Dyscalculia: SLD in Math

Dyscalculia is defined as difficulty acquiring basic arithmetic skills that is not explained by low intelligence or inadequate schooling. About 5% of children in primary schools are affected. Dyscalculia does not improve without treatment. Many people with dyscalculia have associated cognitive impairment (e.g., impairment of working memory and visuospatial skills), and 20% to 60% of those affected have other diagnosed conditions such as dyslexia or attention deficit disorder.

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The U.S. Department of Education released guidance on Dyscalculia, as part of the guidance on Dyslexia in October 2015.

“Ensuring a high-quality education for children with specific learning disabilities is a critical responsibility for all of us. I write today to focus particularly on the unique educational needs of children with dyslexia, dyscalculia, and dysgraphia, which are conditions that could qualify a child as a child with a specific learning disability under the Individuals with Disabilities Education Act (IDEA). The Office of Special Education and Rehabilitation Services (OSERS) has received communications from stakeholders, including parents, advocacy groups, and national disability organizations, who believe that State and local educational agencies (SEAs and LEAs) are reluctant to reference or use dyslexia, dyscalculia, and dysgraphia in evaluations, eligibility determinations, or in developing the individualized education program (IEP) under the IDEA. The purpose of this letter is to clarify that there is nothing in the IDEA that would prohibit the use of the terms dyslexia, dyscalculia, and dysgraphia in IDEA evaluation, eligibility determinations, or IEP documents.

Under the IDEA and its implementing regulations “specific learning disability” is defined, in part, as “a disorder in one or more of the basic psychological processes involved in understanding or in using language, spoken or written, that may manifest itself in the imperfect ability to listen, think, speak, read, write, spell, or to do mathematical calculations, including conditions such as perceptual disabilities, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia.” See 20 U.S.C. §1401(30) and 34 CFR §300.8(c)(10) (emphasis added). While our implementing regulations contain a list of conditions under the definition “specific learning disability,” which includes dyslexia, the list is not exhaustive. However, regardless of whether a child has dyslexia or any other condition explicitly included in this definition of “specific learning disability,” or has a condition such as dyscalculia or dysgraphia not listed expressly in the definition, the LEA must conduct an evaluation in accordance with 34 CFR §§300.304-300.311 to determine whether that child meets the criteria for specific learning disability or any of the other disabilities listed in 34 CFR §300.8, which implements IDEA’s definition of “child with a disability.”

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Developmental Dyscalculia often occurs in association with other developmental disorders such as dyslexia or ADHD/ADD. Co-occurrence of learning disorders appears to be the rule rather than the exception. Co-occurrence is generally assumed to be a consequence of risk factors that are shared between disorders, for example, working memory. However, it should not be assumed that all dyslexics have problems with mathematics, although the percentage may be very high, or that all dyscalculics have problems with reading and writing. This latter rate of co-occurrence may well be a much lower percentage.

Typical symptoms of dyscalculia/mathematical learning difficulties:

• Has difficulty when counting backwards.
• Has a poor sense of number and estimation.
• Has difficulty in remembering ‘basic’ facts, despite many hours of practice/rote learning.
• Has no strategies to compensate for lack of recall, other than to use counting.
• Has difficulty in understanding place value and the role of zero in the Arabic/Hindu number system.
• Has no sense of whether any answers that are obtained are right or nearly right.
• Tends to be slower to perform calculations. (Therefore give fewer examples, rather than more time).
• Forgets mathematical procedures, especially as they become more complex, for example, ‘long’ division.
• Addition is often the default operation. The other operations are usually very poorly executed (or avoided altogether).
• Avoids tasks that are perceived as difficult and likely to result in a wrong answer.
• Weak mental arithmetic skills.
• High levels of mathematics anxiety.
• When writing, reading, and recalling numbers, may make mistakes: number additions, substitutions, transpositions, omissions, and reversals
• Difficulty with abstract concepts of time and direction
• Inability to recall schedules and sequences of past or future events
• May be chronically early or late
• Inconsistent results in addition, subtraction, multiplication, and division
• Inability to visualize, appear absent-minded, or lost in thought
• Inconsistent mastery of math facts
• Difficulty with left and right orientation
• Difficulty following sequential procedures and directions in math steps
• Slow in understanding math concepts in word problems
• Confuse operations signs or perform them in the wrong order
• Confuse part to whole relationships
• Difficulty keeping score during games
• Limited strategic planning ability

Since mathematics is very developmental, any insecurity or uncertainty in early topics will impact on later topics, hence to need to take intervention back to basics.

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There aren’t specific therapies for kids with dyscalculia. But you may want to explore educational therapy. This type of therapy helps kids with different kinds of learning and attention issues develop strategies for working around their issues and dealing with frustration. An educational therapist may be able to help your child get better at working with numbers.

Kids with dyscalculia may have trouble reading and articulating the language of math. In these cases, speech therapy could be helpful.

Kids with dyscalculia may also have trouble with visual-spatial skills. For example, they may struggle to judge distances between objects. If this is the case for your child, you might want to explore occupational therapy and/or vision therapy.

Children with dyscalculia may be dealing with other issues that emotional therapy can help with. For example, ADHD and dyscalculia often co-occur. So it may be recommended that your child try therapies to address aspects of his ADHD.

These kinds of therapies may lessen some of your child’s anxiety about school and make it easier for him to perform in class. The same may be said for psychological counseling if dyscalculia takes a toll on your child’s self-esteem or causes anxiety or stress.

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• Allow extra time on tests. Children with dyscalculia will often feel rushed during standard-length math tests. If possible, avoid timed tests of basic facts like multiplication tables, which can be a roadblock for LD kids.
• Provide frequent checks during classwork. It can be especially heartbreaking for an LD student to finish an entire worksheet, only to be told that every answer is wrong and he’ll need to do it again. Instead, teachers should check after every problem, or every three or four. This way, children can learn from mistakes before moving forward.
• List the steps for multi-step problems and algorithms. Post clearly numbered step-by-step instructions on the board, or give students a copy they can keep at their desk.
• Keep sample problems on the board. Students should also copy them down in a notebook for reference.
• Use individual dry-erase boards for students to work at their desks. Students can complete one step of a problem at a time, erasing any mistakes they may make.
• Use plenty of brightly colored, uncluttered reference charts and diagrams. Children with dyscalculia benefit from visual representations of math problems whenever possible.
• Whenever possible, allow calculator use. When testing more complex concepts than addition or subtraction, allow students to use calculators to make these basic steps quicker and more accessible. Then, students can focus on showing what they know — not how good they can add in their head.
• Reduce the number of assigned problems. Assigning ten problems, rather than a full page, is enough to assess students’ understanding.
• Avoid memory overload by assigning manageable amounts of practice work as skills are learned.
• Build retention by providing a review within a day or two of the initial learning of difficult skills.
• Provide supervised practice to prevent students from practicing misconceptions and “misrules.”
• Reduce interference between concepts or applications of rules and strategies by separating practice opportunities until the discriminations between them are learned.
• Make new learning meaningful by relating the practice of subskills to the performance of the whole task, and by relating what the student has learned about mathematical relationships to what the student will learn next.
• Reduce processing demands by pre-teaching component skills of algorithms and strategies.
• Teach easier knowledge and skills before difficult ones.
• Ensure that skills to be practiced can be completed independently with high levels of success.
• Help students to visualize math problems by drawing.
• Give extra time for students to process any visual information in a picture, chart, or graph.
• Use visual and auditory examples.
• Use real-life situations that make problems functional and applicable to everyday life.
• Do math problems on graph paper to keep the numbers in line.
• Use uncluttered worksheets to avoid too much visual information.
• Use rhythm or music to help students memorize.
• Use distributive practice: plenty of practice in small doses.
• Use interactive and intensive practice with age-appropriate games as motivational materials.
• Have students track their progress; which facts they have mastered and which remain to be learned.
• Challenge critical thinking about real problems with problem-solving.
• Use manipulatives and technology such as tape recorders or calculators.

Goal writing is always a pain.  Is the goal SMART?  What’s a good goal?  Often I struggle to come up with goals.  I found some help!

Common Core Aligned Goals for Kindergarten and First Grade

Virginia SMART goals (2009)

Goal and Objective Bank – Covers more than math

2nd and 3rd Grade Math Goals

Goal Bank (Tons of Goals for ALL Grades and Subjects)

2nd Grade Math Goals

Embrace technology when your child has dysgraphia and/or dyscalculia!  There are great apps that can be used to help you and your child. Here are some apps/software you may find helpful:

Dyscalculia

ModMath

Math Curriculum for Dyscalculia

Policy, Research, Identification and Intervention for Maths Learning Difficulties and Dyscalculia

Math Programs and Apps for Dyscalculia

Photomath – Camera Calculator App (Apple and Android)

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Understood.org has a lot of great posts on a variety of topics. Here they outline four types of tests that are given when evaluating for dyscalculia, and examples of each type of test.

Tests That Assess Computation Skills

Example: Woodcock-Johnson IV (WJ IV) Calculation subtest

Similar tests include: Wechsler Individual Achievement Test IV (WIAT-III) Numerical Operations, Mathematical Fluency and Calculations Tests (MFaCTs), certain subtests of the Comprehensive Mathematical Abilities Test (CMAT)

What it measures: Your child’s ability to do math operations efficiently and accurately.

Why it’s important: These are the skills that allow kids to make correct math calculations. They’re involved in all math operations, from addition to trigonometry.

How it works: Your child is given a series of basic math problems to do with pencil and paper. The type of problems she gets depends on her age or grade. Younger kids will get addition and subtraction problems. Older kids will get problems that involve multiplication, division, decimals, and fractions. High-schoolers may get some basic algebra questions, as well.

These tests aren’t timed. If your child gets a low score, the evaluator will assess what types of errors she makes. When kids make an error like 38 − 29 = 19, they may not understand a math concept, like borrowing.

But some kids make mistakes even when they understand the math concepts they’re working with. For instance, after doing two addition problems, a child may do a third problem as an addition problem, too—even though it’s a division problem. This can point to attention issues.

Tests That Assess Math Fluency

Example: WJ IV Math Fluency subtest

Similar tests include: WIAT-III Math Fluency subtest, MFaCTs Fluency Test

What it measures: Your child’s ability to call up math facts, like 3 × 3 = 9, quickly and accurately.

Why it’s important: Having basic math facts at their fingertips frees up kids to spend more energy on learning new concepts and skills. It can really slow them down if they have to count on their fingers or struggle through basic calculations. They’re also more likely to be confused and get lost in the problem.

Having to do problems quickly requires kids to stay focused. So a low score could point to attention issues in addition to math difficulties.

How it works: Your child is given written tests of math computation problems. (These are similar to the problems in the computation test, but easier.) She must complete as many problems as she can within a certain time frame. The amount of time varies by age, but is generally between three and five minutes.

Tests That Assess Mental Computation

Example: Wechsler Intelligence Scale for Children (WISC-V) Arithmetic subtest

Similar tests include: Paced Auditory Serial Addition Test (PASAT), Test of Mental Computation

What it measures: Your child’s ability to do math problems in her head. This is also known as mental math.

Why it’s important: Mental math requires kids to do a few things. They need to remember the information they’ve heard, retrieve math facts and then make calculations. A low score can mean they haven’t mastered basic math strategies. It can also mean they struggle with working memory or anxiety.

How it works: The test can be given in two ways—orally or visually, on a computer. In the oral version, your child listens to a series of problems. She might hear 9 minus 3 plus 6, for instance. In the visual one, she sees numbers flash on the screen. She might see a 3, followed by another 3, which she adds together. Then she might see a 2 on the screen, so she has to add 6 + 2, and so on.

Tests That Assess Quantitative Reasoning

Example: WIAT-III Math Problem Solving subtest

Similar tests include: WJ IV Applied Problems, CMAT Problem Solving

What it measures: Your child’s math problem-solving skills. Specifically, her ability to understand quantitative relationships and set up a computation to solve a word problem.

Why it’s important: Kids need to use reasoning in order to solve math word problems. That requires being able to understand numerical concepts. A low score on this test can signal an issue with math, language, or higher order skills, so more testing may be needed to tell what’s behind it.

How it works: This test uses both verbal and visual prompts. The evaluator gives your child a series of word problems orally. Or your child might read the problem. She also has a pencil and paper to help calculate, and a written version to refer to.

A typical problem may be: John walked to the store. The store was 10 miles away. He bumped into Alice at the store. They both walked back to John’s house. What was the total number of miles walked by both children? (The answer is 30.)

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Here is some of the latest research on Dyscalculia. Please let me know if you have any questions.

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Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia 2018

Abstract

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides the first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8–11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

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Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia  2018

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (=negative math priming effect).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.

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Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children With Mathematics Difficulties

Abstract

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children (N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and that some showed only a basic grasp of the meaning of a fraction even after several years of instruction. Children with low growth in fraction knowledge during the intermediate grades were much more likely to fail to meet state standards on a broad mathematics measure at the end of Grade 6. Although a range of general and mathematics-specific competencies predicted fraction outcomes, the ability to estimate numerical magnitudes on a number line was a uniquely important marker of fraction success. Many children with mathematics difficulties have deep-seated problems related to whole number magnitude representations that are complicated by the introduction of fractions into the curriculum. Implications for helping students with mathematics difficulties are discussed.

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Dyscalculia and Transitions into Higher Education and the Workplace  2018

Abstract

Grant (2013) cites five key factors: past history; current situation; a standardized mathematics test with the score less than a perceptual reasoning score; a mathematics score that does not result from either poor memory or slow processing, and finally, a measure of numerosity. Trott (2015, p. 411) contends that, although provision for one-on-one study skills supports for dyslexic students is available in almost all Higher Education Institutions, a similar service for dyscalculic students is not commonplace. […]work might involve the use of analog and digital clocks, menus, and shopping tasks as well as measures of lengths or weights. Since dyscalculic students often have good language skills and are procedural in their approach, it can be advantageous to take a route that equips students with step-wise algorithms rather than conceptual, notation-laden solutions. […]for Qualified Teacher Status, for those students who wish to become teachers, tests of numerical reasoning are set before a student can enter a postgraduate teacher training course

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Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic

Abstract

Brain disorders are often investigated in isolation, but very different conclusions might be reached when studies directly contrast multiple disorders. Here, we illustrate this in the context of specific learning disorders, such as dyscalculia and dyslexia. While children with dyscalculia show deficits in arithmetic, children with dyslexia present with reading difficulties. Furthermore, the comorbidity between dyslexia and dyscalculia is surprisingly high. Different hypotheses have been proposed on the origin of these disorders (number processing deficits in dyscalculia, phonological deficits in dyslexia) but these have never been directly contrasted in one brain imaging study. Therefore, we compared the brain activity of children with dyslexia, children with dyscalculia, children with comorbid dyslexia/dyscalculia and healthy controls during arithmetic in a design that allowed us to disentangle various processes that might be associated with the specific or common neural origins of these learning disorders.

Participants were 62 children aged 9 to 12, 39 of whom had been clinically diagnosed with a specific learning disorder (dyscalculia and/or dyslexia). All children underwent fMRI scanning while performing an arithmetic task in different formats (dot arrays, digits and number words). At the behavioral level, children with dyscalculia showed lower accuracy when subtracting dot arrays, and all children with learning disorders were slower in responding compared to typically developing children (especially in symbolic formats). However, at the neural level, analyses pointed towards substantial neural similarity between children with learning disorders: Control children demonstrated higher activation levels in frontal and parietal areas than the three groups of children with learning disorders, regardless of the disorder. A direct comparison between the groups of children with learning disorders revealed similar levels of neural activation throughout the brain across these groups. Multivariate subject generalization analyses were used to statistically test the degree of similarity, and confirmed that the neural activation patterns of children with dyslexia, dyscalculia and dyslexia/dyscalculia were highly similar in how they deviated from neural activation patterns in control children. Collectively, these results suggest that, despite differences at the behavioral level, the brain activity profiles of children with different learning disorders during arithmetic may be more similar than initially thought.

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Do Chinese Children With Math Difficulties Have a Deficit in Executive Functioning?

Several studies have shown that Executive Functioning (EF) is a unique predictor of mathematics performance. However, whether or not children with mathematics difficulties (MD) experience deficits in EF remains unclear. Thus, the purpose of this study was to examine if Chinese children with MD experience deficits in EF. We assessed 23 children with MD (9 girls, mean age = 10.40 years), 30 children with reading difficulties and MD (RDMD; 12 girls, mean age = 10.82 years), and 31 typically-developing (TD) peers (16 girls, mean age = 10.41 years) on measures of inhibition (Color-Word Stroop, Inhibition), shifting of attention (Planned Connections, Rapid Alternating Stimuli), working memory (Digit Span Backwards, Listening Span), processing speed (Visual Matching, Planned Search), reading (Character Recognition, Sentence Verification), and mathematics (Addition and Subtraction Fluency, Math Standard Achievement Test). The results of MANOVA analyses showed first that the performance of the MD children in all EF tasks was worse than their TD peers. Second, with the exception of the shifting tasks in which the MD children performed better than the RDMD children, the performance of the two groups was similar in all measures of working memory and inhibition. Finally, covarying for the effects of processing speed eliminated almost all differences between the TD and MD groups (the only exception was Listening Span) as well as the differences between the MD and RDMD groups in shifting of attention. Taken together, our findings suggest that although Chinese children with MD (with or without comorbid reading difficulties) experience significant deficits in all EF skills, most of their deficits can be accounted by lower-level deficits in processing speed.

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The Diagnosis and Management of Dyscalculia  2012

Dyscalculia is defined as difficulty acquiring basic arithmetic skills that is not explained by low intelligence or inadequate schooling. About 5% of children in primary schools are affected. Dyscalculia does not improve without treatment.

In this article, we selectively review publications on dyscalculia from multiple disciplines (medicine, psychology, neuroscience, education/special education).

Many children and adolescents with dyscalculia have associated cognitive dysfunction (e.g., impairment of working memory and visuospatial skills), and 20% to 60% of those affected have comorbid disorders such as dyslexia or attention deficit disorder. The few interventional studies that have been published to date document the efficacy of pedagogic-therapeutic interventions directed toward specific problem areas. The treatment is tailored to the individual patient’s cognitive functional profile and severity of manifestations. Psychotherapy and/or medication are sometimes necessary as well.

The early identification and treatment of dyscalculia are very important in view of its frequent association with mental disorders. Sufferers need a thorough, neuropsychologically oriented diagnostic evaluation that takes account of the complexity of dyscalculia and its multiple phenotypes and can thus provide a basis for the planning of effective treatment.

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