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Running head: DYSCALCULIA
Dyscalculia in the Middle School Mathematics Classroom
Bryan Anderson
Concordia University, St. Paul
ED 590: Research & Complete Capstone Cohort #583
Dr. Karen Kozen-Lien
Second Reader: Dr. Diane Harr
May 17th, 2017
DYSCALCULIA 2
Table of Contents
Abstract............................................................................................................................................4
Chapter One: Introduction...............................................................................................................5
Scope of Research........................................................................................................................5
Importance of the Study...............................................................................................................6
Research Questions......................................................................................................................7
Connection to Essential Question............................................................................................7
Definition of Terms.....................................................................................................................8
Summary......................................................................................................................................9
Chapter 2: Literature Review.........................................................................................................10
Defining Dyscalculia.................................................................................................................10
How Dyscalculia can be Identified............................................................................................14
Instructional Strategies that Support Dyscalculia......................................................................19
Chapter 3: Summary......................................................................................................................30
Review of the Proposed Problem..............................................................................................30
Defining Dyscalculia.................................................................................................................30
How Dyscalculia can be Identified............................................................................................31
Instructional Strategies that Support Dyscalculia......................................................................33
Summary of the Main Points of the Literature Review.............................................................34
Chapter 4: Discussion and Application.........................................................................................36
Insights Gained from the Research............................................................................................36
DYSCALCULIA 3
Application................................................................................................................................37
.......................................................................................................................................................
Recommendation for Future Research......................................................................................39
Conclusion.................................................................................................................................39
.......................................................................................................................................................
References......................................................................................................................................41
DYSCALCULIA 4
Abstract
This paper will examine the effects of Mathematical Learning Disabilities (MLD), the impact on
mathematical learning and the interventions needed to implement it in mathematics. Since no
core deficit has been identified for MLD, it is believed that several different domains of function
contribute to poor math achievement. The causes of Mathematical Learning Disability may
include heredity, environmental and developmental factors. It has been recognized that there are
six types of Dyscalculia dependent on the mathematical processes involved. These types may
appear as difficulties in the following areas: Naming operations, using manipulatives or pictures,
reading mathematical symbols, writing or manipulating math symbols, understanding
mathematical ideas and mental calculations, and performing mathematical calculations. Students
typically fall in one or more of these categories, and many students with MLD also have a
second form of retrieval deficit. Early identification and intervention for students with
Dyscalculia is important since most children with math disabilities in grade five will continue to
perform in the bottom 25% of students in later grades. Although early diagnosis and intervention
are paramount for student success, accurately identifying if a student has MLD, the type(s), and
providing appropriate interventions and support is essential albeit challenging. This paper
includes a guideline for educators to identify a student’s Math Learning Disability and best
teaching practices to meet their student’s educational needs, providing successful experiences in
the classroom.
Keywords: Dyscalculia, Mathematical Learning Disabilities, Cognitive Development in Math,
Learning Disability Strategies.
DYSCALCULIA 5
Chapter 1: Dyscalculia in the Middle School Mathematics Classroom
Introduction
There has been a “back-to-basics” movement in mathematics ever since the release of the
Trends in International Mathematics and Science Study (TIMSS) showed children from 20
countries outperformed our nation’s 8th grade students (Peak, 1995). The focus of this back-to-
basics push has been basic mathematical operations; addition, subtraction, multiplication and
division. Statements similar to “the student will increase the ability to complete division facts (1
to 9) from no understanding of division facts to the ability to complete division facts (1 to 9)
50% of the time through group instruction and use of manipulatives/computers” often appear in
Individual Education Plans (IEPs) for students with learning disabilities (SpEd Forms, 2016).
One thing that has not been addressed as prevalently is the existence of Mathematical Learning
Disabilities (MLD), its role in student’s ability to perform these math operations and what
adaptations and interventions students need to be successful (Mazzocco & Myers, 2003). In an
attempt to answer the question of how Mathematical Learning Disabilities impact a middle
school mathematics classroom this research paper will examine the effects of Mathematical
Learning Disabilities, the impact on mathematical learning and the interventions needed to
implement it in mathematics.
Scope of Research
In the research of mathematical learning disabilties and how it impacts the math
classroom, the author first researched the terms Mathematical Learning Disabilities and
Dyscalculia in order to attain a understanding of the disability and the scope of challenges
associated with it. There are many challenges to correctly identifying when a student has
Dyscalculia, since it typically corresponds to learning difficulties related to mathematical
DYSCALCULIA 6
calculation and reasoning (Raja & Kumar, 2011). It cuts across age, class, and intelligence
(Nakra, 1996). It can affect individuals in various degrees at different stages of life; from early
childhood, elementary years, secondary years, college and adulthood (Raja & Kumar, 2011).
There are six types of Dyscalculia dependent on the mathematical processes involved; difficulty
naming operations, difficulty using manipulatives or pictures, difficulty reading mathematical
symbols, difficulty writing or manipulating math symbols, difficulty in understanding
mathematical ideas and mental calculations, and difficulty in performing mathematical
calculations (Korsc, 1974). Since there didn’t seem to be a specific cause for MLD or stage of
development when it my occur, the author then researched what types of pedogogy a teacher
could provide in their mathematics classroom to support students with MLD. The author also
searched for strategies and interventions that could address a broad range of needs for students
with learning disabilties.
The author encountered limiting factors to the research. The first is that most research
had been conducted primarily in the early elementary (K to 3rd) grades instead of middle or high
school. The second was that research typically focused on learning disabilites in reading and
writing. Mathematical Learning Disabilities typically is considered a secondary disability so it is
often overlooked.
Importance of the Study
The question of the effects of Mathematical Learning Disabilities, the impact on
mathematical learning and the interventions needed to implement it in mathematics is one that
concerns all teachers who instruct students in mathematics, across all grade levels.
Developmental Dyscalculia has been estimated to effect approximately 5 to 7% of the current
student population, roughly equivalent to the presence of developmental dyslexia (Butterworth,
DYSCALCULIA 7
Varma, & Laurillard, 2011). Students with learning disabilities consistently perform in the
bottom 25% of the population throughout their student careers. There is a need for more
longitudinal studies, but early research has indicated that MLD persists through adulthood
(Butterworth et al., 2011). Students may enter the mathematics classroom with an individualized
education plan, but they may not accurately address challenges that the student may encounter in
a mathematics setting, or provide support to enable the student to develop strategies for learning
that will continue through their adult lives.
Since mathematics encompasses a wide range of skills with varying levels of complexity,
the ability to identify and define specific core deficits of MLD has not been possible (Geary,
2004). A reason for this is the fact that different domains of function have been identified with
poor mathematical achievement, including reading levels, working memory, spatial visualization
and executive functions (Mazzocco & Myers, 2003). Typically, MLD research has primarily
focused on a student’s speed and ability in written assessment of basic math facts (Lewis, 2014).
In many cases, Mathematical Learning Disabilities is a secondary disability paired with others in
reading. These factors make MLD difficult to identify, correctly diagnose which area the student
needs support in, and what types of interventions can be put into place to provide the student
with strategies to be successful in mathematics.
Research Questions
This research paper will examine Dyscalculia, how a teacher can identify a student with
the disability, and how teachers can provide interventions to implement in the middle school
mathematics classroom to provide all students a safe, successful learning environment. By
answering this question, the author will address Concordia St. Paul’s Program Essential
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Question. In light of what is known about special education law and policies, what are best
practices for providing inclusive instruction for all learners?
Definitions of Terms
DTI- Diffusion Tensor Imaging is a magnetic resonance imaging technique that provides
information about white matter microstructure. A DTI measures the diffusion of water
molecules restricted by axons in the brain’s white matter (Kucian, Ashkenazi, Hänggi, Rotzer,
Jäncke, Marthin, & von Aster, 2013).
Dyscalculia- Dyscalculia is a specific learning disability in math. Kids with Dyscalculia may
have difficulty understanding number-related concepts or using symbols or functions needed for
success in mathematics (Understood for Learning and Attention Issues, 2017).
IEP- Individualized Education Program is a legal document that defines a child's special
education program. It includes the disability under which the child qualifies for special education
services (also known as his classification), the services the team has determined the school will
provide, his yearly goals and objectives and any accommodations that must be made to assist his
learning (Morin, 2017).
fMRI- Functional Magnetic Resonance Imaging is a technique for measuring brain activity. It
works by detecting the changes in blood oxygenation and flow that occur in response to neural
activity – when a brain area is more active it consumes more oxygen and to meet this increased
demand blood flow increases to the active area. fMRI can be used to produce activation maps
showing which parts of the brain are involved in a particular mental process (Devlin, 2005).
MLD- Math[ematical] Learning Disabilities range from mild to severe and manifest themselves
in a variety of ways. The most common MLDs are difficulties with efficient recall of basic
arithmetic facts and reliability in written computation (Garnett, 2017).
DYSCALCULIA 9
NVLD- NonVerbal Learning Disabilities is a disorder which is usually characterized by a
significant discrepancy between higher verbal skills and weaker motor, visual-spatial and social
skills (Learning Disabilities Association of America, 2017).
TIMSS- The Trends in International Mathematics and Science Study provides reliable and
timely data on the mathematics and science achievement of U.S. students compared to that of
students in other countries. TIMSS started collecting data in 1995, measuring the achievement of
students in grades 4 and 8. (National Center for Education Statistics, 2017).
Summary
Mathematical Learning Disability, or Dyscalculia, is an important learning disability that
is often overlooked and mishandled in today’s classroom. The causes of Mathematical Learning
Disability include heredity, environmental and developmental factors. Although early diagnosis
and intervention are paramount for student success, accurately identifying if a student has MLD
and what type is difficult. Data obtained from a single year is not enough to determine whether a
student has MLD. Students must show a continuing deficiency over multiple years. The
following chapter presents a collection of primary source, peer reviewed, scholarly research
studies that are relevant to this topic and guided by the question: What has research discovered
with regard to what MLD is, how it impacts mathematical learning and how to provide
interventions to implement in the middle school mathematics classroom to provide all students a
safe, successful learning environment.
DYSCALCULIA 10
Chapter 2: Literature Review
This literature review will examine the effects of Mathematical Learning Disabilities
(MLD), the impact on mathematical learning and the interventions needed to implement it in
mathematics. The literature review will first examine what MLD is, providing insight to factors
that influence a learning disability in Mathematics. The review will then examine what types of
Dyscalculia a student may have, and how to distinguish between them. Finally, the literature
review will turn its focus on interventions to implement in the classroom to provide all students a
safe, successful learning environment.
Defining Dyscalculia
Geary stated that Dyscalculia occurs in 5% to 8% of the current student population
(2004). Riccio et al. (2010) and Geary (2004) both stated that MLD is a familial disorder, with
diagnosis rates 10 times more likely for families who had a parent with Dyscalculia than families
in the general public. While this appeared to be solely a genetic disability, environmental factors
also affected mastery of mathematical skills. Students from low socioeconomic communities
were more likely to suffer from Mathematical Learning Disabilities. Since mathematical
knowledge is primarily acquired through academic settings, one should consider whether
curriculum, educational opportunity, or teaching practices play a role in student achievement
(Riccio, Sullivan, & Cohen, 2010).
Neurology plays a role in Dyscalculia, with studies indicating that multiple regions of the
brain are accessed when performing mathematical operations. A quasi-experimental study
conducted by Eliez, Blasey, Menon, White, Schmitt and Reiss (2001) found students with
cognitive disabilities show abnormal brain activation and activity during computational tasks.
They conducted a qualitative study of 16 students ages six to eleven using functional magnetic
DYSCALCULIA 11
resonance imaging (fMRI) to monitor brain regions and activity. The fMRI revealed that the
parietal lobe is responsible for spatial visualization and arithmetic processing. It also is activated
for many mathematical functions. The intraparietal sulcus performs calculations and
comparisons; it also converts words into numbers. The right inferior parietal lobule, left
precuneus, and left superior parietal gyrus all are critical when performing subtraction
calculations. Two parietal areas, the intraparietal sulcus and posterior superior sulcus are all
active when students are asked to estimate and approximate. Although the research conducted
by Eliez et al. was limited to a small number of students tested, their findings support research
that deficits in mathematical performance has been linked to brain development and structure.
A quasi-experimental study conducted by Kucian, Ashkenazi, Hänggi, Rotzer, Jäncke,
Marthin, and von Aster (2013) on 47 children between the ages of eight and eleven, found that
mathematical calculations are highly demanding tasks for the brain, calling upon a complex
network of neural connections to process. Kucian et al. used a diffusion tensor imaging
technique (DTI) during the testing of student’s numerical abilities, intelligence and memory.
The study showed that developmental Dyscalculia was related to disruption in the brain’s white
matter integrity. The white matter tracts in the left hemisphere of the brain is responsible for the
development of mathematical calculations and connections. The study was limited by the DTI
technology, when analyzing specific mathematical tasks there were some children that had to be
excluded because of the quality of the image. The study did find a strong correlation between
students who are successful in mathematics and those who have had constructed effective, fast,
and accurate connections between this neural network.
Research has also shown that the areas of the brain required for exact calculation are the
same as those required for language processing, providing connections between Reading
DYSCALCULIA 12
Learning Disabilities and Mathematical Learning Disabilities (Riccio et al., 2010). Another
closely linked disability is Non-Verbal Learning Disabilities (NVLD). These students typically
struggle with psychomotor, visual-spatial, tactile tasks, and nonverbal methods to form
mathematical concepts. NVLD is also associated with problem solving and concept formation
difficulties in Mathematics. The qualitative study lead by Riccio et al. was conducted on a
thirteen-year-old male who was referred because of his low academic performance, particularly
in mathematics. The study included the following measures of academic, cognitive and
behavioral achievement: Differential Abilities Scale (DAS-II), Wechsler Individual Achievement
Test (WIAT-II), Delis-Kaplan Executive Functioning Systems (D-KEFS), Clinical Evaluation of
Language Fundamentals (CELF-IV), Wechsler Intelligence Scale for Children (WISC-IV),
Neuropsychological Assessment (NEPSY-2), and the Behavior Assessment System for Children
(BASC-II). Although the research was limited to one student, the depth of testing provided a
very strong base of data. Riccio et al. predicted a strong correlation between language formation
and sequential processing. The case study participant demonstrated difficulty with part/detail
and whole/global relationships, which effected his efficiency, accuracy, decision speed, and
monitoring processes. They concluded that those abilities most related to working memory and
executive function seemed to be identified most often in conjunction with difficulties in
mathematics.
Although there are references to earlier experts in Dyscalculia, there is one expert who is
widely acknowledged and referenced when talking about the disability. Ladislav Kosc (1970)
was the first to consider Mathematical Learning Disabilities as a larger, complicated learning
disorder and defined it as follows:
DYSCALCULIA 13
Developmental Dyscalculia is a structural disorder of mathematical abilities which
has its origin in a genetic or congenital disorder of those parts of the brain that are the
direct anatomico-physiological substrate of the maturation of the mathematical
abilities adequate to age, without a simultaneous disorder of general mental functions
(p. 192).
Korsc (1974) performed a qualitative experiment on 375 students (199 boys and 176 girls)
selected at random from fourteen 5th grade classrooms. They were given two sets of tests to
measure mathematical abilities. Through that test, Korsc found that specific parts of the brain
are associated with mathematics and mathematical learning. When these regions are damaged or
are not developing, that individual had MLD as a result. Through that study, Korsc determined
there are six types of Dyscalculia dependent on the mathematical processes involved:
Graphical Dyscalculia: difficulty writing or manipulating math symbols
Ideognostical Dyscalculia: difficulty in understanding mathematical ideas and mental
calculations
Lexical Dyscalculia: difficulty reading mathematical symbols
Practognostic Dyscalculia: difficulty using manipulatives or pictures
Operational Dyscalculia: difficulty in performing mathematical calculations
Verbal Dyscalculia: difficulty naming amounts, digits, numerals, operations, terms
Students with Dyscalculia can appear to have normal ability levels overall if specific screening is
not completed. Students can demonstrate grade level abilities in some mathematical operations
and calculations and still have learning disabilities in others.
Students can fall in one or more of the categories outlined by Korsc, and many students
with MLD also have a second form of retrieval deficit (Geary, 2004). It is now recognized that
DYSCALCULIA 14
Mathematical Learning Disabilities is the second most common academic learning disability,
with reading disabilities being the first (NASET, n.d.). The process of learning mathematics
places a high demand on a student’s cognitive processing. Mathematical abilities are cognitive
skills and are frequently used to measure a student’s cognitive ability (Riccio et al., 2010). Many
of these difficulties develop at a very early age when children experience situations that demand
mathematical thinking and reasoning. They take these experiences with them to an academic
setting and attempt to apply these early understandings to new concepts (NASET, n.d.). When
deficits in Mathematics are identified and represent a delay in developmental functioning or the
ability to process information in one or more of the mathematical domains, that student suffers
from a Mathematical Learning Disability (also known as Dyscalculia).
How Dyscalculia can be Identified
There are numerous ways researchers have attempted to classify Dyscalculia, most
referencing how math skills are taught in an educational setting. Mathematics is typically broken
down into two classifications: calculations and reasoning. Math calculation is the application of
algorithms, computation, and fluency; math reasoning is the ability to assess a situation and
determine what tools and steps are needed to solve it (Riccio et al., 2010). Students presented
with mathematical problems will be expected to flow fluidly between calculation and reasoning.
For a student to retrieve mathematical facts from memory, they also need to conceptualize the
cardinality, quantity or ordinality of those numbers at the same time. Eliez et al. (2001) and
Butterworth et al. (2011) both found that when this link has not been established, students are not
able to activate appropriate regions of the brain, and calculations are impaired. Dyscalculia
disrupts this flow by inhibiting a student from accessing knowledge or context based on the type
of Mathematical Learning Disability.
DYSCALCULIA 15
Since mathematics encompasses a wide range of skills with varying levels of complexity,
the ability to identify and define specific core deficits of MLD has not been possible (Geary,
2004). In a qualitative study of over three hundred 4th grade urban students from all over the
world (the United States, Europe, and Israel), he found that between 5 and 8% of school age
children have some form of MLD. Geary also stated that defining MLD is further complicated
by poor achievement due to inadequate instruction versus poor achievement due to an actual
cognitive disability. Due to this complication in delineating between these achievements, a
measure specifically designed to diagnose MLD is not currently available. Tests designed for
specifically measuring a student’s counting, arithmetic skills, cognitive memory, procedural
knowledge, semantic memory, and visuospatial skills are vital to pinpointing student need.
Relatively little research has been conducted on a student with mathematics learning disability
and their ability to perform and solve complex mathematical problems. Most research focused
on math facts and simple arithmetic. Current practices use standardized testing combined with
measures of intelligence (IQ). A single score from each of these tests do not imply that a student
has MLD, but consistently low scores over multiple academic years often indicate some form of
cognitive or memory deficit, and a diagnosis of MLD is warranted.
Mazzocco and Myers (2003) learned that different domains of function have been
identified with poor mathematical achievement, including reading levels, working memory,
spatial visualization and executive functions. Their study had 209 students from a suburban
public-school district. There were 103 boys and 106 girls from grades Kindergarten, 1st and 2nd
grade; nine of which repeated a grade during the study. Students were assessed for IQ,
mathematics and reading. Mazzocco and Myers found that the prevalence of Mathematical
Learning Disabilities depended on the criteria used to define it. Their criterion of MLD as
DYSCALCULIA 16
students who persistently have poor mathematical achievement (when compared to the student’s
IQ) over time. Mazzocco and Myers also found that during the four years the study was in
effect, over half of all children met at least one criterion for MLD. There is no one fixed set of
assessments to determine Math Disabilities, and recommend that teachers be familiar with a wide
array of assessments to correctly identify when a student has a disability. Since no one fixed set
of criteria is used to defined Mathematical Learning Disabilities, and that a holistic approach to
identifying a disability and determining which type is present. They also found that the presence
of MD is not consistent across the early grades, only 63% of student met the criteria for math
disabilities for two or more years. “At a given point in time, a very different group of children
meets the criteria for MD depending on which measure(s) are used for identification” (p. 242).
Although this study did not specifically provide a time constraint on persistent poor math
achievement, it did provide evidence that it is difficult to provide a specific definition for MLD
and consistently identify children who have Dyscalculia.
Raja and Kumar (2011) conducted a meta-analysis of Dyscalculia and found that in
children ages eight to nine, Mathematical Learning Disabilities are often the result of the
student’s basic number processing ability. They go on to state that individuals with MLD do not
automatically associate numbers with quantity or magnitude, but typically have no problem
associating letters with phonemes. Dyscalculia cuts across social class, age, gender, and
intelligence. Raja and Kumar stated that MLD can affect individuals differently at different
stages in their life, but that early identification is important. In the primary years, dyscalculics
demonstrate difficulty in reading and writing numbers larger than two digits, cannot reproduce
sequences, and struggle with solving mathematical relationship problems. Raja and Kumar also
stated that students with MLD were able to compensate for their weakness in number sense by
DYSCALCULIA 17
compensating with phonological processing skills, and that if the compensations are not
discovered at an early age, it would create problems when working with higher-level
mathematical processes. In secondary students, Raja and Kumar found that more students were
struggling with the application of strategies than background knowledge of the mathematics.
Riccio et al. connected neuropsychological domains and Mathematical Learning
Disabilities (2010). This provides special education staff and professionals a guideline to which
tests are appropriate to administer to determine if a student has MLD.
Table 1: Neuropsychological Domains and Mathematical Learning Disabilities
Neuropsychological Domain
Mathematical Learning Disability
Auditory-linguistic/Language Function
Problems in verbal organization of numbers and proceduresDifficulty with understanding of directions and word problems
Visual Perception and Constructional Praxis
Difficulty with reading the arithmetic signsDifficulty in reading numbersDifficulty in forming the appropriate numberDifficulty copying the problemsDifficulties in placing numbers in columnsConsistently working right to left, following correct directionality for processNonverbal ability predicts math skills in grade 1 but variance accounted for dissipates over time
Learning and Memory Problems in recall of facts or procedures, fact retrievalProblems with verbal memory when problems and directions are provided verballyDeficits in visual short-term memory predicts math achievement
Executive Function Omission or addition of a step in the processProblem in sequencing of steps in the procedure, attentional-sequential problemsApplication of procedure to the wrong type of problemErrors that imply impossible results, lack of application of reasoning skillsDifficulty in understanding of mathematical ideas and conceptsDifficulty in shifting between one operation and anotherRepetition of the same number
DYSCALCULIA 18
(Riccio et al., 2010, p. 49).
Venkatesan and Vasuda (2014) conducted a qualitative study in an attempt to develop a
standardized test to determine Mathematical Learning Disabilities. They tested 196 Indian
children whose ages ranged from seven to eighteen. There were 146 boys and 50 girls included
in the study. The participants of the study were screened by case study reviewal and intelligence
testing to eliminate mental retardation, attention deficit disorders of emotional and behavioral
disorders. The grade placements of the students ranged from two to ten but their mathematical
performance grade levels ranged from lower kindergarten to grade four. The study revealed that
a student’s math skills are characteristically located at a different developmental or grade levels,
can be identified, discriminated against, and grouped separately from the norm. Venkatesan and
Vasuda also found that there were cases of students who could not perform higher level
mathematical tasks, and theorized that they would not reach that level of proficiency in their high
school years.
Identifying the specific type of Dyscalculia a student has is not an easy task. Students
with Mathematical Learning Disabilities in the primary years typically show problems with
numerical quantity or basic arithmetic concepts. Students in the middle or high school years
often demonstrate deficits in problem solving and reasoning (NASET, n.d.). There are a wide
range of warning signs to students with Mathematical Learning Disabilities: slowness in
providing answers, difficulties with mental calculations, using fingers during problem solving,
mistakes in interpreting word problems, basic math fact errors, difficulty remembering solution
steps in a multistage process, difficulties with number position, and spatial organization (Raja
and Kumar, 2012).
DYSCALCULIA 19
Instructional Strategies that Support Dyscalculia
Early identification and intervention for students with Dyscalculia is important.
According to Rico et al., most children with math disabilities in 5th grade will continue to
perform in the bottom 25% of students in 11th grade (2010). Venkatesan & Vasudha affirm this
by stating “there are seldom cases of middle or high school level students who could ever
perform certain higher-level tasks” (2014, p. 93). Geary also observed that the ability to retrieve
basic facts does not improve throughout the elementary years (2004). He also stated that many
children with MLD do not show a shift from procedure-based to memory-based problem solving.
Riccio et al. (2010) also observed that students with Dyscalculia have difficulty in acquiring new
procedures or correcting existing ones. This implies that teachers need to identify the learning
needs of children early and adapt their curriculum to meet these needs. Teachers need to allow
students to use the tools they have and build new understanding and procedures using those
tools.
Lewis supported the idea of using a student’s specific tools with her research on
persistent understandings. She stated that students who have learning disabilities in mathematics
originate from a cognitive deficit, leading to a distinctly different error pattern that those of their
peers- even low achieving peers without learning disabilities in mathematics (2014). Teachers
currently attempt to address each student’s need (through a response to intervention, or RTI)
without an accurate method to identify those needs or effective instructional support designed
specifically for that need. Lewis conducted a quasi-experimental experiment on 11 students with
a potential learning disability. The age of the students ranged from middle school to community
college. Participants were interviewed, given a pretest to determine a baseline, provided with
tutoring sessions, and finally completed a posttest. Tutoring sessions were designed to address
DYSCALCULIA 20
two instructional goals generally believed to be effective in instruction of students with MLD;
building context/understanding, and using manipulatives/representations. Lewis found that
students had different persistent understandings, ways to examine problems and the tools they
use to solve them. She also stated that many persistent understandings often were resistant to
instructional methods to correct them and often blocked the student’s ability to construct new
understanding through tutoring or manipulative strategies. Lewis further explained the
implications when she stated students with MLDs do not need more instruction but need diverse
kinds of instruction and experiences.
Differentiated instruction was highlighted by Meyen and Greer who stated that
instructional design is an essential skill for mathematics instruction to students with learning
disabilities. They conducted a qualitative experiment implementing Blending Assessment With
Instruction Program (BAIP) over the span of five years. Meyen and Greer found that the
difference between instructional effectiveness and content knowledge was due to the amount of
instructional planning time teachers spent on their lessons. This instructional planning included
developing the lesson, reflecting on how the lesson went and modifying daily lessons according
to student need. Meyen and Greer also found that students showed an increase in mathematical
achievement when instructed by teachers who held certification in mathematics. Successful
mathematics instruction requires strong mathematical content knowledge, a thorough
understanding of students as learners, and pedological strategies. The key to decreasing the
learning gap between students is to increase teacher content knowledge, instructional planning
skills, reflection practices, and knowledge of multiple research-based instructional strategies for
students. Meyen and Greer stated that a BAIP lesson format contains five elements essential for
effective instruction: context, teaching, lessons, application, and extension. The contextual
DYSCALCULIA 21
element is an introduction to the concept or learning point for the day. It contains the state
standards addressed as well as any benchmarks or indicators. The teaching element is designed
to enhance the teacher’s knowledge of the standard. The standard is typically broken down into
smaller skills and concepts to master. The lesson element contains all instructional components
needed to teach the lesson: introduction, manipulatives, presentations, prerequisite skills,
vocabulary, and lesson outline. The application element is the task assigned to students to
practice the concept and demonstrate mastery. It can take many forms such as investigations,
explorations, group work, or individual problems. It also includes guided practice for
clarification, feedback on student thinking, or work and review. The extension element contains
modifications and accommodation for students with learning disabilities and enrichment tasks.
Meyen and Greer found that through the BAIP program, teachers must:
1. Understand the mathematical concepts or learning points they are teaching
2. Transform curriculum standards into a daily script for instruction
3. Align instruction with content standards
4. Identify prior and background knowledge needed to engage in the lesson
5. Understand the relationships of standards, instruction and assessment
6. Apply effective instruction on a daily basis
Special education teachers have to reassess their practices, they can no longer rely on the regular
education teachers to provide instruction, strategies and necessary interventions for students with
Mathematical Learning Disabilities.
One strategy for students is to increase their math literacy. Kiuhara and Witzel
conducted a meta-analysis of mathematical literacy; the ability to perform a variety of
mathematical calculations for various situations (2014). These situations range from everyday
DYSCALCULIA 22
situations such as paying bills and interpreting maps to solving geometric or calculus problems
(such as rocket trajectory and flight duration). Math literacy encompasses more than calculation,
fact retrieval or order of operations; students need to be able to engage in mathematical
reasoning, analyze relationships, modify strategies, and reflect on solutions. Kiuhara and Witzel
stated that teachers must implement the eight mathematical practices (as presented by the
National Council of Teachers of Mathematics, or NCTM) to develop students’ approaches and
reasoning. The eight mathematical practices are: 1) make sense of problems and persevere in
solving them, 2) reason abstractly and quantitatively, 3) construct viable arguments and critique
the reasoning of others, 4) model with mathematics, 5) use appropriate tools strategically, 6)
attend to precision, 7) look for and make use of structure, and 8) look for and express regularity
in repeated reasoning. Effective teachers who followed these practices developed the math
reasoning skills of struggling students. They used the following instructional strategies with
students with Mathematical Learning Disabilities: explicit instruction, student verbalization of
reasoning, visual representation of problems, use of heuristics, sequence of examples, and peer
assisted learning.
Wadlington and Wadlington (2008) provide many intervention strategies for students
based on the eight mathematical practices and the curriculum and evaluation standards of
NCTM. For general instruction, students with MLD should be seated near the focus of
instruction or presentation. Students should be actively engaged, and should receive an overview
of the lesson and learning point before instruction begins. Wadlington and Wadlington also
stated that teachers should start instruction with concrete examples and objects, then move to
pictures and diagrams. Abstract examples should not be introduced until the student has had
multiple experiences and success. For students to continue to experience success, prerequisite
DYSCALCULIA 23
skills must be mastered before they are introduced to new materials. At the close of each lesson,
students should reflect and summarize their learning. Students should receive smaller tasks and
assignments, and teachers should provide immediate feedback on performance. Teachers should
also provide more time for students to learn and practice skills, so that fluency becomes
automatic. Wadlington and Wadlington stated that students should have multiple opportunities
to communicate about mathematics, their strategies and solutions. Students should write about
math through reflections, journals, summaries or informal assessments. Teachers need to explain
new vocabulary, allowing students to create connections using concrete models and examples.
Students should have access to audio textbooks or lessons, alternate assignment layouts, or even
word processors. Classroom assessments should be a mix of formal and informal and should
allow student multiple attempts and ways to demonstrate mastery. Written tests should be in a
font size easily read by every student and written formats should be spaced appropriately for all
students. Wadlington and Wadlington suggested that interviews are the best way to assess
student understanding and mastery. Word problems should relate to student’s experiences, and
teachers should use student-created problems when appropriate. Word problems should not be a
measure of a student’s reading ability, and teachers should read the problems to students and
discuss them with students before any solution attempt is made. Wadlington and Wadlington
stated that although all of these interventions have been found to be successful in classrooms,
that teachers should continue to monitor students and develop new strategies to effectively
connect students with mathematics.
Krawlec, Huang, Montague, Kressler, & de Alba (2012) conducted a quantitative study to
determine if the Solve It! strategy could be effective for middle school students with learning
disabilities. Solve It! is a cognitive strategy that teaches the process that proficient problem
DYSCALCULIA 24
solvers use to solve math word problems. Students read the problem for understanding, then
paraphrase it in their own words. They visualized the problem and created a representation of
the problem through the use of manipulatives or diagrams. Students hypothesize what
mathematical strategies are needed to solve the problem and estimate an answer. The next step
was to solve the problem and check their answer for reasonableness. Krawlec et al. stated that
students with learning disabilities often are inconsistent and ineffective in the use of known
strategies. Many students are unable to determine which strategies are effective, and typically
implement random strategies to a task. Krawlec et al. conducted the experiment over two years
on 680,000 students in seventh and eighth grade. The nationality of the population was 9%
White, 30% African American, 59% Hispanic, and 2% Other. The overall student population
qualifying for free and reduced lunch was 60%. Their study showed that math problem solving
is a complex task that requires students to comprehend information, create mental images of the
situation, consider strategies to implement to find an answer, and calculate and check their
solution. Krawlec et al. reported that students who received the intervention outperformed their
peers who did not. They used more strategies to solve problems, regardless of ability level.
They attributed the performance to the fact that the intervention is explicitly teaching students
higher order concepts and skills.
Selling (2016) provides a similar picture in the use of teaching explicit mathematical
practices in urban middle and high school classrooms. She stated for students to be able to learn
mathematical practices, they need opportunities to engage in them. Constructing arguments or
making generalizations is an integral part of solving mathematical problems. Engaging in
mathematical practices can support all students and allow them to make strong conceptual
connections and understanding. The mathematical practices Selling referred to are
DYSCALCULIA 25
representation, generalizing, problem solving, and justifying. Mathematical practices are
developed in groups and then stored and implemented on an individual basis. Students should be
taught how to create mathematical practices and interact within those groups to build knowledge.
Selling conducted a parallel qualitative case study of three classrooms: a 6th grade mathematics
classroom, a 10th grade geometry classroom, and a 10th grade advanced algebra class. Using this
study, Selling developed a framework for making mathematic practices explicit in the classroom.
The first step is to name a student’s engagement in mathematical practices. Teachers should use
appropriate mathematical terminology and vocabulary to specifically map a student’s actions.
The second step is to highlight specific aspects of how a student engaged in mathematical
practices. This draws attention to what happened mathematically with a student’s work. The
third step is to evaluate a student’s engagement in mathematical practices. This provides
students with a positive message about the value of the practice. The fourth step is to explain the
goal or rationale. Students need to understand why the work they are about to engage in is
meaningful. The fifth step is connecting different student’s engagement in mathematical
practices. This step is critical to providing students with connections between steps and
strategies, as well as developing deep understanding of the concepts. The sixth step is framing
student engagement into a bigger discussion that can be generalized. This will provide students
with the skills to think critically, generalize and promote transfer of skills and strategies to new
situations. The seventh step is to elicit student self-assessment to mathematical practices.
Students need to be able to self-regulate their actions to become successful individuals. The last
step is to refer to a teacher narrative about mathematical practices. Teachers deliberately design
learning experiences and draw student’s attention to why the lesson was designed in that manner.
DYSCALCULIA 26
Selling stated that in creating an explicit mathematical practice in the classroom, student
engagement increases which promotes understanding and success.
Gonsalves and Krawec (2014) demonstrated that the use of explicit mathematical
practices increases student engagement and success. They conducted a qualitative case study on
ten students who had learning disabilities. The study lasted four months, with students receiving
35 minutes sessions three times a week. Students were given a process measure after each
session to assess progress. Gonsalves and Krawec stated that students with learning disabilities
struggle with word problems primarily due to deficits in representation. Teachers need to
provide students with problem-solving instruction that addresses their ability to represent
situations described by word problems. One way is through the use of number lines. Students
with learning disabilities should receive explicit instructed how to translate the information from
these problems in a number line format. Numbers line representations shifts the problem from a
language format into a visual one. This helps students organize their thought process and allows
them to formulate solution plans. According to Gonsalves and Krawlec, there are two parts to
this strategy: translating the problem to a number line and interpreting the number line
representation. To translate the problem to a number line, there are three important components
students must consider. The components are: relevant information given in the problem,
connections or relationships of that information, and the outcome of the problem in relation to
the information.
“It is necessary that, during instruction, teachers focus on these three components of the
representation explicitly, so that students truly understand how to identify this
information in the problem, incorporate it into the representation, and then translate that
representation into a means of solving the problem” (p. 162).
DYSCALCULIA 27
After constructing the model, students must be able to examine and interpret their model to find
a solution. Since students make their own model, it should provide connections to other
understandings and strategies needed to solve the problem. Number lines promote student
understanding of quantity, magnitude, relations between numbers, and mathematical operations.
Gonsalves and Krawlec found that the number line strategy increased student’s accuracy. This
accuracy continued two months after the instructional sessions ended, but was lost after four
months. This implied that strategies must be continually reviewed and practiced in order for
students to maintain proficiency.
This does not mean that students should only be exposed to one method of solving
problems. Lynch and Star (2014) conducted a qualitative case study on 23 students from ten
different schools. Six of those students were identified as having low academic achievement in
mathematics. The students were in 8th and 9th grade, and taking algebra. Students received daily,
55 minute instruction in a curriculum designed to teach students multiple strategies to solve
problems. Strategies were presented simultaneously on a page for students to analyze, compare
and contrast. Lynch and Star found that the struggling students has a positive perception to
learning multiple strategies, and rarely cited issues confusing strategy steps. All of the students
reported that they gained an improved understanding of the problem and the mathematical
knowledge behind it, which reduced math anxiety and improved accuracy. To ensure that
students has a clear understanding of the different procedures, the researchers carefully and
purposefully planned each lesson. Each lesson included: already worked examples, carefully
selected routines to be compared, engaging visual layout, explicit step-by-step presentation of
work, and a structured implementation of instruction.
DYSCALCULIA 28
The final study researched was done by Eren and Henderson (2011), examining the
importance of homework. They stated that homework has not always been viewed as a vital
element in learning; there was a strong anti-homework sentiment in America during the late
nineteenth and early twentieth centuries. Eren and Henderson conducted a large qualitative
study on eighth grade students across the nation. Students selected for the study represented
national demographics with respect to race, sex and academic achievement. There were more
than 25,000 students tested in two of four core curriculums; mathematics, English, history and
science. Eren and Henderson found that an extra 30 minutes of homework practice per night in
7th to 11th grade would advance a student nearly two grade levels in mathematical achievement.
While math homework was consistently found to have a statistically meaningful impact,
homework in the other three areas was found to have little or no effect on testing scores.
Another factor to consider with homework is parental education. Eren and Henderson
discovered that for students whose parents did not attain a high school diploma, homework’s
affect was insignificant, especially in math. Students with parents who have a high school
diploma (or above) showed a large and significant impact on achievement. Teacher’s treatment
of homework (if it is done for completion or graded) does not appear to affect the impact it has
on student achievement. With regards to race, Eren and Henferson stated that African-American
student benefit the least from homework, while White and Hispanic students benefit the most.
There was no statistical difference with regards to gender and achievement gains through
homework.
Geary (2004) and Raja and Kumar (2011) agreed that most cases of Mathematical
Learning Disability also involved a reading disability or attention-deficit disorder. Teachers
must be aware of how those secondary disabilities interact with a student’s MLD. Learning
DYSCALCULIA 29
strategies students employed for reading literacy should also be used in the mathematics
classroom. Interventions would include oral accommodations, large print text, alternative note
taking strategies, graphic organizers and the use of technology. Manipulatives, alternative
seating or learning areas, and segmented class periods should be employed in class for students
with an attention-deficit disorder. Accommodations for homework, assessments and
performance should be integrated into the daily routine of class, providing opportunities for
success.
DYSCALCULIA 30
Chapter 3: Summary
Review of the Proposed Problem
In order to answer the questions of “What is Dyscalculia, how a teacher can identify a
student with the disability, and how teachers can provide interventions to implement in the
middle school mathematics classroom to provide all students a safe, successful learning
environment?” educators must consider the research on learning disabilities. This includes how
they connect to mathematical practices, how Dyscalculia can be identified through observation
and testing, and what intervention strategies are proven successful for students with
Mathematical Learning Disabilities. Dyscalculia is not an easy disability to define or identify;
there are multiple difficulties students can experience in math during various stages of their
educational development. Teachers need to be aware of these difficulties and how to provide
support and instruction to students so they can find success in the mathematics classroom.
Defining Dyscalculia
There are numerous ways researchers have attempted to classify Dyscalculia, most
referencing how math skills are taught in an educational setting. Mathematics is typically broken
down into two classifications: calculations and reasoning. Math calculation is the application of
algorithms, computation and fluency; math reasoning is the ability to assess a situation and
determine what tools and steps are needed to solve it (Riccio et al., 2010). Students presented
with mathematical problems will be expected to flow fluidly between calculation and reasoning.
For students to retrieve mathematical facts from memory, they also need to conceptualize the
cardinality, quantity, or ordinality of those numbers at the same time. Butterworth et al. (2011)
and Eliez et al. (2001) both found that when this link was not established in students, they were
not able to activate appropriate regions of the brain, and calculations are impaired. Dyscalculia
DYSCALCULIA 31
disrupts the brain’s ability to activate appropriate regions by inhibiting a student from accessing
knowledge or context based on the type of Mathematical Learning Disability.
Neurology plays a part in MLD, with multiple regions of the brain responsible for various
mathematical calculations (Butterworth et al., 2011; Eliez et al., 2001; Kucian et al., 2013).
Testing for Mathematical Learning Disabilities must be just as complex; multiple test types and
sessions are required to accurately identify if a student has a Mathematical Learning Disability
and what type of the disability is present. Students with MLDs do not necessarily differ in a
distinct way; many appear to have normal developmental and skill levels as their peers (Korsc
1974). Most students with Mathematical Learning Disabilities also have a second form of
learning disability, with approximately 40% of MLD students also having reading disabilities
and 50% of students with a learning disability having an IEP goal in mathematics (Geary, 2004;
NASET, n.d.).
How Dyscalculia can be Identified
Identifying that a student has Dyscalculia in the primary grades is critical due to the type
of mathematics introduced. Primary mathematical skills include cardinality, quantity, fact
fluency, and operations. These skills are the building blocks to a student’s access to higher level
mathematic. Some early signs that a middle school student may have a Math Learning Disability
include slowness in answer response, mental calculation difficulties, using fingers for counting,
inability to interpret word problems, math fact errors, difficulty following a multistep process,
misalignment of numbers and difficulties with spatial organization (Raja and Kumar, 2012).
Correctly identifying what type of Dyscalculia a student has is also paramount in the
success of implementing differentiated instruction that will support the student. Many IEP
DYSCALCULIA 32
documents address fact fluency, but that is one of many types of difficulties a student can
experience. The types of Dyscalculia a student may experience are:
Graphical Dyscalculia: difficulty writing or manipulating math symbols
Ideognostical Dyscalculia: difficulty in understanding mathematical ideas and mental
calculations
Lexical Dyscalculia: difficulty reading mathematical symbols
Practognostic Dyscalculia: difficulty using manipulatives or pictures
Operational Dyscalculia: difficulty in performing mathematical calculations
Verbal Dyscalculia: difficulty naming amounts, digits, numerals, operations, terms
(Korsc, 1974; NASET, n.d.; Raja & Kumar, 2012).
These types are vastly different in what type of cognitive demand they place on the brain, what
region of the brain they activate, and what mathematical concepts and procedures they address.
A final step in correctly identifying Dyscalculia is linking the type to the
neuropsychological domain. The four function domains are auditory-linguistic and language,
visual perception and constructional praxis, learning and memory and executive functioning.
The audio-linguistic and language function has been associated to disabilities in verbal
organization of numbers and procedures as well as difficulty in understanding directions and
word problems. The visual perception and constructional praxis led to difficulties in reading
math signs and numbers, copying problems, organization and directionality of work (working
right to left for standard algorithms). The learning and memory function influenced problems
with fact retrieval, verbal memory of directions and problems and visual short-term memory.
The executive function is linked to omission of steps, sequencing errors, applying incorrect
DYSCALCULIA 33
concepts, difficulties in understanding concepts and math ideas, inability to shift between
operations and repetition of numbers.
Instructional Strategies that Support Dyscalculia
Although there are many different types of strategies that teachers could implement in
their classroom to support students with Mathematical Learning Disabilities, the first change
teachers needed to make is in their own professional development and lesson planning.
Instructional planning, increasing teacher’s content knowledge, reflection practices implemented
by the teacher, and familiarity with research-based instructional strategies were a key component
for teachers to develop (Meyer & Greer, 2009). Another focus for math teacher’s professional
development was integrating NCTM’s eight mathematical practices into their daily classroom
routine (Kiuhara & Witzel, 2014; Wadlington & Wadlington, 2008). They reported that teachers
who implemented these practices on a daily basis were able to increase student engagement and
developed mathematical reasoning skills in struggling learners. The changes teachers made in
their own practices and preparation of lessons had the largest impact on their student’s
achievement.
Another strategy teachers could provide to students with MLD is seating arrangements.
This was not a mathematical content intervention; students with disabilities should be seated near
the focus of the lesson (Wadlington & Wadlington, 2008). Teachers should note that this does
not always mean students are seated at the front of the class; student seating should be adaptive
to the lesson or task. Having students with disabilities seated at the back or side of the room is
for the teachers’ convenience only; it is not improving their experience or achievement in class.
Multiples sources researched stated that students who engaged in mathematical practices
demonstrated growth in understanding and achievement in mathematics (Gonzalves & Krawlec,
DYSCALCULIA 34
2014; Kiuhara & Witzel, 2014; Krawlec et al., 2012; Selling 2016). The practices found to be
most important were: representation, generalization, problem solving and justifying. Students
transformed information provided in math problems into diagrams, drawings or other
representations. This allowed them to better visualize problem, compare quantities, organize
their thought processes and connect previous knowledge needed to solve the problem. After
students had demonstrated mastery of concepts, they were ready to construct generalizations to
apply to new situations. Students then used relationships they constructed and solved problems.
They were then expected to justify their work, which was done in multiple ways depending on
the task.
Another instructional strategy that proved to be effective for learners with learning
disabilities was when students were provided with multiple methods to solve problems. Methods
were presented simultaneously and students analyzed the strategies, compared them to their own
mathematical understanding, and contrasted the differences. These lessons were purposefully
designed with step-by-step examples, topics and tasks students found engaging, carefully
selected routines to be compared, and structured instruction (Lynch & Star, 2014).
The final strategy considered for successfully supporting students with Mathematical
Learning Disabilities was homework. Homework was shown to have significant impact for
increasing student achievement in mathematics. Parental education was found to be a crucial
factor when considering homework. Special consideration was needed for parents who did not
have a high school diploma, as well as minority students. These groups needed modification to
the amount of homework provided as well as access to resources to assist in skill practice.
Summary of the Main Points of the Literature Review
DYSCALCULIA 35
The literature review consistently revealed there were two main points of learning from
the research of Dyscalculia. The first was that there are several types of Mathematical Learning
Disabilities. The variation of MLD was dependent on the types of mathematical calculation
required and the cognitive functioning domain of the student. The 6 types of Dyscalculia were:
Verbal Dyscalculia, Practognostic Dyscalculia, Lexile Dyscalculia, Graphical Dyscalculia,
Ideognostical Dyscalculia and Operational Dyscalculia (Krosc, 1974). The four cognitive
functioning domains associated with MLD were: Auditory-linguistic/Language Function, Visual
Perception/Constructional Praxis, Learning/Memory, and Executive Functioning (Riccio et al.,
2010). Mathematical Learning Disabilities typically occurred in conjunction with another
Learning Disability; which required careful testing and analysis of the student.
The second main point of learning of the literature review was evident in all the research
examined by the author: explicit instruction. Teachers made their instruction explicit by using
terminology and vocabulary to name a student’s mathematical engagement, highlighted specific
aspects of student mathematical practices, evaluated and acknowledged a student’s mathematical
practice, explained mathematical goals or rationale, connected different student’s engagement to
a mathematical practice, framed student engagement into rich classroom discussions, elicited
student self-assessment, and constructed a narrative script of the lesson and mathematical
practices (Selling, 2016). By consistently referring and connecting student work to mathematical
practices teachers, teachers enriched their student’s math background. This promoted student
confidence and engagement, which resulted in increased achievement. These two main points
provide teachers with a quick-reference with which to modify their daily instructional planning,
classroom procedures, and lessons.
DYSCALCULIA 36
Chapter 4: Discussion and Application
Insights Gained from the Research
The research on Dyscalculia provided many answers to the questions of understanding
Dyscalculia, how a teacher can identify a student with the disability, and how teachers can
provide interventions to implement in the middle school mathematics classroom to provide all
students a safe, successful learning environment. Many teachers are not aware of the presence of
Mathematical Learning Disabilities beyond the inability to quickly retrieve facts or solve word
problems. Teachers have often overlooked the disability, as it is often present with other types of
learning disabilities.
To meet the needs of students teachers must be able to correctly identify what type of
Dyscalculia a student has, along with any other cognitive deficits, and implement strategies to
provide a positive and successful learning experience. Most special education testing measures a
student’s ability in language arts. What many teachers overlook is how Reading Disabilities also
translate into the mathematics classroom. When a cognitive deficit is found to be present in a
student, the teacher must administer additional testing in the corresponding mathematical
concepts associated with the deficit. The use of Table 1 provides teachers with a guide to what
additional tests a student requires to determine if a Math Learning Disability is also present.
Many of the strategies suggested are not specific to special education alone, they are best
teaching practices. Teachers will effectively meet the needs of all the learners in their classroom
if they plan and design lessons for students with learning disabilities.
In order for teachers to do this, a closer look at professional development must be taken.
General education teachers should be provided research and resources to aid them in instructing
students with disabilities. They need special education teachers to create a quick reference card;
DYSCALCULIA 37
a card that references the student’s disability and what types of interventions were found to be
successful for that student in prior grades. Special education teachers also need to become more
familiar with mathematical content standards and pedagogy for instructing math content. Studies
have shown that teachers that have strong mathematical content have been successful in
increasing achievement among students with learning disabilities.
When teachers have a strong content knowledge, it is easier for them to differentiate
instruction to meet every student’s learning needs. Teachers first must consider all prerequisite
skills needed to complete a task, and ensure that students have mastery of those skills. Teachers
should start the lesson or unit with an overview of concepts and daily learning points. Lessons
should remain as concrete tasks until students have had multiple opportunities to demonstrate
mastery. When students have demonstrated mastery; teachers can slowly stretch student
thinking into abstract models. Tasks should remain at a smaller, manageable size for students
and teachers should provide immediate feedback on student understanding and skills. At the end
of the lesson students should be asked to reflect on the lesson to construct deep, meaningful
relationships with the mathematics practiced. All assessments should be a mix between formal
and informal; allowing students multiple means with which to demonstrate mastery.
Applications
The results of this research can be used by policy makers, district coordinators, building
administrators, general education teachers, and special education teachers to accurately identify
Dyscalculia and provide students with this learning disability the appropriate instruction and
interventions to be successful in the classroom. Policy makers at the federal and state levels
must ensure that proper testing and identification is being done for students with learning
disabilities. The findings of this research concerning the difficulties finding testing resources
DYSCALCULIA 38
that quickly and accurately determines a student’s disability; and funding should be made
available for further research grants to develop testing tools for educators. Based on the
research, policy makers should also provide more funding, allowing school districts to provide
more robust professional development for instructing student with learning disabilities.
Programs for parental or guardian support should also be examined to ensure that families have
access to resources needed to support their student in academics and life.
District coordinators and building administrators can use the conclusions of this research
to form committees to analyze district needs in special education. The research has shown that
Dyscalculia is often not tested, and that IEP goals related to mathematics are limited to fact
fluency and computation. Mathematical Learning Disabilities must become a larger concern for
school districts, effective testing measure for MLD must be implemented and extensive training
for educators must be provided so students will receive the services they require to experience
success in the mathematics classroom. Extra-curricular programs and tutoring services must also
be examined, and professionals in those roles must receive the same training as the rest of the
district’s staff.
General education and special education teachers can use the conclusions of this research
as a model to compare to their current methods and practices. The findings of this research paper
have made the author more aware of his own practices, and have provided insight into areas
where he must modify instruction and practices to support the students in his classroom. General
education and special education teachers must work to build a strong rapport; they must work to
refine their educational background and build understanding of each other’s knowledge,
responsibilities and duties. They must create a network of knowledge and support that will
DYSCALCULIA 39
provide consistent support to students with Mathematical Learning Disabilities throughout the
school day.
Recommendation for Future Research
This research has revealed several areas for future studies. Most studies of Dyscalculia
have been done at the primary level, future studies need to expand that research into the middle
and high school years. Research needs to examine how Dyscalculia affects a student over the
course of their education. The research done in this study has implied that different students can
display Mathematical Learning Disabilities depending on cognitive development and academic
level, yet studies on upper level students have not been conducted.
Another topic for future research is testing for MLD. This study found that testing for
Mathematical Learning Disabilities is convoluted and typically overshadowed by Reading
Disabilities. Research must be done on developing a reliable testing measure for all students
from grades Kindergarten to 12th grade. Testing should also determine what cognitive deficits a
student may have and what type of Dyscalculia support services should target.
A final topic for future research is what type of homework support families need to assist
their student with learning disabilities. This research found that math homework does increase
student achievement. This research also found that the effectiveness of homework varies
dependent on parental education. Research needs to be conducted on what types of support or
programs families need to not only increase their student’s achievement in mathematics, but their
own as well.
Conclusion
Mathematical Learning Disability, or Dyscalculia, is an important learning disability that
is often overlooked and mishandled in today’s classroom. The causes of Mathematical Learning
DYSCALCULIA 40
Disability include heredity, environmental and developmental factors. Although early diagnosis
and intervention are paramount for student success, accurately identifying if a student has MLD
and what type is difficult. Data obtained from a single year is not enough to determine whether a
student has MLD, students must show a continuing deficiency over multiple years. Many
students with Dyscalculia also have other learning disabilities, such as Reading Disabilities or
Attention-Deficit Disorders. To adequately support these students, teachers need to build upon
the student’s prior knowledge and procedures since students with MLD typically inhibit new
algorithms. Students with learning disabilities consistently perform in the bottom 25% of the
population throughout their student careers. This is not a topic that can remain hidden behind the
lack of fact fluency, teachers need to address students’ needs so they can be successful in the
mathematics classroom.
DYSCALCULIA 41
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