Mathematics

10 Key Math Practices for All Elementary Schools
This brief resource lists concepts and examples for teaching math based on evidence of effectiveness from high-quality research.
Publication Date: 2017
Publisher: Meadows Center and University of Texas Austin

A Counting-Focused Instructional Treatment to Improve Number Sense: An Exploratory Classroom-Based Intervention Study
This study explored variations in 7- and 8-year-old students’ number sense outcomes as they engaged in a counting focused instructional treatment for differing durations. The study provided preliminary results about an instructional practice, based in numerical cognition theory, for elementary mathematics teachers to facilitate opportunities for students to develop their number sense.
Authors: Jessica Shumway and Patricia Moyer-Packenham
Publication Date: 2019
Publisher: The Mathematics Enthusiast

A Guide for Evaluating the Mathematics Programs Used by Special Education Teachers
This article provides special education teachers with a practical guide for assessing and evaluating the extent to which mathematics programs contain validated principles of explicit mathematics instruction. An example illustrates how teachers can apply the evaluation guide and use the results to address potential instructional shortfalls of mathematics programs.
Authors: Christian Doabler, Jean Louise Smith, Nancy Nelson, Ben Clarke, Tricia Berg, and Hank Fien
Publication Date: 2018
Publisher: Hammill Institute on Disabilities

Arizona Department of Education AT Short Term Loan Library
Arizona Department of Education, Exceptional Student Services works in partnership with Northern Arizona University Institute for Human Development Arizona Technology Access Program to make available at no cost, a wide variety of assistive technology devices, equipment, software and professional development materials to school personnel in order to improve access to assistive technology.
Publisher: Arizona Department of Education

Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades
This practice guide provides evidence-based practices that can help teachers tailor their instructional approaches and/or their mathematics intervention programs to meet the needs of their students.
Authors: Lynn Fuchs, Rebecca Newman-Gonchar, Robin Schumacher, Barbara Dougherty, Nicole Bucka, Kare Karp, John Woodward, Ben Clarke, Nancy Jordan, Russell Gersten, Madhavi Jayanthi, Betsy Keating, and Seth Morgan
Publication Date: March 2021
Publisher: Institute of Education Sciences

Continuing the Journey: Mathematics Learning 2021 and Beyond
This document addresses three key areas that have implications for equitable access to high-quality mathematics teaching and learning. The three areas are a focus on grade-level content; instruction through equitable, effective teaching practices; and planning for advocacy.
Publication Date: July 2021
Publisher: National Council of Teachers of Mathematics and Leadership in Mathematics Education

Developing the Use of Visual Representations in the Primary Classroom
This report outlines the research on using visual representations of mathematical ideas in the classroom and provides the design of the project in terms of the training for teachers and also in terms of measuring the outcomes of the project. The results of the project are presented with the conclusions that are drawn from the project. The final section of this report looks at the results of the external evaluation carried out for the project.
Authors: Patrick Barmby, David Bolden, Stephanie Raine, and Lynn Thompson
Publication Date: November 2019
Publisher: Nuffield Foundation

Effective Word-Problem Instruction Using Schemas to Facilitate Mathematical Reasoning
This article explains schema instruction can be a powerful tool for helping students understand and solve word problems. Schema instruction facilitates mathematical reasoning by helping students understand the underlying structures within word problems that will be used across grade levels and with whole and rational numbers. Many examples are provided.
Authors: Sarah Powell and Lynn Fuchs
Publication Date: 2018
Publisher: TEACHING Exceptional Children

Effects of a Word-Problem Intervention on Word-Problem Language Features for Third-Grade Students with Mathematics Difficulty
This study indicates to adequately prepare students with or at-risk for learning disabilities in mathematics for the language demands presented within word problems, students benefit from explicit modeling and practice related to identifying irrelevant information and providing word-problem labels.
Author: Sarah Powell, Elizabeth Stevens, and Katherine Berry
Publication Date: 2019
Publisher: Learning Disabilities: A Multidisciplinary Journal

High-Quality Mathematics Instruction: What Teachers Should Know
This IRIS Center module describes the components of high-quality mathematics instruction: a standards-based curriculum and evidence-based practices. It highlights several evidence-based practices and other classroom practices that teachers can use to teach mathematics.
Publication Date: 2022
Publisher: Vanderbilt University

How to Use Retrieval Practice to Improve Learning
Established by nearly 100 years of research, retrieval practice is a simple learning technique that is easy to implement, with lasting results. This guide discusses how to use retrieval practice to improve learning.
Authors: Pooja Agarwal, Henry Roediger, Mark McDaniel, and Kathleen McDermott
Publication Date: 2020
Publisher: Washington State in St. Louis

Improving Mathematical Problem Solving in Grades 4 Through 8
This practice guide offers five recommendations that provide teachers with a coherent approach for regularly incorporating problem solving into their classroom instruction to achieve this end. It presents evidence-based suggestions for putting each recommendation into practice and describes roadblocks that may be encountered, as well as possible solutions.
Authors: John Woodward, Sybilla Beckmann, Mark Driscoll, Megan Franke, Patricia Herzig, Asha Jitendra, Kenneth Koedinger, and Philip Ogbuehi
Publication Date: 2018
Publisher: Institute of Education Sciences

Intensive Interventions in Mathematics
Intensive intervention is an individualized, demanding, and concentrated approach to instruction. This article presents the evidence-based elements of intensive intervention that teachers should consider when planning for, implementing, and monitoring intensive intervention in mathematics.
Authors: Sarah Powell and Lynn Fuchs
Publication Date: 2015
Publisher: Learning Disabilities Research and Practice

Interleaved Mathematics Practice Giving Students a Chance to Learn What They Need to Know
This guide describes interleaved practice, a learning method that is backed by science. The method is easy to use and does not require teachers to change how they teach. Students can use it in class or at home and with or without computers.
Authors: Doug Rohrer, Robert Dedrick, and Pooja Agarwal
Publication Date: 2017
Publisher: University of South Florida

Interleaving in Math A Research-Based Strategy to Boost Learning
This article discusses how teachers can ensure students are learning math and improving their skills in the short term and the long term with interleaving, the simple strategy of mixing up concepts to be learned, can increase math learning.
Authors: Pooja Agarwal and Anne Agostinelli
Publication Date: Spring 2020
Publisher: American Educator

Principles for Designing Intervention in Mathematics
The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics.
Publication Date: 2016
Publisher: National Center on Intensive Intervention

Retrieval Practice Consistently Benefits Student Learning: a Systematic Review of Applied Research in Schools and Classrooms
This review makes eight recommendations for future research and provides educators with a better understanding of the robust benefits of retrieval practice across a range of school and classroom settings.
Authors: Pooja Agarwal, Ludmila Nunes, and Janell Blunt
Publication Date: March 2021
Publisher: Educational Psychology Review

School Accommodation
This webpage lists strategies to teach students with a math disability, characteristics of learners with a math disability, and instructional strategies to support those students.
Author: Renee Newman
Publication Date: February 2020
Publisher: Dyscalculia.org

Specific Learning Disability in Mathematics: A Comprehensive Review
This article reviews the changing terminology for specific learning disabilities in math and describes the emerging genetics and neuroimaging studies that relate to individuals with math disability. It discusses the importance to maintain a developmental perspective, as presentation changes with age, instruction, and the different models of identification. \ Newer directions in behavioral, educational, and novel interventions are described.
Authors: Neelkamal Soares, Teresa Evans, Dilip Patel
Publication Date: January 2018
Publisher: Translational Pediatrics

Strategies and Interventions to Support Students with Mathematics Disabilities
This document provides an overview of strategies and resources to support students with, or at-risk for, mathematics learning disabilities.
Authors: Brittany Hott, Laura Isbell, and Teresa Oettinger Montani
Publication Date: December 2014
Publisher: Council for Learning Disabilities

Strategies to Improve All Students’ Mathematics Learning and Achievement
This series of articles cover reflecting on the achievement gap, providing key characteristics of effective diversity training for teachers, building on strengths of a kindergarten student, providing high quality math instruction for all, supporting English learners in the mathematics classroom, and helping children from low-income communities become young mathematicians.
Authors: Courtney Arthur, Eden Badertscher, Paul Goldenberg, Babette Moeller, Matt McLeod, Johannah Nikula, and Kristen Reed
Publication Date: 2017
Publisher: Education Development Center

Taking the Guesswork Out of Locating Evidence-Based Mathematics Practices for Diverse Learners
This paper provides guidance to educators seeking out the latest scientifically based research to improve the likelihood of improving mathematics performance for students with mathematics disabilities and to give teachers a degree of confidence on the effectiveness of their instruction.
Authors: Elizabeth Hughes, Sarah Powell, Erica Lembke, and T. Chris Riley-Tillman
Publication Date: 2016
Publisher: Learning Disabilities Research and Practice

Teaching Math to Young Children
This practice guide provides five recommendations for teaching math to children in preschool, prekindergarten, and kindergarten. Each recommendation includes implementation steps and solutions for common roadblocks. The recommendations also summarize and rate supporting evidence.
Authors: Douglas Frye, Arthur Baroody, Margaret Burchinal, Sharon Carver, Nancy Jordan, and Judy McDowell
Publication Date: November 2013
Publisher: Institute of Education Science

Teaching with Accessible Math
This webpage introduces text-to-speech technologies that are becoming smarter and more capable of interpreting math notation accurately to support access and understanding. Many of the tools mentioned on this page also provide multiple options for creating math notation: you can type it, speak it, or even draw it.
Publisher: National Center on Accessible Educational Materials

The UDL Guidelines
The UDL Guidelines are a tool used in the implementation of Universal Design for Learning. These guidelines offer a set of concrete suggestions that can be applied to any discipline or domain to ensure that all learners can access and participate in meaningful, challenging learning opportunities.
Publication Date: 2018 Publisher: CAST

Using 4 Learner-Centered Routines to Build Positive Math Identity in Equitable Classrooms
This article focuses on four learner-centered routines: Turn and Talks, Stop and Jots, Step Backs, and Quick Writes. It explores how these four routines can be used to foster a positive math identity in students by creating space for voice, agency, and actually doing mathematics.
Authors: Laurie Speranzo and Kristin Klingensmith
Publication Date: December 2020
Publisher: Institute for Learning