning outcomes would

be optimal if the teaching materials are designed in such a way so that students’ learning

barriers can be minimized (SURYADI, 2010). Beside the teaching material optimization

through a series of DDR studies, it was also found that the mathematical prior knowledge

affected enough to the final achievement of PGSD students' mathematical creative thinking

ability. This is in line with findings of Suryadi (2005), Maulana (2007), and Ibrahim (2011)

that students who initially have a superior prior knowledge would have a tendency to achieve

a higher mathematical creative thinking ability.

25

From the point of view of the approaches and learning strategies, a significant

influence toward PGSD students’ mathematical creative thinking ability achievement was

found. It means that PBL-MURDER learning provides the opportunity for PGSD students to

be able to achieve higher mathematical creative thinking ability than conventional learning.

Related to the increase in mathematical creative disposition, all the approaches that

had been successfully used to significantly increase the disposition, and in fact all of that

approaches can increase disposition with a relatively small difference (or it can be said that

each approach provides a disposition increase that relatively equal). All students’

mathematical creative thinking disposition averagely increased by 11%. If it seen from the

benchmark of gain achievement, it was perceived that it was still a slow improvement. This

can only be understood as a theory of conditioning by Pavlovian (RUSEFFENDI, 1992), that

in order to develop attitude aspects (affective) of students can not be carried out instantly, but

habitually in a long time.

Related to the interactions between the types of approaches that had been selected and

educational background behind the students in learning can be considered more, that although

from the beginning the students have a keen interest in science major, but when conventional

approach was used in learning, that interest that initially was great will be eroded and the

increase was not higher than the students who was interested in the non-science field which

both of them used conventional learning.

4 Conclusion

a) Raw input shows that PGSD students had initial ability or mathematical prior

knowledge which was relatively same. Mathematical prior knowledge (high, middle,

and low) greatly affected on the increase of PGSD students’ mathematical creative

thinking ability. Students who initially had a higher achievement would have a

tendency to achieve a high creative thinking ability.

b) The increase of PGSD students’ mathematical creative thinking ability followed the

problem-based learning with mood-understand-recall-detect-elaborate-review strategy

using teaching materials from the result of didactical design research (PBL-MURDER

and DDR) was better than regular PBL-MURDER and conventional learning, as well

as the general PBL-MURDER learning was better than conventional learning in

increasing the mathematical creative thinking ability of PGSD students. Thus, an

attempt to minimize learning barriers (learning obstacles) through a good teaching

26

materials design and more appropriate for the needs of students will be able to

optimize the learning outcomes of those students.

c) In terms of the educational background, a significant effect on the increase of the

mathematical creative thinking ability of PGSD students could not be ignored. Since

the potential of students at science group was significantly better than the potential of

non-science group in increasing mathematical creative thinking ability. In other words,

students who came from the science group had a tendency to equip and prepare

themselves to face the problems that deplete their creative thinking ability.

d) Learning sets with PBL approach with "MURDER" strategy, whether using DDR

teaching materials or not, gave a better effect than conventional learning in terms of

increasing mathematical creative disposition of PGSD students. It is very possible to

happen, since the PBL process with "MURDER" strategy requires students to be more

active and creative in learning activities, compared to conventional learning which

makes students be more "notified" rather than "finding out".

e) The interaction between the type of the selected approach and educational background

which became the background of students in learning, it was found to have a

significant effect in increasing PGSD students’ creative thinking ability. There was a

tendency that the students who from the beginning had a keen interest in majoring in

science, but because of the conventional approach that was used in learning, their

creative thinking ability was not higher than the students that were interested in non-

science which used the same conventional learning.

References

ABDI, A. Senyum guru matematika dan upaya bangkitkan gairah siswa (The math teacher’s smiles and their efforts awaken the students’ passion). Available at: http://www.waspada.co.id/serba_serbi/pendidikan/artikel.php?article_id= 6722 . 2004.

ARENDS, R.I. Learning to Teach. New York: Mc Graw-Hill, Co. Inc. 2004.

BARRET, T. Understanding problem based learning. Available at: http://www.aishie. org/readings/2005-2/chapter-2.pdf. 2005.

ÇATLIOĞLU, GÜRBÜZ, R., AND BIRGIN, O. Do pre-service elementary school teachers still have mathematics anxiety some factors and correlate. Bolema, Rio Claro (SP), v. 28, n. 48, p.110-127, 2014.

DARHIM. Pengaruh pembelajaran matematika kontekstual terhadap hasil belajar dan sikap siswa sekolah dasar kelas awal dalam matematika (Effect of contextual mathematics

http://www.aishie.org/readings/2005-2/chapter-2.pdf

http://www.aishie.org/readings/2005-2/chapter-2.pdf

http://www.waspada.co.id/serba_serbi/pendidikan/%20artikel.php?article_id=6722

27

learning attitudes toward learning results and early grade elementary school students in math). 2004. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2004.

EVANS, J.R. Creative thinking in the decision and managementsciences. Cincinnati: South-Western Publishing, Co. 1991.

FRAENKEL, J.C.; WALLEN, N.E. How to design and evaluate research in education. 2nd

ed. New York: McGraw-Hill, Inc. 1993.

HULUKATI, E. Mengembangkan kemampuan komunikasi dan pemecahan masalah siswa SMP melalui pembelajaran generatif (Developing mathematical communication and problem solving skills through the learning generative in junior high school students). 2005. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2005

IBRAHIM. Peningkatan kemampuan komunikasi, penalaran, pemecahan matematis, serta kecerdasan emosional, melalui pembelajaran berbasis masalah pada siswa sekolah menengah atas (Increasing mathematical communication, reasoning, problem solving, and emotional intelligence, through the problem based learning in high school students). 2011. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2011.

JENNINGS, S.; DUNNE, R. Discussion papers. Available at: http :// www.ex.ac.uk/telematics/t3/maths/mathfram.htm . 1998.

MAIER, H. Kompendium didaktik matematika (Didactic compendium of mathematics). Bandung: CV. Remaja Rosdakarya. 1985.

MAULANA. Alternatif pembelajaran matematika dengan pendekatan metakognitif untuk meningkatkan kemampuan berpikir kritis mahasiswa PGSD (Metacognitive approach as an alternative of mathematics learning for improving critical thinking skills of PGSD students). 2007. Unpublished master’s thesis, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2007.

MAULANA. Mathematical creative thinking which is necessary. Proceeding of the 2nd

International Conference on Basic Education, Indonesia University of Education, Sumedang, Oct. 2011.

POMALATO, S.W.D. Pengaruh penerapan model trefinger dalam mengembangkan kemampuan kreatif dan pemecahan masalah matematika siswa kelas 2 sekolah menengah pertama (Effect of application of trefinger model in enhancing mathematical creative thinking and problem solving abilities in 2nd class of junior high school). 2005. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2005.

RESNICK, L.B. Education and learning to think. Committee on Research in Mathematics, Science, and Technology Education, University of Pittsburg. 1987

http://www.ex.ac.uk/telematics/T3/maths/mathfram.htm

28

RIF’AT, M. Pengaruh pola-pola pembelajaran visual dalam rangka meningkatkan kemampuan menyelesaikan masalah-masalah matematika (Effect of visual learning patterns to improve the mathematical problem solving ability). 2001. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2001.

RUSEFFENDI, E.T. Pengantar kepada: Membantu guru mengembangkan kompetensinya dalam pengajaran matematika untuk meningkatkan CBSA (Introduction to: Helping teachers to develop competence in teaching mathematics to improve student’s active learning). Bandung: Tarsito. 1992.

RUSEFFENDI, E.T. Dasar-dasar penelitian pendidikan dan bidang eksakta lainnya (Fundamentals of educational research and other exact sciences). Semarang: Unnes Press. 2003.

SANTYASA, I.W. Pembelajaran berbasis masalah dan pembelajaran kooperatif (Problem-based and cooperative learning). Papers on training on innovative learning and assessment for secondary school teachers in the District of Nusa Penida, Indonesia, August 22-24, 2008.

SIEGEL, S.; CASTELLAN, N.J. Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill. 1988.

SISWOYO, T.Y.E. Identifying creative thinking process of students through mathematics problem posing. Proceeding of the International Conference on Statistics and Mathematics and Its Application in the Development of Science and Technology. Bandung Islamic University, p. 85 – 89, October 4-6, 2004.

SLETTENHAAR Adapting realistic mathematics education in the indonesian context. Proceeding of National Conference on Mathematics X, Bandung Institute of Technology. July 17-20, 2000.

SUMARMO, U. Pendidikan budaya dan karakter serta pengembangan berpikir dan disposisi matematis: Pengertian dan implementasinya dalam pembelajaran (Culture and character education serta pengembangan mathematical thinking and disposition: definition and implementation in learning). Paper presented at a national seminar on mathematics education at Siliwangi University, Tasikmalaya, Indonesia, Oct. 15, 2011.

SURYADI, D. Penggunaan pendekatan pembelajaran tidak langsung serta pendekatan gabungan langsung dan tidak langsung dalam rangka meningkatkan kemampuan berpikir matematik tingkat tinggi siswa SLTP (Comparing the indirect learning approach to the combined direct and indirect learning approaches in order to improve mathematical high order thinking skills ini junior high school). 2005. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2005.

SURYADI, D. Didactical design research (DDR) dalam pengembangan pembelajaran matematika (Didactical design research (DDR) in the development of mathematics learning). Paper presented at national seminar on mathematics and science education, Muhammadiyah University, Malang, Indonesia, Nov. 13, 2010.

29

SUZANA, Y. Meningkatkan kemampuan pemahaman dan penalaran matematis siswa smu melalui pembelajaran dengan pendekatan metakognitif (Improving mathematical comprehension and reasoning ability through metacognitive learning approach in high school). 2003. Unpublished master’s thesis, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2003.

WAHAB, A. A. Pendidikan kewarganegaraan (Civic education). Jakarta: Depdikbud. 1996

WAHYUDIN. Kemampuan guru matematika, calon guru matematika, dan siswa dalam mata pelajaran matematika (The ability of mathematics teachers, preservice mathematics teachers, and students in mathematics subject). 1999. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 1999.

WARDANI, S. Pembelajaran inkuiri model silver untuk mengembangkan kreativitas dan kemampuan pemecahan masalah matematis siswa SMA (Silver inquiry learning model for improving creativity and mathematical problem solving ability in high school). 2009. Unpublished doctoral dissertasion, Department of Mathematics Education, Indonesia University of Education, Bandung, Indonesia. 2009.

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