# Math

## Common Characteristics of Students with a Mathematics Learning Disability

Though every learner is unique, students with a mathematics learning disability typically have a number of characteristics in common:

• Difficulty processing information; an underdeveloped sense of how to apply strategies.

• Difficulty identifying the important information in mathematics problems, especially in word problems.

• Low motivation; passive learners; attribute successes and failures to external, uncontrollable factors (e.g., luck).

• Problem maintaining attention, a tendency to focus on irrelevant details.

• Poor reasoning and problem-solving skills.

• A difficulty with self-monitoring and self-regulation during problem-solving; impulsive.

• Deficits in the areas of basic math facts and computational skills.

• Memory and vocabulary difficulties.

• Weak visual/ spatial representational skills.

The Iris Center Peabody College Vanderbilt University

The information and resources below address many of the issues that are listed for students with mathematics learning disabilities. They are based on the recommendations made by The Center on Instruction (COI) in a document titled, *Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics A Guide for Teachers*. COI was funded by the U.S. Department of Education to support the 16 Regional Comprehensive Centers as they helped state education leaders raise student achievement, close achievement gaps, and improve teaching and learning for all students in their state.

To read the document in full, click on the image below.

## Math Resources

**Visually Represent Information**

Visual representations are ways to symbolize, describe and refer to a mathematical idea. They are used to understand, develop, and communicate about mathematics. Examples include graphs and diagrams, tables and grids, videos, concrete models, physical and virtual manipulatives, and pictures. Representations are thinking tools for explaining and doing mathematics.

MathVIDS is an interactive website for teachers who are teaching mathematics to struggling learners made possible through funding by the Virginia Department of Education. The CRA approach is highlighted here.

Doing What Works helps educators understand and use research-based practices.The following address the concrete-representational-abstract (CRA) approach for instruction.

The book below can be found in the lending library at the T/TAC at Virginia Tech. Click on the book to see details.

This document from Bemidji Area Schools, Independent School 31 in Bemidji, MN, has a table suggesting manipulatives to use based on math concept as well as a student observation sheet for progress monitoring and an integrity check sheet for the teacher.

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and coherent evidence-based recommendations. Recommendation 5 addresses opportunities for students to work with visual representations.

This website is created by teachers to provide an economical resource for everyone wishing to improve their practice in teaching elementary mathematics. This page addresses the concrete-representational-abstract approach.

Hands-On Standards Books:

These books contain lessons that detail how to use manipulatives to teach math concepts by grade level.

Math Playground is a popular learning site filled with math games, logic puzzles, step-by-step instructional videos, math practice, and a variety of problem-solving activities. The Thinking Blocks area is a great way to visually represent word problems.

is an upper-elementary online resource that has free online tools for visually representing fractions.

**Explicit Instruction**

To be explicit, concepts need to be clearly explained and the skills modeled without any ambiguity. Language needs to be concise and focused on the skill and concept. This needs to include high-level interaction between the teacher and student as they progress through the “I do, we do, you do” stages of explicit instruction.

Anita Archer is nationally recognized as an expert in explicit instruction. Below is a link to her book from the lending library at the T/TAC at Virginia Tech as well as a video example from an 8th-grade geometry vocabulary lesson.

MathVIDS is an interactive website for teachers who are teaching mathematics to struggling learners made possible through funding by the Virginia Department of Education. This Math Vids link explores explicit instruction and contains video examples as well as written information.

Doing What Works helps educators understand and use research-based practices. Below is a link to a video example additional resources.

The Iris Center is funded by the U.S. Department of Education’s Office of Special Education Programs (OSEP). The following information about explicit instruction comes from the module called “High-Quality Mathematics Instruction:What Teachers Should Know”

**Multiple Instructional Examples**

Teachers need to spend some time planning their mathematics instruction, particularly focusing on selecting and sequencing their instructional examples. The goal is to select a range of multiple examples of a problem type. The underlying intent is to expose students to many of the possible variations and at the same time highlight the common but critical features of seemingly disparate problems. Multiple examples can be presented in a specified sequence or pattern such as concrete to abstract, easy to hard, and simple to complex.

Doing What Works helps educators understand and use research-based practices. The first image below will take you to a video explaining alternating worked examples with examples, also known as interleaved worked examples. The second image takes you to the Doing What Works resource page. Type “alternating worked examples” in the search bar for additional resources

This guide explains the research to support how and why to use interleaved mathematics practices.

Edutopia is funded by the George Lucas Educational Foundation created to identify and spread evidence-based approaches to help K-12 students learn better. The image below links to multiple examples.

**Verbalize Decisions and Solutions**

Encouraging students to verbalize, or think-aloud, their decisions and solutions to a math problem is an essential aspect of scaffolded instruction (Palincsar, 1986). Many students with learning disabilities are impulsive behaviorally and when faced with multistep problems frequently attempt to solve the problems by randomly combining numbers rather than implementing a solution strategy step-by-step. Verbalization may help to anchor skills and strategies both behaviorally and mathematically. Verbalizing steps in problem-solving may address students’ impulsivity directly, thus suggesting that verbalization may facilitate students’ self-regulation during problem-solving.

### Talk/Think Aloud Resource:

Power Up What Works has customizable resources to improve teaching and learning for struggling students and those with disabilities: teaching strategies supported by technology, technology use in schools and classrooms and Universal Design for Learning (UDL) and differentiated instruction. This link has a presentation about Think Aloud Strategy.

The NYC Department of Education created resources to provide summaries of promising practices to improve student outcomes for use by professional learning communities. This document specifically summarizes Math Think Aloud.

**Solve Problems Using Multiple/Heuristic Strategies**

A heuristic is a method or strategy that exemplifies a generic approach to solving a problem. Using heuristics shows some promise with students with learning disabilities. Multiple/heuristic strategy instruction has been used in addressing computational skills, problem-solving, and fractions.

The Iris Center is funded by the U.S. Department of Education’s Office of Special Education Programs (OSEP). The following comes from the module High-Quality Mathematics Instruction: What Teachers Should Know and contains information about comparing multiple solutions.

Edutopia is funded by the George Lucas Educational Foundation created to identify and spread evidence-based approaches to help K-12 students learn better. The page below has 2 examples of using multiple examples.

**Provide peer-assisted instruction to students**

Students with LD sometimes receive some type of peer assistance or one-on-one tutoring in areas in which they need help. In the newer within-classroom approach, two students in the same grade tutor each other. In many cases, a higher performing student is strategically placed with a lower performing student but typically both students work in both roles: tutor (provides the tutoring) and tutee (receives the tutoring).

MathVIDS is an interactive website for teachers who are teaching mathematics to struggling learners made possible through funding by the Virginia Department of Education. This MathVIDS link explains why and how to use Structured Peer Tutoring.

The Access Center was a national technical assistance center funded by the Office of Special Education Programs (OSEP) within the Department of Education. This link below gives detailed examples of peer tutoring.

TES, formerly known as the Times Educational Supplement, is a weekly UK publication aimed primarily at school teachers in the UK. The link below gives an overview of peer tutoring, or paired mathematics. There is a link to a document called Learning Together in Mathematics that goes into detail about the role of the tutor and how to set up meaningful peer tutoring.

**Vocabulary**

Vocabulary is not listed in The Center on Instruction (COI) document Mathematics Instruction for Students with Learning Disabilities or Difficulty Learning Mathematics A Guide for Teachers. But extensive information exists about the importance of vocabulary instruction for students with disabilities. Below are articles to explain the importance of vocabulary as well as resources for instruction:

*“Why Are There So Many Words in Math?”: Planning for Content-Area Vocabulary Instruction*

*What’s the Big Deal About Vocabulary?*

Follow the Virginia Department of Education link below to go to vocabulary word wall cards

**Other**

### Here are some additional resources about evidence strategies for math instruction:

Below is a link to modules that focus on teaching students with math disabilities:

The Institute of Education Science (IES) gather research to ensure the use if evidence-based practices. The guide below explains retrieval practice and how and why it improves learning:

The Iris Center is funded by the U.S. Department of Education’s Office of Special Education Programs (OSEP). The following comes from the module High-Quality Mathematics Instruction: What Teachers Should Know and contains information about comparing multiple solutions.

The Quantile Framework for Mathematics site will allow you to search for a lesson based on the SOL. It will offer lessons for prerequisite skills, SOL skills, as well as extension skills using the quantile level of the student.

### Growth Mindset Resources:

### Instruction:

### ESS:

### Virtual Manipulatives:

### Evidence-Based Programs: