Specific Learning Difficulties
ADD/ADHD | Mathematics Difficulties | Dyslexia

Mathematics Difficulties

by Phillip Howell, Academic Dean

Mathematics involves a way of thinking which is considered by some to be a specific type of intelligence. Everyone has this intelligence, but whether it is as strong as one's language abilities or physical abilities varies from one individual to the next. Mathematical thinking involves seeing patterns in everyday life, thinking logically, thinking geometrically, recognizing relationships between numbers, having a sense of whether or not a solution to a problem is reasonable, and devising strategies for solving novel mathematical problems. One's strength with this intelligence stems both from natural predisposition and from one's learning experiences.

Some students experience great difficulty in mathematics which is unrelated to their mathematical intelligence. These children and adults have the potential to learn much more than what they are achieving. They are not experiencing emotional, behavioral, or severe environmental issues which prevent their learning; they have a learning difference.

It is common practice to group mathematics difficulties into two categories of learning disabilities: mathematics computation disabilities and mathematical reasoning disabilities. These categories are based on the child's performance in class -- the outcome of her learning differences. However, the teacher and child are usually better served by focusing on the underlying causes of the difficulties, since there are various reasons why a child may have severe deficits in computation or reasoning. In fact, the underlying cause may not be directly related to mathematics at all.

Visual-Spatial and Organizational Difficulties

Children with learning differences often have trouble organizing their materials and their written work. They seem to create clutter rather than order. Their handwriting may be illegible, and their placement of words, numbers, or pictures on a page is not organized. Individuals who have visual-spatial deficits often have poor visual memory, as well.

While such difficulties do not stem from the realm of mathematical thinking, they can greatly impair a student's ability to succeed in a mathematics class. A disorganized child often has trouble keeping columns lined up in computation, and may lose steps such as "carrying" or "borrowing" during difficult problems. Even working with hands-on learning tools ("manipulatives") may become confusing for the child, because she cannot organize them appropriately. Solving problems through drawing pictures, finding patterns, or creating graphs require visual-spatial organization. In addition, poor visual memory of geometric shapes can hinder the child's success.

Memory Difficulties

Individuals with learning differences often have difficulty transferring short-term memory to long-term memory. These children tend to need much practice with a new concept or skill in order to learn it. Once a concept or fact is learned, retrieving it quickly and consistently can be problematic, as well. A child might know his addition facts Monday through Thursday, but "lose" them on Friday.

Strong memory is essential for mathematics. Children with memory difficulties might not consistently remember the steps in arithmetic procedures such as long multiplication. They often are unable to recall arithmetic facts. They have a limited "working memory," or ability to hold several pieces of information in their minds as they work with them. Since their performance varies from day to day, their teachers may not accurately assess their true knowledge of mathematics.

Language-Related Difficulties

A child with deficits in language skills may find that these difficulties impact learning in mathematics. This child may have trouble remembering or interpreting directions. Her deficits in expressive language may prevent her from explaining how well she understands a concept. Because of her poor reading and writing skills, she may avoid math assignments which involve these tasks. She may have difficulty with the vocabulary of mathematics. On the surface, any of these difficulties can look like a lack of mathematical knowledge or skill, rather than a problem with language.

Attention Difficulties

The student with attention deficits may find math class his greatest challenge. He may feel easily overwhelmed by tasks, not knowing where to begin. (This characteristic is one diagnostic criteria for ADHD.) He may take an impatient, impulsive approach to problem solving, being unwilling to plod through work which seems tedious. He may give too much attention to irrelevant details in a language problem or class activity. His impatience with details makes editing his work seem torturous. The student with attention difficulties often tires quickly when doing written computation, and his accuracy quickly drops after the first few problems.

Difficulties with Math Concepts

This is perhaps the only area of difficulty which should truly be called a mathematics disability, because it arises from the realm of mathematical thinking. Students with learning differences in this area have trouble with abstract concepts and symbols. They demonstrate poor number sense (estimation, seeing number relationships, recognizing when an answer is unreasonable). They have trouble strategizing an approach to solving a novel problem. They have an extremely hard time applying concepts to real-world tasks and experiences. These students often become totally dependent upon memorized procedures for solving problems, rather than using reasoning abilities.

It is important to identify the root cause of difficulties in mathematics for two reasons. First, such diagnosis enables the teacher to provide the appropriate interventions. In some cases, teaching a student how to organize his work and how to deal with visually confusing material will completely change his performance in math. Other students may need to build their memory skills while learning strategies to compensate when their memory fails them. Students with conceptual deficits need many more concrete experiences with objects and real-world practice than are generally offered to students.

Secondly, the teacher cannot accurately assess the child's knowledge of mathematics unless the causes for difficulties are identified. Often, children appear to have very limited knowledge in mathematics, when they actually have attention difficulties or language deficits.

It is vital to provide proper interventions before the child experiences ongoing failure in mathematics. Once the child feels defeated, math anxiety, avoidance, and teacher dependence can become as great a threat to learning as the learning difference itself. Children with learning differences respond well to structured, carefully-crafted lessons which address the sources of the child's difficulties.

For a discussion of appropriate teaching methodology, click here