The Effectiveness of Geometry Learning Tools in Increasing the Level

of Thinking of Junior High School Students

Sukayasa

1,* a

, I N. Murdiana

and A. Zainal

Mathematics Education Study Program, Tadulako University, Jl. Soekarno Hatta Km. 9, Palu, Indonesia

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

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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

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

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;

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

Studen

t Book

Works

heet

Lesson

Plans

Practice

Question

1 Contents 3.40 3.70 3.47 3.60 3.54

Constructio

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

3.50 3.63 3.56 3.63 3.58

Conclusion Vali

vali

Vali

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

∑

Presentation of material in

Student Books and Student

Worksheets is interesting

Presentation of material in the

Worksheet Students can find the

concept being studied.

The content of the Student

Worksheet is in accordance with

the Student Book

The teaching method used by the

teacher is fun and interesting.

The learning method used by the

teacher can raise students'

interest in learning.

The learning method used by the

teacher can improve

understanding of the concepts

being studied.

Learning process activities can

improve thinking skills.

Learning process activities

increase the attitude of respect

and cooperation in groups.

The language in the Student

Books, Student Worksheets and

Practice Questions is

understandable.

The questions in the Problem

Practice challenge the thinking

process.

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

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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