Dyscalculia: problems with maths
Defining the problem
The DfES defines dyscalculia as:
‘a condition that affects the ability to acquire arithmetic skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems learning number facts and procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence.’
Two modes of thinking
The two major thinking styles in which learning happens are verbal and non-verbal. Verbal thinking is thinking with the sounds of words (“talking in your head”); non-verbal thinking is thinking with sensory impressions (“thinking in pictures”).
Any symbol has three parts:
- how it looks on the page: its appearance
- how it sounds when it is spoken: its sound
- what it means
Verbal thinking allows us to connect the appearance of a symbol with its sound: for example, look at the above image. Verbal thinkers see the x symbol and think “times”. They see the numerals and symbols and hear, “Seven times four equals twenty eight.” or something similar. Verbal thinkers can usually ‘learn by heart’, understanding of the meaning can come later.
Non-verbal thinking allows us to connect the appearance of a symbol with its meaning: for example, look again with the above image. The non-verbal thinker looks at the numerals and symbols and sees 4 rows with 7 objects in each, giving an image of 28, perhaps as above, or in any other way the individual’s non-verbal imagery works for them.
Non-verbal thinkers need to learn through meaning. Moreover, if they do not grasp the meaning behind the mathematical symbols they see, dyscalculia will develop. To resolve maths difficulties these meanings need to be mastered. The Davis programme uses plasticine clay to establish the concrete meaning of the abstract symbols in the real world.
Maths depends on foundation concepts like sequence
Mathematical processes all rest on a series of foundation concepts or universal laws, which have to be fully understood before maths can be mastered. For example, it is important to understand the idea of sequence, which is the way that one thing (such as a number or quantity) follows another. The starting point for dyscalculia correction is to master the concepts of change; consequence; cause; effect; before; after; time; sequence; order and disorder. Once again, plasticine clay is used to bring clarity to areas of confusion.
Note on use of plasticine clay
Plasticine rarely makes an appearance in the learning process beyond the age of pre-school. The Davis approach regards it as a powerful learning medium at all levels of the learning process. In particular, it looks at how confusion can arise in the learning process as a result of symbols, terms, concepts and processes that are not understood and sees how these confusions can be “clayed out” through the plasticine medium, often with dramatic results.
The Davis approach acknowledges the individual’s preferred learning style, namely to learn through meaning and hands-on explanation, rather than by repetition or learning by heart. Therefore it uses multi-sensory teaching strategies before moving to the traditional paper and pencil medium.
Dyscalculia and the Davis methods
Dyscalculia typically occurs in thinkers who need to learn through meaning and hands-on exploration rather than by rote or repetition, and who have failed to grasp the meanings behind some or all of the mathematical symbols they have encountered. Once the meanings are mastered, the problems are resolved.
The Davis approach acknowledges this and, in a unique and different approach uses plasticine clay, which is a multi-sensory medium for multi-sensory thinkers, to model and master these meanings. It takes away the confusion that can arise in the learning process as a result of abstract ideas that are not fully understood. Symbols, terms, concepts and processes are made a reality using the clay, and confusions are laid to rest, often with dramatic results.
Maths begins to make sense as it becomes related to real-life concepts.
The Davis approach acknowledges the dyscalculic person’s preferred learning style. which is to learn through meaning and hands-on exploration, rather than by repetition or by heart. Davis methods therefore use multi-sensory teaching strategies before linking those to the traditional paper and pencil medium.
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Prevention is better than correction.
Children who never develop the problems by which Specific Learning Difficulties (SpLD) are recognised, do not need to overcome the baggage of low self esteem and loss of confidence. They can simply use their Gift without interference.
Dyscalculia in the Early Years is an article that explains some of the developmental reasons why dyscalculia happens and gives ideas about how to prevent it.