Mathematical Learning Difficulties - Dyscalculia

Dyscalculia is a learning difficulty faced by an individual. The purpose of this study is to investigate the level of problems of dyscalculia in primary schools. The researchers employed quantitative design to carry out the study. Survey method is used to collect the data. Descriptive and inferential statistics are used to analyze the survey data. A study was conducted with 381 primary schools Mathematics teachers in Malaysia. Means and standard deviation were used to analyze the level of problems of dyscalculia, whereas independent t-test were used to compare the level of problems of dyscalculia between school locations. The results show that the level of problems of dyscalculia is medium high (M=3.31, σ=0.97). On the other hand, the problem of dyscalculia in rural area is slightly higher (M=3.822, σ=0.697) than the urban area (M=3.717, σ=0.696). In short, there is no significant difference for the level of problems of dyscalculia between different school locations (p=0.147, p>0.05). This study is able to bring significances to Ministry of Education Malaysia, educators, teachers, and researchers. The result is useful to determine the allocations of funding and resources for the students with learning difficulties. It is also able to create the awareness of dyscalculia among the people. As a conclusion, interventions and diagnosis need to be carried out in order to improve the capabilities of these pupils to the maximum.

At  least  20%  of  adults  have  very  low  numeracy  (Bynner  &  Parsons,  1997)  and  about  5-8%  of  the  population has severe specific  Mathematical  Learning  Disabilities  (Butterworth,  Varma  &  Laurillard,  2011).  Failure  to  acquire  basic  mathematical skills  may  have  serious  life-long  consequences.  Thus,  it  is  important  to  find  ways  of  enabling  children  with  MLD  to  acquire numeracy skills. The present study involved 10 children in Grade 3 (7 to 8 years old), identified by their teachers as struggling with mathematics.  They were assessed using the Dynamo Assessment, which provides a profile of strengths and weaknesses in  important  components  of  mathematics.  Five  children  acted  as  controls,  while  the  otherfive  followed  the  Dynamo Intervention  programme.    The  intervention  lasted  for  eight  weeks.    All  the  children  were  subsequently  re-assessed  using Dynamo  Assessment.  The  profiles  of  the  children  who  had  undergone  intervention  showed  improvement  in  most components, while the control group did not

Mathematics is an important subject for every pupil. We learn mathematics since early childhood education, primary school, secondary school, and even in higher education. It is needed in our everyday life, yet there are many pupils who afraid of this mathematics subject. This is happening especially among the dyscalculic pupils. Dyscalculia is a type of learning disabilities as the same categories as dyslexia. However, dyscalculia remains behind dyslexia in terms of research and understanding. Dyscalculic pupils are a group of pupils with special educational needs. More researches in this field are very crucial to be developed. Hence, the purpose of this study is to introduce the symptoms, instruments, diagnosis and interventions of dyscalculia. This introduction of dyscalculia will be explained based on the previous
literature reviews and previous studies. The impact of this study is it will provide a fundamental knowledge for researchers in future researches as well as special education teachers or mainstream teachers to understand about their pupils who might have symptoms of dyscalculia. By this knowledge, they can also learn about some instruments,  diagnosis, and interventions to improve the mathematics learning and even reduce the impact of dyscalculia on the pupils.

Hakkarainen, Airi
The relationship between mathematical and reading difficulties, upper secondary
education and enrolment to post-secondary education or work life
Joensuu, University of Eastern Finland, 2016, 53 pages
Publications of the University of Eastern Finland.
Dissertations in Education, Humanities, and Theology; 82
ISBN: 978-952-61-2034-8 (nid.)
ISBN: 978-952-61-2035-5 (pdf)
ISSNL: 1798-5625
ISSN: 1798-5625
ISSN: 1798-5633(pdf)
Abstract
This dissertation examined how mathematical and reading difficulties during comprehensive
education and the long-term effects of cumulative learning difficulties affect a young
person’s upper secondary education and subsequent enrolment to further studies or work
life. Further emphasis was put on the effects that educational support for upper secondary
studies and cumulative learning difficulties have on a successful educational track or on the
development of a negative educational track. The research material consisted of longitudinal
data from the Staying on Track of Learning research project conducted at the University
of Eastern Finland. Since 2004, the research project has followed the educational paths of
Year 9 students (N = 585) from a city in Eastern Finland through upper secondary education
into further studies or the transitional phase into work life. The research data was analysed
using structural equation modelling, which enabled us to investigate how learning difficulties
as whole and as distinct difficulties affect a young person’s education and career.
The research project’s three sub-studies examined young people’s educational tracks at
different stages. The first sub-study investigated how mathematical and reading difficulties
(measured in Year 9) and self-reported learning difficulties are linked to young people’s
enrolment to upper secondary education. The results of the study suggest that mathematical
and reading difficulties affected the young people’s school achievement by lowering
it significantly. Mathematical and reading difficulties along with low school achievement
contributed to young people – boys markedly more than girls – choosing vocational education
(i.e. a vocational track) rather than general upper secondary academic education (i.e. an
academic track) after compulsory education. Furthermore, if a young person experienced
difficulties in their learning during compulsory education, they were more likely to choose
a vocational track instead of an academic one.
The second sub-study examined how mathematical and word-level reading difficulties
that were measured in Year 9 were linked to educational support for upper secondary studies.
In particular, we examined how the aforementioned learning difficulties along with the
educational support received affected a young person graduating from upper secondary
education. The results of the sub-study suggest that young people with learning difficulties
did not receive educational support at the beginning of upper secondary education. Mathematical
and word-level reading difficulties were not a basis for receiving educational support until the second year of studies. In addition, the educational support given did not always
correct a negative educational path. Eighty-two participating young people dropped
out of upper secondary education, with half of them having mathematical or word-level
reading difficulties. It was also notable that mathematical difficulties were directly linked to
the discontinuation of studies during upper secondary education, while word-level reading
and mathematical difficulties weakened school achievement during upper secondary
education and increased the risk of dropping out.
The third sub-study investigated how young people’s mathematical and reading difficulties,
along with externalising and socio-emotional disorders, affected their graduation
from upper secondary education, continuing studies after upper secondary education, and
contributed to exclusion from education and employment. The results suggest that mathematical
and reading difficulties noticeably affected their graduation from upper secondary
education and subsequent education and employment opportunities. A notable finding was
that mathematical and reading difficulties seem to affect young people’s educational paths
in different ways. Mathematical difficulties contributed to them not continuing their studies
after upper secondary education. Furthermore, mathematical difficulties combined with
low prosocial skills put a young person at risk of joining the ranks of those not engaged in
education, employment or training five years after completing basic education. Reading difficulties,
combined with externalising disorders seemed above all to delay graduation from
upper secondary education.
The results suggest that mathematical and reading difficulties clearly increase the risk
of dropping out or delaying graduation from upper secondary education. They also add to
the possibility of exclusion from education and employment. Learning difficulties can thus
be regarded as factors that can push young people to the brink of marginalization. The basis
of the Finnish educational system is to create equal learning opportunities, regardless of
students’ circumstances. The results of this study suggest that educational equity does not
sufficiently materialise for those with learning difficulties.
Keywords: mathematical difficulties, reading difficulties, externalising problems, socioemotional problems, school achievement, transition, support, secondary education,
educational career, dropout

In recent years there have been significant advances in the use of ICTs (Information and Communication Technologies) in the education of students with learning disabilities. In this paper we represent some important studies which highlight the importance of using ICTs, with special reference to online and mobile learning applications, both for assessment and intervention required for students with dyscalculia. Results of the studies revealed that the use of ICTs in education and especially in children with dyscalculia, may in the future become an integral part of the global education process, however there are still many parameters to be investigated.

Dyscalculia is one of the less well-known learning problems in mathematics due to lack of exposure and study. Children with dyscalculia usually face arithmetic and symbolic number comparison issues, with about 3-6 percent of individuals affected. The lack of wide-ranging study and inconsistency in the condition's characterizations through studies have impeded progress in identifying the root causes of dyscalculia and how best to handle it. This problem can be more serious because it can prolong up to adulthood. Therefore, this paper will discuss the general aspects related to dyscalculia problems and their effects on children in their lives. This paper also explains the signs and symptoms that are needed to understand children who may have dyscalculia. Finally, this paper discusses what treatments or methods can be used significantly to help children improve their mastery and mathematical skills, including treatment for co-occurring issues. The implications are society should be aware of possible problems with their children related to dyscalculia and should always increase their initiative to use various methods to address the symptoms of dyscalculia, especially for children who also have other learning problems such as dyslexia and ADHD. Besides, increased knowledge of this distinction going forward, combined with longitudinal observational studies, provides tremendous potential to deepen our understanding of the condition and establish successful educational approaches.

Although learning disabilities study is in advanced stage, research related in algorithmic procedures is limited, since interest in this field is recently displayed. This discourse describes some cognitive and algorithmic principles, which rule the development of a software related to dyscalculia. More specifically,this software design is based on principles related to the diagnostic evaluation of dyscalculia . The proposed software is based on the assumption that dyscalculia is noticed due to a lack of understanding of mathematical concepts and aims at understanding the cerebral reproductions of algorithmic procedures. One of the challenges is the analysis and evaluation the difficulties related to algorithmic mathematical thinking. A key point is maping the features of people with problems in algorithmic thinking.

Dyscalculia is estimated to have a prevalence of 3-5% of the population and is defined as a condition that affects the ability to acquire mathematical skills. This presentation will provide an introduction to dyscalculia in higher education. It discusses key concepts and how dyscalculia impacts students, for example, number concepts and relationships, and  discusses resources and strategies to support concepts and relationships, to support students in the maths element of their course

Visualization of data has recently gained great importance in education and use of infographics is regarded as an important
tool in teaching mathematics since it presents information in a clear and abstract way. Therefore, use of infographics for helping
individuals with mathematical learning difficulties has become an important research question. This study aims to provide an
overview on the use of infographics in teaching mathematics to individuals with mathematical learning difficulties. This is a
qualitative study in which document analysis was used the collect the data. Results provided information about the definition
of infographics, effectiveness of using infographics in education and facilitative role of infographics in enhancing learning of
individuals with mathematical learning difficulties, namely dyscalculia. Results were discussed with relevant literature and
recommendations for further research and practices were also presented.
Key words: Infographics, Teaching mathematics, Mathematical learning difficulties, Dyscalculia, Visualization

The aim of this study was to determine the dimensions of the relationship between math anxiety and mathematics achievement of the third grade students with and without mathematics learning difficulties. Data were collected from 288 elementary school students using math anxiety scale and math achievement test tools. The mathematics achievement test scores reveal that the students were classified into four groups: math learning difficulties (0-10%), low achievers (11-25%), normal achievers (26-95%), and high achievers (96-100%). The findings reveal that there was a strong correlation (r=-.597) between the math anxiety and math achievement of the participants, while there was no significant difference between the mean scores of the mathematics anxiety of the lower two groups as it was between the two upper groups. This indicates that the math anxiety level of the students with math learning difficulties does not differ from the low achievers. However, the results depict a significant difference between the mean scores of the math anxiety of the low achievers and the normal achievers.

Only six states in India currently identify learning disabilities as a category of disability. This article highlights the challenges students with math learning disabilities face in their transition from secondary school to higher secondary education and Bachelor of Commerce degree programs in the state of Maharashtra. While the current educational policy aims to help students with learning disabilities participate in the general education curriculum and pass the 10 th standard secondary exam, the implementation of curricular modifications has repercussions in post-secondary settings when students lack the math content knowledge for a required math course in their Bachelor's degree program. This qualitative study highlights the transitional experiences of secondary and post-secondary individuals with math learning disabilities in Mumbai through interviews with students, college administrators, and lecturers; and a document review of Maharashtra's special education policies. The results suggest that current special education policies and college practices in Mumbai do not prepare students with math learning disabilities with the math knowledge that they need to succeed in post-secondary mathematics courses. Current higher secondary and post-secondary interventions in Mumbai are reviewed and implications for policy and practice for all levels of education are discussed.

It is essential to keep in mind if we want to understand the problem of learners with dyslexia, that the most frequent type of dyslexia is caused not only by phonological difficulties. The difference of these learners’ way of learning is an overall speciality in the information processing. Problems may arise in non-literal areas, like math, too. The best math teaching practices can help to avoid difficulties in math and help to be successful in the subject not only for learners with dyslexia, but for all learners.
This section provides insight of the similarities and differences in dyslexia and dyscalculia, a difficulty in learning or comprehending arithmetic and learning facts in mathematics. Clarification of the concepts can lead to a more directed intervention.
The teaching and learning methods that are suggested in this guide are methods proven to be efficient teaching and learning methods, and ground an inclusive teaching environment.

Στην παρούσα εργασία διερευνώνται οι αιτολογικοί παράγοντες και τα χαρακτηριστικά των Μαθησιακών Διαταραχών. Εξετάζεται μεμονωμένα η κάθε διαταραχή και αναλύονται οι τρόποι αξιολόγησης/διάγνωσης και θεραπευτικής παρέμβασης που ακολουθούνται στη χώρα μας.

The aim of the study is to investigate the effects of using computer for
developing arithmetical skills of students with mathematics learning difficulty (MLD). The study was carried out with pre-test –post-test single subject research design. The participants of the study consist of a girl and two boys who attend 3rd grade at elementary school. The contents of the computeraided instruction materials consist of counting skills, place value and addition subjects which are related to 1st and 2nd grade mathematics course learning outcomes of primary school. The materials have been prepared in the light of educational neuroscience findings about mathematical cognition. Participants were given a total of 75 lessons of individual instruction for five weeks, every
day on weekdays and 20-30 minutes a day with the materials developed.
Achievement tests developed by the researcher were used as data collection tools. Test response times and correct answers of the participants were identified in the achievement tests. It was found that progress was achieved in counting skills and place value concepts and they could solve addition problems. However, it was revealed that the difficulties of students at the second grade level continued with addition, especially when the numbers were given side-by-side. It can be stated that computer assisted instruction used in this study developed students’ arithmetical skills and increased their speed. Triple code and the models which help reduce the workload of working memory are advised to be used in the instruction of the students having MLD.

The aim of this study is to examine the effects of computer assisted instruction materials on approximate number skills of students with mathematics learning difficulties. The study was carried out with pretest-posttest quasi experimental method with a single subject. The participants of the study consist of a girl and two boys who attend 3rd grade at elementary school. The contents of the computer-aided instruction materials which have been designed consist of counting skills, place value concepts and addition subjects which are related to mathematics lesson's learning outcomes of 1st and 2nd grades of primary school. With the materials prepared, participants were given 75 lessons of individual instruction during five weeks, each weekdays and approximately 20-30 minutes a day. Dyscalculia screening tool and Panamath program were used as data collection tools. Panamath program calculates test response time, the percentage of accuracy and weber fraction data of participants. In the dot counting and comparison symbolic tests of DST, response time tests and number of correct answers of the participants were calculated, while mean absolute error were calculated in the mental number line tests. The findings of the study indicate that the approximate skills of the participants have developed and there has been significant increase in their speed of answering. INTRODUCTION Mathematics is a complex course which includes different domains like arithmetic, arithmetic problem solving, statistics, geometry, algebra, probability, and calculus. This condition means that variety of basic abilities related to sense of quantity, symbolic decoding, memory, visual-spatial capacity, and logics must be mobilized. Students who have difficulties with any of these abilities or in their coordination can experience mathematics learning disability (MLD) (Karagiannakis, Baccaglini-Frank, & Papadatos, 2014).

Dyscalculia occupies four to six percent among the population of our pupils. It is as common as dyslexia but it is a learning disability in mathematics instead of reading. However, the dyscalculic pupils are hardly detected and identified due to the lack of awareness and checklist for adults in order to detect them. The purpose of this study is to discuss about the needs and significance to design and develop a checklist for dyscalculia for dyscalculic pupils. The results show that the needs to develop a dyscalculia checklist are prevalence of dyscalculic pupils,
lack of awareness among teachers and parents, and the need of standardized dyscalculia checklist to be officially applied in our country’s education system. If a dyscalculia checklist is being developed, it will bring significance to Ministry of Education, teachers and parents, dyscalculic pupils, and researchers. As a conclusion, the needs to
design and develop a checklist for dyscalculia has been identified based on literature reviews. The implication of this paper is that a dyscalculia checklist will be developed by the researchers in order to detect the dyscalculic pupils among the population.

Uno de los problemas que se presenta en la enseñanza del Cálculo consiste en que prevalece el trabajo mecánico en las aulas, dejando a un lado la construcción de los conceptos, así como la evasión de con-sideraciones visuales al abordarlos. Este trabajo se enfoca en propo-ner elementos que permitan al alumno visualizar situaciones en las que está inmerso el concepto de derivada, como es el caso de la razón de cambio instantánea. Para ello se recurre a la tecnología disponible para los jóvenes, como los dispositivos móviles y aplicaciones de cómputo de uso específico. También se empleó realidad aumenta-da debido a que esta tecnología ha sido reconocida como apoyo en ciertos aspectos educativos tales como: la atención y relación viso-espacial. Para evaluar el sistema se consideró una muestra de 2 grupos de 30 estudiantes cada uno, un grupo fue el de control (GC) y el otro el de estudio (GE), ambos fueron evaluados después de haber trabaja-do una secuencia de enseñanza, en donde se utilizó la misma prueba y diferentes herramientas. Los resultados mostraron que el grupo de estudio identificó el concepto de derivada resolviendo de forma correcta un porcentaje mayor de reactivos en el cuestionario final en relación al grupo de control. El incremento en promedio del GE fue de 2.6 a 7.4 y del GC fue de 2.08 a 4, por lo que se concluye que actividades apoyadas con dispositivos móviles contribuyen a mejorar la visualización y la construcción de los conceptos.

abstract
One of the problems presented in the teaching of calculus is that mechanical work prevails in the classrooms, reducing the time for the construction of concepts, as well as preventing visual consider-ations when they are approached. This paper focuses on proposing elements that allow students to visualize situations that incorporate the concept of the derivative, such as the case of the reason for instantaneous change. To this end, we used the technology available to young people, such as mobile devices and specific computer  applications. We also used Augmented Reality since this technology has been considered a successful support in certain educational aspects, such as attention and visual-spatial relationships. To evaluate the system a sample of two groups of 30 students each was used; one was a control group (CG) and the other a research group (RG). Both were evaluated after having worked through a sequence of teaching in which the same test was used with different tools. The results showed that the research group identified the concept of the derivative and correctly solved a higher percentage of problems in the final questionnaire compared with the control group. The aver-age increase of the RG was from 2.6 to 7.4, and the CG was from 2.08 to 4, which led to the conclusion that activities supported by mobile devices contribute to the improvement of visualization and the con-struction of concepts.

The domain of numerical cognition still lacks an assessment tool that is theoretically driven and that covers a wide range of key numerical processes with the aim of identifying the learning profiles of children with difficulties in mathematics (MD) or dyscalculia. This paper is the first presentation of an online collectively administered tool developed to meet these goals. The Mathematical Profile Test (MathPro Test) includes 18 subtests that assess numerical skills related to the core number domain or to the visual-spatial, memory or reasoning domains. The specific aim of this paper is to present the preliminary evaluation both of the sensitivity and the psychometric characteristics of the individual measures of the MathPro Test, which was administered to 622 primary school children (grades 1-6) in Belgium. Performance on the subtests increased across all grades and varied along the level of difficulty of the items, supporting the sensitivity of the test. The MathPro Test also showed satisfactory internal consistency and significant and stable correlation with a standardized test in mathematics across all grades. In particular, the achievement in mathematics was strongly associated with the performance on the subtests assessing the reasoning and the visuospatial domains throughout all school grades, whereas associations with the core number and memory tasks were found mainly in the younger children. MD children performed significantly lower than their peers; these differences in performance on the MathPro subtests also varied according to the school grades, informing us about the developmental changes of the weaknesses of children with MD. These results suggest that the MathPro Test is a very promising tool for conducting large scale research and for clinicians to sketch out the mathematical profile of children with MD or dyscalculia.

Number sense is critical to the development of higher order mathematic abilities. However, some children have difficulty acquiring these fundamental skills and the knowledge base of effective interventions/remediation is relatively limited. Based on emerging neuro-scientific research which has identified the association between finger movement/representation and numerical cognition, this one-year study examined the effectiveness of a finger calculation program for at-risk and non-at-risk school children. Specifically, the study sought to determine the impact of learning Chisanbop (Korean finger calculation method) on the number sense, computational, quantitative concepts, and problem solving skills, as well as attitudes towards mathematics, of children at the grade 2 and grade 5 levels. The findings indicate a significant impact on attitudes for math for at-risk grade 2 students.

The book reports from recent or on-going research and development in teaching and learning mathematics for pupils with mathematical difficulties in the Nordic countries. Topics discussed are learning environment and social setting, learning communities and teaching approaches, inquiry, and creative learning contrasting traditions of rote and imitative learning. Relations between test anxiety, working memory, and pupils’ self-image are discussed as well as inclusion and the right of every student to understand and enjoy mathematics.

Mathematics is one of the main subjects in our education system. However, there was around five percent among the population are facing learning difficulty in Mathematics, which is also known as dyscalculia. The purpose of this study is to evaluate the content in Dyscalculia Module for dyscalculic pupils in primary schools. The researcher had invited eleven experts in the field of dyscalculia, mathematics, remedial education, and special education to evaluate the content of this module. Four basic arithmetic skills in the module were addition, subtraction, multiplication, and division. There was a number of 45 items in the content evaluation questionnaire. The data was analysed by using Fuzzy Delphi Method. The findings showed that the threshold values, d all of the elements in Dyscalculia Module were below 2, the experts consensus was above 75 percent, and the fuzzy scores were above 0.5. As a conclusion, Teacher’s Manual, Pupil’s Exercise Book, PowerPoint games, and whole Dyscalculia Module were accepted by all of the experts. This study implicated that a module specifically for dyscalculic pupils shall be complementary with the manual, exercises, and interactive games. It is important to evaluate the content of Dyscalculia Module so that the dyscalculic pupils are able to learn effectively. By developing this module, the basic arithmetic skills among dyscalculic pupils will be improved. In addition, this study will also bring significance to Mathematics teachers, parents of dyscalculic pupils, school administrators, policy makers, and Ministry of Education Malaysia.

Visualization of data has recently gained great importance in
education and use of infographics is regarded as an important tool in
teaching mathematics since it presents information in a clear and abstract
way. Therefore, use of infographics for helping individuals with mathematical
learning difficulties has become an important research question. This
study aims to provide an overview on the use of infographics in teaching
mathematics to individuals with mathematical learning difficulties. This
is a qualitative study in which document analysis was used the collect the
data. Results provided information about the definition of infographics,
effectiveness of using infographics in education and facilitative role of
infographics in enhancing learning of individuals with mathematical learning
difficulties, namely dyscalculia. Results were discussed with relevant literature
and recommendations for further research and practices were also presented.

This study reports the psychometric properties of a Basic Number Processing Test (BNPT), which was developed in order to determine elementary school students at risk for Mathematical learning disorder. A total of 478 primary school students were selected from 12 different public schools with an attempt to get a representative sample. The reliability and validity of the Dyscalculia Screening Tool were assessed with approximately 120 students from each of the First to Fourth grade. Results showed that, except for the First grade, the test scores predict the significant portion of the student's curriculum based Math achievement scores for Second, Third and Fourth graders with having the highest variance in the Second grade. These findings indicate that BNPT could be used as a screening tool in order to determine the students at risk for Mathematics learning disorders in those grades. It could also be deduced that at least very important portions of the causes of low achievement in Mathematics might originate from either the core systems of number or the system for accessing numbers from symbols. It is also suggested that symbolic or non-reading measurement paradigms would be more appropriate for screening First graders.