Showing posts with label symbols. Show all posts
Showing posts with label symbols. Show all posts

Wednesday, March 7, 2012

International Dyslexia Assoc: The Impact on Mathematics

While teachers and parents are well aware of the effect of dyslexia on reading, they often overlook its impact on mathematics.

The mastery of the symbolic language of mathematics involves many verbal cognitive processes that can be affected by dyslexia.

Ignoring the impact of dyslexia on the mastery of mathematics can hamper a child’s progress in school and in life.

Dyslexia is the inability to decode and obtain meaning from the printed word. It is a learning disability, not a condition due to inadequate instruction or intelligence.

Estimates of the incidence of dyslexia in school age children range from 5 to 10% (Shaywitz, Shaywitz, Fletcher, & Esteban, 1990).

Dyslexia most clearly impacts reading, spelling, and written expression. However, dyslexia may also affect mathematics achievement.

Approximately 5.9 % of students are identified with a math disability, a number similar to those with a reading disability (Fuchs, Fuchs, Powell, Seethaler, Cirino, & Fletcher, 2008).

Mathematics has a symbolic language whose practical function is to express spatial and quantitative relationships.

Number sense is acquired in developmental stages similar to those in the acquisition of language.

The process begins as soon as children begin to move and explore their environments, placing one box into another, stringing beads, learning “all gone”, etc.

 Spatial relations concepts are based on identification of objects in space, distinguishing right from left, reasoning with abstract designs, and visualizing objects in other positions.

 Children first assimilate and integrate non-verbal experiences; then they associate numerical symbols, numbers, and mathematical words such as “less” to these experiences.

 Children need to have both experiences with mathematical relationships and the words to express them.

Reading numbers and recalling number names are prerequisites for using them to represent abstract quantities.

However, associating the names with the numerals, and recalling them when needed, may be difficult for children with dyslexia.

Mastery of numerical operations also involves retrieval of basic facts. Some children work diligently to learn the multiplication tables but cannot recall them, much to the frustration of teachers and parents.

Such retrieval problems were evident when Rosie , a bright ten year old with dyslexia, and her grandmother worked on learning the names of coins in a homework assignment.

“Grandma,” she said wearily, “ I can tell you that it’s worth ten cents but I don’t know its name.” The task of recalling, sequencing, and manipulating figures, shapes, letters, designs, patterns and numerals and associating them with quantities is analogous to associating letter names with the corresponding sounds, a task many children with dyslexia find challenging.

Instruction in mathematics is most frequently verbal instruction. This may be problematic for children with poor verbal comprehension and poor short term auditory memories.

They hear the teacher but do not fully comprehend or recall the concepts and operations she is describing because of language issues.

With faulty understanding, they are unable to apply the information correctly. Since mathematical concepts build on one another, this shaky foundation can adversely affect mastery of future concepts.

Moreover, the vocabulary of mathematics is unique and can be confusing. Subtraction problems can be phrased as “less than” “ take away”, “minus”, “subtract”, all of which refer to the same process.

Such multiple meanings should be directly taught but frequently it is simply assumed that children have learned them.

Word problems embed the math calculations in language. Performance here is impacted by problems with syntax and vocabulary, as well as calculation problems.

To obtain the correct answer, children must first comprehend the syntax and vocabulary, understand what the problem is asking, ignore extraneous information, devise a strategy to solve it, and retrieve and apply the requisite facts and operations.(Bryant & Bryant, 2008)

Solving algorithms also involves performing operations in correct sequence and reading operational signs correctly.

The symbolic language of math notations, such as decimal points, using x to signify the unknown, exponents, and parentheses, can be confusing.

Some children learn this language incidentally but for others this language must be frequently reinforced.

One eleven year old requested of his teacher, “Tell me which sign it is—the add one or the times one” before starting his calculations.

Dyslexia may make mastering mathematics difficult. Teachers and parents must be aware of potential issues and provide the supports necessary to ensure success in mathematics as well as in reading.

Sunday, December 13, 2009

Orthography: the relationship between written symbols and sounds

In our previous 2 blogs we discussed briefly the sounds of letters and the sounds found inside words; 'Print Awareness' and 'Phonics and Phonemics'.

Taking this a step forward, we would like to introduce you to another term that is often used in describing language and one that has a big part to play in the detection of Dyslexia and the difficulties a child may have in learning to read and spell in a specific language; Orthography.

Orthography
Orthographies are writing systems, the relationship between the words we speak and how we write that down. Conversely, it is how we interpret and speak the words and letters that we see written on a page.

Orthography in Languages
It may surprise you to learn that the orthography of some languages are easier to interpret and learn than others. The complexity of a language's orthography, or writing system, can be a significant contributing factor to the difficulties experienced by readers who suffer from Dyslexia.

Symbols in Language
Languages such as Chinese have very simple orthographies because it has a pictorial languagee. Their written language is based on symbols that represent a picture of the word. Dyslexia is unknown in China.

The difference in the complexity of language and it's symbols versus sound interpretation is best described as the depth of the Orthography.

Shallow orthographies
Shallow Orthographies have a more straightforward, one-to-one relationship between sounds (graphemes) and letters (phonemes), and the spelling of words is very consistent. Italian and Finnish, which are examples of shallow orthographies and consequently, children and new readers, have very little trouble learning to decode words and match them to their sounds.

As a result, children who wish to learn to read in those languages, do so relatively quickly and with greater ease. Most readers who suffer from Dyslexia and are learning to read in a shallow orthography, learn to decode words with relative ease. Unfortunately, they can experience more difficulty with reading fluency and comprehension.

The hallmark symptom of dyslexia in a shallow orthography is the speed of rapid automatised naming (RAN - the speed of recalling and naming an object, word or letter once it is recognised).

Deep Orthographies
Unfortunately, one of the languages considered to be 'deep' is English, as well as Arabic, for example. They do not have a one-to-one correspondence between sounds (phonemes) and the letters (graphemes) that are intended to represent those sounds. As a result, children learn to read more slowly and with the potential for introducing more difficulties.

Overcoming this difficulty
Research has shown that the symptoms of Dyslexia in a deep orthography are a deficit in phonological awareness and difficulty in reading at the word level. For these readers who suffer from Dyslexia, learning to decode words may take a long time but the good news is, that once some level of decoding has been overcome, many of these readers have relatively fewer problems with fluency and comprehension. This is the opposite of the 'shallow' orthographies.

Comparative Studies
Studies between German and English have shown that the greater depth of English orthography had a "marked adverse effect on reading skills" among dyslexic children.