Alfredo is eighteen years old, and he excels in drama and art. He’s an avid reader and writes poems and short stories in his spare time. However, he is unable to graduate with his senior class because he doesn’t have the required credits in mathematics.
Although he has normal intelligence, Alfredo has consistently done poorly in mathematics since primary school. After intensive tutoring and years of practice, he has finally become somewhat competent at basic facts and operations, but he has no idea how or when to apply them. When taking a math test, he simply takes numbers from each problem and inserts them in the algorithms that he memorized when studying for the test. He always carries his personal telephone book in his book bag because he can’t remember his own phone number or those of his friends.
Like Alfredo, many people have problems in learning mathematics. The nature of their problems vary. Some students can master basic facts but can’t do higher mathematics. Some can do higher math but can’t master basics. Some can follow math procedures one day but are unable to follow them the next day. Others may perform mathematical algorithms well in one situation but can’t apply them to new situations. Math disabilities can be very frustrating due to the complexity and variety of problems.
Dyscalculia, which means inability to calculate, is the most widely used term for disabilities in arithmetic and mathematics. Sometimes the term acalculia is used to refer to complete inability to use mathematical symbols and the term dyscalculia is reserved for less severe problems in these areas. Developmental dyscalculia may be used to distinguish the problem in children and youth from similar problems experienced by adults after severe head injuries, according to Hallahan et al. in Introduction to Learning Disabilities.
No one seems to know when the word dyscalculia came to life — the earliest we have come across is an advertisement in The New York Times from May 1968 (see below). We do, however, know that researchers have used other words for what they considered to be some sort of disability in math: arithmetic disability, arithmetic deficit, mathematical disability, and so on. The media has been using words like digit dyslexia, number blindness and the obvious math dyslexia.
As with other learning disabilities, reports of dyscalculia’s prevalence vary depending upon the definition and situation. However, research suggests that its prevalence is at least 6 percent of the school-aged population. Specifically, Badian reports a prevalence rate of 6.9 percent with 3.9 percent of these students low in arithmetic only, and 3 percent of these students low in arithmetic and reading. She suggests that researchers differentiate between children with arithmetic difficulties and those with both arithmetic and reading problems, in order to prevent distorted interpretations of research.
Dyscalculia symptoms include:
- Poor understanding of the signs +, -, ÷ and x, or may confuse these mathematical symbols.
- Difficulty with addition, subtraction, multiplication and division or may find it difficult to understand the words “plus,” “add,” “add-together.”
- Poor mental arithmetic skills.
- May have trouble even with a calculator due to difficulties in the process of feeding in variables.
- May reverse or transpose numbers for example 63 for 36, or 785 for 875.
- Difficulty with conceptualizing time and judging the passing of time.
- Difficulty with everyday tasks like checking change.
- Difficulty keeping score during games.
- Inability to comprehend financial planning or budgeting, sometimes even at a basic level, for example, estimating the cost of the items in a shopping basket or balancing a checkbook.
- Inability to grasp and remember mathematical concepts, rules, formulae, and sequences.
- May have a poor sense of direction (i.e., north, south, east, and west), potentially even with a compass.
- May have difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 10 or 20 feet away).
- Extreme cases may lead to a phobia of mathematics and mathematical devices.
According to the website Dyslexia in Ireland dyscalculia can be broken down into three subtypes:
- Quantitative dyscalculia, a deficit in the skills of counting and calculating.
- Qualitative dyscalculia, a result of difficulties in comprehension of instructions or the failure to master the skills required for an operation. When a child has not mastered the memorization of number facts, he cannot benefit from this stored “verbalizable information about numbers” that is used with prior associations to solve problems involving addition, subtraction, multiplication, division, and square roots.
- Intermediate dyscalculia involves the inability to operate with symbols, or numbers.
On the basis of his experience with arithmetic learning problems, Kosc described six types:
- Verbal dyscalculia, which refers to problems in naming the amount of things.
- Practognostic dyscalculia, which refers to problems in manipulating things mathematically — for example, comparing objects to determine which is larger.
- Lexical dyscalculia, which refers to problems in reading mathematical symbols, including operation signs (+, – ) and numerals.
- Graphical dyscalculia, which refers to problems in writing mathematical symbols and numerals.
- Ideognostical dyscalculia, which refers to problems in understanding mathematical concepts and relationships.
- Operational dyscalculia, which refers to problems in performing arithmetic operations.
These types of dyscalculia have not been independently verified — the data Kosc reported about students in Czechoslovakia were not directly supportive of the categories — and they are quite difficult to differentiate in students who have arithmetic learning disabilities. Nevertheless, Kosc’s discussion illustrates the many problems students may have in arithmetic and mathematics.
Successful intervention is dependent on finding the cause or causes of a problem. Most problems can only be solved if one knows their causes. A disease such as scurvy claimed the lives of thousands of seamen during their long sea voyages. The disease was cured fairly quickly once the cause was discovered, viz. a vitamin C deficiency. A viable point of departure would therefore be to ask the question, “What causes dyscalculia?”
It is important to understand that mathematics is a subject that consists of three aspects:
- Foundational skills: Research has shown that visual perception, visual memory, visual-spatial memory and logical thinking (which makes problem solving possible) are the most important foundational skills of math.
- Mathematical skills: There are many things in mathematics that the learner must learn to do, like, for example, the skills of counting, adding and subtracting, multiplication and division, applying place value and fractions, reading time etc.
- Knowledge: There is much in math that one simply has to know and therefore has to learn, for example many terms, definitions, symbols, theorems and axioms. These are all things that the learner must know, not things that he must know how to do.
It should also be noted that learning is a stratified process. Certain skills have to be mastered first, before it becomes possible to master subsequent skills.
In order to be a basketball player, a person first has to master the foundational skills, e.g. passing, dribbling, defense, and shooting. In the same way, in order to do math, a child first has to learn the foundational skills of math, like visual perception and visual memory. The child who confuses the signs +, -, ÷ and ×, may have a problem with visual discrimination of forms and/or visual discrimination of position in space. A child who has a poor sense of direction (i.e., north, south, east, and west), may have a problem with visual discrimination of position in space, etc.
The second step would be to master mathematical skills, which must be done in a sequential fashion. One has to learn to count before it becomes possible to learn to add and subtract. Suppose one tried to teach a child, who had not yet learned to count, to add and subtract. This would be quite impossible and no amount of effort would ever succeed in teaching the child these skills. The child must learn to count first, before it becomes possible for him to learn to add and subtract.
The third step would be to ensure that a learner catches up on the knowledge aspect of math.
Edublox’s math help aims at (1.) addressing the underlying shortcomings that interfere with math performance, such as poor visual-spatial memory and logical thinking, (2.) teaching math skills in a sequential fashion, which may include counting and skip-counting, adding and subtracting, multiplication and division, applying place value and fractions, using money, reading time etc., as well as (3.) math knowledge. Visit the Edublox website for more information.
Below is an example of a child’s progress after receiving math help from Edublox. She was diagnosed with dyscalculia as well as dyslexia, ADHD and low IQ. Click here to follow her amazing journey to learning success.
.Below is an example of a child’s progress after rec
Below is the report of another child whose math marks improved from 43% in the first term to 70% in the fourth term. Many of his other subject improved as well, as a result of the cognitive training he received:
The bottom line
The only solution for a problem like dyscalculia is to address the causes. Until we have done that, the child will continue to struggle.