ABSTRACT
After getting a low score on the 2018 PISA Result in mathematics, Indonesia
faced a significant crisis in 2018. Geometry, which is one of the core principles of
studying mathematics and the relationship between studies and daily life, is one of
the sources of student challenges. Furthermore, Van Hiele is mentioned as having
the greatest influence on geometric thinking, yet this would make it difficult for
each student in a diverse class to change their comprehension. Through the Van
Hiele Model, this study intends to provide an alternative to improve Indonesian
students' geometry thinking. The PRISMA technique is used to conduct
systematic literature reviews on 10 primary and some supplementary publications
in four stages: identification, screening, eligibility, and inclusion and exclusion
criteria. The gathered data is then analyzed and classified into two categories:
personalized learning to improve students' geometric thinking and Geogebra via
MOOC to support effective geometry learning. Finally, the data analysis results
highlight the possibilities of personalized learning by using Geogebra via MOOCs
to improve Indonesian students' geometry thinking using the Van Hiele Model.
Keywords: Personalized Learning, Van Hiele Model, Geogebra via MOOC
INTRODUCTION
Indonesia faced a severe crisis in mathematics in 2018 after receiving a low score
on the 2018 Programme For International Student Assessment (PISA) Result in
mathematics (OECD, 2018). One of the sources of student difficulties is
Geometry, a topic in mathematics with conceptual learning (Faruk Tutkun &
Ozturk, 2013; Hutkemri, 2014). Whereas, one of the fundamental concepts of
learning mathematics is the relationship between subjects and daily life (Faruk
Tutkun & Ozturk, 2013).
According to (S. et al., 2022), the ability to think geometrically is one factor
contributing to geometry's success. Furthermore, Van Hiele indicated that
geometric thinking level is influenced by geometry instruction, although grade
level and biological maturity have less of an impact. (Škrbec & Čadež, 2015). Van
Hiele's model is one of the mathematical learning models with five geometry
stages to acquire knowledge and progress to the next level (Kandaga et al., 2022).
The stages start from level 1, namely visualization; level 2, namely analysis; level
3, namely abstraction; level 4, namely deduction; and the last stage, namely Rigor.
On the other hand, the difference in levels would make it difficult for each student
in a heterogeneous class to alter their comprehension. According to (Abu &
Abidin, 2013), lower-level students still need to establish critical reasoning for a
higher thinking process. In contrast, a higher-level student would challenge to
express their ideas effectively in lower-level terms. Students in Indonesia scored
lower than the OECD average in mathematics, with 28% scoring at Level 5 or
higher (PISA, 2018).
As a result, this study attempts to address the alternative to improving Indonesian
students' geometry thinking by utilizing the Van Hiele Model, emphasizing the
possibilities of personalized learning and Geogebra via MOOCs applied in
geometry learning. To achieve these goals, the current systematic review must
examine literature that discusses the Van Hiele Model, Personalized Learning
Implementation, and Geogebra through MOOC Application.
Research Questions
This study investigated the alternative to improve Indonesian Students’ Geometry
Thinking Through Van Hiele Model to address the major question, “How to
improve Indonesian students’ geometry thinking?” In order to provide an answer
to the main research question, the main question is divided into three subquestions is:
1. How does personalized learning improve students’ geometry thinking through
Van Hiele Model?
2. How is Geogebra via MOOC can support effective geometry learning?
3. How is the application of using Geogebra via MOOC in personalized learning
through the Van Hiele Model?
Objectives
The objective of this study is to provide an alternative to improve Indonesian
students’ geometry thinking in three stages:
1. To investigate the implementation of personalized learning in improving
students’ geometry thinking through the Van Hiele Model.
2. To investigate the application of Geogebra in geometry class.
3. To describe the application of Geogebra via MOOC in personalized learning
through the Van Hiele Model.
Benefits
This study offers several benefits for Indonesian students to improve their
geometry thinking, as follows:
1. To guide Indonesian teachers and students implemented personalized learning
to improve students’ geometry thinking.
2. To guide Indonesian teachers and students using Geogebra via MOOC to
support personalized learning in GeoGebra learning
3. Geogebra via MOOC to support personalized learning in GeoGebra learning
4. To provide a reference for further researchers in developing Geogebra via
MOOC to improve students’ geometry thinking
METHOD
This qualitative study aims to provide an alternative to improve Indonesian
students' geometry thinking by presenting evidence of Geogebra via MOOC in
personalized learning that can successfully contribute to students' geometry
thinking improvement. Therefore, following (Serhan & Yahaya, 2022), a
systematic literature review (SLR) is conducted in this study to discuss the
implementation of the alternative in improving students' geometric thinking. This review typically covers the above-mentioned specific research questions using
evidence from the studies.
Data Source and Search Strategy
Data used for this study were acquired from two sorts of sources: primary and
secondary, which were found on Google Scholar using a combination of search
terms such as "Students' Geometry Thinking", "Mathematics Personal Learning",
and "The Application of Geogebra." This analysis only looked at literature
between the years of 2012 and 2022; no older literature was considered.
The selected literature was assessed applying the Preferred Reporting Items for
Systematic Reviews and Meta-Analyses (PRISMA) technique. PRISMA creates a
standardized, peer-reviewed technique that includes guideline checklists to
contribute to the quality assurance and replicability of the revision process (Conde
et al., 2020). PRISMA has four stages: identification, screening, eligibility, and
inclusion. This study might accurately search for the best-personalized learning
practices using Geogebra via MOOC to improve Indonesian students' geometry
thinking by adhering to PRISMA principles (Mohamed et al., 2022). Figure 2
represents the PRISMA flow chart used in this investigation, which was
developed and modified by Mohamed et al (2022).
Figure 1. PRISMA flowchart
Table 1. Inclusion and Exclusion Crieteria
--
Systematics Review Process
Identification
Google Scholar was used for the search. We developed two main search terms
based on our primary research areas: Van Hiele Model, Personalized Learning,
and Geogebra through MOOC. As a result, the search phrases and tactics are
broadened to include as much relevant research as possible. This study searched
using the following key terms: "Students' Geometry Thinking," "Mathematics
Personal Learning," and "The Application of Geogebra." As a result, at this point
in the process, 2980 journal articles were categorized.
Screening
The PRISMA principles were followed during the selection process, as shown in
Figure 1 (Mohamed et al., 2022). In this method, this study used a range of
inclusion and exclusion criteria. There were no non-Indexed literature or article
reviews, and focusing solely on English-language literature articles reduced the
likelihood of translations that are complicated or uncertain being necessary. Then
this study looked at articles from the prior one decade (between 2012 and 2022).
This study focused on publications with at least one reference to mathematics in
the final step of the screening process. After the screening stage, 150 publications
were determined to be non-compliant with the study's requirements 2830 articles
were left.
Eligibility
The eligibility phase was caused by incomplete articles, as seen in Figure 1. First,
any book that did not match the requirements for improving students' geometry
thinking using the Van Hiele Model was discarded. The title, abstract, technique,
findings, and discussion of each of the 150 works of literature were then thoroughly assessed to ensure they satisfied entry requirements and goals for the
study. Currently, 123 articles have been rejected because they need to adequately
describe the improvement in Students' Geometry Thinking through Van Hiele
Model or clearly describe and review the study findings data. As a result, in the
final stage of the review process, 17 articles were chosen for publication.
Inclusion and Exclusion
Criteria
After obtaining all of the information from all recognized sources, this study used
filtering factors such as timeframe, document type, language, and subject area to
eliminate extraneous articles. The inclusion and exclusion criteria must be
explicitly established when picking items for inclusion and exclusion to guarantee
that the studies selected are pertinent to the primary research goal. The inclusion
and exclusion criteria for this review study, as well as the research findings, are
summarized in Table 1. The significance of 17 papers was established, and fulltext articles from these publications were obtained.
RESULT AND DISCUSSION
The Implementation Of Personalized Learning In Improving Students’
Geometry Thinking Through Van Hiele Model
The van Hiele concept has been proposed as the best and most well-defined
explanation for students' geometry-level thinking levels (Alex & Mammen, 2016).
he model's basis is based on students' engagement in activities identified to attain
the intended goals and discovering aspects connected to geometric ideas that
consist of thinking levels that describes the students' geometric thinking styles
(Faruk Tutkun & Ozturk, 2013). The transition from one level to the next is the
most crucial point in the Van Hiele paradigm. This critical point's advancement
depends on the quality of education supplied.
Hohol (2019) detailed the degrees of geometric thinking were divided into five
stages. The first stage is visual whereby students understand geometric shapes as
gestalt primarily visually, without taking into account components, sections, and
geometric characteristics. The level after that is description or analytic. Children
may visually recognize not only their design and identity, but also their merge
with essence and the relationships between them. The abstract or relational level
is defined by students' grasp of the hierarchical link between geometric qualities
and geometric conceptions relating to sufficient and necessary circumstances. The
next level is standard deduction, where students get definitions, axioms, theorems,
and proofs. The meta-mathematical level is the most significant.
However, gaps in the learning process in the classroom cannot be avoided in this
model (Abdullah & Zakaria, 2013; Abu & Abidin, 2013). Each student will
struggle to share levels in order to comprehend one another. Students at higher
levels will need help to express themselves appropriately in lower-level
vocabulary. On the other hand, students at lesser levels have not yet mastered
critical reasoning for higher cognitive processes. Personalized education in the
present study is considered an educational approach using individual educational
trajectories. Eventually, teachers have issues effectively personalizing and
individualizing learning for each student in the class when they have students with
varying levels of preparation (Dixon et al., 2014; Goddard et al., 2015).
To address this issue, (Thai et al., 2022) have attempted to address this issue by
operationalizing personalized learning based on mastery as an adaptation of the
difficulty level to each student's capability to grasp the subject at a studentfriendly speed. The study discovered that one-on-one tutoring delivers the most
significant learning increases when teachers change the instruction to maintain the
adapted learning to the individual student's level demands. In addition, teachers
expressed a favorable opinion of the systems’ flexibility to distinguish instruction
and address the needs of students where they were at in their comprehension. It
highlights the necessity of individualized mathematical learning, which can
provide more complex information for students who are prepared for the high
level, students may be overlooked by teachers whose time and focus are needed
by students who are failing to master the fundamental levels.
Geogebra to Support Effective Geometry Learning
GeoGebra is a dynamic public software for teaching and learning mathematics
that includes features appropriate for courses such as geometry and algebra by
simply downloading the software from its website www.geogebra.org (Azizul,
2016). GeoGebra software, which includes mathematical features such as symbols
and graphs, can also assist teachers in improving students' grasp of mathematical
ideas and methods (Hutkemri, 2014).
Previous research conducted by (Faruk Tutkun & Ozturk, 2013) has demonstrated
GeoGebra's effectiveness in improving students' geometric understanding. The
study focused on the role of GeoGebra mathematics software on scholastic
achievement and Van Hiele's geometric thinking. The findings revealed that
students utilized dynamic geometry software outperformed students who learned
without GeoGebra. The study also recognized that technology-based applications,
particularly GeoGebra, aid in successful teaching and learning. Meanwhile, Wan
Salleh and Sulaiman (2013) examined the efficiency of GeoGebra application on
instructors' conceptual and procedural mathematics expertise. The topics covered
included the use of differentiation and integration. The results showed that using
GeoGebra increased conceptual knowledge. Aside from that, the use of
technology, particularly GeoGebra, may aid in improving and stabilizing
information for lecturers in the areas of differentiation and integration application.
The Application Of Using Geogebra Via MOOC In Personalized Learning
Through Van Hiele Model
In order to meet the demands of personalized learning to improve students'
geometry thinking, the most significant online public class, a Massive Open
Online Course (MOOC) using the OpenLearning platform, is considered. A
MOOC is a global online learning platform that can handle many learners while
offering various courses tailored to individual needs (Weller & Anderson, 2013).
A program integrated into the teaching and study of mathematics via MOOC can
develop a generation of tech-savvy and open-minded users. It is because
GeoGebra is not only a dynamic software that fosters constructive abilities but
also individual originality (Erlina & Zakaria, 2014; Syairatul, 2014 Furthermore,
MOOCs are participatory, allowing learners to share their perspectives and
improve software-related activities as time passes (Weller & Anderson, 2013;
Baturay, 2015). Therefore, learning Geometry with GeoGebra via MOOC fosters
If teachers provide personalized learning for their students by strategically change
the atmosphere and environment to suit the student's needs level needs in
geometry thinking through Van Hiele Model.
CONCLUSION
After getting a low score on the 2018 PISA Result in mathematics, particularly
geometry, Indonesia faced a major crisis in mathematics in 2018. The ability to
think geometrically, which is separated into five stages called Van Hiele's Model,
is one component contributing to geometry's success. Van Hiele's Model phases
are a five-level aim of obtaining information that begins with level 1, which is
visualization; level 2, which is analysis; level 3, which is abstraction; level 4,
which is deduction; and the final stage, which is rigor. Personalized Learning
becomes an option to improve students' geometry thinking by adjusting the level
of each student's thinking to handle the topic at a student-friendly pace to
maximize the implementation of the Van Hiele Model in Geometry class.
Teachers can benefit from the program's flexibility to differentiate instruction and
meet students where they were in their comprehension by incorporating
personalized learning in the Van Hiele Model.
Furthermore, GeoGebra has been demonstrated to be an effective software for
improving students' geometric understanding. GeoGebra can help Mathematics
concepts be accepted and applied systematically. As a result, in order to meet the
need for personalized learning and Geogebra application in implementing the Van
Hiele Model, the Massive Open Online Course has been modified to improve
students' geometry thinking. Due to the study's entirely theoretical nature,
additional research, including the development of Geogebra via MOOC, as well
as the effectiveness of the application towards users, is advised.
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