A math disability, like other learning disorders, can stand in the way of a child's potential to succeed. As with other learning problems, early recognition of a math disability is the best first step toward helping a struggling child overcome it. Even so, parents commonly dismiss math difficulty as a normal part of life, especially if they too struggled with the subject when they were young. In the minds of many, mathematics is a subject that either comes naturally to a person or remains forever out of intellectual reach; either you get it or you don't. For many students today, getting it is no longer optional.
In 1970, only nine percent of all jobs in the U.S. were considered technical. As the world's reliance on technology has grown, so too has the demand for people who can think in the abstract terms of math and science and, today, technical jobs make up nearly one-third of all employment opportunities. Schools have tried to keep pace with the demands of an increasingly competitive technological world by stiffening their mathematics requirements and invoking a system of high-stakes testing, resulting in a widening disparity between those who learn math with relative ease and those who struggle with math disabilities.
While it is true that people can still succeed without achieving advanced competency in math, a deficiency in certain basic math skills dramatically limits a child's opportunities. The following statistics suggest why and underscore the importance of early recognition:
* In the 1950s and 1960s, the United States, pushed by the space race with the Soviets, introduced "new math," a movement away from everyday problem-solving toward a focus on abstract structures, patterns, and relationships.
* In the early 1980s, schools raised graduation requirements for math and introduced minimum competency testing in response to a government report on the state of education titled "A Nation at Risk."
* In the late 1980s, the National Council of Teachers of Mathematics revised content and methods standards for the teaching of mathematics. At the same time, standards-based tests with rigorous math sections were included as part of the graduation requirements in many schools.
While tougher graduation requirements in mathematics have had a generally positive effect — improving overall math proficiency in the U.S. — many students are failing to graduate or go on to college because of them. This can have a profound effect on a young person's future. For example, in 1997, the typical college graduate's income was 73 percent higher, on average, than that of the typical high school graduate.
Tuesday, January 5, 2010
Easier Said Than Done
Whether we are proficient in mathematics or struggle with the simplest calculations, we seldom, if ever, think about the neurological or cognitive functions involved in solving math problems. In fact, math requires the use of many complex brain functions working together toward a common goal.
To solve even simple math problems, students must use their memories to recall rules and formulas, recognize patterns, invoke rules about sequential ordering to solve multi-step problems, use advanced language skills to understand vocabulary and instructions and explain processes and rationale. In addition, students must be able to use spatial ordering to recognize symbols and to understand three-dimensional representations of objects. Perhaps more importantly, higher-order cognition allows students to consider alternative strategies while solving problems, to monitor their thinking, to assess the reasonableness of their answers, and to transfer and apply learned skills to new problems. Usually several, or all, of these brain functions occur simultaneously in the process of solving a single math problem.
The complexity of the mathematical process provides multiple opportunities for breakdowns to occur, and math disabilities can arise at nearly any stage of a child's development. Although very little is known about the biological causes of math disabilities, many experts attribute these problems to deficiencies in one or more of six different skills. These deficits can exist independently of one another or can occur in combination. All can impact a child's ability to progress in mathematics.
To solve even simple math problems, students must use their memories to recall rules and formulas, recognize patterns, invoke rules about sequential ordering to solve multi-step problems, use advanced language skills to understand vocabulary and instructions and explain processes and rationale. In addition, students must be able to use spatial ordering to recognize symbols and to understand three-dimensional representations of objects. Perhaps more importantly, higher-order cognition allows students to consider alternative strategies while solving problems, to monitor their thinking, to assess the reasonableness of their answers, and to transfer and apply learned skills to new problems. Usually several, or all, of these brain functions occur simultaneously in the process of solving a single math problem.
The complexity of the mathematical process provides multiple opportunities for breakdowns to occur, and math disabilities can arise at nearly any stage of a child's development. Although very little is known about the biological causes of math disabilities, many experts attribute these problems to deficiencies in one or more of six different skills. These deficits can exist independently of one another or can occur in combination. All can impact a child's ability to progress in mathematics.
Signs of Struggle
Math skills are often cumulative in nature, one skill building upon previously learned skills. Algebraic manipulation, for example, would be impossible without an understanding of basic arithmetic.
Computer Training Online
Unfortunately, the effects of math disabilities can also be cumulative. Computational weakness can keep a student from reaching higher-level math, regardless of that student's potential for abstract mathematical thinking. Because of this, children with math disabilities stand the best chance of reaching their potential when developmental differences are dealt with promptly — before students lose confidence or develop a fear of the subject.
Free Training Courses
The following is a list of math skills and warning signs that may indicate a math disability:
Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) that students are required to memorize in the earliest grades of elementary school. Recalling these facts automatically is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations. A student with a deficiency in this skill may:
* be unable to recall basic math facts, procedures, rules, or formulas
* be very slow to retrieve facts or pursue procedures
* have difficulties with precision during mathematical work
Computation
Many students, despite a good understanding of mathematical concepts, are inconsistent at computing. They make errors because they may misread signs, carry numbers incorrectly, or not write numerals clearly enough or in the correct column. These students often struggle — especially in primary school, where basic computation and correct answers are stressed — they often end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking. A student with a deficiency in this skill may:
* have difficulties with handwriting that slow down written work or make it hard to read later
* have difficulty remembering previously encountered patterns
* forget what he or she is doing in the middle of a math problem (this may also indicate an attention problem)
* have difficulties sequencing multiple steps
* lose appreciation of the final goal and overemphasize individual elements of a problem
* feel overloaded when faced with a worksheet full of math exercises
* not be able to copy problems correctly
Knowledge Transfer
One fairly common difficulty experienced by people with math problems is the inability to easily connect the abstract or conceptual aspects of math with reality. Understanding what symbols represent in the physical world is important to how well and how easily a child will remember a concept. Given a description of an equilateral triangle, for example, a student with this problem may find it impossible to visualize, or draw, such a triangle. A student with a deficiency in this skill may:
* not be able to distinguish between what is important in a math problem and what is not, particularly in word problems that include irrelevant information
* be unable to appreciate the appropriateness or reasonableness of solutions generated
* find it difficult to switch between multiple demands in a complex math problem
* have difficulty interpreting and manipulating geometric configurations
* find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
The Language of Math
For some students, a math disability is driven by problems with language. These students may also experience difficulty with reading, writing, and speaking. In math, however, their language problem is confounded by the inherently difficult terminology, some of which they never hear outside of the math classroom. These students find word problems especially difficult to translate, as they have difficulty understanding written or verbal directions or explanations. A student with a deficiency in this skill may:
* be confused by language in word problems
* have trouble learning or recalling specialized terms
* have difficulty understanding directions
* be unable to explain their confusion about math concepts and procedures
* have difficulty reading texts to direct their own learning
* have difficulty remembering assigned values or definitions in specific problems
Spatial Organization
This problem is similar to, but more severe than, knowledge-transfer problems. In general, it is an inability to effectively visualize math concepts. Students who have this problem may, for example, be unable to judge the relative size among three dissimilar objects. This disorder requires that a student rely almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. A student with a deficiency in this skill may:
* have difficulty laying out problems in a neat and organized manner
* be unable to describe what a three-dimensional object would look like if the object is rotated and viewed from a different angle
* be unable to comprehend what quantities and mathematical formulas represent in the real world
[ Back to Top ]
Produced by WGBH. Copyright 2003
Support for PBS Parents provided by:
Click here to find out more!
Sponsored Links
Visual Learning
Model and simulate real-world problems to engage students
www.iseesystems.com/STELLA
Math Basics Practice
Comprehensive site for grades 1-6. Practice, win awards, and have FUN!
www.ixl.com/math
Official Berard AIT
Certified Berard AIT Practitioner Training from world leading expert
www.ideatrainingcenter.com
What's this?
Computer Training Online
Unfortunately, the effects of math disabilities can also be cumulative. Computational weakness can keep a student from reaching higher-level math, regardless of that student's potential for abstract mathematical thinking. Because of this, children with math disabilities stand the best chance of reaching their potential when developmental differences are dealt with promptly — before students lose confidence or develop a fear of the subject.
Free Training Courses
The following is a list of math skills and warning signs that may indicate a math disability:
Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) that students are required to memorize in the earliest grades of elementary school. Recalling these facts automatically is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations. A student with a deficiency in this skill may:
* be unable to recall basic math facts, procedures, rules, or formulas
* be very slow to retrieve facts or pursue procedures
* have difficulties with precision during mathematical work
Computation
Many students, despite a good understanding of mathematical concepts, are inconsistent at computing. They make errors because they may misread signs, carry numbers incorrectly, or not write numerals clearly enough or in the correct column. These students often struggle — especially in primary school, where basic computation and correct answers are stressed — they often end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking. A student with a deficiency in this skill may:
* have difficulties with handwriting that slow down written work or make it hard to read later
* have difficulty remembering previously encountered patterns
* forget what he or she is doing in the middle of a math problem (this may also indicate an attention problem)
* have difficulties sequencing multiple steps
* lose appreciation of the final goal and overemphasize individual elements of a problem
* feel overloaded when faced with a worksheet full of math exercises
* not be able to copy problems correctly
Knowledge Transfer
One fairly common difficulty experienced by people with math problems is the inability to easily connect the abstract or conceptual aspects of math with reality. Understanding what symbols represent in the physical world is important to how well and how easily a child will remember a concept. Given a description of an equilateral triangle, for example, a student with this problem may find it impossible to visualize, or draw, such a triangle. A student with a deficiency in this skill may:
* not be able to distinguish between what is important in a math problem and what is not, particularly in word problems that include irrelevant information
* be unable to appreciate the appropriateness or reasonableness of solutions generated
* find it difficult to switch between multiple demands in a complex math problem
* have difficulty interpreting and manipulating geometric configurations
* find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
The Language of Math
For some students, a math disability is driven by problems with language. These students may also experience difficulty with reading, writing, and speaking. In math, however, their language problem is confounded by the inherently difficult terminology, some of which they never hear outside of the math classroom. These students find word problems especially difficult to translate, as they have difficulty understanding written or verbal directions or explanations. A student with a deficiency in this skill may:
* be confused by language in word problems
* have trouble learning or recalling specialized terms
* have difficulty understanding directions
* be unable to explain their confusion about math concepts and procedures
* have difficulty reading texts to direct their own learning
* have difficulty remembering assigned values or definitions in specific problems
Spatial Organization
This problem is similar to, but more severe than, knowledge-transfer problems. In general, it is an inability to effectively visualize math concepts. Students who have this problem may, for example, be unable to judge the relative size among three dissimilar objects. This disorder requires that a student rely almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. A student with a deficiency in this skill may:
* have difficulty laying out problems in a neat and organized manner
* be unable to describe what a three-dimensional object would look like if the object is rotated and viewed from a different angle
* be unable to comprehend what quantities and mathematical formulas represent in the real world
[ Back to Top ]
Produced by WGBH. Copyright 2003
Support for PBS Parents provided by:
Click here to find out more!
Sponsored Links
Visual Learning
Model and simulate real-world problems to engage students
www.iseesystems.com/STELLA
Math Basics Practice
Comprehensive site for grades 1-6. Practice, win awards, and have FUN!
www.ixl.com/math
Official Berard AIT
Certified Berard AIT Practitioner Training from world leading expert
www.ideatrainingcenter.com
What's this?
Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) that students are required to memorize in the earliest grades of elementary school. Recalling these facts automatically is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations. A student with a deficiency in this skill may:
* be unable to recall basic math facts, procedures, rules, or formulas
* be very slow to retrieve facts or pursue procedures
* have difficulties with precision during mathematical work
* be unable to recall basic math facts, procedures, rules, or formulas
* be very slow to retrieve facts or pursue procedures
* have difficulties with precision during mathematical work
Computation
Many students, despite a good understanding of mathematical concepts, are inconsistent at computing. They make errors because they may misread signs, carry numbers incorrectly, or not write numerals clearly enough or in the correct column. These students often struggle — especially in primary school, where basic computation and correct answers are stressed — they often end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking. A student with a deficiency in this skill may:
* have difficulties with handwriting that slow down written work or make it hard to read later
* have difficulty remembering previously encountered patterns
* forget what he or she is doing in the middle of a math problem (this may also indicate an attention problem)
* have difficulties sequencing multiple steps
* lose appreciation of the final goal and overemphasize individual elements of a problem
* feel overloaded when faced with a worksheet full of math exercises
* not be able to copy problems correctly
* have difficulties with handwriting that slow down written work or make it hard to read later
* have difficulty remembering previously encountered patterns
* forget what he or she is doing in the middle of a math problem (this may also indicate an attention problem)
* have difficulties sequencing multiple steps
* lose appreciation of the final goal and overemphasize individual elements of a problem
* feel overloaded when faced with a worksheet full of math exercises
* not be able to copy problems correctly
Knowledge Transfer
One fairly common difficulty experienced by people with math problems is the inability to easily connect the abstract or conceptual aspects of math with reality. Understanding what symbols represent in the physical world is important to how well and how easily a child will remember a concept. Given a description of an equilateral triangle, for example, a student with this problem may find it impossible to visualize, or draw, such a triangle. A student with a deficiency in this skill may:
* not be able to distinguish between what is important in a math problem and what is not, particularly in word problems that include irrelevant information
* be unable to appreciate the appropriateness or reasonableness of solutions generated
* find it difficult to switch between multiple demands in a complex math problem
* have difficulty interpreting and manipulating geometric configurations
* find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
* not be able to distinguish between what is important in a math problem and what is not, particularly in word problems that include irrelevant information
* be unable to appreciate the appropriateness or reasonableness of solutions generated
* find it difficult to switch between multiple demands in a complex math problem
* have difficulty interpreting and manipulating geometric configurations
* find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
The Language of Math
For some students, a math disability is driven by problems with language. These students may also experience difficulty with reading, writing, and speaking. In math, however, their language problem is confounded by the inherently difficult terminology, some of which they never hear outside of the math classroom. These students find word problems especially difficult to translate, as they have difficulty understanding written or verbal directions or explanations. A student with a deficiency in this skill may:
* be confused by language in word problems
* have trouble learning or recalling specialized terms
* have difficulty understanding directions
* be unable to explain their confusion about math concepts and procedures
* have difficulty reading texts to direct their own learning
* have difficulty remembering assigned values or definitions in specific problems
* be confused by language in word problems
* have trouble learning or recalling specialized terms
* have difficulty understanding directions
* be unable to explain their confusion about math concepts and procedures
* have difficulty reading texts to direct their own learning
* have difficulty remembering assigned values or definitions in specific problems
Spatial Organization
This problem is similar to, but more severe than, knowledge-transfer problems. In general, it is an inability to effectively visualize math concepts. Students who have this problem may, for example, be unable to judge the relative size among three dissimilar objects. This disorder requires that a student rely almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. A student with a deficiency in this skill may:
* have difficulty laying out problems in a neat and organized manner
* be unable to describe what a three-dimensional object would look like if the object is rotated and viewed from a different angle
* be unable to comprehend what quantities and mathematical formulas represent in the real world
* have difficulty laying out problems in a neat and organized manner
* be unable to describe what a three-dimensional object would look like if the object is rotated and viewed from a different angle
* be unable to comprehend what quantities and mathematical formulas represent in the real world
Understanding
When seeking help for a child who is struggling in school, parents invariably ask, "What can I do?" Often, the best first step is to take the time to learn more about various learning problems so that you might better understand, recognize, and ultimately respond to your child's specific struggles and needs. This section outlines important aspects of four basic skills: what it takes to exhibit them well, where and when developmental breakdowns occur, and how to recognize problems early.
Struggle For Education
Millions of American school children struggle with serious learning problems. Each day they face tasks that, for reasons unknown to them, never become automatic and always seem to stand in the way of their progress as students. For parents and teachers of a struggling child, the picture is not much clearer or any less frustrating. Specific learning problems are difficult to identify; their causes are generally unknown; and the long-term effects are hard to predict.
The tension between the stubborn reality of learning problems and the demand for academic success in an increasingly competitive society has created one of the most contentious issues in education today. Decades of research have shed light on the causes and effects of learning disabilities and yielded effective strategies for dealing with them. Yet, at the same time, increasing numbers of school districts have embraced standardized, high-stakes testing as a means of evaluating students.
It comes as no surprise, then, that when a child can't read, write, do math, or pay attention —and when the problem doesn't go away— parents, educators, experts, and policymakers often collide in an earnest struggle to find answers. The result is a landscape filled with a range of expert opinions and approaches to treatment.
In the middle of this landscape there is common ground. Nearly everyone agrees that no single teaching method is appropriate for all students. More pragmatically, experts also acknowledge that the term "disability" has important legal ramifications, because all of the funding to support children with learning problems is tied to the Individuals with Disabilities Education Act. And while learning disabilities don't go away, the work of learning experts continues to translate into more and more effective strategies that help children succeed.
The tension between the stubborn reality of learning problems and the demand for academic success in an increasingly competitive society has created one of the most contentious issues in education today. Decades of research have shed light on the causes and effects of learning disabilities and yielded effective strategies for dealing with them. Yet, at the same time, increasing numbers of school districts have embraced standardized, high-stakes testing as a means of evaluating students.
It comes as no surprise, then, that when a child can't read, write, do math, or pay attention —and when the problem doesn't go away— parents, educators, experts, and policymakers often collide in an earnest struggle to find answers. The result is a landscape filled with a range of expert opinions and approaches to treatment.
In the middle of this landscape there is common ground. Nearly everyone agrees that no single teaching method is appropriate for all students. More pragmatically, experts also acknowledge that the term "disability" has important legal ramifications, because all of the funding to support children with learning problems is tied to the Individuals with Disabilities Education Act. And while learning disabilities don't go away, the work of learning experts continues to translate into more and more effective strategies that help children succeed.
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