What Is Mathematics Disorder?

The most obvious manifestation is that their scores on standardized mathematical tests are significantly inconsistent with their own age, intelligence, and grade level and expected standards. However, such performance is not caused by visual or auditory nervous system problems, mental retardation and other reasons. Mathematical obstacles can be divided into 6 subtypes: speech disorder, semantic disorder, graphic disorder, arithmetic disorder, physical manipulation disorder, and understanding disorder.

Cui Yonghua

(Deputy Chief Physician)

Department of Pediatrics, Beijing Anding Hospital, Capital Medical University

Mathematics learning disability (MLD) refers to the level of students who are significantly behind the students of the same age or grade in mathematics learning due to defects in mathematics. It is a subtype of learning disabilities. The incidence of mathematics learning disabilities in China is basically the same as in other countries, about 6% to 11%. There are currently 360 million children in China, and it is estimated that the number of children with learning disabilities in mathematics at this stage in China will reach 21.6 million to 39.6 million.

Western Medicine Name: Mathematical Learning Disabilities
English name: Mathematics learning disability, MLD
Affiliated Department: Gynecology-Pediatrics

The main symptoms: Calculation errors, messy algorithms, reading and writing difficulties, etc.
Main cause: Lack of attention, students' motivation for learning, defects in the nervous system, etc.
Contagious: Non-contagious

Clinical manifestations of learning disabilities in mathematics

Research has shown that mathematics learning disabilities are specifically manifested as calculation errors, confused algorithms, reading and writing difficulties, poor problem solving skills, and spatial organization difficulties. Among them, poor mathematical problem solving skills are particularly prominent. Compared with ordinary children, children with math learning disabilities have less knowledge and cannot effectively use them in the problem solving process. They have poor metacognitive skills when solving mathematical problems, do not know how to solve the problem, and have not shown The transition from program-based problem solving to memory-based problem solving.

Causes of Mathematical Learning Disabilities

Since Samuel Kirk first proposed learning disabilities in 1963, four foreign theories have tried to explain the causes of learning disabilities. The first theory is that learning disabilities are caused by defects in the nervous system, that is, children with learning disabilities face each other, Listening and other sensory channel information are produced by conflicts; the second theory is also called the lack of attention theory, which believes that lack of attention is the main cause of low academic achievement; the third theory is that the causes of learning disabilities and students The fourth theory holds that there are problems with the information processing of children with learning disabilities, such as incorrect information coding, storage, and retrieval. Because the research on learning disability in China is later than abroad, and most of the research focuses on the characteristics of learning disability, there is less research on its cause. In terms of the causes of mathematics learning disability, its literature is less discussed, but it is only relevant when discussing the cause of learning disability. For example, some scholars believe that the shortcomings of learning strategies are the main causes of difficulties in mathematics learning, which are mainly manifested by poor mathematical representation ability, lack of flexible problem solving strategies, and lack of effective metacognitive skills. Of course, when analyzing the causes of learning disabilities, attention deficits, sensory integration disorders, and learning strategy defects are also the main causes of poor mathematics performance. Disorders of sensory integration and accompanying attention deficits can easily lead to uncontrollable children and affect academic performance. Although there is no systematic research on the causes of mathematics learning obstacles, these studies have initially shown that Chinese scholars have also begun to notice the psychological and physiological mechanisms of mathematics learning obstacles and have obtained some preliminary research results.

In addition, many scholars have studied the cognitive characteristics of children with math learning disabilities, and their cognitive deficits may also be related to the formation of math learning disabilities. At present, the research on the cognitive characteristics of mathematics learning disabilities in China can be summarized into the following two aspects:

1. Short-term memory and working memory

At present, most scholars believe that short-term memory and working memory are one of the most important cognitive support systems affecting mathematical learning. Defects in working memory and insufficient short-term memory are a key factor leading to mathematical learning disorders. Foreign studies have found that children with math learning disabilities have worse short-term memory abilities than children with normal learning, and also have insufficient working memory abilities related to digital information processing. Chinese scholars' research on short-term memory and working memory of mathematics learning disabilities is basically similar to foreign countries. First of all, it is thought that children with learning disabilities in mathematics have defects in working memory. That is, the defects of visual space templates, language circuits, and central actuator functions in the working memory model of exponential learning disabilities are obvious. Secondly, the information processing speed is slow and short-term memory is insufficient. Children with learning difficulties in mathematics not only have defects in working memory, but also have obvious shortcomings in speech processing speed, short-term memory, central executive function, and overall working memory ability. In addition, research has found that children with learning difficulties in mathematics have insufficient breadths of working memory in speech and visual space. This deficiency is mainly manifested in developmental delays, but appropriate educational counselling may promote the expansion of their working memory breadth.

2. Characterization and organization strategy of problem solving

At present, there are many materials abroad that reflect the research results on the problem-solving strategies of children with math learning disabilities, which are mainly manifested in the research of problem-representation strategies, arithmetic strategies and problem-solving strategies. Some scholars have proposed a change model of arithmetic strategy. The model distinguishes four dimensions of developmental changes in strategic capabilities: the type of strategy (different strategies a student can use to solve a problem), the distribution of strategies (the relative frequency of each strategy used), and the effectiveness of strategies (referring to the accuracy of strategy execution And speed), strategy choice (refers to the adaptation of personal strategy choice). In terms of strategy types, it was found that children with math learning disabilities are the same as ordinary children, and they have developed extraction strategies and counting strategies. In terms of strategy distribution, children with math learning disabilities rely more on immature counting strategies. In terms of the accuracy of strategy effectiveness, Children with math learning disabilities are not as good as ordinary children; in strategy selection, ordinary children know how to choose strategies based on the difficulty of the problem, use counting strategies for difficult problems, and use extraction strategies for easy problems, but there are few adaptive strategies for mathematics learning disabilities. . Chinese scholars' research on the representation and organization strategies of problem solving generally reflects the lack of language and mathematics knowledge of children with mathematical learning disabilities, a single type of problem representation, or inaccurate representation, individual knowledge accumulation, and lack of knowledge structure. feature.

Diagnosis of Mathematical Learning Disabilities

Mathematical learning disorder diagnosis description

(1) Diagnosis characteristics

The basic characteristic of mathematical obstacles is that their mathematical ability (such as mathematical calculation or reasoning ability in individual standardized tests) is significantly lower than the expected level of the individual's actual age, intelligence and education level (standard A). This mathematical obstacle significantly affects an individual's academic achievement or activities that require mathematical skills in daily life (Standard B). If an individual has other sensory defects, the difficulty in mathematical ability will far exceed the level caused by his sensory defects (criterion C). If an individual has neurological or other medical or sensory conditions, it should be diagnosed as axis III. In the case of mathematical obstacles, many skills may be impaired, including language skills (such as understanding or naming mathematical proper nouns, manipulating, conceptualizing or interpreting applied problems or mathematical calculations); perceptual ability (such as understanding or reading numbers or Arithmetic symbols and classifying individuals); attention (for example: copying numbers or figures correctly, remembering to carry, and observing arithmetic symbols); and mathematical abilities (for example, following mathematical steps, calculating objects, learning multiplication tables).

(2) Accompanying features and defects

Mathematical defects are often accompanied by dyslexia or expression problems.

(3) Prevalence

Because many studies focus on the prevalence of learning disabilities rather than on individual reading, math, and text expression defects, the prevalence of dyslexia is difficult to establish. It is estimated that one in five individuals with a learning disability will have only a mathematical disability (not accompanied by other learning disabilities). Its prevalence in the United States is about 1% of school-age children.

(5) Course of disease

Although symptoms of math disorders may appear as early as in kindergarten or first grade (for example: confusion of numbers and inaccurate counting), math defects are rarely diagnosed before the end of first grade, as most school education usually occurs here There is very little complete math teaching before the point in time, and symptoms usually do not become apparent until the second or third grade. Especially when people with math disabilities appear with high IQ, children in lower grades may be able to perform within or close to the level, and math obstacles will not show up until the fifth grade or later.

Mathematical learning disorder diagnostic criteria

A. The mathematical ability assessed in individual standardized tests is significantly lower than the expected level of the individual's actual age, intelligence and education.

B. The situation in Standard A seriously affects the individual's academic achievements or activities that require mathematical skills in daily life.

C. If an individual has other sensory defects, the difficulty in mathematical ability will exceed the degree caused by his sensory defects.

Note: If an individual has neurological or other medical or sensory problems, it should be diagnosed as axis III. ^[1-4]

Mathematics learning disability treatment

Early intervention in mathematics learning disabilities is feasible. As long as education is available, every child with normal intelligence can learn to communicate using mathematics. Therefore, mathematics learning disabilities can be cured. The sooner we find that children with math learning disabilities, the sooner we can formulate an intervention plan. If we can identify children at high risk for math learning disabilities earlier, we can prevent the real occurrence of math learning disabilities. The common treatments are as follows.

Perceptual Integration Training for Mathematical Learning Disabilities

Perception is the overall reflection of the human brain on the various parts and attributes of objective things that directly affect the sensory organs; perception is produced on the basis of sensation and is the integration and interpretation of sensory information. Perceptual integration ability refers to the ability of the brain to combine the information perceived by the sensory organs into correct information. Insufficient perceptual integration is one of the causes of developmental dysfunction, and such patients are unable to coordinate the "seeing", "hearding" and "doing" in a unified manner. For these patients, we should encourage them to participate in more hand-eye coordination activities to improve their perceptual integration capabilities, such as skipping rope, roller skating, table tennis, and so on. Through hand-eye coordination training activities to help patients improve balance, control and coordination , Thereby alleviating or eliminating the adverse effects of developmental computing disorders on patients.

Learning Strategy Training for Mathematical Learning Disabilities

In recent years, strategic guidance has increasingly become an important method of intervention for children with math learning disabilities, and it has also become a trend in intervention studies for children with math learning disabilities. The study found that there is a significant difference in the use of learning strategies between students with math learning disabilities and outstanding students, that is, the use of learning strategies by students with math learning disabilities is significantly lower than that of students with excellent learning. Learning strategies refer to the procedures, rules, methods, techniques, and control methods that learners learn effectively in their learning activities. It can be either an implicit rule system or an explicit operating procedure and steps. The reason for some children's difficulty in learning mathematics is not their lack of ability, but that they will not effectively use learning strategies in mathematics. Compared with normal students, they lack appropriate problem-solving steps and rules systems, and cannot distinguish related quantitative relationships. , Unable to correctly understand the meaning of the question and choose effective learning strategies. In practice, there are several practical mathematical learning strategies that we can use for reference.

(1) Imitation acceptance learning strategies. Imitation refers to the study of the operating procedures described in the textbook and the teacher's explanation and demonstration of the steps in mathematics learning. Acceptance refers to actively accepting the teacher's explanation and internalizing the mathematical knowledge and forming its own cognitive structure. Imitation and acceptance are shown as some continuous activity procedures in the operation. In this procedure, our intervention teaching should pay attention to guide students to comprehensively use and optimize the methods of combined observation, imitation, operation, practice and internalization, so as to realize the Learn in-depth understanding of mathematical knowledge.

(2) Transfer analogy learning strategies. Mathematical learning is inseparable from transfer and analogy, and the study of new knowledge that is closely related to the knowledge that has been learned is especially inseparable from forward transfer and analogy. Forward transfer refers to the impact of previous learning on subsequent learning. The study of most mathematical knowledge requires us to use the method of forward transfer. Analogy refers to the introduction of the same or similar characteristics and laws in the same type of knowledge according to the characteristics and laws of certain knowledge. It can guide students to draw on new knowledge and methods to derive new knowledge. It is a student An effective way to acquire new knowledge. Learners must have a knowledge base that can be transferred and analogized is a prerequisite for the transfer analogy learning strategy, which emphasizes the importance of reviewing and consolidating the learned knowledge. At the same time, intervention teaching should also highlight the connection between new and old content, pinpoint the connection point between new and old content, and use this connection point as a bridge link, so as to realize the transfer or analogy of learned knowledge in new situations. Finally, we use this strategy to intervene in teaching to achieve the further integration of new and old knowledge in the learner's mind, to form a relatively systematic knowledge structure, thereby improving the mastery of the learned knowledge.

(3) "Small value" counting strategy. This strategy assumes that there is a counting device in the human brain. The larger addend is used as the base number, such as m, and then counted up n times. After the counting is completed, the total is displayed on the counting device, and the answer is finally obtained. This strategy is suitable for simple addition operations.

In addition, operation-aware learning strategies and collaborative learning strategies are also two more practical mathematical learning strategies.

(4) Cognitive and metacognitive strategy training

Effective mathematical problem solving is based on selecting and adopting appropriate cognitive and metacognitive processes to understand, describe, and solve problems. Cognitive processes can be used as "do" strategies, and metacognition can be used as "reflection" strategies. Cognitive strategy is a kind of psychological operation that points to cognitive goals. The subject can use the strategy to solve the problem. The application of cognitive strategy is based on specific mathematical content. The teaching of cognitive strategy should become an important part of teaching tasks. . In intervention teaching, students can learn mathematical cognition gradually by providing contexts in which strategies can be applied. This requires us to pay attention to intervention teaching: to penetrate cognitive strategies in the process of knowledge formation, teach cognitive strategies according to the rules of procedural knowledge learning, and use cognitive strategies to guide variant training.

(5) Characterization technology training

Representation, also known as psychological representation or knowledge representation, refers to the way information or knowledge is expressed and recorded in psychological activities, and is the internal representation of external things in psychological activities. Representation is a process and result of constructing a good problem space. Its quality affects the effect of problem solving. Good representation is the core of problem solving and the key to solving mathematical problems. The study found that children with mathematical learning disabilities have a single type of problem representation, insufficient processes, and lack of effectiveness. Representation training This method refers to the interpretation and representation of information and concepts presented in mathematical problems. Representation methods when solving mathematical problems include illustrations (such as drawing diagrams), specific (such as hands-on operation), verbal (such as language training), and insinuation guidance (based on illustration). One of the important points is to guide students Identify important relationships between key components of the problem. In intervention teaching, attention should be paid to the use of "operational perceptual learning strategies". This strategy refers to the special emphasis on teaching abstract mathematical knowledge in a vivid, concrete, and vivid form in teaching so that students can mobilize in activities such as operations and observations. A variety of senses to achieve understanding of abstract mathematical knowledge.

In addition, the widespread popularity of computers has provided good conditions for the correction of children with mathematical learning disabilities, because computer-assisted instruction provides unique opportunities for children with mathematical learning disabilities to adapt to many situations, thereby making up for their own weaknesses. The study found that computer-assisted instruction promotes self-monitoring learning ability in mathematics. For students with excellent, medium, and poor self-monitoring learning ability in mathematics, they are in the feedback and remedial, planning, and methodological styles. As well as the consciousness and methodological aspects have a significant promotion effect. ^[5-7]