Math Disabilities

PART 1: CRITICAL DISTINCTIONS - LD vs. LEARNING DIFFICULTY vs. INTELLECTUAL DISABILITY

1.1 Why This Distinction Matters

The difference between a Learning Disability, a Learning Difficulty, and an Intellectual Disability is often misunderstood but critically important for proper diagnosis, intervention, and support.

1.2 Learning Disability (LD)

Definition: A specific Learning Disability is diagnosed when an individual meets established diagnostic criteria (DSM-5, OPA, LDAO) in reading, writing, or math (or any combination).

Key Characteristics

Important: A Learning Disability is a formal diagnosis, not just a description of difficulty.

1.3 Learning Difficulty

Definition: A learning difficulty can arise due to various factors but is not in and of itself a formally diagnosed Learning Disability.

Causes of Learning Difficulties

The ASD/ADHD Confusion

ASD and ADHD are often mischaracterized as Learning Disabilities. While they are Neurodevelopmental Disorders (like LDs), they are not Learning Disabilities in and of themselves.

Key Points:

• ASD and ADHD can create learning challenges → may be referred to as "learning difficulties"

• Some individuals with ASD and/or ADHD have coexisting Learning Disabilities

• If diagnostic criteria are met for both, an individual can be diagnosed with all three disorders

Clinical Reality: This complexity will be discussed further in Unit 10.

1.4 Intellectual Disability (ID)

Definition: An intellectual disability is a neurodevelopmental disorder diagnosed when an individual has both intellectual and adaptive functioning deficits in conceptual, social, and practical domains (American Psychological Association, 2013).

Key Characteristics

Critical Rule: ID and LD Cannot Coexist

Why? Because LD requires average cognitive abilities while ID involves significantly below average cognitive abilities.

Case Study Reference: Olivia (from Unit 4)

Olivia's profile exemplifies Intellectual Disability:

But Wait—There's More: For an ID diagnosis, Olivia would also need low adaptive functioning skills:

• Social skills (interaction, communication)

• Conceptual skills (academic concepts, money, time)

• Practical skills (daily living, self-care)

These would be assessed using parent and teacher rating scales.

1.5 Coexisting Conditions Involving ID

Clinical Caution: Given the complex nature of ASD and ADHD, an additional Intellectual Disability diagnosis must be given very carefully and cautiously.

1.6 Summary Comparison Table

PART 2: THE IMPORTANCE OF MATHEMATICS

2.1 Foundational Quotes

2.2 Why Math Matters

In Daily Life

We use math in some way every day, whether we realize it or not:

• Managing money and budgets

• Cooking and measuring ingredients

• Telling time and scheduling

• Shopping and calculating discounts

• Understanding statistics in news

In Society

Our society would not function without numbers and math:

• Engineering and construction

• Technology and computing

• Medicine and dosage calculations

• Transportation and navigation

• Scientific research

In Education

Math is essential for understanding other subjects:

• Science (data analysis, formulas)

• Social studies (statistics, timelines)

• Music (rhythm, notation)

• Art (perspective, symmetry)

2.3 The Spectrum of Math Experience

2.4 A World Without Numbers

(Based on video content referenced in lecture)

Consider what life would be like without numbers:

• No way to tell time

• No monetary system

• No measurements for cooking or building

• No way to count inventory

• No age calculations

• No sports scores

• No GPS coordinates

We take numbers for granted, but they are fundamental to modern civilization.

PART 3: MATH DEVELOPMENT - PIAGET'S FOUNDATIONAL CONCEPTS

3.1 Piaget's Contribution

Piaget spent much of his career investigating children's concepts of number, quantity, and early skills related to quantity.

Piaget's Four Foundational Skills for Math

Enduring Relevance: These skills are still believed to be important foundational skills for math development.

PART 4: MATH DEVELOPMENT BY AGE

4.1 Comprehensive Developmental Table

(Source: PBS Learning Media, 2024)

Number Concepts and Relations

Number Operations

Geometry and Spatial Sense

Measurement and Comparison

Patterns

PART 5: UNDERSTANDING MATH DISABILITIES

5.1 What Are Math Disabilities?

Many students struggle with math—it's a complex subject requiring focus and effort. However, for some students, math presents significant challenges due to underlying processing deficits. These students may be diagnosed with a math disability.

DSM-5 Terminology

Formally: "Specific Learning Disorder with impairment in mathematics"

DSM-5 Diagnostic Criteria (Applied)

Using the DSM-5 criteria for Specific Learning Disorder, a math disability would be diagnosed if criterion 5 OR criterion 6 is met in Section A, along with criteria B, C, and D.

Important Distinction: An individual may meet only one criterion and still receive a diagnosis. This means someone could:

• Struggle primarily with calculation but reason well about math concepts, OR

• Understand calculations but struggle to apply them in problem-solving, OR

• Struggle with both (most common)

5.2 Dyscalculia

DSM-5 Definition:

Key Features of Dyscalculia

PART 6: SKILLS REQUIRED FOR MATH SUCCESS

6.1 Overview: Math as a Cumulative Skill

Analogy: Learning math is like building a house. If the foundation (number sense, counting) is weak, everything built on top (arithmetic, algebra, calculus) will be unstable.

6.2 Number Sense

Definition: The first developing skill related to math. It develops fairly naturally in most children.

Components of Number Sense

Subitizing: A Critical Early Skill

Definition: The ability to instantly recognize a small number of objects (1-4) without counting them.

Real-World Example: When playing a game with dice, you can look at the dice and immediately know the number of dots without counting each individual one. That's subitizing.

Why It Matters:

• Foundation for number sense

• Builds automaticity with small quantities

• Frees cognitive resources for more complex math

Beyond 5: When there are more than five objects, we can't subitize the entire array. Instead, we naturally use visual skills to group objects, making them easier to count efficiently.

Activity: Try looking at a pattern of dots and notice how your brain automatically groups them—this demonstrates your visual grouping skills at work.

6.3 Counting Knowledge

Counting seems simple, but it actually requires understanding several principles. For some children, counting does not develop typically, leading to significant math challenges.

The Three Principles of Counting

Common Counting Errors

(Based on video content referenced in lecture)

Early Counting Confusion Example

When very young children are shown three buttons and asked to count them, they might:

• Point to each button and say "button, button, button" (instead of "one, two, three")

• Or say "one, two, three" but not connect this to "three buttons"

They need to understand that the numbers they're assigning are just labels for quantity, not related to what the objects are.

6.4 Arithmetic

Definition: Basic arithmetic skills include addition, subtraction, multiplication, and division.

Developmental Timeline

Skills Required for Arithmetic

Required Reading: Flanagan & Alfonso (2011), pages 54-56, details:

• Memory skills required for arithmetic

• Procedural competence needed

• Specific challenges individuals with math disabilities face

6.5 Graphomotor Implementation

The Problem: Some children struggle with the paper/pencil aspect of math, which can interrupt the entire process.

How Graphomotor/Visual-Spatial Challenges Affect Math

Consequences

• Can't solve problem correctly despite understanding concept

• Makes careless errors due to cognitive overload

• Struggles compound over time

Helpful Supports

6.6 Memory

Working Memory's Role in Math

Definition: Working memory is the mental workspace that controls, regulates, and actively maintains information to accomplish complex tasks.

Why Working Memory Matters for Math:

• Math requires solving problems while holding partial information

• Need to process new information while retaining intermediate steps

• Must keep track of where you are in multi-step problems

Research Findings

Clinical Observation

The Working Memory System

From previous psychology courses, recall the three components:

Required Reading: Flanagan & Alfonso (2011) provides further detail on:

• Specific roles of these working memory systems in math development

• Role of processing speed in math skill development

6.7 Attention

Why Attention Matters for Math

Common Attention-Related Math Errors

ADHD Symptoms That Complicate Math Learning

The resource "Math Learning Disabilities and ADHD: How Symptoms Relate" describes:

Important Caveat

Hyperfocus Factor: As discussed in Unit 5, individuals with ADHD can sometimes hyperfocus on tasks they find interesting. If math is one of those interesting tasks, they might excel.

6.8 Cognitive Ability

When to Consider a Full Assessment

Some math difficulty is expected. However, consider a psychological assessment when students:

• Continually struggle with math despite extra help

• Seem to lack basic building blocks of numeracy

• Don't respond to typical interventions

Role of Cognitive Assessment (WISC)

The WISC measures skills relevant to math:

PART 7: IMPACT OF MATH DISABILITIES ON DEVELOPMENT

7.1 Cumulative Nature of Math Difficulties

The Snowball Effect:

1. Weak number sense in preschool

2. Counting difficulties in kindergarten

3. Trouble with basic arithmetic in Grade 1

4. Fractions become impossible in Grade 4

5. Algebra inaccessible in middle school

6. Calculus out of reach in high school

Critical Point: Once children have fallen behind in math, it can be very challenging to get them caught up. Early intervention is essential.

7.2 Research Findings on Long-Term Outcomes

Academic Trajectory

Employment Outcomes

Key Insight: Poor math skills have negative employment consequences independent of reading ability. Strong readers with math disabilities still face employment challenges.

7.3 Math Anxiety

What Is Math Anxiety?

Math anxiety is a unique phenomenon—a high level of anxiety specifically associated with mathematics.

How It Works:

1. Anxiety consumes working memory resources

2. Less working memory available for math

3. Math performance suffers

4. Negative experience reinforces anxiety

Critical Insight

This means:

• Someone can understand math perfectly well

• But anxiety blocks their ability to access that knowledge

• They perform poorly despite having the skills

Resource for Math Anxiety

The American Psychological Association article "How to help kids manage math anxiety" covers:

• What math anxiety is

• Consequences of math anxiety

• Strategies to combat it

PART 8: ASSESSMENT FOR MATH DISABILITIES

8.1 Psychological Assessment Process

Assessment follows the process outlined in Unit 4, with specific focus on math skills.

Core Assessment Battery

KeyMath Test Details

8.2 Case Study Application

Review Olivia's profile from Unit 4:

This profile, combined with low adaptive functioning, would indicate Intellectual Disability, not a specific math disability.

Distinction: For a specific math disability diagnosis, we would expect:

• Average cognitive ability (not 2nd percentile)

• Significant discrepancy between cognitive ability and math achievement

PART 9: INTERVENTION FOR MATH DISABILITIES

9.1 School-Based Programs

The Challenge

What Schools Do Instead

Many school boards have robust plans for improving math scores, implemented through:

• Classroom teacher training

• Curriculum changes

• General instructional improvements

Note: These are typically not specific programs for students with math disabilities, but rather system-wide approaches.

9.2 Individual Education Plan (IEP) Accommodations

Students with math disabilities would likely receive an IEP with accommodations including:

9.3 Levine's General Recommendations (1999, pg. 424-426)

Levine outlines comprehensive recommendations for supporting students with math disabilities:

Foundational Principle

Example: Students who haven't fully automatized multiplication tables will feel stressed during long division and fractions.

Intervention Implication: Remedial assistance must often include a return to fundamentals.

Leveraging Strengths

Example: If a student has strong verbal skills but weak visual-spatial skills, use verbal explanations and self-talk strategies for math.

Creating a Supportive Environment

Modeling Techniques

With the student watching, the teacher solves the first example on the page. This provides a model to which the student can refer.

At home: Parents can do the same.

Integration: Combine modeling with discussions of the conceptual content or rationale for the processes being demonstrated.

Evaluation Approaches

Using Breakdown Points

Identify the student's "breakdown point" and make it the end object of assignments.

Examples:

• Student who struggles with identifying operations in word problems → give problems and ask them to write what operation is needed (multiplication, subtraction)

• Student who misses regrouping needs → go through worksheet and circle all instances where regrouping is required

• Student who can't identify extraneous information → go through examples and cross out superfluous information

Goal Setting

Test-Taking Support

Using Games

Highly motivating games alleviate the tedium of drill:

Advantage: Games provide direct feedback, preventing students from practicing errors.

Homework Guidelines

High-Interest Materials

Instruction and practice using materials related to high-interest subject matter makes learning more meaningful:

• Sports statistics

• Woodworking measurements

• Trip planning (distance, time, budget)

• Cooking (measuring, fractions)

Resource Room/Tutoring

Many students benefit from individualized help in a resource room or tutorial setting.

Key Elements:

• Strong alliance with student

• Non-threatening setting

• Cheerful ambiance

• Combats apprehension about math

Teacher Modeling

Make demonstration (accompanied by talking through the sequence) a part of classroom instruction.

Warning: Simply having students mimic examples from the board or textbook can result in misleading lack of real understanding and acquisition of poor work habits.

Preventing Skill Loss

Recommendation: Require all students to maintain a cumulative notebook or file of math concepts and procedures throughout elementary and junior high school. Give regular review tests. Continue reviews in all high school math courses.

9.4 Commercially Available Programs

CogMed

Claim: Improves attention and working memory skills, leading to significant improvement in math skills.

Important Caution:

Questions to Ask:

• What does the research actually show?

• Are studies peer-reviewed?

• Were there control groups?

• How large were the effects?

• Do results generalize to classroom math performance?

PART 10: GLOSSARY OF KEY TERMS

PART 11: SUMMARY AND KEY TAKEAWAYS

11.1 Critical Distinctions

1. Learning Disability = Specific academic impairment with average cognitive ability

2. Learning Difficulty = Learning challenges from any cause; not a formal diagnosis

3. Intellectual Disability = Global impairment in intellectual AND adaptive functioning; cannot coexist with LD

11.2 About Math Disabilities

1. Affect number sense/calculation (criterion 5) and/or mathematical reasoning (criterion 6)

2. "Dyscalculia" is alternative term for math disability

3. Can be diagnosed even if only one area is impaired

4. Often under-researched compared to reading disabilities

11.3 Skills Required for Math

Nine Key Areas:

1. Number sense (including subitizing)

2. Counting knowledge (three principles)

3. Arithmetic

4. Graphomotor implementation

5. Working memory

6. Attention

7. Cognitive ability

8. Visual-spatial skills

9. Procedural competence

11.4 The Cumulative Nature of Math

• Math builds on previously learned skills

• Early difficulties snowball into later challenges

• Early intervention is essential

• Math difficulties at school start predict difficulties at school end

11.5 Math Anxiety

• Anxiety consumes working memory resources

• Can affect even students with strong math skills

• Creates vicious cycle of poor performance and more anxiety

• Requires supportive teaching approaches

11.6 Assessment Essentials

• Psychologists use WIAT, WISC, KeyMath

• Must rule out Intellectual Disability first

• School-based assessments (KeyMath) can inform intervention but not diagnose

11.7 Intervention Approaches

1. IEP accommodations (calculator, manipulatives, extended time)

2. Levine's comprehensive recommendations (mastery of prerequisites, supportive environment, modeling, games)

3. Commercial programs (evaluate claims carefully)

4. Prevention of skill loss through cumulative review

11.8 The Research Gap

Math disabilities are less well understood and remediated within our education system than reading disabilities. This remains an important area for further research.