The Effectiveness of Geometry Learning Tools in Increasing the Level
of Thinking of Junior High School Students
Sukayasa
1,* a
, I N. Murdiana
1b
and A. Zainal
2c
1
Mathematics Education Study Program, Tadulako University, Jl. Soekarno Hatta Km. 9, Palu, Indonesia
2
Mathematics Education Study Program, Ar-Raniry State Islamic University, Jl. Hamzah Fansuri, Banda Aceh, Indonesia
Keywords: Effectiveness, Increase, Thinking.
Abstract: This study aims to obtain a learning device for junior high school geometry based on Van Hiele's theory to
improve students' thinking levels from the level of analysis to the level of informal deduction. The researcher
uses the Four D-Model development method which consists of several stages, namely: define, design,
develop; and (d) disseminate. The definition stage includes examining student characteristics, reviewing
curriculum content, and analyzing tasks and learning objectives. The draft I of the learning tool was made at
the design stage based on the results of the define stage. This draft consists of a Lesson Plan, Student Books,
Student Worksheets, and an evaluation instrument. Then in the develo stage, the activities carried out were to
validate Draft I and test the readability of Draft I (trial I). These results were used to revise Draft I and produce
Draft II. At this development stage, a second trial of Draft II was also carried out. Trial II was used to
determine the practicality and effectiveness of the resulting learning tools. The results of the development of
these learning tools are a set of junior high school geometry learning tools based on Van Hiele's theory,
namely Student Books, Lesson Plans, Student Worksheets, and evaluation instruments that can improve
students' thinking levels from the analysis level to the informal deduction level. This learning tool is needed
by teachers in remedial learning to improve students' thinking from level 1 to level 2.
1 INTRODUCTION
Geometry is a mathematical part that discusses the
concept of mathematics related to planes and spaces.
One of the basic goals of teaching mathematics is to
improve the students' geometric thinking levels (Al-
ebous, 2016). Having Al-Ebous also argues that
geometry is one of the materials in the mathematics
curriculum that can develop spatial abilities and
reasoning (Al-ebous, 2016). According to the theory
of Van Hiele that someone in learning geometry must
go through five levels of thinking that are
hierarchical. The fifth levels are visualization,
analysis, informal deduction, deduction, and rigor
(Erdogan, 2020). Crowley explained the five levels of
thinking as follows: Level 0 (visualization), students
only understand the geometric form of objects but do
not understand the parts of the geometry object
a
https://orcid.org/0000-0003-1058-7397
b
https://orcid.org/0009-0009-2469-2260
c
https://orcid.org/0000-0002-3245-0204
*
Corresponding author
component; Level 1 (analysis), students can
recognize different forms of geometry and their
properties, but not yet understand the relationship of
the properties of the forms of geometry; Level 2
(informal deductive), at this stage students can
identify and classify the properties of geometry and
use the relationship between the properties of
geometry; Level 3 (deductive), at this stage students
can make more meaningful geometry forms and can
construct logical evidence; and level 4 (rigor), at this
stage students can understand the axiomatic system in
a geometry system and be able to verify the impact of
the axiomatic system. The five stages of thinking this
is hierarchical and sequential (Moru et al., 2020). It
means that a student who learns geometry is expected
to increase their level of thinking as the level rises.
According to the theory of cognitive development
from Piaget, ideally, the levels of thinking of junior
420
Sukayasa, ., Murdiana, I. and Zainal, A.
The Effectiveness of Geometry Learning Tools in Increasing the Level of Thinking of Junior High School Students.
DOI: 10.5220/0012230400003738
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 4th International Conference on Innovation in Education (ICoIE 4 2022) - Digital Era Education After the Pandemic, pages 420-426
ISBN: 978-989-758-669-9; ISSN: 2975-9676
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
high school students in learning geometry have
reached the level of informal deduction, although the
axiomatic system has also been introduced. Based on
several research results (Luneta, 2015)(Fuys et al.,
1988)(Clements & Battista, 1992) found students in
learning geometry are still in level 0 and level 1. This
indicates that geometry learning at the junior high
level needs serious attention. According to Van
Hiele, the level of thinking students in learning
geometry from a certain level can be increased to the
next level depending on the learning experience
(Kusuma et al., 2021). This means that the increase in
the level of thinking students is influenced by the
design of learning. Middle school geometry learning
tools that aim to increase the student thinking level of
a certain level to the next level based on Van Hiele's
theory is still very lacking. Though these tools are
needed to help students understand higher geometry
concepts.
Characteristics of the concept of geometry is
abstract and hierarchical. This means that to
understand the C concept is needed a good
understanding of the concept of A and B. Because all
concepts in the mathematical system include
mutually related geometry and hierarchical. For this
reason, the ability to think about the characteristics of
the concept are learned. In the 2013 Mathematics
Curriculum, it has presented junior high school
geometry teaching materials about the concepts of
two parallel lines cut by tranversal lines and their
applications in proving the theorem that is simple. For
example, prove: "The number of sizes of the corners
of a triangel is 180
0
".
To prove the theorem, students must be able to
understand the relationship between traits in the
concept of two parallel lines cut by transverse lines.
This shows that students in learning the concept of
geometry is expected to have achieved a full stage of
thinking 2 (informal deductive) and thinking phase 3
(formal deduction) although relatively simple. Thus,
both based on Piaget's theory and the characteristics
of junior high school teaching materials turned out to
be the level of thinking of junior high school students
in learning geometry is expected to have reached the
level of thinking 2 and the thinking level 3. Based on
this and the results of the research described above
that most of the junior high school students in
learning geometry are still in level 0 and level 1, it is
deemed necessary to have a geometry learning tool to
increase the student thinking level from level 1 to
level 2. Based on the study of several references,
researchers have not found research results that
produce special learning tools like this. This learning
tool is specifically used for remedial purposes in
small groups. This learning tool is designed on a
constructivist basis, so that the geometric concepts
learned are more meaningful. Therefore this study
aims to develop Junior Geometry Learning Tools
based on Hiele's theory of Van to increase the student
thinking level of the analysis level to the informal
deduction level through a development research.
2 METHOD
This research is a development and research. Things
to note in development research are the quality of
products produced. Plomp and Nieveen provide
product quality criteria namely valid (reflecting the
state-of-the art and consistent internal assessment),
have added value, practical and effective (Palupi &
Khabibah, 2018)(Nieveen, 1999). The product is said
to be valid if the material components are based on
state-of the art knowledge (validation of content) and
all components are consistently related (construct
validation). The product is said to be of practical
quality if according to other teachers or experts are
useful and easy to implement by teachers and
students.
Categorized as effective, if it reflects student
experience and expected student learning outcomes.
Therefore the focus of this development research is a
quality product produced by valid, practical and
effective criteria. This learning tool is said to be valid,
if the validator has declared it as such and feasible to
use, even though there is a revision. This learning tool
can be declared to meet practical criteria, if the
respondent (user) of the learning device tends to
provide a positive response. This learning device can
be declared effective, if it can increase the student
thinking level of the analysis level to the level of
informal deduction. The learning tool development
model used in this study is the Four D-Model
proposed by Thiagarajan and Semmel (Thiagarajan,
1974), namely (a) the definition stage, (b) the design
stage, (c) the development stage and (d) the stage of
dissemination. The activities carried out at the
definition stage are examining the content of junior
high school geometry in the curriculum and the
characteristics of students in geometric thinking.
While the activities at the design stage are compiling
and making learning tools based on the results of
activities at the defining stage. The results of the
activities at the design stage are in the form of an
initial prototype (Draft I) of learning tools. The next
activity at the development stage is to carry out trial I
and trial II. Trial I to determine the readability of
Draft I and trial II to determine the effectiveness of
The Effectiveness of Geometry Learning Tools in Increasing the Level of Thinking of Junior High School Students
421
the learning tools developed. The results of the
development in the first trial resulted in Draft II. Then
this Draft II was developed in the second trial and
resulted in a final draft that met the specified criteria.
The data in this study are quantitative and qualitative.
The data collection techniques used in this study
consisted of (a) Van Hiele Geometry Test (VHGT)
developed by Usiskin (Usiskin, 1982). This test is
used to classify students' thinking stages in
understanding geometric concepts; (b) Interview.
Test-based interview activities (VHGT) to confirm
the data obtained from the test results (VHGT); (c)
The researcher used a questionnaire to obtain data on
student responses in writing to test the practicality of
the learning tools developed. Data analysis in this
study used descriptive data analysis. Meanwhile,
specifically for qualitative data, it refers to the
qualitative data analysis of the Miles and Huberman
model, namely: data reduction, data display and
conclusions/verification.
3 RESULTS OF RESEARCH
The results of the development of these learning tools
are as follows:
3.1 Results of the Defined Phase
The results that the researchers obtained at this stage
were: (a) the results of the study of curriculum content
and mathematics textbooks for grade 7 semester 2 for
the 2013 Curriculum, showed that the description of
the concept material for the types of rectangles was
not detailed and did not comprehensively explain the
relationship between the properties of the types of
rectangles and how to define each type of
quadrilateral; (b) the results of the survey and initial
test of the trial development of this learning tools at
SMPN 12 Palu from 15 students tested, which yields
the results of 14 students in the visualization level of
thinking, 4 students in the analytical thinking level
and 1 student in the informal deduction level. This
shows that learning geometry at the junior high
school level needs attention. According to Piaget's
theory of cognitive development, junior high school
students in learning geometry should have reached
the level of informal analysis and deduction thinking;
(c) the geometric concepts obtained from the concept
analysis are the concept of the types of quadrilaterals
regarding their properties, the relationship between
the properties of the types of quadrilaterals and the
definition of the types of quadrilaterals. The types of
quadrilaterals are parallelogram, rectangle, square,
rhombus, kite, and trapezoid; (d) the results of the
task analysis developed are Student Worksheets and
independent assignments contained in the Student
Book; (e) the learning objectives to be achieved are
as follows: determine the properties of each type of
quadrilateral; determine the relationship between
certain types of quadrilaterals and other types of
rectangles; define the concept of a certain type of
quadrilateral based on its properties.
3.2 Results of the Design Phase
The result of development at this design stage is
called Draft I or the initial prototype. This initial
prototype is packaged in Student Books, Lesson
Plans, Practice Questions, and Student Worksheets.
The Student's Book contains teaching materials for
quadrilaterals, especially the properties of types of
rectangles, the relationship between the properties of
types of rectangles, and definitions of types of
rectangles. The material on the types of rectangles
contained in the Student Book includes
parallelograms, rectangles, squares, rhombuses, kites,
and trapezoids. These teaching materials are
presented or packaged on constructivist grounds. This
means that the properties of the types of
quadrilaterals, the relationship between the properties
of the types of rectangles, and the definition of each
type of quadrilateral that students must learn are
expected to be found by students themselves.
Meanwhile, the steps of the Lesson Plan are packaged
based on the syntax of the Van Hiele learning model
which consists of five phases, namely: (a) the
information phase; (b) the directional orientation
phase; (c) the affirmation phase; (d) free orientation
phase and; (e) integration phase. The design of this
learning tool is based on Van Hiele's theory, namely
the theory of thinking levels and Van Hiele's learning
model.
The characteristics of this learning tool are
specifically to improve the thinking level of junior
high school students in learning geometry from the
analysis level to the informal deduction level. While
the teaching materials include rectangular shapes.
The quadrilaterals in question are parallelograms,
rectangles, squares, rhombuses, kites, and trapezoids.
3.3 Results of the Develop Phase
At this development stage, three things are produced,
namely: (a) validation results from the validator; (b)
the results of trial I (readability test), and; (c) the
results of the second trial (effectiveness test and
practicality test). Based on the results of the
ICoIE 4 2022 - The Fourth International Conference on Innovation in Education
422
development at the design stage, it was then validated
by two mathematics lecturers teaching geometry and
three junior high schools.
Table 1: Validation Results.
No.
Analyzed
Area
Average Validator Rating
Avera
ge
Studen
t Book
Works
heet
Lesson
Plans
Practice
Question
s
1 Contents 3.40 3.70 3.47 3.60 3.54
2
Constructio
n
3.50 3.50 3.60 3.70 3.58
3 Language 3.60 3.70 3.60 3.60 3.63
Total
10.50
10.90 10.67 10.90 10.75
Avera
g
e
3.50 3.63 3.56 3.63 3.58
Conclusion Vali
d
vali
d
vali
d
vali
d
Vali
d
Based on Table 1 above, it turns out that all the
learning tools developed meet the valid criteria,
although there are still revisions and the revision
results produce an initial prototype (Draft I).
Meanwhile, in the first trial results, several
words/terms and sentences were found in the Student
Book and Student Worksheets that needed to be
revised. The results of this revision resulted in Draft
II. Then this Draft II was tested (trial II) on class IIB
students of SMPN 12 Palu. This second trial,
involved four test subjects whose thinking level was
at the analysis level, namely IT subjects, AZ subjects,
MA subjects, and EP subjects. Trial II was carried out
for five meetings of learning activities. The results of
this second trial are listed in Table 2 below.
Table 2: Final test results in trial II.
No Trial
Subject
Number of Correct
Answers for Each
Question
Level
Category
1-5 6-10 11-15
1 IT 3 2 2 Level 2
2 AZ 3 1 0 Level 1
3 MA 3 1 2 Level 2
4 EP 3 1 1 Level 2
After triangulating the method with interviews,
the results remained the same as in Table 2 above.
Thus, it can be concluded that the developed learning
tools can improve the subject's thinking level from
level 1 (analysis) to level 2 (informal deduction),
although one subject (subject AZ) is still at the
analysis level. Furthermore, the practicality test of
using the resulting product (learning tool) is shown in
Table 3 below.
Table 3: Student responses to the application of learning
tools during trial II.
No.
Statements in the
questionnaire responded by the
students
∑
1
Presentation of material in
Student Books and Student
Worksheets is interesting
19
2
Presentation of material in the
Worksheet Students can find the
concept being studied.
19
3
The content of the Student
Worksheet is in accordance with
the Student Book
19
4
The teaching method used by the
teacher is fun and interesting.
19
5
The learning method used by the
teacher can raise students'
interest in learning.
19
6
The learning method used by the
teacher can improve
understanding of the concepts
being studied.
19
7
Learning process activities can
improve thinking skills.
19
8
Learning process activities
increase the attitude of respect
and cooperation in groups.
19
9
The language in the Student
Books, Student Worksheets and
Practice Questions is
understandable.
19
10
The questions in the Problem
Practice challenge the thinking
process.
19
Total 190
Percentage (%) 100.00
Total Percentage of Positive/Negative
criteria (%)
(Posi
tive)
0.94
(Negat
ive)
19.05
Number of Students Filling Out
Questionnaire
19
Based on Table 3 above, in general, the students'
responses to the learning tools and processes during
the second trial obtained the average student response
in the positive category reaching 19.05% and in the
negative category reaching 0.95%. This shows that
the learning tool meets the criteria of practicality.
Thus, it can be concluded that the SMP geometry
learning tools, especially the quadrilaterals that have
been developed, have met the valid, practical and
effective criteria. The dissemination stage for the
The Effectiveness of Geometry Learning Tools in Increasing the Level of Thinking of Junior High School Students
423
development of learning tools is carried out at this
seminar and positive suggestions are highly expected.
4 DISCUSSION OF RESEARCH
RESULTS
At the stage of defining the development of these
learning tools, especially the results of the analysis of
the K-13 curriculum, it turns out that in the
curriculum the content of the material does not
explain the properties of the types of rectangles in
detail and comprehensively. In the Mathematics
Package Book for grade VII for K-13, there is also no
correlation between the properties of the
quadrilaterals; so students understand the concepts of
quadrilateral types not comprehensively. As a result,
students find it difficult to find interrelationships
between concepts of the quadrilateral type. This is by
the opinion of the researchers, that students are not
accustomed to doing formal proofs in learning
geometry at school, but more informal geometry
learning is needed (Alex & Mammen, 2016).
Therefore, it is necessary to present the material in an
orderly, systematic, and comprehensive manner, so
that students have complete knowledge and
understanding of the types of quadrilaterals. For this
reason, it is also necessary to have a concept map
between the concepts of the types of quadrilaterals as
a means for students to understand the properties and
definitions of the concepts of the types of
quadrilaterals.
Based on the results of the initial test, most of the
students of SMPN 12 Palu in learning geometry 14
were at the visualization level, 4 students were at the
analysis level and 1 person was at the informal
deduction thinking level. According to intellectual
development theory, junior high school students
should be able to think formally. This means that
students' understanding of geometric concepts should
be more abstract and not at the visualization level.
Students should be able to understand more abstract
geometric concepts, whether presented in the form of
definitions or theorems of the relationship between
concepts. Therefore, based on the characteristics of
students who are still in visualization thinking and the
ideal competencies that junior high school students
should have, it is appropriate that the development of
this learning tool was developed through this
research. According to intellectual development
theory, junior high school students should be able to
think formally. This means that students'
understanding of geometric concepts should be more
abstract and not at the visualization level. Students
should be able to understand more abstract geometric
concepts, whether presented in the form of definitions
or theorems of the relationship between concepts.
Therefore, based on the characteristics of students
who are still in visualization thinking and the ideal
competencies that junior high school students should
have, it is appropriate that the development of this
learning tool was developed through this research.
According to De Villiers (Alex & Mammen, 2016),
the revision of the curriculum on geometry material
in elementary schools will determine the success of
students in learning geometry in junior high schools.
Related to this, the design of learning tools
developed, especially Student Books and Student
Worksheets are designed with the aim of increasing
students' thinking stages from the analysis level to the
informal deduction level. Construction of Student
Books and Student Worksheets on a constructivist
basis. This means that the core concepts being studied
can be found by students themselves through
activities in learning.
At the development stage, the learning tools
developed were validated by mathematics education
lecturers and junior high school mathematics
teachers. Aspects that are validated include aspects of
material content, construction, and language aspects.
The validation results show that the developed
learning tools meet the valid criteria, although there
are several revisions. Most of the revisions are related
to language aspects, especially terms/words, and
sentences. This is also related to the results of trial I,
it turns out that there are terms/words or fragments of
sentences that students do not understand, so
revisions are needed. Then revisions were made and
then the revised draft was tested in the second trial to
determine the effectiveness of the developed learning
tools. This is by Van Hiele's opinion that the
language used in learning geometry is very important
(Al-ebous, 2016). Therefore, the language factor in
the form of writing, symbols or verbal in learning
geometry greatly affects students' understanding of
the concepts being taught.
The results of this second trial indicate that the
learning tools developed meet the effective criteria. It
is evident that the four experimental subjects
experienced an increase in the thinking level from the
analysis level to the informal deduction level,
although there was one experimental subject that did
not experience an increase in the thinking level. This
shows that the learning tools developed are quite
effective in increasing the thinking level of junior
high school students in learning geometry from the
analysis level to the informal deduction level. At the
ICoIE 4 2022 - The Fourth International Conference on Innovation in Education
424
transition level of thinking from the analysis level to
the informal deduction level, conceptualization skills
are needed. Some research results show that
conceptualization is a cognitive process that is often
experienced by students when solving problems
(Noor & Alghadari, 2021)(Aghadari, 2021).
The weak mastery of geometric concepts
experienced by students is due to the lack of student's
ability to solve problems (Noviana & Hadi,
2021)(Aghadari, 2021). The low level of thinking
ability of students is caused by the learning strategies
used in schools. Therefore, learning geometry should
place more emphasis on problem solving, reasoning
and spatial abilities (Hassan et al., 2020)(Cahyanita et
al., 2021). In addition, language also plays an
important role in learning geometry. A teacher in
teaching geometry must use language that is in
accordance with the development of students'
thinking (Pasani, 2019). Students at the abstraction
thinking level have understood the concept definition
well. This means that students have been able to
understand the meaning of the definition, even though
the representation is different from the definition
presented formally. A student in constructing the
meaning of a concept depends on his ability to
understand the definition of the concept. Therefore,
the role of definition is very important in constructing
the meaning of a concept (Haj-Yahya, 2021).
The results of the practicality test of using
learning tools also indicate a positive thing. Because
most of the students' responses to learning tools in the
second trial process were in the positive category with
an average of 19.05% and only an average of 0.95%
in the negative category. This means that students are
quite good at responding to the learning tools used
and it means that the learning tools developed meet
the practical criteria.
Thus the geometry learning tool for junior high
school level developed through this research has met
the valid, practical, and effective criteria for
improving students' thinking level from the analysis
level to the informal deduction level.
5 CONCLUSION
Based on the results of this development research, a
geometry learning device for junior high school level
based on Van Hiele's theory has been obtained which
can improve students' thinking levels from the
analysis level to the informal deduction level. These
learning tools are Student Books, Lesson Plans,
Student Worksheets, and Practice Questions. The
specifications of this learning tool are as follows: (a)
this learning tool is based on Van Hiele's theory, both
the theory of the thinking levels and Van Hiele's
theory of learning; (b) constructivist-oriented
learning tool activities. This means that the geometric
concepts learned are constructed by students through
learning activities; (c) this learning tool specifically
aims to improve students' thinking level from the
analysis level to the informal deduction level on the
material of quadrilateral concepts in junior high
school. The concepts of quadrilaterals that are the
focus of the study are the properties of quadrilaterals,
the relationship between the properties of the types of
quadrilaterals, and the definition of each type of
quadrilateral; (d) this learning tool is used for
remedial purposes, both individually and in small
groups.
ACKNOWLEDGMENTS
This research was funded by the Tadulako University
FKIP DIPA fund. Therefore, the researcher would
like to thank you very much for the funds provided to
finance this research process.
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