Learning Disabilities and Math Interventions: Strategies for Educators

Mathematics can inspire creativity and provide proof of grand ideas, yet many students find it inaccessible. Educators face the challenge of improving math proficiency levels in the next generation of problem solvers. Math interventions are designed to support students who are behind in their math learning, particularly those who are two or more grade levels behind in a specific math topic. Some schools offer specialized classes with smaller sizes and multiple teachers for intensive math intervention.

Understanding Math Intervention

In broad terms, math interventions encompass strategies to assist students who are struggling with math. These interventions align with the Response to Intervention (RTI) framework, a multi-tiered system of supports within the core classroom. Math interventions can be implemented across all tiers of instruction to support students who are falling behind. The specific supports provided will vary based on the district, school, and individual student needs.

Assessment and Identification of Learning Disabilities in Mathematics

Assessment of learning disabilities in mathematics occurs within a Multi-Tiered System of Supports (MTSS), a framework that provides academic, behavioral, and social-emotional supports for all students. The Individuals with Disabilities Education Act (IDEA) allows students to qualify for special education services under two categories of Specific Learning Disability (SLD) in math: math calculation and/or math reasoning.

The delivery of evidence-based interventions within an MTSS for students not acquiring basic academic skills, while closely monitoring student instructional response, is essential in identifying Specific Learning Disability (SLD). Students who struggle to learn mathematics need evidence-based instructional practices matched to their stage of learning within the instructional hierarchy, along with accommodations that support their unique needs. Good math instruction remains effective regardless of a student's label. Data-based decision-making intensifies as students show greater need.

The Importance of Early Intervention

Research indicates that prevention activities at preschool, kindergarten, or first grade can significantly improve math performance. For example, tutoring programs in first grade have demonstrated substantial improvements in computation, concepts, applications, and story problems. However, students are not always universally responsive, and some may continue to manifest severe mathematics deficits.

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Core Principles of Effective Math Intervention

Several principles guide effective math intervention for students with learning disabilities. These principles include:

Explicit and Systematic Instruction: Interventions should be explicit and systematic, with verbalization of thought processes.
Targeted Instruction: Focus on specific areas of need, such as number combinations or story problems.
Progress Monitoring: Regularly monitor student progress to ensure the intervention is effective.
Intensive Intervention: Provide individualized, demanding, and concentrated instruction.

Specific Learning Disabilities: Dyscalculia and Dysgraphia

Some students experience specific learning disabilities like dyscalculia and dysgraphia that cause them to face deeper challenges in learning math. These challenges go beyond the typical frustrations of learning math, they affect how students process numbers, understand relationships, and communicate. Math learning disabilities aren’t a reflection of intelligence or effort, they are learning disorders that affect a person’s ability to work with numbers. It’s clear that dyscalculia and dysgraphia bring challenges with to learning math, but there are classroom accommodations and strategies that help students find success in math.

Dyscalculia is a math-related learning disability that makes it difficult to understand and process numbers, affecting a student’s math skills and number sense. This often leads to struggles with math facts and basic math. Three to seven percent of all children, adolescents, and adults have dyscalculia. Students with dyscalculia experience difficulty in all areas of mathematics. Basic arithmetic operations and word problems are difficult to process and solve. Students may not understand that “7” is the same thing as the word “seven.” Phone numbers or zip codes are tricky to remember. They find it hard to decide which number is greater or less than another number.

Dysgraphia is a writing-related learning disability that affects reading, writing, and typing skills. This can affect a student’s ability to organize math problems and communicate. One in five children struggle with it. The learning disorder presents itself in math class because the ability to learn, apply, and communicate math skills is affected. Learners with dysgraphia in math class may experience frustrations with place value, fractions, and equations.

Strategies and Interventions for Math Learning Disabilities

Teachers have a variety of dyscalculia accommodations to use in the classroom; some are spelled out specifically for a student with an IEP. A few intervention strategies to try:

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Start with manipulatives because seeing and touching objects help with connections to the concepts.
Talk about math using specific math vocabulary.
Let students draw pictures and make models to illustrate math problems.
Allow extra time for work completion and calculators when appropriate for the skill.
Use edtech resources to provide alternative ways for students to learn and practice concepts.
Provide graph paper to use for keeping numbers in line when solving problems.

Because dysgraphia involves the physical task of writing, evidence-based interventions for dysgraphia eliminate struggles with the writing process itself. Writing accommodations for students with dysgraphia include:

Use pencil grips.
Write on wide-ruled paper or graph paper to help with keeping numbers in line.
Try paper that has raised lines so students feel the spacing.
Get notes from the teacher when possible.
Use computers or tablets.
Write big, and don’t expect perfection. Aim for legibility.
Build muscle strength and control in the hands by squeezing stress balls.

Effective Math Intervention Strategies

Here are some strategies to help educators maximize and accelerate students’ growth, no matter where they are on their mathematical journeys:

Account for the Whole Student: Consider the student's interests, hobbies, and feelings about math to create a connection and make learning more engaging.
Schema-Based Word Problems: Use schemas to help students understand and solve word problems by providing an underlying blueprint or structure.
Peer Tutoring: Pair students to teach math concepts to each other, fostering rich math conversations and deeper understanding.
Targeted Fact Practice: Set aside time for practicing math facts to improve confidence and competency.
Metacognitive Strategies: Encourage students to think critically about their own mathematical thinking and address negative mindsets.
Number Lines: Utilize number lines to model magnitude, arithmetic, and other mathematical concepts, helping students visualize and develop a mental model.
Verbalize Thought Processes: Encourage students to verbalize their thought processes when solving problems to identify specific areas of difficulty.
Fast Draw: Use the Fast Draw strategy to help students with learning disabilities solve math word problems by providing a concrete, step-by-step approach.
Multiple Representations: Present math concepts in different ways to provide students with a variety of mental models and make comprehension more likely.

A Closer Look: Math Flash Intervention

The Math Flash protocol relies on scripts (a) to clarify for tutors how to frame precise, effective explanations; and (b) to provide tutors a concrete model for how to implement the lessons. Tutors study scripts; they do not read them. Math Flash addresses the 200 number combinations with addends and subtrahends from 0 to 9. Math facts are introduced in a deliberate order. For the first two lessons, tutors address facts of + 1 and - 1, using manipulatives and the number line, teaching the commutative property of addition, and emphasizing that this property does not apply to subtraction. In the next two lessons, facts of + 0 and - 0 are introduced, again using manipulatives and the number line.

In lesson seven, students begin learning doubles that run from 0 through 6 (i.e., 0 + 0, 1 + 1, 2 + 2, 3 + 3, 4 + 4, 5 + 5, 6 + 6, 0 - 0, 2 - 1, 4 - 2, 6 - 3, 8 - 4, 10 - 5, 12 - 6). Students work on these doubles using manipulatives and rehearsing doubles chants. At this point in Math Flash, mastery criteria are introduced, and students spend a minimum of one day on each lesson topic (so they do not waste time on facts they already know) and a maximum of four days on each lesson topic (to avoid students getting “stuck” on a topic and losing content coverage). Mastery is assessed in each lesson during computerized practice.

After doubles, students learn facts with + 2 and - 2. Next, students are taught to use two strategies for answering a math fact. They are taught that if they “just know” the math fact, they “pull it out of your head.” However, if they do not know an answer immediately, they count up. Counting-up strategies for addition and subtraction are taught using the number line and their fingers. To count up addition problems, students start with the bigger number and count up the smaller number on their fingers.

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For subtraction counting-up, new math vocabulary is introduced. The minus number is the number directly after the minus sign. The number you start with is the first number in the equation. To count up subtraction problems, students start with the minus number and count up to the number you start with. The answer is the number of fingers used to count up. Because students are now equipped with two strategies for answering math facts, the tutor introduces additional sets of number combinations, beginning with the 5 set. This includes all addition problems equaling 5 and all subtraction problems with 5 as the minuend: 0 + 5, 1 + 4, 2 + 3, 3 + 2, 4 + 1, 5 + 0, 5 - 0, 5 - 1, 5 - 2, 5 - 3, 5 - 4, 5 - 5.

After mastery of the 5 set, students progress to the 6 set, then the 7 set, and so on: 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17-18. The tutor works with the student on each set for a maximum of four days. Between the 12 set and the 13 set, students work on doubles of 7 through 10 (i.e., 7 + 7, 8 + 8, 9 + 9, 10 + 10, 14 - 7, 16 - 8, 18 - 9, 20 -10). Each of the 48 Math Flash daily lessons comprises five activities: flash card warm-up, conceptual and strategic instruction, lesson-specific flash card practice, computerized practice with mastery assessment, and paper-pencil review.

With flash card warm-up, tutors show flash cards, one at a time, for 2 minutes. The cards are a representative sample of the pool of the 200 number combinations addressed in Math Flash. Flash cards answered correctly are placed in a “correct” pile. When students answer incorrectly, the tutor instructs them to “count up.” Students count up to produce the correct answer, but the card is placed in the “incorrect” pile.

During conceptual and strategic instruction, tutors introduce or review concepts and strategies. Throughout, tutors emphasize the two strategies for deriving answers -“Know It or Count Up”- provide practice in counting up, and require students to explain how to count up addition and subtraction problems. After the tutor-led lesson, tutors conduct lesson-specific flash card practice for 1 minute. Lesson-specific flash cards consist of the math facts that are the focus of the day's lesson. (For example, if a lesson focuses on the 5 set, lesson-specific flash cards are facts with addends that sum to 5 and with minuends of 5.) Correctly answered flash cards are placed in the “correct” pile. When students answer incorrectly, tutors require them to “count up.” The cards for which an incorrect answer is given are placed in the “incorrect” pile. After 1 minute, the lesson-specific flash cards answered correctly are counted, but the score is not graphed. On the second, third, and fourth days of a given lesson topic, students get a chance to beat their lesson-specific flash card score. Tutors remind students what their score on the first minute was and encourage them to answer more cards during the upcoming minute. Scoring and feedback are the same as in the first minute.

For the next 7.5 minutes, students complete computerized practice to build fluency with number combinations and to assess their mastery of the day's number combination set. The game goes like this. A math fact flashes on the screen for 1.3 seconds. Students rehearse the fact (e.g., 3 + 2 = 5) while it briefly appears; when the fact disappears, students retype the entire fact (e.g., addends and answer). If the answer is correct, the student hears applause and earns a point. If it is incorrect, the student has another chance to enter the problem correctly. The computer game ends after the student has answered each of the 10 lesson-specific facts correctly twice or after 7.5 minutes. Mastery on the lesson-specific number combinations set is assessed automatically as the student completes the computer game. Immediately after the game ends, the computer provides a report to the tutor. If the student answers each of the 10 lesson-specific facts correctly twice before 7.5 minutes elapses, mastered appears on the screen. If not, review appears on the screen.

Finally, students complete a paper-and-pencil review. The student has 1 minute to complete 15 lesson-specific facts on one side of a paper and then has another minute to complete 15 review facts on the other side of the paper. At the end of 2 minutes, tutors circle correct answers and write the score at the top of the paper. A systematic reinforcement program is also incorporated. Tutors award gold stars following each component of the tutoring session, with the option to withhold stars for inattention or poor effort. At the end of a session, each gold star is placed on a “Star Chart.” Sixteen stars lead to a picture of a treasure box and, when this goal is reached, the student chooses a small prize from a real treasure box.

Additional Resources

Sesame Street in Communities: Bilingual multi-media tools for early childhood education.
99Math: A fun way to practice math facts in the classroom.
AAA Math: Interactive arithmetic lessons with practice exercises.
NRICH: Mathematics resources for children, parents, and teachers.
Virtual Manipulatives for Math | Didax: A great way to enhance at-home learning.
Against All Odds: Inside Statistics: Shows students the relevance of statistics in real-world settings.
Summer Math Challenge: A free, six-week program for practicing math skills.
XtraMath: A nonprofit organization dedicated to math achievement.
Center on Instruction: Research-based resources on instruction.
Mathematics Interventions | Education Northwest: Strategies for struggling learners or students with learning disabilities.
National Council of Teachers of Mathematics: An online hub for the mathematics education community.
Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students | WWC: Recommendations for teaching algebra.
ExploreLearning: Math solutions that target students’ critical learning needs.

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