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Development of SMP Student Mathematical Inductive
Reasoning and Beliefs With Guided Inquiry Learning
Nurmuludin
Mathematics Education Department
Universitas Pendidikan Indonesia
Bandung, Indonesia
[email protected]
Abstract—Most of students still believe that the mathematics problems only can be
solved by the formula. This belief cause the student mindset cannot be developed.
Inductive reasoning ability is very important to be had by everyone, because they
always must to take everyday decision inductively. Taking decision on an action to
solve everyday problems depend on they subjective knowledge about the object that
can be the problem solver. This subjective knowledge are called by beliefs. The
Objectives of this research are to knowing about mathematical inductive reasoning
ability and beliefs student of Junior High School development with Guided Inquiry
Learning. The research methodology used literature study about Guided Inquiry
Learning concepts, principles, and procedures so that can developed mathematical
inductive reasoning and beliefs. From the results of study found that eight steps, six
principles, and six strategies of Guided Inquiry Learning supported the mindset of
student inductive reasoning and beliefs development. In Open-Immerse-Explore steps,
support students to explore the ideas of the topic based on their knowledge that they
have in their scheme. Those steps need student beliefs about mathematics and
developed transductive, analogy and generalization abilities. The Identify-GatherCreate steps are the focus guessing, focus inquiring, and concept formation steps from
the ideas that converse to a problem which will developed prediction, formation, and
generalization abilities. While the Share and Evaluate steps are communication and
reflection steps on inquiring results during learning process. Those steps are the peak
of learning and can supported a good mathematical beliefs for students as well as
developed interpretation abilities.
Keywords: Guided Inquiry, Inductive Reasoning, Mathematical Beliefs
I.
INTRODUCTION
Mathematics is a universal science that underlying the modern technology (Depdiknas, 2006).
Mathematics has a important role in some of discipline science and increase the thinking power of people.
Role of mathematics scopes all of people life aspect. Mathematics is way of thinking for people to solving
the problem (Copi & Cohen, 1990). Because of that, if one have been solving the problem, whatever
problems, so he have been doing mathematics.
Many people who mistake to belief mathematics as knowledge. They believe that mathematics is a
calculating science and just learn about formula. Many of them unconscious that doing mathematics
activities always have been done in their life day. Mathematics is not only about calculating ability, but
reasoning ability too. Where the problem has been solved, there the people have been doing mathematics.
Knuth et al. (2011) in his study of reasoning in young children, stating that secondary schools
teenagers is very limited understanding of the general rules of a fact and truth in mathematics. Teenagers
more demonstrate the tendency of empirical facts through inductive reasoning rather than deductive
reasoning. Yopp (2009) states that a mathematical proof is an expression of deductive reasoning (draw
conclusions from the previous statement). However, often inductive reasoning (conclusions drawn on the
basis of examples) that help learners to form their deductive argument, or evidence. Inductive arguments
are generalizations that have been made on the basis of evidence, in this case, the empirical evidence.
Furthermore Michalski (Watters & English, 1995) describes the relationship between inductive reasoning,
deductive reasoning, and analogical reasoning. Where the processing of recognize the existence of an
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analogy between knowledge stored and a real incident intrinsically is inductive reasoning. While the
process of making decisions about the common use of analogical mapping is deductive reasoning.
In mathematics, inductive reasoning is the basis for building a concept. Facts mathematically
identified through inductive reasoning in order to obtain an initial pattern is used as a conjecture as a first
approximation of a mathematical concept. Heit (2007) states there are three (3) study the reasons for the
importance of inductive reasoning. First, that inductive reasoning has regarded to opportunities,
uncertainties, estimates, and the others where it is most associated with everyday reasoning. Second, that
inductive reasoning is a cognitive activity that is very complex and diverse. Inductive reasoning can be
assessed by giving a small child a simple question involving a cartoon or give adults some verbal
statements varied to determine a conclusion. Third, that inductive reasoning associated with a number of
other cognitive activities such as grouping, common ground, the possibility of the decision and
conclusion.
Knuth et al. (2011) identify beliefs involvement of students in the process of inductive reasoning. The
process of identifying a similar pattern is strongly influenced by the belief of students to conjecture the
truth. Where, conjecture is alleged conclusions. Confidence in the truth of conjecture has guided students
in identifying a similar pattern on the facts available. The beliefs in mathematical knowledge possessed
termed mathematical beliefs. Pehkonen (Kislenko et al, 2007) states that the beliefs an individual's
subjective knowledge of a stable, involving feelings or particular attention to the object which the reasons
are not always found in an objective consideration. Beliefs recognize the existence of a very close
relationship between thinking and feeling. It cannot be avoided, because on the one hand beliefs is part of
a person's knowledge is highly subjective and on the other side of the conception of beliefs and feelings
often have in common (Kartini, 2011; Isharyadi, 2015).
According to the language, the Oxford dictionary, beliefs defined as the feeling that something is true
or something accepted as true. Thus, the sense beliefs include two things, namely, the feeling (feel) and
truth (true). Still cannot be determined precisely how the definition of beliefs. However, in everyday
terms, beliefs often interpreted as an attitude, disposition, opinion, perception, philosophy, and values
(and Forgasz Leder, 2002). Given these concepts are difficult to observe and closely interconnected, it is
difficult to find a precise definition of beliefs.
To encourage the activity of inductive reasoning and increase students' mathematical beliefs in doing
math, we need a model of learning that gives students the opportunity to be directly involved in
investigations of mathematical concepts. With this investigation activity, the students will be directly
involved in the process of understanding the mathematical knowledge and improve students'
mathematical beliefs.
Kuhn et al. (2000) defines the inquiry learning as an educational activity in which students
individually and in groups to investigate a set of phenomena (virtual or real) and draw conclusions based
on the phenomenon. In inquiry learning, student do inductive reasoning, where the conclusions obtained
in the learning process is the result of an analysis of the facts observed by the knowledge of the students.
This may indirectly increase the ability of inductive reasoning and mathematical beliefs of students.
Kuhlthau et al. (2007: 2) states that the inquiry is an approach to learning in which students find and
use various sources of information and ideas to improve their understanding of the problem, topic or
issue. Inquiry is not just how to answer questions or get the right answer, but the inquiry to support the
process of investigation (investigation), exploration (exploration), search (search), attempts (quest),
research (research), pursuit (pursuit) and learning ( study). Colburn (2000: 42) describes the Inquiry as the
creation or management of a classroom where students are involved in basic problems of open (openended), centered on the student, and the practical activities of students. Although the student-centered and
emphasizes the open-ended problems, but the inquiry learning does not mean students without guidance,
inquiry forms provide intervention to students in the form of scaffolding.
However, the Inquiry learning students often experience frustration at the exploratory stage (Kuhlthau
et al., 2007). The frustration caused by the inability of students in finding a focus on the ideas expected in
the learning objectives. Therefore we need guidance in investigating and identifying the focus of learning.
Inquiry guided by teachers to enable students gain a depth of understanding and personal perspective
through a variety of sources of information is called Guided Inquiry. Guided Inquiry allows students to
determine the importance of establishing a focus, make decisions, manage investigations, interpreting
facts and organize ideas and share their learning with others. In the model of Guided Inquiry Learning,
teachers and students play an important role in asking questions, developing answers, structuring
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materials and cases (Bilgin, 2009), and jointly create learning materials more meaningful and also inspire
intellectual curiosity (Gialamas et al, 2000).
II.
MATHEMATICAL INDUCTIVE REASONING
Mathematical reasoning is usually divided into two types, namely deductive and inductive reasoning
(Smith et al., 1992; Watters & English, 1995; Klauer et al., 2002; Sumarmo, 2010). Shye (Klauer et al.,
2002) states that inductive reasoning means making the rule essentially, while deductive reasoning
applying the rules. Deductive reasoning is an activity mathematically to draw conclusions on a specific
facts according to the general rules, whereas inductive reasoning is the opposite, namely to draw general
conclusions according to the specific facts (Polya, 1957; Copi & Cohen, 1990; Watters & English, 1995;
Sumarmo, 2010; Lassiter & Goodman, 2014; Molnar et al., 2013; Hayes et al., 2013; Yopp, 2009).
According to Molnar et al. (2013), described as a generalization inductive reasoning to an observation
and experience to find a common conclusion or making a broad rule. Inductive reasoning involves the
expansion of knowledge of which is known to be examples of new ones (Hayes et al., 2013), involves the
facts are there to make the same conclusion (likely) and reasonable (plausible) but not necessarily true
(Lassiter & Goodman , 2014), combines observations and explanations to deduce a rule of something
special into something common (Mantere & Ketokivi, 2013). Inductive reasoning is the formation of
concepts, generalizations facts, and estimate the sample obtained from specific statements into something
more general.
Klauer (De Koning et al, 2002; Hamers et al., 1998) defines the inductive reasoning as an activity to
compare systematically and analytically that aims to find order in the chaos that is real and chaos in the
real regularity. With inductive reasoning, one can find order, rules, generalizations, and also the opposite
can find irregularities (Klauer et al., 2002). Inductive reasoning is an important strategy in problem
solving (Tomic, 1995; Nisbett et al, 1983). Inductive reasoning is the process whereby a person to
generalize based on a number of examples, facts or observations were limited to finding an idea that can
be implemented thoroughly. Inductive reasoning allows one to make predictions on a possible new ones
based on existing knowledge to anticipate solutions to problems (Tomic, 1995; Hayes et al., 2010).
Experts have outlined some of the activities of inductive reasoning. Nisbett et al (1983) suggest that
the formation of the concept (concept formation), a generalization of the facts (generalization from
instances), and the estimate (prediction) are all examples of activities of inductive reasoning. Csapo
(1997) revealed that the majority of inductive reasoning includes the analogies (analogy), completing the
pattern or series (series completions), and create a classification (classifications). Haverty et al. (2000)
states that there are three fundamental activity in the inductive reasoning of data collection (Data
Gathering), discovery of patterns (Pattern Finding), and the formulation of hypotheses (Hypothesis
Generation). Klauer (De Koning et al, 2002; Molnar, 2011; Molnar et al., 2013) divides the task
characteristics of an inductive argument into three classifications: (1) the similarity (similarity) includes
recognize similarities in the nature or generalization (generalization) and recognize the similarity
relationships (recognizing relationship); (2) the inequality (dissimilarity) includes distinguishing
characteristics or discrimination (discrimination) and distinguish the relationship (differentiating
relationship), and (3) a combination of both covers the classification of cross (cross-classification) and the
build system (system construction). Sumarmo (2010) reveals more about the operational activities of
inductive reasoning which includes six (6) activities, among others, (1) Transductive: draw conclusions
from one case or the specific nature of which one is applied to the other special cases; (2) Analogy:
drawing conclusions based on the similarity of data or processes; (3) Generalization: general conclusion
is based on a number of the observed data; (4) Prediction: predict the answers, solutions or trends; (5)
Formation: using patterns of relationships to analyze the situation and draw up a conjecture; and (6)
Interpretation: explain to the model, the facts, nature, relationships, or the existing pattern.
III.
MATHEMATICAL BELIEFS
Researchers felt difficult to separating the concept of attitudes and beliefs. Kartini (2011) states that a
person's beliefs is the attitude of an object as a result of deep involvement and introduction of the object.
Kloosterman (2002) looked at the existence of a direct relation between effort and beliefs. Where, beliefs
have been expressed as the feeling and the knowledge that students bring the influence to their efforts in
their act. Understanding fairly easy to understand and widely expressed by Rokeach (Kislenko et al.
2005) where beliefs are simple statements, whether consciously or not, based on the conclusions of the
words or actions that can begin with the phrase "I believe that ...". To see one's beliefs, can be seen from a
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simple statement. Because, a simple statement is a reflection of the attitudes and knowledge as a result of
its beliefs.
Epistemologically (Op't Eynde et al, 2002), the differences of knowledge and beliefs are that beliefs
have been formed from individual aspects while knowledge formed from the social aspect. Beliefs are
believed to focus on something and deny the fact that other people agree or not. Furthermore, Thompson
and Scheffler (Op't Eynde et al, 2002) suggests knowledge is an aspect that demands a correct conditions,
while beliefs are not bound by elements of accuracy. So that what is disclosed is based on beliefs can not
be used as a reference the truth.
Developments in beliefs form a system of beliefs. Beliefs systems are dynamic and will be
restructured if there is an evaluation of others to one's beliefs. The same thing happens when a change in a
person's cognitive structure. Scheme someone will change as we get experience. Thus, beliefs also will
change beliefs with increasing experience as one component in the cognitive element. The same thing
was disclosed by Muis & Duffy (2013) that a person's beliefs evolved through the dynamic interaction
between the individual and the environment to form a belief in a sustainable manner.
Based on these opinions above it can be concluded that students' beliefs strongly influenced by
environmental conditions and the school where the student resides. Like in the mathematics classes. Then
the conditions and environment in the mathematics classroom will greatly influence the beliefs of
students towards mathematics. Experience during the learning of mathematics will form correct
mathematical beliefs in students.
Op't Eynde et al (2002) found that students' beliefs about mathematics are subjective view clearly and
completely student who is regarded as a truth that affects the way they solve problems and learn
mathematics.
Beliefs about knowledge of a person referred to as epistemic beliefs (Corkin et al, 2015). Epistemic
beliefs include three (3) things: (1) a person's beliefs about where knowledge comes, (2) the core material
or subject knowledge, and (3) how did one known the truth of knowledge. Based on that, if viewed as a
mathematical science, the students 'mathematical beliefs is the students' beliefs about mathematics that
includes the origins of mathematics, the core of mathematics, and how to learn mathematics.
Muis & Duffy (2013) epistemic beliefs more clearly divide students into four (4) dimensions that can
be developed over time and through experience in education, namely (1) certainty/simplicity; (2)
justification of beliefs; (3) source of knowledge; and (4) the attainability of truth.
Dimensions certainty / simplicity is the individual's beliefs about the nature of a knowledge. In
mathematics education, then this dimension expresses the beliefs of students to the nature of mathematics.
Components of certainty on these dimensions reflect whether students saw math as knowledge of both
fixed and variable. While component of simplicity reflect students' beliefs towards mathematics as simple
or complex knowledge.
Dimensions justification of beliefs about students' beliefs that reflect the true knowledge obtained
based on expert opinion or the opinion of students through direct experience. In mathematics education,
the dimension is revealed about the students' beliefs about how to learn is how to obtain evidence of
mathematical truths. This dimension reveals whether mathematical truth is based on the concept of the
experts or the student's own direct observations.
Dimension source of knowledge reflects students' beliefs that knowledge comes from outside himself
and sourced in others such as teachers, other experts or can be derived from the others with him in which
knowledge can be created personally. In mathematics education reveals the dimension of students' beliefs
about mathematics teaching strategies. This dimension reveals that the mathematical knowledge obtained
by the students is the result of discussions with other people instead of himself.
Dimensions attainability of truth reflects a person's beliefs are the truth can finally be achieved. In
mathematics education then this dimension to the efforts of students expressed confidence in solving
mathematical problems. This dimension also encompasses beliefs of students towards mathematics
problems, that all problems can be solved in mathematics.
IV.
GUIDED INQUIRY LEARNING
Kuhlthau et al. (2007: 17) revealed that there are problems that occur in students during the initial
Inquiry, which is in the process of identifying problems and developing hypotheses. In such a step is
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necessary exploration (exploration) and the formulation of hypotheses (formulation) which requires
students to conduct an investigation, raises key questions, the issue of the right or the key issues to be
searched information on the data collection phase.
This stage often causes most students find it difficult and frustrating in the learning process. This stage
is crucial because it determines the success of learning. Uncertainty is the beginning of learning (Kuhlthau
et al., 2007). Initial information students need to keep the quality of learning outcomes through problems
instead of reducing it. Students need to be made aware of their problems and learn to work through the
ideas that led them to the understanding and reduce confusion. Teachers' guidance in the form of initial
information is then that creates learning models Guided Inquiry.
According Kuhlthau et al (2007: 1) Guided Inquiry is an integral part of the Inquiry planned and guided
by the teacher in order to provide a way for students to gain a deep understanding of the concept of
learning materials and information. There are 6 (six) counseling strategies undertaken in Guided Inquiry
among others (1) Collaborate by working with others, (2) Converse are talking about focusing ideas for
clarity and follow-up question, (3) Continue namely the development of understanding all the time, (4)
choose which choose what is in demand and relevant, (5) chart that depicts the idea of using images,
timelines and graphs, (6) Compose ie write whatever occurs during learning.
There are six principles that underlie learning Guided Inquiry (Kuhlthau et al, 2007: 24), namely: (1)
students learn to engage actively and reflect on the experience; (2) students learn to build on what they
already know; (3) students develop higher-order thinking through guidance at critical points in the learning
process; (4) students have ways and different learning styles; (5) students learn through social interaction
with others; and (6) students learn through instruction and experience according to their cognitive.
Steps Guided Inquiry learning by Kuhlthau et al (2012) consists of 8 stages, namely the Open,
Immerse, Explore, Identify, Gather, Create, Share, and Evaluate.
The first stage is Open (Orientation). Open an interesting stage of the students' attention to the
beginning of the investigation process. This stage is very important to set the rhythm / rules and directions
of investigation. The first team learning has decided learning objectives, then makes strong apperceptions
and introduces a general topic that involves all students. The main objective of this phase is to open
students' minds and stimulate curiosity and inspire them to be motivated in pursuit of the investigation.
Apperception designed to spark conversation and stimulate students to think about the content of the entire
investigation and connect with what they already know from personal experience and knowledge.
The second stage is Immerse (Introduction to the problem). Immerse the stage of building the
knowledge base of students together through the experience embedded in students' thinking. Team learning
makes the design ways to engage students so immersed in the whole idea of learning materials by reading
books, stories or articles, watch videos, visit museums, historic sites and pay attention to the experts. The
main objective of this phase is to guide students to connect with the content as a whole and to discover
interesting ideas that they want to explore further. When they build a knowledge base together, each
student find ideas that are important to him and worth reading further to be used as a probe.
The third stage is the Explore (Browsing issue). Explore a variety of sources of information search
phase to explore interesting ideas obtained in phase Immerse. Teacher guides students to apply reading
strategies, view and scan multiple sources. Teacher led them keep an open mind and reflect new
information that they face and begin to find a question that seems very important to them. Guiding students
through this stage will bring them to form a meaningful question.
The fourth stage is the Identify (Invention focus). Identify the pause stage in the investigation process
to develop meaningful questions and forming focus. The main objective of this phase is to build a question
of ideas that are interesting, pressing problems, and bring up the theme.
The fifth stage is a Gather (Research focus). Gather is the stage of collecting information vital to the
question of focus. Team learning guide students discover, evaluate, and use information that leads to
deeper learning.
The sixth stage is the Create (Formation of concept). Create a step to integrate the ideas to the
understanding of the concept of a stronger and deeper. Team learning guide students to explore the facts
and make a simple statement to summarize, interpret and extend the meaning of what they had found and
created a way to share what they have learned.
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The seventh stage is Share (Share the concept). Share a peak stage of the investigation process when
students share the products they have created and show what they have learned. They now have the
opportunity and responsibility to share insights with their peers and communicate to others. An important
component of Guided Inquiry is a collaborative learning happens when students share what they have
learned in the investigation process.
The eighth stage is the Evaluate (self-assessment). Evaluate the closing stages of the investigation
process and an integral part of the Guided Inquiry. This stage also guides students to reflect on the selfassessment of the learning material and their progress through the investigation process. During the process
of reflection will refresh their minds and strengthen learning materials and build good habits in learning.
So, based on the description above, Learning Guided Inquiry as defined in this study is a model
learning Inquiry planned and guided by the teacher in order to provide a way for students to gain a deep
understanding of the concept of learning materials and information with 8 lesson, namely the Open,
Immerse , Explore, Identify, Gather, Create, Share, and Evaluate.
V.
DISCUSSION
Through guidance at critical points in the learning process, Guided Inquiry support high-level thought
processes such as inductive reasoning is maintained. Guidance will rekindle students' beliefs (beliefs) to
continue to investigate and discover the ideas embedded in students.
Although students learn through social interaction with others but Guided Inquiry recognizes that
students have ways and different learning styles. There are no way and learning styles better than others.
Student is a unique person. Nothing is better than the other, they are together have a way and style to
enhance its capabilities. This belief has been instilled in students. It is strongly associated with beliefs,
where students have to trust and believe with the knowledge and experience that already exists within
them. Each student is accommodated to learn through instruction and experience according to their
cognitive.
At this stage of the Open, teachers provide students the essential information needed in the
investigation process. Apperception will increase students' beliefs about the nature of mathematical
certainty that dimension / simplicity. A discussion of prior knowledge, will encourage students to develop
the ability to draw conclusions on a specific case. Indirectly this will enhance the ability transductive.
Immerse At this stage, the teacher presents a problem and guide the students to describe the problem.
Facts already known to students of the problem will increase students' beliefs dimensional nature of
mathematical problems, namely the attainability of truth. Formulation of the problem will develop students'
skills in connecting facts with the information that is already known. It is specifically an analogy skill.
At this stage of Explore, teachers guide students to find information about the existing problems.
Information can be obtained from the Internet or reading books. Then students make notes so finding a
focus problem that should be investigated. Focus invention is to develop students' beliefs about how
knowledge is acquired and developed the ability to draw conclusions from the data similarity is the ability
of generalization.
In the Identify phase, the students with the guidance of teachers make decisions about the focus of the
problems encountered. This phase emphasizes to students that the knowledge acquired together through
discussion. In particular will bring students' beliefs about the way teachers teach. The focus of the problem
is the claim of a major problem. It will develop the predictive ability of students to solve a problem.
Gather At this stage, the students prove focusing problems with the experiments they do themselves.
Thus, it will develop a belief that the knowledge gained through experience alone. Records of the results of
the experiment the students will also improve the ability of preparing a conjecture through patterns to result
from the data obtained. In particular this is the ability of the formation.
In the Create phase, students make conclusions based on the data obtained in step gather and make
products for presentation discussed with friends the other. This will develop students' beliefs about the true
nature of mathematics, that mathematics is not just about counting, but also to reason. Drawing conclusions
based on the similarity of data in particular will increase the generalization ability.
Share on stage, students discuss their findings with another friend. This will increase confidence that
knowledge does not come from myself, but from the results of cooperation and discussion. At this stage
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students will explain the study results, it will increase the ability of the interpretation of the facts obtained
from the experiments.
Evaluate At this stage, the teacher gives a reflection exercises as a result of the investigation the
students. This will increase the belief that all problems can be solved in mathematics. The evaluation
process will also improve the ability of students in the interpretation of the facts that exist in the given
problem.
In general, the relationship between guided inquiry learning, inductive reasoning and mathematical
beliefs can be described as follows:
Guided
Inquiry Stages
Open
Mathematical Skills Development
Guided Stratgies and
Principles

Immerse 
Explore 
Identify 
Gather

Create

Share

Evaluate 
Guided Inquiry Principles:
 Active reflection
 Based on scheme
 Guided on critical spot
 Difference learning style
 Collaborative learning
 Based on cognitive level






Inductive
Reasoning
Beliefs
Guided Strategies:
Collaborate
Converse
Continue
Choose
Chart
Compose

certainty/simplicity

Transductive

attainability of truth

Analogy

justification of beliefs

Generalization

source of knowledge

Prediction

justification of beliefs

Formation

certainty/simplicity

Generalization

source of knowledge

Interpretation

attainability of truth

Interpretation
FIGURE 1. ASSOCIATION BETWEEN GUIDED INQUIRY LEARNING, MATHEMATICAL INDUCTIVE REASONING AND BELIEFS
VI.
CONCLUSION
The principles and stages of Guided Inquiry learning supports upgrading of mathematical inductive
reasoning and beliefs. Guided Inquiry Learning support students to engage actively and reflect on the
experience and build on what they already know. This is an inductive thinking process. Where students
should be actively to involved in real experiences and build the concept through the transductive, analogy,
formation, generalization, interpretation and prediction skills. By building concept which based on what
students already know, it motivates students to develop mathematical beliefs, because they basically have
experiences in mathematics. The experiences they are used to solve mathematical problems.
ACKNOWLEDGMENT
This research was supported by Department of Mathematics Education Graduate School of
Universitas Pendidikan Indonesia Bandung, West Java and SMPN 4 Satu Atap Kedungreja Cilacap in
Central Java as the place where the writer worked. The author would like to say thank you especially for
Drs. Turmudi, M.Sc., M.Ed. Ph.D. and Dr. Bambang Avip Priatna, M.Pd. as supervisor, Dr. Dadan Dasari,
M.Pd. as counselors, Al.Jupri, M.Sc., Ph.D., and Dr. Ilfiandra, M.Pd. as the validators and Sutar, S.Pd.SD
as head SMPN 4 Satu Atap Kedungreja for their contribution to this study. Thanks also goes to all teachers
in MABEST 2014 and SPENSAFOUR were always devoted to supporting education in Indonesia. Thanks
also to Ummi FM, Naurah, Nadhilah and Nabhan who remained with the author wherever located.
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