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JIPM: Jurnal Ilmu dan Pendidikan Matematika
Vol.1 No.2 Oktober (2023)
e-ISSN: 2988-7763
DOI: 10.33830/hexagon.v1i2.5356
Salisa, R. D. & Rahayu, W. (2023). Conceptual Understanding and Reasoning of Students with Dyscalculia: A Literature Review.
HEXAGON: Jurnal Ilmu dan Pendidikan Matematika, 1(2), 94-102. https://doi.org/10.33830/hexagon.v1i2.5356.
Conceptual Understanding and Reasoning of Students with
Dyscalculia: A Literature Review
Resminati Dinda Salisa1*, Wardani Rahayu2
1,2 Pendidikan Matematika, Universitas Negeri Jakarta, DKI Jakarta, Indonesia
* Corresponding Author. E-mail: resminati_1309822002@mhs.unj.ac.id
i
A B S T R A C T
Dyscalculia is a specific learning condition that affects one's
understanding and manipulation of numerical concepts. Conceptual
understanding is one of the components of mathematics proficiency
that can be developed through reasoning skills. However, neither the
conceptual understanding nor the reasoning abilities of students with
dyscalculia have been thoroughly described. The objective of this
systematic review of the relevant scientific literature is to identify and
analyze existing evidence regarding the conceptual understanding and
reasoning skills of students with dyscalculia by using the following
procedures: (1) developing a research question; (2) selection criteria;
(3) developing the search strategy; (4) study selection process; (5)
appraising the quality of studies; and (6) synthesizing results. The
articles were obtained from various online databases. Subsequently, a
meticulous screening process was undertaken based on predetermined
selection criteria, and the quality of the articles was appraised, resulting
in twenty articles for further analysis. It was discovered that students
with dyscalculia lacked conceptual understanding and reasoning skills,
which could present them with a variety of difficulties, such as processing mathematical facts and further
developing their mathematical skills.
INTRODUCTION
Mathematics plays a significant role in human existence and is utilized in numerous fields. It has
been determined that the strategies and abilities gained from mathematics are necessary not only for
academic success but also for effective functioning in day-to-day living (Aprinastuti et al., 2020; Kißler
et al., 2021; Kunwar & Sharma, 2020; Lazo-Amado et al., 2022; Liu et al., 2022; Ziadat, 2022). This
realization comes as no surprise, given the central role mathematics plays in almost every aspect of our
lives (Hodaňová & Nocar, 2016). This underscores the significance of mathematics education in
institutions as well. Mathematics education plays a crucial role in preparing students for their future roles
in society and the economy, as well as for their personal growth (Bakker et al., 2021)
Since mathematics cannot function without the application of extremely high levels of
mathematical skill and knowledge, the primary reason it is taught and practiced in schools is to benefit
society (Aprinastuti et al., 2020; Kißler et al., 2021; Kunwar & Sharma, 2020; Lazo-Amado et al., 2022;
Liu et al., 2022; Ziadat, 2022). The ability to perform well in school and in life generally requires a high
level of mathematical skills due to the nature of modern society (Lyons & Ansari, 2015; Mitra, 2002;
Vanbinst & De Smedt, 2016). It is crucial that students acquire a comprehensive understanding of
mathematics, which involves actively constructing novel knowledge from their prior experiences and
existing knowledge (National Council of Teachers of Mathematics, 2000). Conceptual understanding is
a fundamental component of knowledge, just as it is a part of mathematical proficiency, and it can be
developed through various mathematical skills, such as reasoning. Mathematical reasoning skill is
important as it serves as a basis for developing new insights and promoting further study, and being
able to reason is essential to understand mathematics (Crooks & Alibali, 2014; Hjelte et al., 2020;
Nurjanah et al., 2021)
A R T I C L E I N F O
Article history:
Received : July 13, 2023
Revised : September 24, 2023
Accepted : October 31, 2023
Available : online October 31, 2023
Kata Kunci:
Diskalkulia, Pemahaman
Konseptual, Penalaran
Keywords:
Dyscalculia, Conceptual
Understanding, Reasoning
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Resminati Dinda Salisa / Conceptual Understanding and Reasoning of Students with Dyscalculia: A Literature Review
Undoubtedly, the mathematics that an individual acquires during their academic years will have
a significant impact on their life (Aprinastuti et al., 2020; Kißler et al., 2021; Kunwar & Sharma, 2020;
Lazo-Amado et al., 2022; Liu et al., 2022; Ziadat, 2022). However, 5-8% of school-aged individuals have
a learning disability that makes it challenging for them to understand the fundamental concepts of
mathematics (Fauzan et al., 2022; Lazo-Amado et al., 2022; Patricia & Zamzam, 2021). This learning
disability, known as dyscalculia, along with dyslexia and dysgraphia, is one of the most common learning
disabilities among school-aged individuals (Ahuja et al., 2022; Kariyawasam et al., 2019). Dyscalculia
is a learning condition that makes individuals who have it face difficulty learning and acquiring basic
mathematical skills (Dehghani, 2019; Jannah & Bharata, 2020; Kariyawasam et al., 2019; Kohn et al.,
2020; Kunwar & Sharma, 2020). Students with dyscalculia might find it difficult to develop the
mathematical skills necessary for mathematics proficiency, as they struggle to fully understand
fundamental mathematical concepts (Ahuja et al., 2022; Fauzan et al., 2022; Jannah & Bharata, 2020;
K. E. Lewis et al., 2022; Noordin et al., 2020; Patricia & Zamzam, 2021; Vigna et al., 2022; Ziadat, 2022).
As one of the components of mathematical proficiency, conceptual understanding and reasoning skills
are essential. Therefore, it is necessary to identify these skills in students with dyscalculia."
Understanding the underlying issues that students with dyscalculia face in conceptual
understanding and mathematical reasoning may assist teachers in gaining a better understanding of the
mathematical skills possessed by these students. These insights can also help teachers determine the
type of intervention required for students with dyscalculia to acquire the necessary mathematical skills.
Only a handful of literature reviews have been conducted to cover the mathematical skills of students
with dyscalculia. According to a study on domain-general cognitive skills in children with dyscalculia,
some cognitive domains in children with mathematical difficulties were compromised (Agostini et al.,
2022). Another study that examined the domain-general and domain-specific aspects of developmental
dyscalculia found that visuospatial working memory and symbolic number processing skills were the
best predictors of math ability in children with dyscalculia (Mishra & Khan, 2022). A comprehensive
review of the literature on dyscalculia will serve as the foundation for this study, which aims to investigate
both mathematical conceptual understanding and mathematical reasoning in students with dyscalculia.
This research endeavour is significant in advancing the field of mathematics learning as it seeks to shed
light on the specific challenges faced by students with dyscalculia, ultimately contributing to the
development of targeted interventions and instructional strategies to enhance their mathematical
proficiency.
METHOD
The present study employed a systematic literature review as its research methodology. The
objective of this study is to conduct a systematic literature review (SLR) by employing transparent and
rigorous research methods (Newman & Gough, 2020). The primary goal of this review is to critically
evaluate the existing body of research on the topic under investigation. This study followed the research
methods of Aisyah and Juandi (Aisyah & Juandi, 2022), which consist of six steps outlined below.
Develop Research Questions
The following are the study's research questions, formulated based on the study's background:
1. How do students with dyscalculia understand mathematical concepts?
2. What are the mathematical reasoning skills of students with dyscalculia?
Selection Criteria
The next step in the study's procedures was to define the selection criteria. This study employed
a rigorous selection process to identify relevant articles that aligned with the research questions. This
process involved the application of multiple sets of inclusion and exclusion criteria in the article search
process. The purpose of these criteria was to ensure that only articles meeting the predetermined
standards were selected for inclusion in the study. Specifically, this study included articles published
within the last five years and written in the English language. Using articles published within the last 5
years in academic writing ensures relevance, accuracy, acknowledgment of contemporary contributions,
avoidance of repetition, awareness of evolving methodologies, and alignment with journal requirements,
all of which collectively enhance the credibility and timeliness of the research. Referencing articles
written in English provides access to a diverse body of research, international readership, alignment
with academic standards, and enhanced credibility within the global scholarly community. Table 1
displays the selection criteria employed in this study
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JIPM. E-ISSN: 2988-7763
Table 1. Selection Criteria
Criteria
Inclusion
1. Articles were the results of primary research published
in a journal or proceeding.
2. Articles published from 2019 to 2023.
3. Articles were written in English
Exclusion
1. Chapter book, thesis, brief report, and non-empirical
study types
2. Articles published outside of the stated timestamp
3. Articles were not written in English
Developing the Search Strategy
The present study conducted an analysis of academic papers obtained from various electronic
repositories, including ERIC (https://eric.ed.gov/), Google Scholar (https://scholar.google.com/), and
Crossref (https://www.crossref.org/). The articles were selected using the software tool Publish or Perish
and subsequently underwent an intensive review process. The current investigation utilized the search
term "dyscalculia" to extract academic papers from various databases. Below are the initial searches for
articles on ERIC and Publish or Perish:"
Figure 1. Initial Search on ERIC
Figure 2. Initial Search on Google Scholar using Publish or Perish
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Resminati Dinda Salisa / Conceptual Understanding and Reasoning of Students with Dyscalculia: A Literature Review
The Study Selection Process
During this study, a search strategy was formulated and implemented. The articles and abstracts
obtained through this strategy were subjected to an initial screening process to assess their relevance
and adherence to predetermined selection criteria. Following the initial screening process, a
comprehensive evaluation of the articles was conducted. Articles that did not satisfy the predetermined
selection criteria and were deemed irrelevant were excluded from further analysis
Appraising the Quality of Studies
After the study selection process, the articles were evaluated for quality based on a set of
predetermined criteria to determine their relevance to this study. The following are the quality
assessment criteria:
AQ1. Is the article the result of primary research?
AQ2. Does the article discuss dyscalculia in the educational domain?
AQ3. Does the article address a research problem relevant to this study?
AQ4. Does the article mention mathematical conceptual understanding and/or reasoning of students
with dyscalculia?
Synthesis Result
This study aimed to provide a comprehensive analysis of the mathematical conceptual
understanding and reasoning abilities of students with dyscalculia. To achieve this objective, the
synthesis procedure was executed in accordance with the research objectives. This study involved a
thorough examination of the contents of each article, followed by the identification of the mathematical
conceptual understanding and reasoning abilities of students with dyscalculia. These findings were then
used to address the formulated research questions.
Figure 3. Research Flow
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JIPM. E-ISSN: 2988-7763
RESULT AND DISCUSSION
Result
A total of twenty articles were found to meet the selection and quality criteria during the selection
process. The majority of the studies were conducted at the elementary school level. Among these
studies, 40% were conducted in 2022, and half of them used quantitative research methods. The
distribution of research locations was relatively uniform, with five studies conducted in Asian countries,
four in both North America and Europe, and one each in South America and Africa.
Table 2. Studies Included in the Review
Study
Method
Level
Country
(Erfurt et al., 2019)
Research and Development
Elementary School
Germany
(Dehghani, 2019)
Research and Development
Elementary School
Iran
(Jannah & Bharata, 2020)
Qualitative
High School
Indonesia
(Cheng et al., 2020)
Quantitative
Elementary School
China
(Kohn et al., 2020)
Quantitative
Elementary School
Germany
(Castaldi et al., 2020)
Quantitative
Adult
Italy
(K. E. Lewis et al., 2020)
Qualitative
Adult
USA
(Decarli et al., 2020)
Quantitative
Elementary School
Italy
(Lu et al., 2021)
Quantitative
Elementary School
China
(Firmasari et al., 2021)
Quantitative
Elementary School
Canada
(Kißler et al., 2021)
Qualitative
Elementary School
Indonesia
(Ahuja et al., 2022)
Quantitative
Elementary School
Germany
(K. E. Lewis et al., 2022)
Quantitative
Elementary School
India
(Lazo-Amado et al., 2022)
Qualitative
Adult
USA
(K. Lewis et al., 2022)
Research and Development
Elementary School
Peru
(Vigna et al., 2022)
Mixed Method
Middle School
USA
(Fauzan et al., 2022)
Quantitative
Adult
Italy
(Gut et al., 2022)
Qualitative
Elementary School
Indonesia
(Nkepah & Atanga, 2022)
Quantitative
Elementary School
Poland
Discussion
Mathematical Conceptual Understanding of Students with Dyscalculia
Students with dyscalculia faced difficulties in understanding mathematical concepts, which
affected their ability to work with numbers and operate with them (Bugden et al., 2020; Castaldi et al.,
2020; Cheng et al., 2020; Decarli et al., 2020; Dehghani, 2019; Erfurt et al., 2019; Fauzan et al., 2022;
Firmasari et al., 2021; Jannah & Bharata, 2020; Lazo-Amado et al., 2022; K. Lewis et al., 2022; K. E.
Lewis et al., 2020, 2022; Nkepah & Atanga, 2022). This difficulty also extended to solving mathematics
problems (Dehghani, 2019; Fauzan et al., 2022). Furthermore, they exhibited unconventional
understandings that could be attributed to cognitive differences (K. Lewis et al., 2022; K. E. Lewis et al.,
2020, 2022). For instance, they may have unconventional understandings of integer quantities and
symbolic notation (K. E. Lewis et al., 2020)
These unconventional understandings among students with dyscalculia may result in difficulties
with basic mathematics, not to mention more complex mathematical concepts (Ahuja et al., 2022;
Dehghani, 2019; Erfurt et al., 2019; Kißler et al., 2021; K. Lewis et al., 2022; K. E. Lewis et al., 2022,
2022; Nkepah & Atanga, 2022). Dyscalculia can make it challenging to perform a variety of arithmetic
and numerical tasks (Ahuja et al., 2022; Dehghani, 2019; Fauzan et al., 2022; Kohn et al., 2020; Vigna
et al., 2022) and to apply mathematical concepts in and out of the classroom (Fauzan et al., 2022;
Firmasari et al., 2021; Vigna et al., 2022)
In simpler terms, students with dyscalculia demonstrated difficulty in processing numbers (Gut et
al., 2022). For example, they made more errors when counting and estimating numbers, comparing
numbers, and performing arithmetic operations (Ahuja et al., 2022; Dehghani, 2019; Fauzan et al., 2022;
Firmasari et al., 2021; Gut et al., 2022, 2022; Vigna et al., 2022). Additionally, they displayed the use of
underdeveloped mathematical strategies, such as verbal and finger counting (Gut et al., 2022). One
study categorized the various obstacles faced by students with dyscalculia that impaired their conceptual
understanding of mathematics into four groups: spatial disruption, difficulty understanding concepts,
difficulty understanding formulas or symbols, and calculation difficulty (Jannah & Bharata, 2020). While
HEXAGON: Jurnal Ilmu dan Pendidikan Matematika Vol. 1, No. 2, 2023, pp. 94-102 99
Resminati Dinda Salisa / Conceptual Understanding and Reasoning of Students with Dyscalculia: A Literature Review
these classifications might be attributed to a lack of understanding of mathematical concepts, unclear
instructions from instructors may have also contributed to the challenges faced by students with
dyscalculia (Jannah & Bharata, 2020).
Conceptual understanding refers to a comprehensive and practical grasp of mathematical
concepts (Crooks & Alibali, 2014; Nurhasanah, 2019). Even though it was not explicitly stated in the
majority of the reviewed papers, it is evident that students with dyscalculia lacked conceptual
understanding. The fundamental requirement for students to have a solid conceptual understanding was
the integration of factual and procedural knowledge. However, students with dyscalculia possessed
different factual knowledge than their peers, making it challenging for them to apply their procedural
knowledge correctly. For instance, students with dyscalculia had unconventional understandings of the
use of mathematical symbols and numbers (K. Lewis et al., 2022; K. E. Lewis et al., 2020, 2022),
hindering their ability to apply them correctly when solving mathematical problems.
The struggles of students with dyscalculia may have had a negative impact on other mathematical
skills, such as reasoning and problem-solving. This not only affected their academic performance but
also their social lives due to a lack of conceptual understanding. Several studies have been conducted
to explore strategies aimed at enhancing conceptual understanding among students with dyscalculia.
These strategies include the use of technologies like the mobile application "Kalcal" (Dehghani, 2019)
and augmented reality (Lazo-Amado et al., 2022), as well as specialized interventions for students with
dyscalculia (Cheng et al., 2020; Erfurt et al., 2019; Fauzan et al., 2022)
Mathematical Reasoning of Students with Dyscalculia
Because dyscalculia makes it challenging for students to understand mathematics, it can also
have an impact on their ability to reason (Castaldi et al., 2020, 2020; Fauzan et al., 2022; K. E. Lewis et
al., 2022). Students with dyscalculia may struggle with reasoning, particularly in tasks that rely on
numerical information, spatial and creative reasoning (Dehghani, 2019; Fauzan et al., 2022). They also
lack nonverbal matrix reasoning, a cognitive skill involving the ability to recognize patterns and
relationships between visual elements (Lu et al., 2021). Additionally, students with dyscalculia may face
challenges in multiplication reasoning, which involves various semantic structures related to
multiplication representations, such as repeated addition, arrays, and equal groups (Firmasari et al.,
2021) The mathematical reasoning skills of students with dyscalculia are an understudied area. Out of
the 20 studies reviewed, only seven briefly discussed the mathematical reasoning of students with
dyscalculia. This could be because students with dyscalculia struggle to comprehend elementary
mathematics, leading to the assumption that their other mathematical skills are also lacking. Students
with dyscalculia exhibit poor mathematical reasoning, especially in solving problems that require spatial,
creative, nonverbal matrix, and/or multiplication reasoning (Dehghani, 2019; Fauzan et al., 2022;
Firmasari et al., 2021; Lu et al., 2021). Several studies have explored interventions to enhance
mathematical reasoning skills among students with dyscalculia, including the use of "Kalcal" (Dehghani,
2019) and abacus training in the mathematics classroom (Lu et al., 2021). It is important to note that the
mathematical reasoning abilities of students with dyscalculia vary depending on the severity of their
condition. As Jannah & Bharata (2020) stated, students with dyscalculia, like students in general, have
different strengths and weaknesses, leading to distinct categories.
CONCLUSION
In conclusion, this study has explored the challenges related to conceptual understanding and
mathematical reasoning in students affected by dyscalculia. The comprehensive review of literature and
empirical evidence has underscored the significant obstacles these students face, ranging from basic
arithmetic to broader mathematical applications. This study emphasizes the need for tailored
interventions and instructional approaches to address the unique needs of students with dyscalculia.
Furthermore, it highlights the importance of clear instructions in mathematics education.
This research contributes to our understanding of dyscalculia, shedding light on its impact on
conceptual understanding and mathematical reasoning. It is hoped that these insights will inform the
development of more effective support strategies, promoting inclusivity in mathematics education.
Continued research in this field is essential to further explore dyscalculia and enhance the support
available to individuals affected by it.
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