### UNDERSTANDING

## Dyscalculia

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##### What is dyscalculia? What is developmental dyscalculia?

##### Are there other types of math learning disabilities?

Yes. Some children have difficulty specifically with mathematical reasoning, which is the ability to apply math to real-world, practical problems. These children may be able to perform calculations without difficulty when the problems are presented in number form but have trouble solving word problems. This includes children with language disorders.

##### What are the symptoms of dyscalculia? What are the signs of dyscalculia / a mathematics based learning disability?

Children with dyscalculia often have the following characteristics. Keep in mind that children with dyscalculia do not necessarily have every symptom below and they will not have every symptom to the same degree. Also realize that some of the concepts below are similar and overlap.

- Learning how to count as young children as well as associating digits to the quantity they represent. These children may have trouble for example writing numbers from dictation (e.g. hearing “five” and writing “5”) or writing the digit that goes with a set of objects (e.g. seeing ///// and writing “5”).
- Number sense. Number sense is an internalized appreciation of the quantity that numbers represent, such as an intuitive appreciation of what “five” means or of how much larger “twenty” is than “three” for example. Children with poor number sense also have difficulty understanding the relationship between numbers, such as all the different ways you can get to 5 (e.g. 2 + 3, 2 + 2 + 1, 4+ 1, etc.).
- Learning and quickly retrieving math facts (e.g. 5 + 8, 9 x 9, etc.). This results in poor math fluency or automaticity.
- Subitizing. Subitizing is the ability to immediately and accurately identify the number of a visual display of objects, such as being able to immediately identify ❑ as 1
- Estimation. Children with dyscalculia often have trouble estimating. For example, a child with dyscalculia would be expected to be more inaccurate guessing how many jelly beans are in a jar compared to a typically developing child of the same age.
- Digit Comparison. Young children who are slow to identify which of two digits is greater (e.g. 7 vs. 9) are at increased risk of later having dyscalculia.
- Immature use of strategy. Typically developing students in grades 1 through 7 quickly retrieve single digit addition and subtraction facts. On the other hand, children with dyscalculia tend to persist using less sophisticated counting strategies across these grades, such as counting on from the larger addend. An example would be computing 5 + 7 by starting with 7 and then counting 5 more numbers in sequence to get to 12.
- Counting on fingers. Research has shown that counting on fingers facilitates math development in Kindergarten and 1st grade. This gives students a concrete visual representation of quantity, helping them associate digits to the quantities they represent. However, if students are still counting on their fingers by the end of 2nd grade, this is associated with poorer math development. This suggests they are having trouble internalizing the association between digit and quantity as well as having difficulty making this knowledge automatic and rote. This is analogous to how children with dyslexia can get stuck habitually decoding words by trying to identify and blend each sound of the word, at the expense of developing an ability to automatically recognize whole words on sight (i.e. develop a sight vocabulary).
- Pattern Identification. The ability to understand and identify patterns underlies many areas of math in some way. For example, a child’s ability to recognize that the pattern below is one in which the boxes keep doubling, sets the stage for skip counting, which is a prerequisite skill for multiplication.

Pattern identification is an important pre-cursor skill for algebraic thinking. It allows a student to comprehend the relationship between numbers as well as mathematical rules. An example would be judging the equivalence of number sentences (e.g. Does 5 + 3 = 4 + 4?) or understanding the converse relationship between addition and subtraction, that if, for example, 2 + 5 = 7, then 7 – 5 = 2.

- Visual – spatial skill. Visual – spatial skill is the ability to understand location and position. We use visual – spatial skill to do things like assemble a piece of furniture from a diagram or figure out how to place our luggage so it fits in the trunk of our car. Visual-spatial skill is also very important in math since, in math, the
*location*of information often determines what the information means. Think of place value for example. The difference in meaning between 13 and 31 is based on which number is located on the right vs. the left. Other examples include fractions, in which the numbers mean part (numerator) or whole (denominator) based on whether they are located on the top or bottom. Knowing the correct direction or route in which to travel when solving a problem also requires visual – spatial skill. For this reason, many math concepts are confusing to children with weak visual – spatial skills. This is also a reason why some students may find areas of math that place an especially high demand on visual – spatial skills, such as geometry, particularly challenging. - Visual memory. Visual memory is the ability to recall what one saw. Visual memory is important in math for several reasons. Math is a very “visual” subject. Visual memory is necessary to recall mathematical and scientific notations, symbols, formulas, and equations. In addition, teachers demonstrate how to solve math problems visually – by solving them on the board as the students watch. To recall how to solve math problems, the student must recall what s/he “saw” when the teacher was illustrating the concept or procedure.
- Working memory, including spatial working memory. Working memory is a complex concept that has multiple aspects. Working memory can be defined as the ability to register and access information and keep it “online,” in our awareness so that we can solve problems. Working memory is necessary to keep track of information in our mind. For example, picture a teacher asking, “If five dogs are in a yard and four more dogs run in, how many dogs are in the yard altogether?” In order to solve this problem, the student must register or “catch” all the important details of the problem in the first place, such as that there were five dogs, four more ran in, and we want to know how many dogs altogether. The student must also “hold” these details in his or her awareness while s/he retrieves relevant math facts / arithmetic procedures necessary to solve this problem. This is part of the job of working memory.Working memory is especially important for math because math places a high emphasis on keeping track of many details at once. Math is also a cumulative subject. One concept builds upon the next so students must be able to readily and easily retrieve previously learned information and have it “top of mind” in order to make sense of the current lesson. For example, in order for a student to be able to understand the concept of multiplying decimals, s/he needs to be able to recall what a decimal is and how to multiply digits.
Children with weaknesses in working memory are prone to losing track of details while solving math problems and making careless errors. For example, they may forget to add a column of numbers when solving a multi-digit problem. The child may also forget what s/he is doing in the middle of the problem and veer off course, such as beginning the problem by performing the correct operation and then inadvertently switching operations in the middle of the problem.

Working memory also includes what has been called a “central executive,” a part of working memory whose job it is to

*keep out*of awareness (i.e. inhibit)*irrelevant*information. Children with dyscalculia have been shown to have a deficit in this area, which interferes with arithmetic fact retrieval. When trying to recall the arithmetic fact that*does*apply to the current problem, arithmetic facts that do*not*apply also pop in their heads.Because of the above relationships between working memory and math, including the ability to notice and keep track of details as well as inhibit irrelevant thoughts, children with Attention Deficit / Hyperactivity Disorder (ADHD), Predominantly Inattentive Presentation (what used to be called Attention Deficit Disorder or “ADD”) are at higher risk for math difficulty.

*Spatial*working memory refers specifically to the ability to actively visualize information. Children with dyscalculia have been shown to have poor spatial working memory, which interferes with their ability to visualize quantity and link quantity to the numbers that represent them. For example, in learning what “five” means, spatial working memory helps a child visualize something like ●●●●● which the child then forms a mental link to “5.” In addition, spatial working memory helps children keep track of the location of information when solving a problem. For example, when solving a multi-digit computation (e.g. 347 x 85), spatial working memory helps the student keep track of where s/he is putting the numbers as s/he performs each computation the problem requires.

- Poor understanding of time. Time is a spatial concept. Points in time are designated by position, location, and direction. For example, “tomorrow” on a calendar (for all but one day of the week) is to the right and “yesterday” is to the left. The root of time concepts in spatial skill is also reflected in the language. Words pertaining to time are often “position” or “location” words (e.g. to look
*ahead*to the future, or look*behind*to the past, etc.). Because time is a spatial concept and because children with dyscalculia often have weaknesses in visual-spatial skill and spatial working memory, children with dyscalculia may also have a poor understanding of time. For example, the child may not understand the difference between something being a week from now and a month from now or the child may not have a sense of how far away his or her birthday is despite multiple explanations from the parent.

##### How many people have dyscalculia?

About 3 – 6% of the population has dyscalculia.*

**Cited from: Kuhn, J.-T. (2015). Developmental dyscalculia: Neurobiological, cognitive, and developmental perspectives. Zeitschrift für Psychologie, 223(2), 69-82. http://dx.doi.org/10.1027/2151-2604/a000205*

##### Does dyscalculia run in families?

**Cited from: Kuhn, J.-T. (2015). Developmental dyscalculia: Neurobiological, cognitive, and developmental perspectives. Zeitschrift für Psychologie, 223(2), 69-82. http://dx.doi.org/10.1027/2151-2604/a000205*

##### Do more girls or more boys have dyscalculia?

**Cited from: Kuhn, J.-T. (2015). Developmental dyscalculia: Neurobiological, cognitive, and developmental perspectives. Zeitschrift für Psychologie, 223(2), 69-82. http://dx.doi.org/10.1027/2151-2604/a000205*

##### What causes dyscalculia? What causes math learning disabilities?

Dyscalculia is associated with dysfunction in the parietal lobes of the brain, in particular the intraparietal sulcus (a part of the parietal lobe). The parietal lobe roughly corresponds to the top back part of the head. Dyscalculia also has been associated with the right frontal lobe of the brain, which corresponds roughly to the area behind the right eye.

This dysfunction can be caused by genetics. It also can be caused by other factors, like in utero exposure to toxins, such as in the case of fetal alcohol syndrome. Dyscalculia also can be caused by brain injury, such as from a blow to the head or a stroke.

##### How can I help my child with dyscalculia?

The specific needs of a student with dyscalculia will vary based on the individual, but potential interventions include:

- Special Education services, including specialized, multi-sensory math instruction from a Special Education teacher, such as in Resource Room or via direct Consultant Teacher services.
- Classroom and test modifications and accommodations, such as: extra explanations, cues, and prompting regarding the spatial aspects of math problems (e.g. where to begin math problems and which direction to “travel” in when solving the problem), and provision of graph paper to help align numbers when performing multi-digit computations.