# Mathematics

## Mathematics Difficulties

What Can Stand in the Way of a Student's Mathematical Development?
Math difficulties 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 weaknesses in one or more of the skill types listed below. These weaknesses can exist independently of one another or can occur in combination. All can impact a child's ability to progress in mathematics.

1. Incomplete mastery of number facts
Number facts (e.g., 9 + 3 = 12 or 2 x 4 = 8) are the basic computations 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.

2. Computational weakness
Many students compute inconsistently. Despite a good understanding of mathematical concepts, they make errors because they misread signs or carry numbers incorrectly. They might 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. At times, they end up in remedial classes, even though they might have great potential for higher-level mathematical thinking.

3. Difficulty transferring knowledge
Students may struggle when they are required to connect the abstract or conceptual aspects of math with reality. Understanding what symbols represent in the physical world is important to how easily a child will remember a concept. For example, inspecting and comparing one third cup of water and one half cup of water in a measuring cup will be much more meaningful to a child than simply being told that one half is more than one third.

4. 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.

5. Incomplete understanding of the language of math
Struggles with math may be driven by difficulty with language. Children may also experience difficulty with reading, writing, and speaking. In math, a language weakness is comes into play when children are presented with difficult vocabulary, some of which they may rarely hear outside of the math classroom. These students may have difficulty understanding written or verbal directions or explanations and find word problems especially difficult to understand.

6. 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 struggle with this may have difficulty judging the relative size among three different objects (e.g., which is taller: a 1 inch paper clip, a 2 centimeter piece of string, or a 1.2 inch blade of grass?).

This weakness 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 thinking with perceptual skills (e.g., determine what shape will result when a complex 3-D figure is rotated).

> Try it yourself. Experience a visualization challenge.

## Observations at Home

When a child is struggling with math, parents might make the following observations.

Output Difficulties
A student struggling 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 struggling with 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 weaknesses 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 explaining and communicating about math, including asking and answering questions
• 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 weaknesses 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 weaknesses in visual, spatial, or sequential aspects of math 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
• have difficulties reading the hands on an analog clock
• have difficulties interpreting and manipulating geometric configurations
• have difficulties appreciating changes in objects as they are moved in space

Difficulties with multiple tasks
A student struggling to manage and/or merge 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
• Struggle to manage all the demands of a complex problem, such as a word problem, even thought he or she may know component facts and procedures

NOTE: This is not an exhaustive list of the types of difficulties a student may have with math and should not be used without considering all of the child’s strengths and weaknesses. If you are concerned about your child’s difficulties with math or other struggles with learning, read more about tips on assessment.

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