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Math literacy is important for survival in modern society. Everyday tasks such as paying bills or budgeting for daily expenses all have to do with numbers. Every job, from the rocket scientist to the sheepherder, requires the use of math. Decisions in life are often based on numerical information: to make the best choices, we need to be numerate. People with math learning disabilities, generally known as dyscalculia, will struggle in everyday life and their career choices will be limited.
What are the characteristics and signs of dyscalculia?
The most generally agreed-upon feature of children with dyscalculia is difficulty in learning and remembering arithmetic facts. The second feature of children with dyscalculia is difficulty in executing calculation procedures, with immature problem-solving strategies, long solution times, and high error rates. Below is a list of dyscalculia characteristics and signs:
- Poor number sense is a core deficit of dyscalculia. Number sense refers to a person’s ability to use and understand numbers.
- Another core deficit is poor subitizing. The word ‘subitize’ comes from Latin meaning ‘sudden’. It refers to the ability to instantly identify the number of objects in a set without counting. Most people can subitize up to six or seven objects. A child with dyscalculia may find this very hard and may need to count even small numbers of objects. For example, if they are presented with two objects they may count the objects rather than just know that there are two.
- 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.”
- Immature strategies such as counting all instead of counting on. The child may work out 137 + 78 by drawing 137 dots and then 78 dots and then counting them all.
- Difficulty with times tables.
- Poor mental arithmetic skills.
- May have trouble even with a calculator due to difficulties in the process of feeding in variables.
- Inability to notice patterns. The world of math is full of patterns and the ability to see, predict and continue patterns is a key math skill. Take the sequence of the 5 x table for example 5, 10, 15, 20, 25, etc. This is a very clear pattern but a student with dyscalculia may not readily spot it.
- Inability to generalize. Being able to generalize makes life so much simpler in math, but a dyscalculic student may find this very hard. They might not see that knowing that 3 + 4 = 7 means they also know that 30 + 40 = 70, or even that 3 inches + 4 inches = 7 inches.
- 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 grasp and remember mathematical concepts, rules, formulae, and sequences.
- Inability to conceptualize and execute math processes (can do correct computation, but doesn’t understand why a strategy worked, so they can’t transfer knowledge to new problems).
Dyscalculia characterictics and signs by age
Toddlers and preschoolers
- Difficulty learning to count
- Difficulty sorting
- Difficulty corresponding numbers to objects
- Difficulty with auditory memory of numbers
- Difficulty counting
- Difficulty subitizing
- Trouble with number recognition
- Difficulty with magnitude comparison
- Trouble learning math facts
- Difficulty with math problem-solving skills
- Over-reliance on ﬁnger counting for more than basic sums
- Anxiety during math tasks
Late elementary through middle
- Difficulties with precision during math work
- Difficulty remembering previously encountered patterns
- Difficulty sequencing multiple steps of math problems
- Difficulty understanding real-world representation of math formulae
- Anxiety during math tasks
- Struggle to apply math concepts to everyday life, including money matters, estimating speed and distance
- Trouble with measurements
- Difficulty grasping information from graphs or charts
- Difficulty arriving at different approaches to the same math problem
- Anxiety during math tasks
How does math anxiety contribute to dyscalculia?
Mathematics anxiety (henceforth, referred to as ‘math anxiety’), is a negative reaction to math associated with negative emotions. Ashcraft and Faust (1994) define math anxiety as a feeling of tension, helplessness, mental disorganization and dread produced when one is required to manipulate numbers or to solve mathematical problems.
Reasons for math anxiety are usually classified as environmental, personal, or cognitive. Environmental causes can include negative experiences in math classes or with particular math teachers. Personal causes include low self-esteem, lack of confidence, and the influence of previous negative experiences with mathematics. Cognitive causes involve innate characteristics, being either low intelligence or simply poor cognitive abilities in mathematics (Rubinsten and Tannock, 2010). Math anxiety may influence students’ choices of courses in school and careers. Math anxiety can be specific: students may experience stress about particular math situations rather than all math situations. Math anxiety can be global: feel incompetent in all math situations and dislike all aspects of mathematics intensely. Extreme cases may lead to a phobia of mathematics and mathematical devices.
Math anxiety is distinguishable from other types of anxiety symptoms (i.e., math anxiety can exist in the absence of more general anxiety traits); and has a direct and deleterious effect on underlying cognitive processes as the individual performs a math task. This is especially true for individuals with dyscalculia — they may experience intense fear, which may cause an inability to learn math concepts and skills or perform well on math tests (Rubinsten and Tannock, 2010).
What are the different types of dyscalculia?
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.
Based on his experience with arithmetic learning problems, Kosc described six types:
- Verbal dyscalculia, which refers to problems in naming the number 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.
Based on the cognitive difficulties that underpin dyscalculia, Karagiannakis and Cooreman (2015) identified four subtypes: core number, reasoning, memory, and visual-spatial. Dyscalculic students may have difficulty in all or maybe just one or two of these areas.
These types of dyscalculia have not been independently verified, and they are quite difficult to differentiate in students who have arithmetic learning disabilities. Nevertheless, these discussions illustrate the many problems students may have in arithmetic and mathematics.
NEXT: Page 4: Causes
Edublox offers live online tutoring to students with dyscalculia. Our students are based in the United States, Canada, Australia, New Zealand, and elsewhere. Book a free consultation to discuss your child’s math learning needs.
Authored by Susan du Plessis (B.A. Hons Psychology; B.D.) who has 30+ years’ experience in the LD field.
Medically reviewed by Dr. Zelda Strydom (MBChB) on May 21, 2021.
Next review due: May 21, 2023.
References and sources:
Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition Emotion 8, 97-125.
Hornigold, J. (2015). Dyscalculia pocketbook. Alresford, Hampshire: Teachers’ Pocketbooks.
Karagiannakis, G. N, & Cooreman, A. (2015). Focused MLD intervention based on the classification of MLD subtypes. In S. Chinn (Ed.), The Routledge international handbook of dyscalculia and mathematical learning difficulties (pp. 265-276). Abingdon, Oxon: Routledge.
Kosc, L. (1974). Development of dyscalculia. Journal of Learning Disabilities, 7, 164–177.
Peard, R. (2010). Dyscalculia: What is its prevalence? Research evidence from case studies. Procedia – Social and Behavioral Sciences, 8, 106–113.
Rubinsten, O., & Tannock, R. (2010). Mathematics anxiety in children with developmental dyscalculia. Behavioral and Brain Functions 6, 46. https://doi.org/10.1186/1744-9081-6-46
Soares, N., Evans, T., & Patel, D. R. (2018). Specific learning disability in mathematics: A comprehensive review. Translational Pediatrics, 7(1), 48–62. https://doi.org/10.21037/tp.2017.08.03