Stories from the Documentary: Nathan V.LaurenSarah LeeAdamNathan S.

MATHEMATICSBasics | Difficulties | Responses

## Difficulties with Mathematics

### What Can Stand in the Way of a Student's Mathematical Development?

Math disabilities can arise at nearly any stage of a child's scholastic development. While very little is known about the neurobiological or environmental causes of these problems, many experts attribute them to deficits in one or more of five different skill types. These deficits can exist independently of one another or can occur in combination. All can impact a child's ability to progress in mathematics.

Incomplete Mastery of Number Facts
Number facts are the basic computations (9 + 3 = 12 or 2 x 4 = 8) students are required to memorize in the earliest grades of elementary school. Recalling these facts efficiently is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations.

Try it yourself. Experience a problem with basic facts.

Computational Weakness
Many students, despite a good understanding of mathematical concepts, are inconsistent at computing. They make errors because they misread signs or carry numbers incorrectly, or may not write numerals clearly enough or in the correct column. These students often struggle, especially in primary school, where basic computation and "right answers" are stressed. Often they end up in remedial classes, even though they might have a high level of potential for higher-level mathematical thinking.

Difficulty Transferring Knowledge
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. Holding and inspecting an equilateral triangle, for example, will be much more meaningful to a child than simply being told that the triangle is equilateral because it has three equal sides. And yet children with this problem find connections such as these painstaking at best.

Making Connections
Some students have difficulty making meaningful connections within and across mathematical experiences. For instance, a student may not readily comprehend the relation between numbers and the quantities they represent. If this kind of connection is not made, math skills may be not anchored in any meaningful or relevant manner. This makes them harder to recall and apply in new situations.

Incomplete Understanding of the Language of Math
For some students, a math disability is driven by problems with language. These children 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 hear nowhere outside of the math classroom. These students have difficulty understanding written or verbal directions or explanations, and find word problems especially difficult to translate.

Difficulty Comprehending the Visual and Spatial Aspects and Perceptual Difficulties.
A far less common problem -- and probably the most severe -- is the inability to effectively visualize math concepts. Students who have this problem may be unable to judge the relative size among three dissimilar objects. This disorder has obvious disadvantages, as it requires that a student rely almost entirely on rote memorization of verbal or written descriptions of math concepts that most people take for granted. Some mathematical problems also require students to combine higher-order cognition with perceptual skills, for instance, to determine what shape will result when a complex 3-D figure is rotated.

Try it yourself. Experience a visualization challenge.

### Signs of Math Difficulties

#### Output Difficulties

A student with problems in output may
• be unable to recall basic math facts, procedures, rules, or formulas
• be very slow to retrieve facts or pursue procedures
• have difficulties maintaining precision during mathematical work
• 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

#### Organizational Difficulties

A student with problems in organization may
• have difficulties sequencing multiple steps
• become entangled in multiple steps or elements of a problem
• lose appreciation of the final goal and over emphasize individual elements of a problem
• not be able to identify salient aspects of a mathematical situation, particularly in word problems or other problem solving situations where some information is not relevant
• be unable to appreciate the appropriateness or reasonableness of solutions generated

#### Language Difficulties

A student with language problems in math may
• have difficulty with the vocabulary of math
• be confused by language in word problems
• not know when irrelevant information is included or when information is given out of sequence
• have trouble learning or recalling abstract terms
• have difficulty understanding directions
• have difficulty reading texts to direct their own learning
• have difficulty remembering assigned values or definitions in specific problems

#### Attention Difficulties

A student with attention problems in math may
• be distracted or fidgety during math tasks
• lose his or her place while working on a math problem
• appear mentally fatigued or overly tired when doing math

#### Visual Spatial or Ordering Difficulties

A student with problems in visual, spatial, or sequential aspects of mathematics may
• be confused when learning multi-step procedures
• have trouble ordering the steps used to solve a problem
• feel overloaded when faced with a worksheet full of math exercises
• not be able to copy problems correctly
• may have difficulties reading the hands on an analog clock
• may have difficulties interpreting and manipulating geometric configurations
• may have difficulties appreciating changes in objects as they are moved in space

A student with problems managing and/or merging different tasks in math may
• find it difficult to switch between multiple demands in a complex math problem
• find it difficult to tell when tasks can be grouped or merged and when they must be separated in a multi-step math problem
• cannot manage all the demands of a complex problem, such as a word problem, even thought he or she may know component facts and procedures

MATHEMATICSBasics | Difficulties | Responses

UP CLOSE:
Statistics

A snapshot of mathematics problems and implications

Math disabilities, like other learning disorders, have the power to keep children from performing up to their potential in school and beyond. At no time in our history has this notion been truer. 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. The disparity between those who learn math with relative ease and those who struggle with math disabilities is widening at an alarming rate. Here are some statistics that suggest why and underscore the importance of early intervention.

Struggling Kids
• Nine-year-olds with math disabilities have, on average, a first-grade level of math knowledge.
• Seventeen-year-olds with math disabilities have, on average, a fifth-grade level of math knowledge.
• Experts estimate that for every two years of school, children with math disabilities acquire about one year of mathematical proficiency.
• Children with math disabilities often reach a learning plateau in seventh grade, and acquire only one year's worth of mathematical proficiency in grades seven through twelve.
• Thirty-five percent of children with learning disabilities drop out of high school.
• Fourteen percent of students with learning disabilities (compared to 53 percent of students in general population) attend post-secondary school within two years of leaving high school.

Changing Emphasis
• 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.
• Schools stiffened math-course requirements for graduation and introduced minimum competency testing in response to a 1983 government report titled "A Nation at Risk."
• In 1983, the typical college graduate's income was 38 percent higher, on average, than the typical high school graduate's income.
• 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.
• In 1997, the typical college graduate's income was 73 percent higher, on average, than the typical high school graduate's income.