Math Disabilities Essay, Research Paper
There seem to be many problems within the American educational system today. Most of the problems refer back to the differences in the students that undergo the education system. Some of these students are handicapped, some are not motivated either at home or by themselves, and some have learning disabilities. The world of learning disabilities is large and seems to receive the least amount of attention. Learning disabilities are apparent in some children while in others they remain hidden. One example of a learning disability exists in children that speak languages different from English, which is spoken the most in schools today. Children that speak different languages seem to have the most trouble in math because their memory works differently, their organizational skills are different and they lack the symbolic understanding that English speaking children possess. Psychologists have also found that there is a link to children with language disabilities, their mathematical skills, and their reading skills. This is especially seen in word problems. ?When solving story problems, children must understand complex language and solve problems presented in meaningful contexts.? (Jordan p. 569)
The most apparent problem found amongst children that are language impaired is their symbolic understanding. This weakness is also found amongst children with other disabilities. The main problem with symbolic understanding is that the children do not seem to realize that things can stand for other things. ?They may fail to come to terms with the notion that one coin can stand for two other coins? (Grauberg p.3)
It is understood that children with a problem with symbolic understanding most likely suffer from other learning disabilities.
?Such children are most probably learning-impaired in a wider sense, but they are often found in special language units and in special schools for children with language impairments.? (Grauberg p. 3) Children who seem to have the most problems with symbolic understanding are the ones that are known as being semantic or pragmatic. These types of children are able to use the symbols that are numbers and letters. However, they can only use them as they learned them causing the children to be unable to see the symbols as constructs which, only stand for a meaning. ?In general, such children will have difficulty in applying acquired number skills to new situations?. (Grauberg p.4)
Some children with very large problems in language development seem to just give up on learning mathematical skills at a very early age. Here the problem of teacher interaction becomes a problem because if the teachers do not spend a lot of time helping and introducing the concepts of symbols to these students at very young ages the students will give up at fail at math later in the future. These children tend to become distracted very easily by their surroundings.
Another problem found in the symbolic understanding is that the children may know a counting system very different to the one that they are learning at their present school. The confusion of the two number systems can be extremely large. ??children will have difficulty in accommodating their own, more global and non-verbal working symbol system?? (Grauberg p.6)
There are ways to help these children with learning mathematics. First, one must begin by concentrating on the cardinal aspect to numbers. Here the relationship between linguistic form and the content in small and simple. Some suggest working with terms that are in relation to numbers and amounts such as a little or a few. ?Before precisely specified quantities like ?three? or ?four? are introduced, it may be useful to work with large nonspecific quantities.? (Grauberg p.9) The next step is to have the child associate specific amounts to the numbers such as five apples or seven shirts. Then, one should introduce the written symbols to the children. Some specialists believe that children should write the number and understand that before they speak the number. They suggest that ?the children will become familiar with the notion that a quantity can be labeled in writing? (Grauberg p15).
Another issue that children with language developmental problems have is organization. The problem of organization relates itself to the other problems found in the children. ?A child with added language difficulties will have even greater problems because the strategy of ?talking a problem through? while solving it- essential for most of us when organizing a problem solving situation- will not come naturally to him.? (Grauberg p.61)
Much like children with problems having to do with symbiotic understanding the children with organizational problems will be learning impaired in a much larger sense because while they may look or act as though they understand their work shows that they do not. Teachers can also use patterns to help them learn the symbols. ?The patterns strategy requires students to examine sequences of numbers or geometrical objects in search of some rule that will allow them to extend the sequence indefinitely.? (Thomas p. 204)
Children who have problems with organizational skills have many features. The features are impulsiveness, lack of concentration, clumsiness, and lack of spatial ability. The impulsiveness is seen when the children continue to test their parents or teachers patience. They will not look further into given information, and they can not sort out the relevant from the irrelevant information. Just as in problems in symbolic understanding if the child does not understand the information or process it quickly enough they begin to show signs of a lack of concentration. Children so clumsiness because research has shown that children with a lack of organization physical movements seem slow and they appear to have no rhythm. ?This results in untidiness and a lack of clarity?? (Grauberg p.62).
Children with this issue have problems with math because they have problems sequencing, halving, sharing, and classifying the numbers. Children need to learn how to explore the various possibilities of grouping in order to make more efficient decisions having to do with organizing themselves. The main problem within the organizational problem is trying to sort out word problems. The relations between the numbers and words must be understood before the problem itself can be solved. Word problems are very complex even at the easiest level. ?some knowledge is needed in at least three different areas: the specific aspect of ?life? in which the story takes place, the mathematical procedures that can be applied to the problem, and the logic and language of the story? (Grauberg p.81).
The area of spatial organization seems to be the hardest to teach children. ?There are serious doubts about methods and transfer and there seems to be very little information about the frequency and severity with which spatial disability occurs? (Grauberg p. 101). Spatial ability is the ability to see and understand the relationships between shapes, spaces, or areas. This area can be noticed in the child?s early years as they play with toys dealing with shapes and placing. When dealing with word problems a teacher should analyze the problem out loud. This allows the child to hear the breakdown of the word problem. ?Teachers should explain their thinking as they test the choice of schema and algorithm.?(Thomas p. 202)
The final area that effects children with language impairments is memory. ?Early research on children with MD suggested that they were deficient in two areas of mathematical cognition: retrieval of number facts and the ability to solve story problems. ? (Jordan p. 1) This area is directly related to organization. ? ?memory is organized and structured, and the more efficiently it is organized, the more successfully it will function? (Grauberg p. 124). Therefore if more problems lye in the child?s organizational skills then more problems are bound to exist in their memory. There are at least two parts to a person?s memory, long-term memory and short-term memory.
Long-term memory has an unlimited amount of storage space however; one can not always recall what they are looking for from the storage space. What makes a teacher?s job so difficult with regards to long term memory is that all of the organization that goes on in the long term memory is done in a very personal way so, when recalling information it can be difficult to recall exact specific?s. ?Learning matter can be offered in a way that the teacher considers well-organized and therefore likely to be remembered and easily produced, but it is by no means certain that all children will accept the organization and store it accordingly in their long-term memory.? (Grauberg p. 127)
Short-term memory can also be called primary memory. It holds what we need for the present. Unfortunately the information that is stored in short term memory can very easily thrown away. ?Its content, supported by consciousness, can be easily accessed, altered and worked with; but, as the name suggests, any information stored in it is liable to fade away quickly.? (Grauberg p. 127) The short-term memory is also called the working memory because there is always room for more information.
While memory might cause difficulty to language impaired children some feel as though it is not a prominent feature in these children others feel that the children can not seen to escape it. ?A weak memory I not a feature that is peculiar to children with language difficulties.? (Grauberg p. 130) Many teachers seem to complain that their student?s memory is their largest problem. ?One does not need to have been teaching a long time in a school with language impaired children to find that anchoring facts in long-term memory takes a lot of targeted effort; that the number of times which can be held in working memory is low, and that word-finding problems among the children are widespread and severe.? (Grauberg p. 130)
The main problem that lies in children with language impairments is that they seem to have difficulties with vocabulary and auditory tests appear low. In reference to long-term memory and the children?s mathematical skills the children seems to have the most problem with learning to count. These difficulties may occur for a long time which, can affect all further number work. The children can not recall what certain numbers amount to and they have to keep learning the equation while normal children learn these amounts quicker.
Short-term memory however, brings up other problems with mathematical skills. Children seem to have problems with all mental arithmetic. ? They will not be able to keep a number question in mind while they hear it, let alone while they think about it.? (Grauberg p. 131) Numerical problems in either written or oral form will give the children problems this is because they often forget the beginning before they get to the end. Following instructions is also a problem for children with language disabilities. The information that the teachers are looking for is unavailable to the students so they can not provide it for the teachers.
While some of the first problems that occur with children who have difficulties with symbolic understanding share those problems that children with memory problems have. However, these problems are made worse by those with memory problems. ?Children with memory deficits may experience the same problems, but they are made worse because the children find it hard to remember the names of first numbers and, more importantly, they find it hard to remember the names in the right sequence.? (Grauberg p. 133)
Much like the other problems that exist in these children the problem of memory can be helped. ?One has to realize that in both forms of retrieval problems help can only be very indirect; the child needs to learn strategies for self-help.? (Grauberg p. 160) of course this solution is easier said then done. The main idea is to turn a difficult ?free recall? into a simpilier easier ?cued recall?. This new ?cued recall? can also be called recognition. Making up cue games is also a good way to help. The child can begin to recognize the numbers through their associations in the games.
As seen above there are many problems within the educational system that seem to go unadvised. The main problems that occur in children with language disabilities are symbolic understanding, lack of organizational skills, and poor memory skills. These problems can be helped if teachers and parents are willing to put in the time and effort.
BibliographyGrauberg, Eva. Elementary Mathematics and Language Difficulties. London: Whurr 1998.
Thomas, David A. Children, Teachers, and Mathematics. Boston: Allyn and Bacon, 1991.
Jordan, Nancy C., & Hanich, Laurie. (2000). Mathematical Thinking in Second-Grade Children with Different Forms of LD. Journal of Learning Disabilities, 33 (6), 567- 578.