Understanding dyscalculia for teaching
Education, Summer, 2004 by Sheila Rao Vaidya
Dyscalculia is a learning problem affecting many individuals. However, less is known about this disability than about the reading disability because the American society accepts learning problems in mathematics as quite normal. This article provides a summary of the research on Dyscalculia and teaching approaches for teachers.
Relative to research on reading disability, research on math learning disability is very much in its infancy. Reading disability researchers have described deficits and possible genetic mechanisms that underlie dyslexia. Also, interventions have been proposed and studied for effectiveness. In contrast, math disability researchers are still working to define math learning disability and to identify underlying cognitive or genetic attributes.
What is Dyscalculia?
Dyscalculia is characterized by a poor understanding of the number concept and the number system. Difficulties are presented in counting, giving and receiving change; tipping, learning abstract concepts of time and direction, telling and keeping track of time and the sequence of past and future events. Children with dyscalculia are unable to function with these mathematical milestones characteristic of their age group.
Dyscalculic children find learning and recalling number facts difficult. They often lack confidence even when they produce the correct answer. They also fail to use rules and procedures to build on known facts. For example, they may know that 5+3=8, but not infer that, therefore, 3+5=8.
In word problems, Dyscalculic children often don't understand which type of arithmetical operation is asked for.
There may be exaggerated difficulties with intensive numbers-i.e. those involving x per y, either explicitly or implicitly -such as speed (miles per hour), temperature (energy per unit of mass), averages and proportional measures. Some have spatial problems, which affects understanding of position and direction.
Dyscalculic children can usually learn the sequence of counting words, but may have difficulty navigating back and forth, especially in twos, threes or more. Their difficulty in estimating number is impaired in comparison to that of their peers. The lack of an intuitive grasp of number magnitudes typical of children in the age group of 7 to 11, is absent in the child with dyscalculia.
According to Mahesh Sharma (2001), The seven prerequisite math skills are:
(1) The ability to follow sequential directions;
(2) A keen sense of directionality, of one's position in space, and of spatial orientation and organization;
(3) Pattern recognition and extension;
(4) Visualization- key for qualitative students- is the ability to conjure up and manipulate mental images;
(5) Estimation- the ability to form a reasonable educated guess about size, amount, number, and magnitude;
(6) Deductive reasoning- the ability to reason from the general principle to a particular instance; and
(7) Inductive reasoning- natural understanding that is not the result of conscious attention or reason. Without these prerequisite skills, any math learning that takes place is essentially temporary.
(1.) Quantitative dyscalculia is a deficit in the skills of counting and calculating and refers to prerequisite skills 1 & 2 above.
(2.) Qualitiative dyscalculia is the result of difficulties in comprehension of instructions or the failure to master the skills required for an operation. It refers to prerequisite skills 3, 4, 5, 6, 7.
MEASURES used to test for Dyscalculia
1. Piagetian test of conservation of number, classification and seriation.
If a child has not mastered the concept of number preservation (the idea that 5 represents a set of 5 things), then they are incapable of making the generalizations necessary for performing addition or subtraction. How can you recognize a low functioning child? He is dependent on counting with his fingers or objects. When told that a hand has five fingers, he will have to manually count them when shown a hand and asked how many fingers are showing (Sharma 1989).
An example of an advanced level of cognition, is a student who uses knowledge of multiplication facts to solve a problem using a least common multiple. At this level of ability, the child is ready for addition and subtraction of fractions (Sharma 1989).
2. The Rey-Osterrieth' Complex Figure Test
This is a visual-motor drawing task like the Bender Gestalt. The Subject is first asked to copy the complex figure made of basic geometric shapes, then to draw it from memory.
It assesses attentive analytical and perceptual-organizational skills and the degree of precision.
Identifies cases of spatial difficulties that interfere with math performance.
Teaching Math as a Second Language
Mathematics is a second language and should be taught as such. The conceptual aspect of mathematics learning is connected to the language. It is exclusively bound to the symbolic representation of ideas. Most of the difficulties seen in mathematics result from underdevelopment of the language of mathematics. Teaching of the linguistic elements of math language is sorely neglected. The syntax, terminology, and the translation from English to math language, and from math language to English must be directly and deliberately taught (Sharma 1989).
Children's ability to understand the language found in word problems greatly influences their proficiency at solving them. In addition to understanding the meaning of specific words and sentences, children are expected to understand textbook explanations and teacher instructions.
Math vocabulary also can pose problems for children. They may find it confusing to use several different words, such as "add," "plus," and "combine," that have the same meaning. Other terms, such as "hypotenuse" and "to factor," do not occur in everyday conversations and must be learned specifically for mathematics. Sometimes a student understands the underlying concept clearly but does not recall a specific term correctly.
Math and Attention
Attention abilities help children maintain a steady focus on the details of mathematics. For example, children must be able to distinguish between a minus and plus sign--sometimes on the same page, or even in the same problem. In addition, children must be able to discriminate between the important information and the unnecessary information in word problems. Attention also plays an important role by allowing children to monitor their efforts; for instance, to slow down and pace themselves while doing math, if needed.
Temporal-Sequential Ordering and Spatial Ordering
Almost everything that a child does in math involves following a sequence. Sequencing ability allows children to put things, do things, or keep things in the right order. For example, to count from one to ten requires presenting the numbers in a definite order. When solving math problems, children usually are expected to do the right steps in a specific order to achieve the correct answer.
Recognizing symbols such as numbers and operation signs, being able to visualize--or form mental images--are aspects of spatial perception that are important to succeeding in math. The ability to visualize as a teacher talks about geometric forms or proportion, for example, can help children store information in long-term memory and can help them anchor abstract concepts. In a similar fashion, visualizing multiplication may help students understand and retain multiplication rules.
SUMMARY OF BEST PRACTICES
1. Teaching the language of mathematics
2. Teaching focusing strategies
3. Using visualization to help with sequencing
4. Providing practice with the understanding of the number concept and underlying concepts such as seriation and classification.
5. Guided Practice in reading word problems
6. Prenumber skills and numeration
7. Action teaching
8. Immersion Therapy
SHARMA, M. (2001) Berkshire Mathematics Project, Cambridge.