Case Study Of Child With Dyscalculia In Adults

What is dyscalculia? It is a specific developmental disorder, biologically based, that deeply affects learning related to mathematics and arithmetic. Many times it is defined as “math dyslexia”. This condition is independent of the level of intelligence of the child and to the teaching methods used. The difficulty is centered around the ability to interpret numeric symbols and arithmetical operations like adding, subtracting, multiplication, and division. A child that suffers from dyscalculia will confuse numbers and signs, and cannot do mental math or work with abstract ideas. These children have a hard time completing assignments and homework.

Dyscalculia could be defined as the dysfunction of the neural connections that process numeric language, making it more difficult to access and process numeric information.

The prevalence of dyscalculia in the school population is about 3% to 6%, with a similar distribution between boys and girls.

How does dyscalculia affect the brain?

Dyscalculia presents itself as a neuronal dysfunction in the intraparietal sulcus of the brain. This dysfunction develops a pattern of cognitive deterioration that usually manifests itself with skills deficits such as:

  • Focus (concentration)

    : Skill related to the pattern of cognitive deterioration linked to dislexia. The structural deficit in these connections of neural networks is also related to inhibition, which affects the mind's sharpness, making it more difficult for the child to learn math.
  • Divided attention

    : This skill is important as it allows for multitasking. Children with math disabilities present problems when responding to a stimulus because they are unable to focus, they get distracted with irrelevant stimuli, and they tire easily.
  • Working memory

    : This cognitive skill refers to temporary storage and the ability to manipulate information in order to complete complex assignments. Some difficulties as a result of this may be trouble following directions, forgetting instructions and tasks, low motivation, incomplete memories, being easily distracted, not remembering numbers, and delayed mental arithmetic.
  • Short-term memory

    : The capacity to retain a small amount of information during a short period of time. This mental deficit explains the inability to carry out math assignments. The problems present themselves when they calculate or attempt math problems. This is also related to the inability to remember numbers or multiplication tables.
  • Naming

    : Implies the ability to recall a word or number and use it later. Children with dyscalculia have difficulties remembering numbers because their ability to process information is deficient.
  • Planning

    : Low levels in this cognitive skill implies difficulties in planning and making sense of numbers and exercises. This inability to anticipate events or outcomes prevents the student from correctly completing the exercise.
  • Processing speed

    : This corresponds to the time it takes for our brain to receive information (a number, a mathematical equation, a problem…), understand it, and respond to it. Children that do not have any learning difficulties complete this process quickly and automatically, while children who have dyscalculia need more time and energy in order to process the information.

In the image above, we can see the area that is affected by dyscalculia. CogniFit is a professional tool that provides a complete cognitive screening for each user. It identifies the cognitive skills that show deficits and automatically proposes different batteries of clinical exercises that stimulate the connections of neural networks that are weak and is individualized training for each child.

The most effective treatment for dyscalculia, just like with dyslexia, is an early diagnosis. The earlier the problem is identified, the earlier that children with this disorder can learn the necessary tools to help them adapt to a new learning process, and the more likely they are to avoid learning delays, self-esteem problems and other more serious disorders.

Thanks to training the neuroplasticity, we can rebuild deteriorated brain functions and help these children develop new brain strategies aimed to efficiently improve the difficulties associated with dyscalculia.

CogniFit's brain training exercises for children with dyscalculia evaluates the level of cognitive deterioration and automatically creates an intervention strategy that is personalized for each profile. This allows for stimulation of the parts of the brain that show deficits through fun clinical games and exercises. Some of the deteriorated brain modules that these exercises work to improve are associated with the ability to concentrate or focus, divided attention, working memory, visual memory and short term memory, naming, and processing or planning speed.

The program was designed by a team of scientists, neurologists, and psychologists that apply the latest discoveries about the brain to simple games that are automatically adapted to the cognitive profile of each user. The games can be practiced online from any computer with internet and they are easy to understand.

What is the cause of dyscalculia? There are numerous investigations conducted by neuroimaging. This technique allows for a live visual of brain activity and the central nervous system. Thanks to these representations, you can see that the deficit in the neural connections associated with dyscalculia is found specifically in the brain module in charge of numeric processing, which is located in the parietal lobe of the brain. Moreover, other areas such as the prefrontal cortex, the cingulate cortex, the back of the temporal lobe and numerous subcortical regions also form part of the proper functioning of mathematical or arithmetic skills.

Dyscalculia occurs due to a congenital condition, meaning it has a genetic component. Normally one of the parents of the child also had trouble learning math.

Some of the causes of dyscalculia correspond to:

  • Cognitive deficit in numeric representation

    : this is a neuronal dysfunction that prevents the correct mental representation of numbers. It makes numeric decoding more difficult and it affects the comprehension of the meaning of assignments or math problems.
  • Cognitive deficit that impedes ability to store information in the brain

    : Children with dyscalculia show a dysfunction in a specific neural connection that prevents them from easily accessing numeric information. Their neural connection networks use alternative routes that a personal without this disorder does not use.

There are other possible causes that related to dyslexia. Neurobiological brain disorders, neurological maturation failures, psychomotor alterations, and even memory problems related to the environment, such as maternal exposure to alcohol, drugs in the womb, or premature birth are some possible causes.

Characteristics and symptoms of dyscalculia

Dyscalculia has an ample network of difficulties associated with mathematics, and its characteristics and symptoms will vary depending on the age of each child. These symptoms may be combined and present themselves differently from child to child.

It starts to become noticeable during pre-school years, when the child begins to develop mathematical learning skills and continues into childhood, adolescence, and even adulthood.

As the children continue to grow, their difficulties become more pronounced, so it is essential to seek help early on. The most important thing in dyscalculia cases is early identification, and for this reason parents as well as teachers should be alert in order to detect the difficulties and symptoms as early as possible.

The earlier we can offer these children the intervention tools necessary to help them adapt to school, the more likely they are to optimize their mental resources and learning strategies.

Symptoms of dyscalculia in pre-school aged children:

  • Difficulties

    learning how to count.

  • Problems associated with the

    comprehension of numbers

    .
  • Inability to classify and measure:

    It is difficult to associate a number with a real life situation, for example connecting the number “2” to the possibility of having 2 candies, 2 books, 2 plates, etc.
  • Problems recognizing symbols associated with numbers

    , for example, inability to associate “4” to the concept “four”.
  • Written errors

    of numbers when they're written or copied.
  • Incorrect symbols:

    for example, confusing 9 with 6, or 3 with 8.
  • Reverse number while writing:

    Write the numbers upside down.
  • Sound errors:

    Confuse numbers that sound similar, like “two” and “three”
  • Symptoms when ordering or sequencing numbers:

    Repeat a number two or more times.
  • When we tell a child with dyscalculia

    to count until 5 and stop

    , many times they do not realize the limit when they reach 5 and continue to count.
  • Omission:

    This is quite common. The child will often forget one or more number in a series.
  • Symptoms relative to sequencing:

    Another characteristic of dyscalculia happens when we ask a child to start counting from 4, for example. The child is not able to start from this number, and instead must say the complete sequence by writing it or saying the previous numbers to him or herself.
  • They have a hard time classifying objects

    by shape and size.

Symptoms of dyscalculia in primary school aged children:

  • Problems recognizing mathematical symbols:

    They confuse the sign + with - and cannot use these or other symbols correctly.
  • Unable to learn or remember

    basic mathematical structures,

    like 1+2=3
  • They are not able to recognize words like

    “more than” or “less than”,

  • They often use their

    fingers to count

    .
  • Difficulties learning and remembering the procedure or

    rules for simple problems

    . They tend to skip steps and/or they do not understand the exercise well.
  • They start

    problems in the wrong order

    . For example, while adding or subtracting they start on the right instead of the left.
  • They have difficulties lining up the problems:

    For example, if there is a horizontal addition problem they do not know how to make it vertical. We can see another example of this symptom while multiplying, where children with dyscalculia have a hard time lining up the columns of numbers (derivative) in the corresponding column, or when they divide they write the quotient and they put the first number on the right and then on the left, inverting the answer.
  • Another very common characteristic is having trouble carrying when adding or subtracting.

    This is because students with dyscalculia do not understand the numeric series or decimals well.
  • Problems reasoning:

    A fairly frequent error is that the answer when subtracting is larger than the original numbers.
  • Difficulties when doing basic math in their head.

  • They do not understand spoken or dictated problems.

    They don't understand the main idea of the problem. They are not capable of visualizing all of the information that they heard, and they have trouble when they try to draw visuals.
  • Symptoms related to the process of reasoning in mathematical problems:

    The mental representation deficit prevents them from relating concepts and they don't know how to differentiate between more and less important data. They especially have trouble when the problem has more than one step.
  • They usually have more general difficulties,

    such as problems telling time and they often get lost easily because they tend to have poor orientation.

Symptoms of dyscalculia in high school:

  • They have a hard time

    applying mathematical ideas in their day-to-day.

    For example, estimating how much they will spend in total, making change, creating a budget, etc.
  • Problems

    measuring variables

    , for example, calculating how much 500g rice, 250ml of milk, or 1/3 kg of flour, etc. corresponds to.
  • Poor orientation or disorientation

    , they have a hard time following directions and often get lost.
  • Unsure of how to solve basic mathematical equations

    and have little creativity with numbers. They do not understand the different formulas or ways to solve the same problem.
  • Hard time

    understanding graphs

    , numeric representations, or maps.
  • They are not generally good drivers

    because they don't calculate speed or distance well.

It is also important to mention that not all children that have trouble doing mathematical equations have dyscalculia, and it is essential to identify the frequency of symptoms. Moreover, dyscalculia is not always related to mathematical equations, children may also have trouble with everyday activities or common games.

Although the symptoms that present themselves in dyscalculia are usually common in different types of dyslexia, dyscalculia usually presents itself in 5 main types.

  • Verbal dyscalculia:

    This type of dyscalculia is characterized by a difficulty naming and understanding the mathematical concepts presented verbally. Children with this type of duscalculia are able to read or write numbers, but have a hard time recognizing them when presented verbally.
  • Practognostic dyscalculia

    : This type of dyscalculia is characterized by a difficulty translating an abstract mathematical concept into a real concept. These children are able to understand mathematical concepts but have trouble listing, comparing, and manipulating mathematical equations.
  • Lexical dyscalculia

    : Trouble reading and understanding mathematical symbols and numbers, as well as mathematical expressions or equations. A child with lexical dyscalculia can understand the concepts when spoken, but may have trouble writing and understanding them.
  • Graphical dyscalculia

    : Difficulty writing mathematical symbols. Children with this type of dyscalculia are able to understand the mathematical concepts but do not have the ability to read, write, or use the correct corresponding symbols.
  • Ideognostical dyscalculia

    : Difficulty carrying out mental operations without using numbers to answer math problems and understand mathematical concepts. They may also have a hard time remembering mathematical concepts after learning them.
  • Operational dyscalculia

    : This type of dyscalculia presents itself with a difficulty to complete written or spoken mathematical operations or calculations. Someone with operational dyscalculia will be able to understand the numbers and the relationships between them, but will have trouble manipulating numbers and mathematical symbols in the calculation process.

Games to beat dyscalculia with the family

Dyscalculia is not easy to diagnose, and most schools do not have any type of early detection system in place to identify this disorder in the classroom and help children get the tools they need. For this reason it is often up to parents and families to be alert and identify the early symptoms. If you think your child has dyscalculia, a cognitive assessment may also be useful, which can be done using CogniFit's cognitive stimulation exercises for children with dyscalculia. Deficits in cognitive skills such as: focus, divided attention, working memory, short-term memory, naming skills, planning, or processing speed may be indicators of dyscalculia.

Once you have the diagnosis, it is important to motivate your child and show them that they can be successful with patience, practice, and effort. They need to be reminded that they have other gifts, and to know that dyscalculia does not have to negatively affect their work. This is why it is also important that you work with them at home. It will help to visualize math homework and give them the necessary time they need so that they understand the exercise. Here we will provide some fun games and activities so that you can play with the family while you beat dyscalculia at home:

  • Cook together

    : Both of you look at a recipe that you are going to make and ask them to be in charge of getting the ingredients together that you'll need to cook. For example, we need 1/5 kg of lentils, 3 carrots, 2 onions, 6 pieces of meat… We have to cut the vegetables into 5 pieces...
  • Play with the clock

    : Tell the child they are in charge of telling you when it is a certain time, celebrate how well they did and how responsible and how “old” they are together.
  • Go to the supermarket

    : Have them help you go shopping, you can play games like them being responsible for how many things you have to buy, identify what and how many things there are on the list and have them get it themselves.
  • Ask them questions about prices

    : If we want to save, how many yogurts should we get, the ones that cost 1.00$, or the ones that cost 1.30$? Celebrate the great “steal” you both made together.
  • Play guess the pile

    : Make little mountains out of rocks, peas, or change and you have to guess which pile has more or less. You can also try to guess how many rocks there are in the pile. You count them together, and whoever get closer, wins.
  • Play counting something

    : Count, for example, all the red cars you see, count the number of people you see with white shoes, count how many stairs you go up...
  • Find numbers

    : As you walk around, you can play “finding numbers”, suggest that they find the number “7”, and you both look for the number on the street, license plates, etc.
  • Play remember telephone numbers

    : For example, you have to call grandma, ask them if they remember the first three numbers and you remember the rest. Call together and if they did it well, you celebrate.
  • Have them help hand things out

    : There's four of us, how can we cut a piece of cake into four equal parts?
  • Play setting the table

    : Hand out the plates, silverware, cups, napkins, and bread. Make sure they realize that it's important that each one must go to a set.
  • Play with CogniFit

    : It's a great way to stimulate weakened brain modules, without the kids noticing. They'll be playing and having fun!
  • Play with stores

    : Imagine that the child is a store clerk, they must choose between all the products you have at home what they wants to sell at “their store”. They must give each item a price and a tag. Later, you go in as a client. With this game, you'll practice quantity, addition, subtraction, and even how to manage money. Its a fun way to spend family time and learn together.

There is one main link with dyslexia, both are genetic and show common cognitive deficits that make it more difficult to learn to read and do math.

Horowitz-Kraus T, Breznitz Z. - Can the error detection mechanism benefit from training the working memory? A comparison between dyslexics and controls- an ERP study - PLoS ONE 2009; 4:7141.

Peretz C, Korczyn AD, Shatil E, Aharonson V, Birnboim S, Giladi N. - Computer-Based, Personalized Cognitive Training versus Classical Computer Games: A Randomized Double-Blind Prospective Trial of Cognitive Stimulation - Neuroepidemiology 2011; 36:91-9.

Thompson HJ, Demiris G, Rue T, Shatil E, Wilamowska K, Zaslavsky O, Reeder B. - Telemedicine Journal and E-health Date and Volume: 2011 Dec;17(10):794-800. Epub 2011 Oct 19.

Preiss M, Shatil E, Cermakova R, Cimermannova D, Flesher I (2013) Personalized cognitive training in unipolar and bipolar disorder: a study of cognitive functioning. Frontiers in Human Neuroscience doi: 10.3389/fnhum.2013.00108.

2.2.1

Single-case study

With mathematics being multidetermined and dyscalculia being heterogeneous, the dynamic process leading to an arithmetic facts deficit is thus difficult to isolate and define. Recently, the analysis of a single-case presenting a very circumscribed deficit of arithmetic facts has shed light on new perspectives. This case study concerned a 42-year-old woman, called DB, whose abilities in mathematics were characterized by a strong (developmental) arithmetic facts deficit in the context of good conceptual knowledge of mathematics and good to superior cognitive abilities (De Visscher and Noël, 2013). This deficit had negative repercussions on her latencies in a global math test, that were significantly longer compared to matched controls, but her good accuracy accounted for her good conceptual knowledge of mathematics. The cognitive investigation reported a very high level of global reasoning and normal performances in all tests assessing attention (visual, divided, and sustained attention), executive functioning (cognitive inhibition, behavioral inhibition, planning, cognitive flexibility), visual and verbal short-term memory, working memory, verbal and visual episodic memory, visuoconstructive processing, motor speed, and finger gnosia. The only noticeable deficit was found in the Brown–Peterson task, where the participant had to repeat three letters after doing an interfering task (orally reversing pairs of digits) for 5 to 15 s. In that task, DB made more errors than the controls, mainly because she incorrectly reported letters learned during the previous (instead of the current) trial, suggesting that her problem came from proactive interference.

The first aim of this single-case study was to establish a profile of her mathematical deficit. The difficulties of DB were seen in multiplication. She showed impaired performance in single-digit multiplication characterized by longer latencies when the task had unlimited time (due to the use of finger counting strategies) and by errors or nonresponses when the task had time limitation. Different multiplication tasks used at different time periods revealed that her deficit was persistent and stable (high correlation across problems, between the same test taken two times, 5 months apart). In a table membership judgment task where participants have to decide whether the number displayed belongs to the answers of the Pythagorean table of multiplications, DB showed impaired performance compared to matched controls. Similarly, in a multiplication verification task with manipulation of the false answer (nontable such as 4 × 8 = 26 or operand-related lures 4 × 8 = 28), DB did not show the classic operand-related lure effect. Because healthy adults have stored multiplication facts in their long-term memory, rejecting an operand-related lure like 28 associated with 4 × 8 =, is more difficult (more error-prone and slower) than rejecting a nontable lure such as 26. Contrariwise, DB similarly performed in the two categories of false answers. In other words, she encountered higher difficulties in rejecting the nontable lures compared to controls and did not show the classical operand-related effect. The findings of these two above-mentioned tests indicated that DB stored very few arithmetic facts in long-term memory.

The second aim was to identify the possible cause of this circumscribed deficit of arithmetic facts. Accordingly, De Visscher and Noël (2013) first considered the potential causes of dyscalculia depicted in the literature, in particular the number magnitude representation deficit (Piazza et al., 2010a; Wilson and Dehaene, 2007) and the rote verbal memory deficit (Dehaene et al., 2003). However, both hypotheses were dismissed since the performance of DB was good in tasks assessing the number magnitude representation (ie, magnitude comparison of symbolic (digits) and nonsymbolic (arrays of bars, or dots) stimuli and estimation) and the rote verbal memory (ie, reciting the alphabet and the months of the years, completing verbal expressions, speaking as quickly as possible the letter following the letter displayed and phonological awareness).

The question of why DB had never stored arithmetic facts in her long-term memory while she tried hard to train her arithmetic facts knowledge remains open. This question is especially compelling given the fact that DB had good performance in all the memory tests of short-, working-, and long-term memory, except for the Brown–Peterson where she seemed to be sensitive-to-proactive interference.

Accordingly, the sensitivity-to-interference of DB has been deeply investigated. First, a general sensitivity-to-interference in memory was tested with a recent-probes task (Monsell, 1978), where participants have to decide whether the displayed target corresponds to one of the stimuli that was presented 3 s earlier. This task includes three conditions; one where the target was presented 3 s before (accept), one where the target has never seen before (reject, no interfering), and one where the target has been seen before but in a previous trial (reject, interfering). In a verbal modality, DB used her high performing phonological loop that permitted her to score at the same level as the matched controls. In a visual condition, however, she showed a high performance in accepting the correct targets, and in rejecting false never seen targets, but was impaired in the condition of interference. A hypersensitivity-to-interference was therefore brought to light in DB.

From these findings, the impact of hypersensitivity-to-interference on learning stimuli that are highly similar had to be tested. To that aim, associative memory tasks with different levels of interference were used. In accordance with the assumption, DB showed a higher sensitivity-to-interference than matched controls in learning tasks, resulting in a deficit in the high interfering condition but normal performance in a noninterfering condition (when the stimuli were dissimilar).

Furthermore, and according to the principles of the interference parameter developed in the previous section, people with heightened sensitivity to similarity interference in memory should show higher sensitivity to the interference parameter in arithmetic facts solving. Therefore, the single-case study of DB should have a heightened sensitivity to the interference parameter (steeper slope) when compared to controls. De Visscher and Noël (2014b) ran a multiple regression with the interference parameter and the problem size for DB and for each of the matched controls. The model with DB's data revealed that the interference parameter was the only significant factor predicting her reaction time across problems. In comparison to the controls, the interference slope of DB was much steeper, while the problem size slope was similar to that of the controls. This confirmed the interpretation of a deleterious effect of the similarity in memorizing arithmetic facts in learners experiencing hypersensitivity-to-interference in memory, at least in this single-case study.

This single-case study shed light on a new potential explanation for one particular mathematical difficulty: hypersensitivity-to-interference in memory prevents subjects from storing arithmetical facts in long-term memory. Indeed, as arithmetic facts are very similar (use combination of the same 10 digits), people with hypersensitivity-to-interference in memory would not succeed in storing them in memory and would use counting or procedural strategies, that long more and are more error-prone. This hypothesis belongs to the domain-general etiologies.

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