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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 03, MARCH 2020 ISSN 2277-8616
4454
IJSTR©2020
www.ijstr.org
Analysis Of Student Spatial Ability Based On Van
Hiele Theory And Mathematical Disposition Ability
Based On Model Realistic Mathematics Education
Erwin P Silalahi , Bornok Sinaga, Ani Minarni
AbstractThis study aims to: 1) To analyze the ability of student space based on Van Hiele's theory based on the Model Realistic Mathematics Education
2) To analyze mathematical dispositions based on learning models of Model Realistic Mathematics Education 3) To find out the number of indicators of
the ability of spatial ability and mathematical disposition of students achieved which are taught based on Model Realistic Mathematics Education. The
subjects in this study involved students of class XII IPA-1 RK Serdang Murni Private High School who were treated with Model Realistic Mathematics
Education based on Van Hiell's theory in odd semester 2019/2020 with a total of 30 students. The results showed that: 1) The thought process of
students with visualization levels has been able to identify patterns in the building and has been able to determine the pattern of subsequent drawings,
students with the level of analysis have the process of thinking by understanding and seeing images that are triangular nets that face together and
contain many fields. In accordance with the indicator that students can solve problems involving projections of points and lines in a field in three-
dimensional space, students with informal deduction levels describe the answer with the appropriate shapes and vertices, students with deduction levels
understand the picture and see the instructions given then draw them , it means students can deduct evidence deductively, students with rigor level can
determine the shape of an object when viewed from various perspectives and certain situations. This is in accordance with rigor level indicators. 2)
Mathematical Disposition of students after learning on Model Realistic Mathematics Education is in the good category. 3) The overall percentage of
active student activity used during teaching and learning activities is within the ideal ideal time tolerance interval.
Keywords : Spatial Ability, Realistic Mathematics Education Learning, Van Hiele's theory, mathematical disposition
————————————————————
INTRODUCTION
According to Sugiyono (2009: 65) education is one
measure of the progress of a nation. Therefore it is very
important to pay attention to the progress of education in
our country. Education is really needed to create the next
generation of the nation that is qualified and has skills. But
in reality the quality of education in Indonesia is still low.
This can be seen from the Human Development Index
(HDI) data released by UNDP (United Nations Development
Program), which is the composition of education, health and
per capita income ranking which shows that Indonesia's
human development index is still ranked below the world.
The improvement of the quality of education in Indonesia is
also pursued with the hope of improving the quality of
Indonesian education in the future. According to Arikunto
(2015: 86) efforts to improve quality are carried out
conventionally and innovatively considering that education
is a container of activities that can create high quality
human resources. As for what is meant by high human
resources is characterized by the existence of reliable
resources in dealing with the changing times that are
increasingly fast and able to master Science and
Technology (Science and Technology). Mastering and
creating technology in the future requires strong
mathematics from an early age. In other words,
mathematics has an important role in various aspects of
life.Geometry is a branch of mathematics. Geometry is the
key to understanding nature in all its forms in the world.
______________________
Erwin P Silalahi , Bornok Sinaga, Ani Minarni ,Department of
Mathematics, Science Faculty, State University of Medan, Jl.
William Iskandar Ps. V, Kenangan Baru, Sumatera Utara
Indonesia* E-mail of the corresponding author:
erwinsilalahi125@gmail.com
According to Kartono (Khotimah, 2013), based on a
psychological point of view, geometry is the presentation of
abstractions from visual and spatial experiences, such as
fields, patterns, measurements and mapping. Geometry not
only develops the cognitive abilities of students but also
helps in the formation of memory, ie concrete objects
become abstract. Based on this opinion, geometry is an
important material in learning mathematics. According to
Ristontowi, (2013: 16), one of the standards given by
geometry in schools is so that children can use
visualization, have the ability to spatial reasoning and
geometry modeling to solve problems. At the high school
level, the geometry of space taught is known as the Three
Dimensional Space. To study geometry, is not the same as
studying other content standards, for example in geometry
of space, there are 4 dimensions studied namely (1)
visualization, drawing and image construction, (2) study of
spatial aspects of the physical world, (3) use as a tool to
present mathematical concepts, (4) presentation as a
formal mathematical system. For this reason a good spatial
understanding is needed so students can understand the
four dimensions of the geometry of space. Understanding
spatial is known as the ability of student space.The ability of
spatial power is not just an ability that students must master
solely to better understand the concept of building space,
but the ability of space itself indirectly influences the overall
learning outcomes of mathematics. This was confirmed by
Indriyani, (2013) that spatial ability also has an influence on
students' mathematical abilities. That is, if the ability of
mathematical space power possessed by students is high,
then the ability of these students to mathematics in general
is also high. Likewise, Nasution (2017) stated that he found
a positive relationship between mathematics learning
achievement and spatial ability.From the observations
made at the RK Serdang Murni Private High School there
are still many teachers who teach mathematics in the
conventional way, where the teacher explains, gives
examples of questions and students answer the questions
given by the teacher. Thus the importance of the ability of
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 03, MARCH 2020 ISSN 2277-8616
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this power space needs to be owned by students so that
teachers are required to pay attention to this ability in
learning in class. But in reality the ability of spatial power
possessed by students is still weak.Besides the importance
of spatial ability, another thing that is considered important
is the role of students in constructing actively based on Van
Hiele's learning theory. In the development of thinking Van
Hiele emphasizes the role of students in actively
constructing knowledge. Students will not succeed if they
only learn by memorizing facts, names or rules, but
students must determine for themselves the
interrelationships between the concepts of geometry rather
than geometry processes (Clements and Battista, 1992:
436 ). Ismail (1998: 45) states that there are five stages of
understanding geometry, namely: Stage of introduction,
analysis, sequencing, deduction, and accuracy. Based on
the above opinion Van Hiele learning theory can improve
the ability of student space based on the stages of Van
Hiele learning theory. The ability of space based on Van
Hiele learning theory is considered important is the attitude
of students in learning mathematics, one of which is Model
Realistic Mathematics Education.yahputra (2013: 63) states
that a realistic mathematics learning approach on the topic
of geometry with the help of a 3D computer cabri program
can improve the spatial abilities of students in both good
and moderate schools. Likewise the realistic Mathematics
learning approach can improve the spatial abilities of
students who have high, intermediate and low background
early math abilities. In addition there is a shared influence
between the learning approach and school categories on
improving students' spatial ability. This is in line with
research Hasratuddin, (2002: 41) explains the realistic
mathematical approach to find that reasoning, achievement
and interest in learning mathematics students are better
when compared with ordinary learning. Based on this
thinking researchers are interested in conducting a study
entitled "Analysis of Student Space Power Ability Based on
Van Hiele Theory and Students' Mathematical Disposition
Abilities Based on Model Realistic Mathematics Education
".
METHODS
Research Pattern
This research is a descriptive study using a qualitative
approach. Qualitative research is research that intends to
understand phenomena about what is experienced by
research subjects such as behavior, perceptions, actions
and others without generalizing what is obtained from
research (Herdiansyah, 2012).
Participants
Subjects in this study involved students of class XII IPA-1
RK Serdang Murni Private High School who were treated
with Model Realistic Mathematics Education based on Van
Hiell's theory in odd semester 2019/2020 with the number
of students 30 people.
Data Collection Technique
This data collection process includes the process of
entering the research site as well as being in the research
location and collecting research data. Data collection
techniques in this research is the survey method.
Instruments in this study include: a test of mathematical
space ability, student realistic mathematics learning
questionnaire, student activity sheets, interview guidelines,
data triangulation, and documentation in the form of sound
recordings and video recordings.
Validity and Reliability
Validation of learning devices and instruments aims to
obtain valid learning instruments and research instruments
that are suitable for use in research. Learning devices and
research instruments are validated by 5 experts. Based on
the results of the learning device validation it was found that
learning devices were good for use in learning. the
validation of the research instruments was carried out
statistical tests (empirically) to see the validity, reliability so
that the validity of the research instruments was getting
better.
Data Analysis
Analysis of the data used in this study, namely qualitatve
data analysis. Qualitative analysis is used to analyze
student capacity data, student realistic mathematics
learning questionnaire data, student activity sheets through
realistic mathematics learning. The qualitative approach
used in this study follows the concept given by Mile and
Huberman consisting of three activities that occur
interactively and continue continuously until completion.
Data analysis in qualitative research is carried out at the
time the data collection takes place, and after the data
collection is completed within a certain period. At the time of
the interview, the researcher has done an analysis of the
answers interviewed after the analysis feels unsatisfactory,
then the researcher will continue the question again to a
certain stage so that credible data is obtained. After the
researchers have collected data, the researchers anticipate
it before carrying out data reduction. Actually, before the
data is actually collected, there is anticipation that there will
be a reduction in the data when the researcher decides on
the conceptual framework, the research area, the research
problem and the data collection approach to choose. After
that the data is presented and conclusions can be drawn.
RESULT AND DISCUSSION
1) Analysis of Students' Mathematical Spatial
Ability According to Indicators according to
Van Hiele's theory
There are the five stages of level thinking according to Van
Hiele's theory, namely: (1) Level 0 (Visualization); (2) Level
1 (Analysis); Level 2 (Formal Deduction); Level 3
(Deduction); Level 4 (Rigor). This test will be tested on 30
students of class XII Markus Medan Private High School
and then examined and given a scoring. From the scoring
results, students will be grouped into five stages of Van
Hiele's thinking level. Based on the explanation above
follows a table of students' level of thinking.
Table 1. Number of Students at Spatial Thinking Level
based on Van Hiele's Theory
Level
Indicators according to Van Hiele's
theory
Total
Students
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0
Students who reach the visualization
indicator
28
1
Students who reach the indicator of
analysis
25
2
Students who reach the formal
deduction indicator
12
3
Students who reach the indicator of
deduction
6
4
Students who reach the rigor indicator
2
2) Analysis of Student's mathematical spatial
ability
After carrying out learning using the Model Realistic
Mathematics Education on geometry material about
building three-dimensional space for 4 (four) meetings
continued with the test of students to see students'
mathematical spatial abilities. Student answer sheets
corrected based on scoring guidelines are judged based on
valid, objective, fair, integrated, comprehensive and
continuous principles, systematically, critically referenced,
accountable (Permendikbud No. 23 Chapter IV Article 5 of
2016).
Table 2. Scoring Interval Test Students' Mathematical
Spatial Ability
Predicate Interval
Total
Students
Percentage
Predicate
10087 skor
4
13,33%
A
8773 skor
6
20%
B
7360 skor
12
40%
C
600 skor
8
26,67%
D
Based on the results of 30 students 'mathematical power
abilities ability, the level of students' mathematical spatial
ability is obtained in four levels.
3) Analysis of Difficulties of Students' Spatial Ability
Based on Van Hiele Theory
Difficulty Analysis of Students 'Space Ability Based on Van
Hiele's Theory was analyzed through the Realistic
Mathematics Learning model which was reviewed from the
results sheet of students' answers in the tests of space
ability. Analysis of students 'geometrical problem solving
difficulties will be described through students'
understanding of mathematical objects, namely: facts,
concepts, procedures, and principles.
Table 3. The large number of students experiencing
difficulties in the Ability of Student Space Ability Based
on Van Hiele Theory
Difficulties
Experienced by
Students
Many students experience difficulties
according to indicator criteria
1. Facts
6
2. Concepts
11
3. Skills
19
4. Principle
26
From the table above, students had the most difficulty with
principles, which were 26 students. Difficulty in skills as
many as 19 students, difficulty in concept as many as 11
and difficulty in fact as many as 6 students.
4) Analysis of Students' Mathematical Disposition
Capabilities
The description of students 'mathematical disposition can
be seen through the mean score of students' mathematical
disposition of each indicator. From the table above we can
see the average score, which is the confidence indicator at
the initial meeting of 10. Then it increased to 20,3 the last
meeting so that the total average became 15,15. The
flexibility indicator at the initial meeting was 7,13 and then
increased to 7,9 at the last meeting so that the total
average was 7,515. The indicators of persistent and
tenacious at the initial meeting of 11,367 then increased to
19,83 at the last meeting so that the total average became
15,5985. In the indicator of curiosity at the initial meeting of
7,9 then increased to 13,63 at the last meeting so that the
total average became 10,765. The reflective indicator at the
initial meeting was 5,867 and then increased to 11,03 at the
last meeting so that the total average was 8,38. In the
application indicator at the initial meeting of 5,73 then
increased to 10,63 at the last meeting so that the total
average became 8,18.
Table 4. Average of Mathematical Disposition Scores
for Each Indicator Student
No
Indicator
Average Mathematical
Disposition Score
Average
Disposition
Score
First
meeting
Final
meeting
1
Confidence
10
20,3
15,15
2
Flexibility
7,13
7,9
7,515
3
Persistent
and
tenacious
11,367
19,83
15,5985
4
Curiosity
7,9
13,63
10,765
5
Reflective
5,867
11,03
8,38
6
Application
5,73
10,63
8,18
DISCUSSION
1) The ability of students' mathematical space
power is based on Van Hiele's theory based on
Model Realistic Mathematics Education
Based on the results of this study indicate that an increase
in the ability of mathematical space power of students who
are given the RME approach It is natural that there are
differences in the improvement of mathematical
communication skills between students who are given the
PMR approach with students who are given conventional
approaches. In the PMR approach, problems raised from a
child's life are more easily understood by children, because
they are real, affordable to their imagination, and can be
imagined, making it easier for him to look for possible
solutions using the mathematical abilities he already has. If
to understand a child's problem is already difficult, then to
find a solution will find it more difficult, so the child cannot
develop the mathematical abilities that he has.This supports
the statement of Verschaffel, et al (1994: 578) stating that
"Realistic Mathematical Modeling provides realistic contexts
that invite or even force pupils to use communication
knowledge and experience in the problem-solving process,
school arithmetic word problems, perceived as artificial,
puzzle like tasks unrelated to the real world ". Realistic
Mathematical Modeling provides a realistic context that can
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 9, ISSUE 03, MARCH 2020 ISSN 2277-8616
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invite or even force students to use their common sense
knowledge and experience in problem solving processes,
such as school arithmetic words that are considered
artificial and arrange tasks that are like puzzles that are not
related to the real world. Using the Realistic Mathematical
Approach will enable students to be able to visualize and
construct their own various geometric shapes that connect
spatial concepts with numbers. Edy Syahputra's research
entitled "Increasing students' spatial abilities through
Learning Realistic Mathematics (2013: 3) concludes the
Research Results that a realistic Mathematics learning
approach can improve the spatial abilities of students who
have high, intermediate and low initial mathematical
abilities.
2) Mathematical disposition of students using
Model Realistic Mathematics Education
The results showed that there was an increase in
mathematical disposition towards students while learning
with realistic mathematics education. In the RME approach
social interaction occurs, especially in group discussion
activities. This encourages students to express their ideas
verbally and compare with their peers' ideas and help
students learn to respect differences when the process of
solving a problem. In addition, interactions that occur during
discussions can help students of medium and low ability to
keep doing, that is, get the opportunity to learn the skills to
ask questions and comment on a problem presented.This
finding is in line with Mahmudi, (2010), mathematical
disposition is one of the requirements to be able to form
mathematical abilities, including one of the ability of
mathematical power space. Students who have high
mathematical disposition will be more persistent and
diligent in the ability of spatial power, and can form good
habits in learning mathematics. This can encourage these
students to have more ability than the rest who do not show
such mathematical disposition tendencies. Then, the more
ability will affect the formation of mathematical abilities,
including one of the students' abilities in spatial abilities.
CONCLUSION
1. Students' thinking processes on spatial ability after
learning with RME are categorized into five categories
namely visualization, analysis, informal deduction,
deduction, rigor as follows:
Students with the level of visualization have
been able to identify patterns in the building and
have been able to determine the next picture
pattern.
Students with Analysis level have the process
of thinking by understanding and seeing images
which are triangular nets that face together and
contain many fields. In accordance with the
indicator that students can solve problems
involving the projection of points and lines in a
plane in three dimensional space.
Students with Informal Deduction level describe
the answer with the appropriate shape and
vertex.
Students with Deduction level understand the
picture and see the instructions that have been
given then draw it. That means students can
construct deductive evidence..
Students with the Rigor level can determine the
shape of an object when viewed from various
perspectives and certain situations. This is in
accordance with rigor level indicators.
2. Mathematical Disposition of students after RME
learning is in the good category.
3. The overall percentage of active student activity used
during teaching and learning activities is within the ideal
time tolerance.
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