DOI: 10.30738/union.v11i1.14048 © Author (s), 2023. Open Access
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Mathematical representation ability: A systematic literature review
Jasmine Salsabila Lutfi*, Dadang Juandi
Mathematics Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi No. 229, Bandung 40154, West Java, Indonesia
* Corresponding Author. Email: jasmines.salsabila@upi.edu Received: 6 January 2023; Revised: 19 April 2023; Accepted: 29 April 2023
Abstract: One of the psychological aspects of students that encourage students' mathematical representation ability is self-confidence. The mathematical representation ability of each student is not the same, because of the student's ability to receive and process the information that the teacher has given during the lesson. Thus, the cognitive style also affects the ability of mathematical representation. This article is a systematic literature review (SLR) of 25 studies published until November 2022 with the help of the Publish or Perish (PoP) application with the Google Scholar database. This article aims to investigate:
(a) the characteristics of the period, index, research approach, subject matter, and demographics of the participants in the identified articles, (b) learning methods that can improve students' mathematical representation and self-confidence abilities, and (c) the most frequently used cognitive style type. The results of research with SLR show that the Problem-Based Learning (PBL) learning model is effective and able to develop students' mathematical representation skills, and student self-confidence. Mathematical representation ability studies based on cognitive style mostly use Field Dependent (FD) and Field Independent (FI) types, and rarely use spatial and visualizer-verbalizer types. The results of this SLR can be useful for other researchers who are interested in researching this topic in the form of research gaps that can be done for the next research.
Keywords: Cognitive style; Mathematical representation ability; Self-confidence; Systematic literature review.
How to cite: Lutfi, J. S. & Juandi, D. (2023). Mathematical representation ability: A systematic literature review. Union: Jurnal Ilmiah Pendidikan Matematika, 11(1), 124-135.
https://doi.org/10.30738/union.v11i1.14048
INTRODUCTION
One of the subjects that must be learned in school education in Indonesia is mathematics.
By learning mathematics, students are aimed at having the ability to think mathematically and then be able to use it to deal with constantly changing real-life situations. There are 5 mathematical thinking skills that students must have, namely representation ability, reasoning ability, problem-solving ability, connection ability, and communication ability (NCTM, 2000).
The ability to perform mathematical representation is one of the 5 mathematical thinking abilities that students must master.
Representation is a way to achieve mathematical concepts in various forms (graphs, symbols, as well as diagrams) (NCTM, 2000). Mathematical representation is a key concept in mathematics learning that allows students to interpret and solve problems easily (Supandi et al., 2018). Mathematical representations can be applied to externalize and present student findings (Kalathil & Sherin, 2000). Good mathematical representation skills are needed to master mathematical concepts, then communicate mathematical ideas and finally solve
mathematical problems (Lutfi & Khusna, 2021). Thus, mathematical representation is needed as a tool to display student work and convey mathematical ideas.
In addition to representation skills, students also need to have good self-confidence. Based on the research of Minarti & Senjayawati (2015), there is a positive relationship between mathematical representation ability and student self-confidence. Self-confidence is confidence in carrying out tasks and choosing a good, appropriate, and effective way of solving (Syaifatunnisa et al., 2015). Self-confidence must be developed in students to be able to interpret the learning process of mathematics in real life, so that later the learning process can be maximized, and can improve the representation ability of students (Eviyanti, 2018). Low student confidence can hinder students from learning and developing. For example, students do not dare to present their work in front of the class because they feel insecure.
Each activity or learning process by students when solving problems cannot be separated from how students process and understand the information given to them which is called cognitive style (Fatri et al., 2019). Furthermore, students' cognitive styles affect how students think to use forms of representation that students understand (Ningtiyas & Rosyidi, 2020;
Rahmatika et al., 2022). The process of representation of each student is not always the same.
The difference in the representation process is caused by many things, one of which is the ability of students to receive and process the information during learning takes place due to different cognitive styles (Ruamba et al., 2022). Cognitive style is how students receive and manage attitudes toward the information obtained, as well as habits related to learning.
According to Witkin (in Junita, 2016), cognitive style describes an individual's tendency to understand, think, remember, assess, and solve problems, and also cognitive style determines cognitive strategies applied in various situations. By paying attention to the cognitive style of students in the learning process and its relation to the ability to express mathematical ideas, it is hoped that it can help students to achieve maximum learning goals and success.
Although a lot of research on the ability of mathematical representation in terms of self- confidence (Siregar et al., 2022; Sari & Karyati, 2020; Anggraini & Andriani, 2019; Herdiana et al., 2019; Ifanda & Septian, 2019; Rista et al., 2019; Rudiya et al., 2019; Eviyanti, 2018; Fadilla et al., 2017; Putri et al., 2017; Minarti & Senjayawati, 2015; Syaifatunnisa et al., 2015) or cognitive style (Rahmatika et al., 2022; Rofiq et al., 2021; Amalia et al., 2020; Deviana &
Pramartha, 2020; M. Khairunnisa & Masrukan, 2020; Ningtiyas & Rosyidi, 2020; Fatri et al., 2019; Kusumawardani & Budiarto, 2019; Rahmah et al., 2019; Umah & Vitantri, 2019; Melinda, 2017; Utomo et al., 2017; Junita, 2016) has been conducted in many schools, several different subjects or locations, some gaps are of concern, and need to get more research to fill those gaps. Therefore, the author wants to investigate the ability of mathematical representation in terms of self-confidence or cognitive style using the Systematic Literature Review (SLR) method. SLR is the process of collecting all publications and related documents that have met the inclusion criteria to answer certain research questions (Mengist et al., 2020). Thus, researchers can synthesize general conclusions and find research gaps through SLR to conduct further research.
To date, no SLR research on the ability of mathematical representation in terms of self- confidence or cognitive style has been discussed in previous existing studies. Thus, the Research Questions (RQ) in this systematic literature review of the identified articles are:
RQ1. How does the description of students' mathematical representation based on self- confidence or cognitive style in terms of the year of publication?;
RQ2. How does the description of students' mathematical representation based on self- confidence or cognitive style in terms of publication index?;
RQ3. How does the description of students' mathematical representation based on self- confidence or cognitive style in terms of research approach?;
RQ4. How does the description of students' mathematical representations based on self- confidence or cognitive style in terms of educational level?;
RQ5. How does the description of students' mathematical representation based on self- confidence or cognitive style in terms of research demographics?;
RQ6. How does the description of students' mathematical representation based on self- confidence or cognitive style in terms of subject matter?;
RQ7. What learning methods can improve students' mathematical representations and self- confidence?;
RQ8. What cognitive style type is most often used?
METHOD
This research applies the systematic literature review (SLR) method. The purpose of this study is to accumulate secondary data collected from research results related to mathematical representation ability based on self-confidence or cognitive style. SLR consists of three main stages, namely review planning, review implementation, and review reporting. At the planning stage, researchers identify the need for reviews, determine research questions, and develop review protocols. At the review stage, the researcher identifies and selects the main research, extracts analyze, and synthesizes the data. At the review reporting stage, researchers write reports to disseminate findings from the literature review (Xiao & Watson, 2019). This study uses descriptive quantitative data analysis techniques.
In this study, the data collection technique was to collect research related to mathematical representation capabilities based on self-confidence or cognitive style by utilizing the Publish or Perish (PoP) application with the Google Scholar database. The data are sorted using inclusion criteria that will determine which research will be included in the relevant selected research collection (Stapić et al., 2012). The research instrument in this SLR is in the form of a set of inclusion criteria. The following are set of inclusion criteria defined to establish review limits:
1. This article discusses mathematical representations based on self-confidence or cognitive style regardless of school level.
2. Sinta-indexed articles
3. Articles whose research was conducted in Indonesia.
4. This article is published until November 2022 (the last month in which the article search was conducted), because the researchers wanted to know to what extent the research related to the ability of mathematical representation based on self-confidence or cognitive style was carried out.
5. Focuses on articles that report empirical findings based on quantitative, qualitative, and mixed methods. Thus, theoretical articles and literature reviews are excluded.
6. Articles published in Indonesian or English.
The protocol used for the main study selection process is the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyzes) protocol. PRISMA refers to four steps, namely identification, screening, feasibility, and inclusion (final results of article selection) (Juandi & Tamur, 2020; Moher et al., 2009). Below are the stages of the PRISMA protocol developed by Xenofontos & Mouroutsou (2022) shown in Figure 1.
As presented in Figure 1, at the identification stage, several keywords are used to get a broader article. Overall, the ability of mathematical representation based on self-confidence was obtained in 53 studies, while the ability to mathematical representation based on cognitive style was obtained in 53 studies. Furthermore, at the screening stage, the elimination of studies in the form of a thesis amounted to 61 studies of which 31 studies of mathematical representations based on self-confidence, and 30 studies of mathematical representations based on cognitive style. So, the articles that come in at this stage are articles published in journals only. At the elimination stage, the process of elimination of each of the 7 studies of each keyword that did not meet the inclusion criteria was carried out because it was not indexed. Furthermore, at the final stage, that is, it was included, the researcher eliminated 3
duplicate articles in relation to self-confidence, while 3 duplicate articles in relation to cognitive style were eliminated.
Figure 1. PRISMA Flow Diagram
The final result obtained 12 articles on mathematical representation ability based on self- confidence and 13 articles on mathematical representation ability based on cognitive style.
Thus, 25 articles met all the inclusion criteria that have been identified that will be analyzed in this systematic literature review.
RESULTS AND DISCUSSION
This research resulted in an analysis and summary of a systematic literature review obtained from the Google Scholar database with the help of the Publish or Perish (PoP) application. A total of 25 articles were identified that met all the inclusion criteria in the study. The final result obtained 12 articles on mathematical representation ability based on self-confidence and 13 articles on mathematical representation ability based on cognitive style. The following is presented an overview of the diversity or heterogeneity of the ability of mathematical representation of research based on self-confidence or cognitive style based on the year of
publication, publication index, research approach, subject demographics, subject and class level, as well as the scope of material used in the research to be analyzed.
Research by year of publication (RQ1)
The search for research in this SLR is not limited to the lower limit of the research year related to the ability of mathematical representation based on self-confidence or cognitive style, because the researcher wants to know the extent of developments regarding the research. Based on the final search results, the publication of the first article was found in 2015.
Details of the distribution of research until 2022 are presented in Figure 2.
Figure 2. Research by Year of Publication
Based on Figure 2, it is concluded that the number of published studies related to mathematical representation ability based on self-confidence or cognitive style varies and fluctuates between 2015 to 2022. Based on inclusion criteria, research related to mathematical representation ability based on self-confidence was first published in 2015. The most published mathematical representation ability articles based on self-confidence were in 2019 with a total of 5 articles. Meanwhile, the articles on mathematical representation capabilities based on cognitive style were first published in 2016 and were published the most in 2019 and 2020 with 4 articles each.
Research by publication index (RQ2)
Research related to the ability of mathematical representation in terms of self-confidence or cognitive style was identified and indexed starting from Sinta 1 to Sinta 6. Details regarding the distribution of publication indices related to mathematical representation ability in terms of self-confidence or cognitive style are shown in Figure 3.
Figure 3. Research-based on Publication Index
From Figure 3 it can be concluded that the results of the article are related to the ability of mathematical representation in relation to self-confidence, the majority indexed by Sinta 4 with
2
0 2
1
5
1 0
1 0
1 2
0
4 4
1 0
2 4 6
2015 2016 2017 2018 2019 2020 2021 2022
Total
Year
Year of Publication
Self-Confidence Cognitive Style
0 1 1
9
1 0
0
3
5
3 2
0 0
5 10
Sinta 1 Sinta 2 Sinta 3 Sinta 4 Sinta 5 Sinta 6
Total
Index
Publication Index
Self-Confidence Cognitive Style
a total of 9 articles. Then, followed by articles published and indexed by Sinta 2, Sinta 3, and Sinta 5 with 1 article each. For article results related to mathematical representation capabilities in relation to cognitive style, the majority are indexed by Sinta 3 for a total of 5 articles. Followed by Sinta 2 and Sinta 4 with 3 articles each. The fewest articles are indexed by Sinta 5 with a total of 2 articles. Neither article is a mathematical representation ability based on self-confidence or cognitive style, both have not been published on Sinta 1 and Sinta 6.
Study by research approach (RQ3)
Research related to the ability of mathematical representation in relation to self-confidence or cognitive style identified in SLR uses qualitative, quantitative, and mixed-method research approaches. Details on the distribution of research approaches are presented in Figure 4.
Figure 4. Study by Research Approach
Based on Figure 4, the number of articles on mathematical representation ability in relation to self-confidence is at most using a quantitative approach of 11 articles, followed by a qualitative approach of 1 article, and no one has used a mixed-method approach yet. While the number of articles on mathematical representation ability in relation to cognitive style using the most qualitative approach is 8 articles, followed by a mixed-method approach of 3 articles, and a quantitative approach of 2 articles.
Study by education level (RQ4)
Research related to the ability of mathematical representation in relation to self-confidence or cognitive style is divided into elementary school level, up to university level. Details on the distribution of levels and classes of the subjects of the study are presented in Figure 5.
Figure 5. Study by Education Level
In Figure 5, research on the ability of mathematical representation in relation to self- confidence is dominated at the junior high school level with a total of 9 articles, followed by
1
11
0 8
2 3
0 5 10 15
Qualitative Quantitative Mixed-Method
Total
Research Approach
Research Approach
Self-Confidence Cognitive Style
0
9 3
0
0
7 5
1
0 2 4 6 8 10
Elementary School Junior High School Senior High School University
Total
Education Level
Education Level
Cognitive Style Self-Confidence
the high school level with 3 articles. Meanwhile, research on the ability of mathematical representation based on cognitive style is also mostly carried out at the junior high school level with 7 articles, then high school with 5 articles, and finally at the university level with 1 article.
Research related to mathematical representation based on self-confidence or cognitive style, both dominate at the junior high level. Meanwhile, at the elementary school and university levels, no studies have been conducted yet. The ability of mathematical representation in terms of self-confidence or cognitive style at the primary school level is necessary because the child at the age of 7 to 12 years, according to the stages of cognitive development Piaget is in a concrete phase of operational development. In that phase, the child uses concrete thinking to solve problems (Hamilton & Ghatala, 1994). Mathematical representation acts as a tool to display the student's work and convey students' mathematical ideas.
Study by research demographics (RQ5)
Research related to the ability of mathematical representation in relation to self-confidence or cognitive style identified in this SLR is divided into Sumatra, Java, Kalimantan, Sulawesi, Nusa Tenggara, and Papua. Details on the demographic distribution of the subjects of study are presented in Figure 6.
Figure 6. Study by Research Demographics
In Figure 6, research on the ability of mathematical representation in relation to self- confidence is dominated by Sumatra with a percentage of 75% or a total of 9 studies, while for Sulawesi, Nusa Tenggara, and Papua there has been no research published in the Sinta indexed journal. Sumatra became the most researched area for mathematical representation ability based on self-confidence. This is interesting because in general research on mathematical abilities is dominated by Java Island. This is in line with the research results of Ariati & Juandi (2022) and Khairunnisa et al. (2022) that mathematical ability research dominates in Java and the least in Papua. Meanwhile, research on the ability of mathematical representation in relation to cognitive style was carried out in Java with a percentage of 85% or a total of 11 studies. For the regions of Kalimantan, Sulawesi, and Papua, no research related to mathematical representation capabilities and cognitive style has been published. Therefore, research needs to be carried out in various provinces in Indonesia related to the ability of mathematical representation based on self-confidence or cognitive style.
Study by subject matter (RQ6)
0 2 4 6 8 10 12
9
2 1
0 0 0
1
11
0 0 1
0
Total
Research Demographics
Research Demographics
Self-Confidence Cognitive Style
Research on mathematical representation skills in relation to self-confidence or cognitive style identified in SLRs includes the scope of algebra, statistics, trigonometry, geometry, and PISA questions. Details of the distribution of the scope of the research material are presented in Figure 7.
Figure 7. Research by Subject Matter
In Figure 7, research on the ability of mathematical representation based on self-confidence mostly tests geometric matter with a total of 6 articles. As for trigonometric and statistics material have not found any research publications. Therefore, researchers recommend the need for research on trigonometric material, and statistics related to the ability of mathematical representation in terms of self-confidence. Research on mathematical representation capabilities based on cognitive style mostly tests geometry material with a total of 10 articles.
As for other material still little even on trigonometric material, no article has been found. Thus, research on the ability of mathematical representation based on cognitive style still needs to be studied a lot in other materials, especially trigonometry.
Studies based on self-confidence (RQ7)
Of the 12 articles on mathematical representation ability based on self-confidence, 11 of them are experimental studies used to test a learning method or approach to improve students' mathematical representation ability and self-confidence. The following are the results of research from articles on the ability of mathematical representation based on self-confidence can be seen in Table 1.
Based on Table 1, there is a learning method that does not affect students' mathematical representation ability and self-confidence, namely the guided discovery learning model. Based on the research of Fadilla et al. (2017) and Putri et al. (2017), Guided Discovery Learning model is ineffective in terms of students' mathematical representation ability and self-confidence. In addition, core learning with a scientific approach is not effectively reviewed against the ability of mathematical representation, and student self-confidence (Sari & Karyati, 2020). To improve students' mathematical representation and self-confidence skills, teachers can apply the Problem-Based Learning (PBL) method. 4 experimental studies show positive results using the Problem-Based Learning method on mathematical representation ability, and self- confidence. Based on the results of the research of Herdiana et al. (2019), Rudiya et al. (2019), Eviyanti (2018), and Syaifatunnisa et al. (2015), learning with the PBL model can help foster the development of students' mathematical representation abilities. Students' self-confidence ability develops classically and has a positive impact on students' mathematical representation ability of the PBL learning process.
0 2 4 6 8 10
3
0 0
6
0
3
1 1
0
10
1 0
Total
Subject Matter
Subject Matter
Self-Confidence Cognitive Style
Table 1. Research Results of Mathematical Representation Ability Study based on Self-Confidence
Researchers Research Results
(Minarti & Senjayawati,
2015) Experimental Research. There is no difference in the mathematical representation ability and self-confidence of students who learn using a contextual approach with those who use a contextual approach with a cooperative script.
(Syaifatunnisa et al.,
2015) Experimental research. Problem-based learning is effective in terms of students' mathematical representation and self-confidence skills.
(Fadilla et al., 2017) Experimental research. Guided discovery learning is not effective in terms of students' mathematical representation ability and self- confidence.
(Putri et al., 2017) Experimental research. Guided discovery learning generally does not affect students' mathematical representation ability and self-confidence.
(Eviyanti, 2018) Experimental research. The increase in mathematical representation ability and self-confidence of students who were given the Problem- Based Learning (PBL) model was higher than that of students who were given regular learning.
(Ifanda & Septian, 2019) Experimental research. There is a significant relationship between increased mathematical representation ability and self-confidence of students using ARIAS learning.
(Rudiya et al., 2019) Experimental research. Problem-based learning is effective in terms of students' mathematical representation ability and self-confidence.
(Rista et al., 2019) Experimental research. The increase in mathematical representation ability and self-confidence of students who were given PMR-based humanistic learning was higher than that of students who were given regular learning.
(Herdiana et al., 2019) Qualitative research. Learning with the PBL model can help foster the development of students' mathematical representation abilities. The ability of self-confidence students develop classically and has a positive impact on the ability of students' mathematical representation of the PBL learning process.
(Anggraini & Andriani,
2019) Experimental research. There are differences in mathematical representation abilities between students who take part in exploratory learning and students who obtain conventional learning or are reviewed based on student self-confidence.
(Sari & Karyati, 2020) Experimental research. Core learning with a scientific approach is ineffective in terms of mathematical connection ability, mathematical representation ability, and student self-confidence.
(Siregar et al., 2022) Experimental research. This is the influence of learning models (reciprocal teaching & student facilitator and explaining) on mathematical representation and student self-confidence.
Study by type of cognitive style (RQ8)
The following is an elaboration of the use of the types of learning styles of each of the articles identified in this SLR in Figure 8. Based on Figure 8, the research on mathematical representation ability based on cognitive style mostly uses Field Dependent (FD) and Field Independent (FI) types with a total of 6 articles. According to Slameto, a person with a cognitive style field dependent tends to accept something globally and has difficulty in separating themselves from the surrounding circumstances (Ningtiyas, 2020). Thus, students with field dependent cognitive style can solve problems according to what the teacher has taught.
Meanwhile, students with an independent cognitive style field solve problems according to what they think and can analyze problems without relying on the teacher's explanation.
Figure 8. Research by Type of Cognitive Style
Field independent learners are better at representation skills than field-dependent learners (Junita, 2016). Male subjects with a field-independent style have a stronger tendency to use the help of unconventional representations before expressing them in more conventional representations in the form of graphs (Umah & Vitantri, 2019). Students with Cognitive style FI tend to have fulfilled the three components of attitudes and stages of mathematical representation; Students with cognitive style field dependent tend to have not been able to show attitudes that refer to the three components of mathematical attitudes and have been able to understand problems but are less able to represent and have not been able to solve the solution of given problems (Deviana & Pramartha, 2020). There are differences in the mathematical representation of students through the GeoGebra-assisted PBL model with the RME model in terms of FI learning styles, while for FD there are no significant differences (Amalia et al., 2020).
Students with the field-independent category are able to present ideas or information from a representation, make mathematical equations or models (mathematical ideas) from representations that have been made, solve tasks involving equations or mathematical models, and write representations of solving mathematical problems in words. Students with the field- dependent category are able to present ideas or information from representations, and make mathematical equations or models (mathematical ideas) from the representations that have been made (Rofiq et al., 2021). From Figure 8, research on mathematical representation capabilities based on cognitive spatial style and visualizer-verbalizer are still very rare.
Therefore, this can open up opportunities for researchers who are interested in researching and adding new knowledge about representation capabilities based on cognitive style.
CONCLUSION
Based on the results of the analysis of 25 articles identified by the SLR method, it was concluded that problem-based learning (PBL) is effective and able to develop students' mathematical representation skills, and student self-confidence. Some models are ineffective in mathematical representation ability based on self-confidence, namely the guided discovery learning model and the CORE learning method with a scientific approach. Mathematical representation ability studies based on cognitive style mostly use Field Dependent (FD) and Field Independent (FI) types, and rarely use spatial and visualizer-verbalizer types. Field independent students' mathematical representation ability is better at representation ability than field-dependent learners.
6, 46%
5, 38%
1, 8%
1, 8%
Type of Cognitive Style
Field Dependent (FD) - Field Independent (FI) Reflective - Impulsive
Spatial
Visualizer - Verbalizer.
Based on the inclusion criteria in this study, research on representation ability based on self- confidence has not been carried out at the elementary school & university level, using a mixed- method approach, statistical material, and trigonometry. In addition, research must also be carried out in Java Island and other areas, especially in the regions of Sulawesi, Nusa Tenggara, and Papua. Meanwhile, research on the ability to represent mathematics based on cognitive style has not been carried out at the elementary school level, and trigonometric material. In addition, research should be conducted in the regions of Kalimantan, Sulawesi, and Papua.
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