Most people consider the rules of maths are consistent, some more consistent than the rules of spelling (Riddick, 1996). In fact there are many inconsistencies in mathematics, which are often invisible. Maths has more exclusion to the rules than many people believe (Riddick 1996). These incompatibilities can especially hinder the dyslexic child in that they challenge the security of learning. Many of these inconsistencies happen in numeracy and in that way the seeds of disorder and failure are sown very early (Henderson 1989b).
This is one reason why endeavours to deal with problems in maths have to move back a long way in the individual’s learning history. For instance in fractions, which are considered as problematic by many learners, we write 1/5 + 3/5 = 4/5 and merely the top numbers are added. Yet in 3/5 x 2/5 both top and bottom numbers are multiplied. We carry sums and decompose in subtraction sums, yet both are trading actions, trading ten ones for one ten and trading one ten for ten ones.
We expect absolute exactness in answers and then expect students to abandon this strict regime and estimate. In entire numbers the succession of words from left to right of the decimal points are units, tens, hundreds, and thousands. For decimals, the succession from right to left of the decimal point is tenths, hundredths, thousandths. There are some factors, which can affect the learning of mathematics. These may happen in seclusion or may interact to make a possible learning difficulty.
Each person is an individual and will have a personal mixture of various levels of severity of these factors. With proper help most of the difficulties connected with these factors can be lessened. Here are some main areas that dyslexia learner may have difficulties in mathematics: Language. Mathematics has its individual vocabulary, for instance, algebra is only a maths word. But maths also shares words with other activities; so “take away” connect with food as well as subtraction (Riddick, 1996).
In numeracy there is a series of words used to mean the same maths operation, so we could use add, more, and, plus to mean add. But we can also use more to imply subtract as in “Nick has three more pens than Ann”. Nick has ten pens, how many pens does Ann have? ” Maths word questions often use a special mathematical form of the English language. It is not enough just to be able to read the words; the students have to understand the meaning that is pertinent to maths.
Thus it is not unexpected that people list word difficulties as one of the most difficult fields of maths, even if they are not dyslexic (Miles, Haslum & Wheeler, 2001). Short Term Memory. Most dyslexic people have poorer short-term memories than their non-dyslexic peers (Chin & Ashcroft, 1998). The results of this are that they can lose track in the middle of doing a multistep intellectual arithmetic problem or fail to realise a sequence of instructions.
For instance, in adding 234 + 93 in mind, the learner may try to add mentally using a written method, so starting with the units, there is 4 + 3 = 7, then the tens, 3 + 9 = 12, carry on the 1 to end as 2 + 1 = 3, then reverse these numbers (7, 2, 3) to give 327. It is improbable that dyslexics can retain by rote learning basic number facts especially times table facts (Chinn, 1998) or it may be that they can not remember the succession of steps needed to finish a long division sum, particularly if the process has no sense or logic to confirm memory.
Direction. This tendency for learners to look for logicality (and thus patterns, rules and connections) in what they learn. There are much more inconsistencies in direction in maths than many people understand, for example the teen numbers, fourteen, fifteen (14, 15) and so on are discordant with other two digit numbers such as forty six, fifty six (46, 56, where the digits are written in the same order as the words). Any inconsistency can affect an uncertain learner and many maths learners are insecure.
Visual. This may be a difficulty with recognising differences between symbols, such as + and x; or + and ч or the plan of work on the page of a book can be reason of difficulties, for example if the distance between examples are very close. Speed of Work. One of the odd things about maths is the need to do it quickly. This requirement tends to increase disquiet and thus decrease precision. Dyslexics usually are slower in maths with many factors furthering to this, such as slow recall of basic facts.
In a classroom study (Chinn & Ashcroft , 1998) found that dyslexic pupils took about 50% more time to finish a set of arithmetic questions than their non-dyslexic peers. It is difficult for dyslexic children to concentrate on high numbers and this highly slows their work. This is a perfect example of an area where by choosing proper techniques of work with dyslexic children, simple awareness and adjustment can reduce stress and help learning. Sequencing. Maths needs sequencing capabilities. These might be the ability to count on, or back, in eights or sixes or they might be the complex sequence of the steps in the long division procedure.
This problem can connect with language problems in questions such as ‘Take 17 away from 36” which presents the numbers in the reverse sequence for calculation to “26 minus 16” which presents the numbers in the sequence in which the subtraction is computed. The succession of negative numbers can be bewildering as in negative co-ordinates (-3, -6). Going from coordinates which are positive to coordinates which are negative can make a very high anxiety level or understanding problem for some dyslexics. Anxiety. Maths can make anxiety in most learners (and some teachers) (Henderson & Miles, 2001).
For example, fractions often are reason of disorder. It is a feature of dyslexics (and probably other learners, too) that if they pre-judge a question as too difficult to solve then they escape failure by not begin to try to solve the question. This is the hidden factor that have connection with above. The dyslexic pupils demonstrate a much higher proportion of “no attempts” in the arithmetic test, which is they determine they are unable to get the question accurate, so they avoid failure by not trying the question. Learning needs the learner to take a risk and get inveigled in the learning process.
Dread of default can stop the learner taking the risk necessary for learning. Conceptual Ability. There is just a usual spread of conceptual ability in maths for dyslexics and they can reach at or above this potential with proper teaching and motivation (Henderson & Miles, 2001). Unfortunately the speed of working and the other factors included here can imply that they do not get the experience and practice necessary to develop skills and concepts. Another significant factor is the problem that an early misconception and initial wrong practise of an idea may create a dominant memory.
For example, if pupils write 51 for 15 when they first meet this number, then unless the correction comes immediately, that will be a dominant memory. It is important to make sure that each new idea is practised accurately. Thinking Style. Dyslexic strengths and difficulties share the same source – the dyslexic thinking style. Dyslexics tend to think originally through pictures and images rather than through the internal monologue used by verbal thinkers (Yeo,2003). Nowadays researchers have identified two thinking styles (Yeo, 2003).
Basically one style is pattern and sequential and the other is intuitional and entire. Most learners lie somewhere on a continuum between the two extremes of style and indeed this mixture is likely to be the most successful style as success in maths tends to need flexibility in thinking. Understanding a learner’s thinking style can be one of the most important pieces in the jigsaw of realizing the learner. Each style needs sub-skills, but this does not mean that the learner chooses to use the style more appropriate to his own sub-skills. 10. Notation.
Some dyslexic children may have problem if a new piece of notation is introduced, for instance an algebraic symbol, such as “x”, a geometric term such as “obtuse angle”, a trigonometric term such as “cosine”, the use of a colon to express ratio, or the use of the symbols > and < to mean “greater than” and “less than”. Fractional and decimal notation may also prove confusion. 11. Understanding place value. Some dyslexics do not readily understand the idea of place value, especially when there are zeros in a number (20,040). They may also take longer to understand the patterns of multiplying and dividing by 10, 100, 1,000 etc.