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How do UDL Principles Apply to the Design of the Cockpit of a Fighter Jet and a Math Lesson?

First, let's provide a bit of context. In this popular Ted Talk video , best-selling author and Harvard professor Todd Rose tells the story of a problem the United States Air Force faced in the 1950s. Despite having good pilots and better planes, they were getting poor results. After ruling out other possible causes of declining performance, such as the pilots themselves, the technology, and the flight instructors, the air force realized that the problem was with the cockpit in its fighter jets. It didn't fit the pilots.

The thinking behind the existing configuration was that a cockpit designed to fit the average-size pilot would accommodate most pilots. As part of the troubleshooting effort, a researcher measured 10 different body dimensions (height, shoulders, torso, etc.) of over 4,000 pilots to determine how many pilots had average measurements of all 10 dimensions. The air force discovered that no one had average measurements of all dimensions; there was no average pilot. In fact, every pilot had what they described as a "jagged size profile"-some measurements were average, some above, some below. As a result, the air force banned designing for the average, instead requiring companies that built the planes to "design to the edges" of pilots' dimensions, ensuring that the cockpit would fit the variability of pilots' sizes. The result was a cockpit that accommodates all pilots by providing flexible components such as adjustable seats.

Just as the air force discovered that there is no average-size pilot, neuroscience research tells us that there is no average learner. As an article by CAST , a nonprofit education research and development organization, explains, no two brains are alike (2018a). Therefore, instruction should not be designed for the "average learner." Instead, instruction should provide flexible options-just like the adjustable seat in the cockpit of a fighter jet. CAST's Universal Design for Learning Guidelines (2018b), help educators design instruction that proactively addresses barriers to learning by designing for the predictable variability of all learners.

Why is the Universal Design for Learning Important?

UDL is a framework based on current research from cognitive neuroscience that recognizes learner variance as the norm rather than the exception. The guiding principles of the UDL framework are based on the three primary networks of the brain.

Brain Networks

Guiding Principle

The Affective networks

Provide multiple means of Engagement (the why of learning)

The Recognition networks

Provide multiple means of Representation (the what of learning)

The Strategic networks

Provide multiple means of Action & Expression (the how of learning)

(Image Source: CAST)

According to CAST, the UDL framework "offers an overarching approach to designing meaningful learning opportunities that address learner variability and suggests purposeful, proactive attention to the design of goals, assessments, methods, and materials." ( n.d. ) The UDL Guidelines provide a set of concrete suggestions organized by the three guiding principles: Engagement, Representation, and Action & Expression. Educators can use the UDL Guidelines to evaluate their goals, assessments, methods, and materials and identify potential barriers to student learning. Teachers can then proactively design instruction that maintains desirable challenges and eliminates unnecessary barriers. Here is an overview of each guiding principle and its instructional implications.

1. . Use a variety of methods to engage students. For example, provide choice, address student interest, and arrange for students to monitor their own learning, such as with goal setting, self-assessment, and reflection.Provide Multiple Means of Engagement : Learners differ markedly in the ways in which they can be engaged or motivated to learn

2. . Use a variety of strategies, instructional tools, and methods when presenting information and content.Provide Multiple Means of Representation : Learners differ in the ways they perceive and comprehend information that is presented to them

3. Provide Multiple Means of Action & Expression: Learners differ in the ways they can navigate a learning environment and express what they know . Offer students a variety of strategies and instructional tools and allow for multiple ways to demonstrate new understanding.

Read more about how the UDL principles can be applied to all subjects, including math, science, and English language arts.
How do You Provide Multiple Means of Engagement in Math?

The following examples show how Eureka Math ² lesson s apply the UDL principle of Engagement to various lesson components.

Provide Options for Recruiting Interest

According to CAST, "individuals are engaged by information and activities that are relevant and valuable to their interests and goals." ( UDL Guidelines, Engagement, Checkpoint 7.2 ) In this grade 1 lesson, students collect data about their preferences and make a graph by representing each student choice with a cube on a number path. Sharing favorite activities through a class survey engages students by tapping into their interests and experiences. A margin note encourages teachers to tailor the sample questions to match student interests. Adjusting questions to make them more meaningful to students provides options for recruiting interest by personalizing and contextualizing the content to learners' lives.

Provide Options for Sustaining Effort and Persistence

According to CAST, " feedback that orients students toward mastery and that emphasizes the role of effort and practice rather than 'intelligence' or inherent 'ability' is an important factor in guiding students toward successful long-term habits of mind. " ( UDL Guidelines, Engagement, Research for Checkpoint 8.4 ) In this grade 7 lesson, students work on a problem with a partner by writing the expression as an equivalent addition expression and decomposing the mixed number. A margin note prompts teachers to provide feedback that focuses on students' application of strategies as they work. Offering timely, relevant, consequential, practical feedback and asking students to explain their choices provides options for sustaining effort and persistence .

Provide Options for Self-Regulation

According to CAST, "the ability to self-regulate ... is a critical aspect of human development. While many individuals develop self-regulatory skills on their own, many others have significant difficulties in developing these skills." ( UDL Guidelines, Engagement, Guideline 9 ) In this grade 2 lesson, students share strategies and reason about ways they can combine addends to make an easier problem. Students make connections between the different solutions and their own work, and then they try a strategy one of their classmates used. A margin note encourages teachers to provide feedback that promotes students' belief in themselves. Encouraging students to consider a peer's success and connecting this to the potential for their own success provides options for self-regulation by strengthening students' belief in their own abilities.

How do You Provide Multiple Means of Representation in Math?

The following examples show how Eureka Math² lessons apply the UDL principle of Representation to various lesson components.

Provide Options for Perception

According to CAST, "information conveyed solely through sound is not equally accessible to all learners and is especially inaccessible for learners with hearing disabilities, for learners who need more time to process information, or for learners who have memory difficulties... . To ensure that all learners have access to learning, options should be available for any information, including emphasis, presented aurally." ( UDL Guidelines, Representation, Checkpoint 2 ) In this grade 8 lesson, students factor and use the properties of exponents to simplify numerical expressions and write exponential expressions by using the fewest number of prime bases. A margin note encourages teachers to activate students' prior knowledge of common squares and cubes. Additionally, the margin note suggests displaying the examples in a chart for student reference. Posting the chart provides options for perception by offering alternatives for auditory information and presenting the information in more than one mode.

Provide Options for Language and Symbols

According to CAST, " c lassroom materials are often dominated by information in text. But text is a weak format for presenting many concepts and for explicating most processes. Furthermore, text is a particularly weak form of presentation for learners who have text- or language-related disabilities. " ( UDL Guidelines, Representation, Checkpoint 2.5 ) In this example from a grade 3 lesson , students use tape diagrams to make sense of and solve word problems about liquid volume . Working with a partner, s tudents identify what each part of the tape diagram represents. Then students discuss how the tape diagram helps them find the solution path. Presenting the text-based word problem paired with the tape diagram , which is an example of a visual representation , provide s options for language and symbols by making the word problem more comprehensible . In addition , visual representation s are an example of an evidence-based practice , h elp ful for all students, particularly students with learning disabilities.

Provide Options for Comprehension

According to CAST, " l earning can be  cognitively inaccessible  when it requires the ability to select and prioritize among many elements or sources, and where there are no options for individuals who differ in that capability. One of the most effective ways to make information more accessible is to provide explicit cues or prompts that assist individuals in attending to those features that matter most while avoiding those that matter least . " ( UDL Guidelines, Representation, Research for Checkpoint 3.2 ) In this Algebra I lesson, students use a graphic organizer to highlight the relationships associated with the addition property of inequality and the multiplication property of inequality. Throughout the lesson , students complete each section of the graphic organizer by adding examples . Graphic organizers are another example of the evidence-based practice of using visual representations (IRIS Center 2021) , as they p rovide o ptions for c omprehension by emphasizing key ideas and relationships.

How do You Provide Multiple Means of Action & Expression in Math?

The following examples show how Eureka Math² lessons apply the UDL principle of Representation to various lesson components.

Provide Options for Physical Action

According to CAST , " l earners differ widely in their capacity to navigate their physical environment. To reduce barriers to learning that would be introduced by the motor demands of a task, provide alternative means for response, selection, and composition . " UDL Guidelines, Action & Expression, Checkpoint 4.1 ( provides options for physical action by suggesting alternative ways students can complete their arrays. ) In this grade 3 lesson, students transition from concrete to pictorial representations of the break apart and distribute strategy with arrays by tracing and shading a large array on grid paper. Margin notes in this lesson suggest offer ing alternative materials to minimize fine motor challenge s presented by tracing and shading . Teachers are encouraged to offer square-inch tiles and inch grid paper for completing the array. O ffer ing square-inch tiles and inch grid paper

Provide Options for Expression & Communication

According to CAST, " t here is a tendency in schooling to focus on traditional tools rather than contemporary ones. This tendency has several liabilities: 1) it does not prepare learners for their future; 2) it limits the range of content and teaching methods that can be implemented; 3) it restricts learners ' ability to express knowledge about content (assessment); and, most importantly, 4) it constricts the kinds of learners who can be successful . Current media tools provide a more flexible and accessible toolkit with which learners can more successfully take part in their learning and articulate what they know. " ( UDL Guidelines, Action & Expression, Checkpoint 5.2 ) In this example from Algebra I , s tudents study an animation of a person jumping on an in-ground trampoline and sketch a graph that models the elevation of the jumper as a function of time. S tudents use dynamic features of the digital platform to show key features of functions and their graphs and participate in discussions informally describing those key features. Using the digital tool provides options for expression and communication by allowing students to show what they know in a flexible and nontraditional way.

Provide Options for Executive Functions

According to CAST, " l earning can be inaccessible when it requires planning and strategy development, and where there are no options for individuals who differ in such  executive functions . Young children, older students in a new domain, or any student with one of the disabilities that compromise executive functions (e.g. , ADHD, ADD, Autism Spectrum Disorders) often are weak at planning and strategy development and impulsive trial and error dominates their learning. " ( UDL Guidelines, Action & Expression, Research for Checkpoint 6.2 ) In this example from a grade 5 lesson, students work with a partner to draw a model to solve a division problem involving fractions . Then the class discusses the reasonableness of their quotient. A margin note prompts teacher s to provide guiding questions to support students in planning, monitoring, and evaluating their progress . The guiding questions provide options for executive functions by supporting students with planning, strategizing, and metacognitive thinking as they consider what worked well and what they may do differently next time .

What is the Importance of Universal Design for Learning in Math

So back to our original question, how is a lessons provide options to address the variability of learners. Rather than designing for the illusory average student, Great MindsEureka Math² lesson like the cockpit of a fighter jet? Just as the United States Air Force provided options to address the variability of their pilots, Eureka Math² average ® prioritizes learner variability, recognizing that is a myth and variability is the norm.

Although the concept of UDL has roots in special education, UDL is for all students. When instruction is designed to meet the needs of the widest range of learners, all students benefit. This is especially important since, according to the National Center for Learning Disabilities report The State of Learning Disabilities: Understanding the 1 in 5 , "1 in 5 children in the U.S. have learning and attention issues, but only a small subset are formally identified with a disability in school ... while millions of children with learning and attention issues are not formally identified." The report recommends policy changes, one of which is to "drive innovation for effective teaching and learning." A key aspect identified to accomplish this change is to use UDL to reach every student. As the report states, "Children with learning and attention issues are as smart as their peers and, with the right support, can achieve at high levels" (Horowitz, Rawe, and Whittaker 2017).

Learning Acceleration for All: Planning for the Next 3-5 Years , a recent report by TNTP , an education nonprofit, cautions school systems to recognize and address pitfalls that may hinder their long-term learning acceleration strategy. One of these pitfalls is "centering on the mythical "average" student rather than considering how to plan for high expectations for a diverse set of learners." TNTP recommends that school systems work "in partnership with parents, teachers, students, and community partners to develop a comprehensive education support plan that will provide equitably high-quality academic experiences to all of [their] students." A critical component of a high-quality academic experience for students is a high-quality curriculum that is explicitly designed to attend to the needs of all learners in its instructional design, not just the "average" learner because the average does not exist. Each student arrives to school with their own strengths, areas for growth, and approach to engaging with academic content. School systems can be confident when selecting Eureka Math ² that the curriculum materials were designed to address learner variability from the outset.

Interested in learning more about designing UDL-aligned lessons? Check out these planning questions our writers used to plan for learner variability.

Download the Article as a Free PDF

Great Minds

Great Minds PBC is a public benefit corporation and a subsidiary of Great Minds, a nonprofit organization. A group of education leaders founded Great Minds® in 2007 to advocate for a more content-rich, comprehensive education for all children. In pursuit of that mission, Great Minds brings together teachers and scholars to create exemplary instructional materials that provide joyful rigor to learning, spark and reward curiosity, and impart knowledge with equal parts delight.

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How To Support Math Students With The Universal Design For Learning Principles

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Introducing Eureka Math2 - an exponentially greater math curriculum, written to unlock greatness for every student.

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EF+Math contributes to the broad education and learning sciences fields by publishing research,reports, conference proceedings, and other content on the topics of the relationship between executive function skills and math learning, equity, and inclusive research and development. Discover a selection of EF+Math's resources from across our work. Our entire collection of resources is in development in AERDF's .

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EF+Math contributes to the broad education and learning sciences fields by publishing research,reports, conference proceedings, and other content on the topics of the relationship between executive function skills and math learning, equity, and inclusive research and development. Discover a selection of EF+Math's resources from across our work.

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress. The tools are relevant to any curriculum that seeks to deepen students' understanding of mathematical concepts and develop their ability to apply that knowledge to non-routine problems.

More about the Math Assessment Project

100 lessons for formative assessment, some focused on developing math concepts, others on solving non-routine problems. A Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time.

A set of 94 exemplar summative assessment tasks to illustrate the range of performance goals required by CCSSM. The tasks come with scoring rubrics and examples of scored student work.

Complete summative test forms and rubrics designed to help teachers and students monitor their progress using a range of task types similar to the 'Tasks' section.

5 Prototype modules that encourage groups of teachers to explore the practical and pedagogical concepts behind the materials, such as formative assessment, collaborative learning and the use of unstructured problems.

The Teaching for Robust Understanding of Mathematics (TRU Math) suite is a set of tools with applications in Professional Development and research based around a framework for characterizing powerful learning environments.

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The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students' mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress.

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Fraction Division Support for EL Students

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Fraction Division Support for EL Students

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The Three Reads strategy is a language access support that can facilitate sense-making of mathematics text such as word problems during the launch or sense-making when introducing a new task. It consists of three structured readings of a mathematics task with a different purpose and focus during each read. It facilitates the process of understanding the meaning in word problems, thus boosting access for English learners, and in the ADSEL lessons it specifically supports students in linking task information to their work on drawing or analyzing a diagram.

Rationale. Reading a word problem requires a different approach than reading prose, in part because the purpose (e.g., the question to be answered) typically does not appear until the end of the passage. Since the reader does not know the purpose until the end, it can be difficult to determine the importance of the information within the text. In addition, math problem text is often dense and may include unfamiliar academic language, complex long sentences, or unfamiliar ways to express relationships. Reading it more than once may strengthen students' understanding of a text. A focus on the mathematical context, rather than the specific vocabulary, grammar, or sentence structure, also supports students in building upon the mathematical skills and concepts they already know.

Implementation. Although the Three Reads strategy can be successfully used individually or quietly, repeated reading out loud in a small group or whole class provides additional support to ELs by providing opportunities to hear and see the language multiple times. In each lesson, we present the Three Reads Strategy on the first page of the lesson, and there is a prompt to complete after each read focused on the purpose for that read:

The Gardener's Flower Pots

1. The first read is to get a sense of context in order to understand the "story" or context of the text. Students should not focus on the quantities or relationships between them during this reading. Responses should be more like a title for the problem, such as "Ice cream," "Sharing ice cream," "flowerpots and soil". Students complete the sentence, "The problem is about....".

2. The second read is to discern the question or the goal of the task. The problem is read again in its entirety, looking specifically for information about what needs to be answered, or if there is no question in the task then what the students are supposed to do. Students complete the sentence starter, "I need to find out...". Focus students on what they need to find out for a final answer, and not just an operation (for example, encourage, "I need to find the number of servings," rather than, "I need to subtract/divide").

3. The third read of the text is to gather important information that is needed to solve the problem or achieve the purpose of the task, such as specific quantities and their relationships. Students complete the sentence starter "The important information is...".

After each read, provide students with brief think time to complete the prompt, and then have a couple students share their responses. Having multiple students share allows all students to hear the information and compare it with their ideas and ensures that more ideas are on the table and promotes connections between different ways of phrasing the ideas (e.g., running laps and ran laps). Record students' responses and indicate which pieces of "information" shared for the third read are correct or important to keep in mind before moving on to working on the task.

The information from the third read should be used as students draw a diagram or do the next step in the lesson. In the lessons, we explicitly prompt students, for each task, to draw a diagram that captures the important information (of the third read). This is a critical step that supports students in linking the important information from the task to the mathematical work that students need to do to solve the task. Remind students to reference what they did in the Three Reads as they work on the task individually or with a partner.

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The Three Reads strategy is a language access support that can facilitate sense-making of mathematics text such as word problems during the launch or sense-making when introducing a new task. It consists of three structured readings of a mathematics task with a different purpose and focus during each read.

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Math Teaching Models: Universal Design For Learning

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GAISE Guidelines for Assessment and Instruction in Statistics Education

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GAISE Guidelines for Assessment and Instruction in Statistics Education

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Lots of resources for exploring simulation-based inference, which is an approach to introductory statistics informed by the GAISE guidelines (and UDL best practices)

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Our goal is to provide a discussion forum for those interested in using simulation- and randomization-based inference as a large component of their introductory statistics courses. We will have postings from developers of several curricula, with their insights as to why and how to use these methods. See Overview for more information.

Follow the links below to access these discussion topics:

We look forward to your comments.

Please email Jill VanderStoep <vanderstoepj@hope.edu> or Todd Swanson <swansont@hope.edu> if you have any problems or suggestions for future posts.

This material is based upon work supported by the National Science Foundation under Grant Number DUE-1323210. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Our goal is to provide a discussion forum for those interested in using simulation- and randomization-based inference as a large component of their introductory statistics courses. We will have postings from developers of several curricula, with their insights as to why and how to use these methods. See Overview for more information.

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Exploring the Art and Practice of Statistics Teaching

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Exploring the Art and Practice of Statistics Teaching

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Recent professional development (live webinars and recorded sessions) on GAISE-aligned pedagogy in Statistics.

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Digital version of the card sort activity we did in class.

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Sentence Stems to Build Academic Language

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Sentence Stems to Build Academic Language

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Sentence Stems for Discussing Multiple Representations

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Sentence Stems for Discussing Multiple Representations

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Guide to Designing Your UDL Lesson - updated2 (1)

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How do UDL Principles Apply to the Design of the Cockpit of a Fighter Jet and a Math Lesson?

First, let's provide a bit of context. In this popular Ted Talk video , best-selling author and Harvard professor Todd Rose tells the story of a problem the United States Air Force faced in the 1950s. Despite having good pilots and better planes, they were getting poor results. After ruling out other possible causes of declining performance, such as the pilots themselves, the technology, and the flight instructors, the air force realized that the problem was with the cockpit in its fighter jets. It didn't fit the pilots.

The thinking behind the existing configuration was that a cockpit designed to fit the average-size pilot would accommodate most pilots. As part of the troubleshooting effort, a researcher measured 10 different body dimensions (height, shoulders, torso, etc.) of over 4,000 pilots to determine how many pilots had average measurements of all 10 dimensions. The air force discovered that no one had average measurements of all dimensions; there was no average pilot. In fact, every pilot had what they described as a "jagged size profile"-some measurements were average, some above, some below. As a result, the air force banned designing for the average, instead requiring companies that built the planes to "design to the edges" of pilots' dimensions, ensuring that the cockpit would fit the variability of pilots' sizes. The result was a cockpit that accommodates all pilots by providing flexible components such as adjustable seats.

Just as the air force discovered that there is no average-size pilot, neuroscience research tells us that there is no average learner. As an article by CAST , a nonprofit education research and development organization, explains, no two brains are alike (2018a). Therefore, instruction should not be designed for the "average learner." Instead, instruction should provide flexible options-just like the adjustable seat in the cockpit of a fighter jet. CAST's Universal Design for Learning Guidelines (2018b), help educators design instruction that proactively addresses barriers to learning by designing for the predictable variability of all learners.

Why is the Universal Design for Learning Important?

UDL is a framework based on current research from cognitive neuroscience that recognizes learner variance as the norm rather than the exception. The guiding principles of the UDL framework are based on the three primary networks of the brain.

Brain Networks

Guiding Principle

The Affective networks

Provide multiple means of Engagement (the why of learning)

The Recognition networks

Provide multiple means of Representation (the what of learning)

The Strategic networks

Provide multiple means of Action & Expression (the how of learning)

(Image Source: CAST)

According to CAST, the UDL framework "offers an overarching approach to designing meaningful learning opportunities that address learner variability and suggests purposeful, proactive attention to the design of goals, assessments, methods, and materials." ( n.d. ) The UDL Guidelines provide a set of concrete suggestions organized by the three guiding principles: Engagement, Representation, and Action & Expression. Educators can use the UDL Guidelines to evaluate their goals, assessments, methods, and materials and identify potential barriers to student learning. Teachers can then proactively design instruction that maintains desirable challenges and eliminates unnecessary barriers. Here is an overview of each guiding principle and its instructional implications.

1. . Use a variety of methods to engage students. For example, provide choice, address student interest, and arrange for students to monitor their own learning, such as with goal setting, self-assessment, and reflection.Provide Multiple Means of Engagement : Learners differ markedly in the ways in which they can be engaged or motivated to learn

2. . Use a variety of strategies, instructional tools, and methods when presenting information and content.Provide Multiple Means of Representation : Learners differ in the ways they perceive and comprehend information that is presented to them

3. Provide Multiple Means of Action & Expression: Learners differ in the ways they can navigate a learning environment and express what they know . Offer students a variety of strategies and instructional tools and allow for multiple ways to demonstrate new understanding.

Read more about how the UDL principles can be applied to all subjects, including math, science, and English language arts.
How do You Provide Multiple Means of Engagement in Math?

The following examples show how Eureka Math ² lesson s apply the UDL principle of Engagement to various lesson components.

Provide Options for Recruiting Interest

According to CAST, "individuals are engaged by information and activities that are relevant and valuable to their interests and goals." ( UDL Guidelines, Engagement, Checkpoint 7.2 ) In this grade 1 lesson, students collect data about their preferences and make a graph by representing each student choice with a cube on a number path. Sharing favorite activities through a class survey engages students by tapping into their interests and experiences. A margin note encourages teachers to tailor the sample questions to match student interests. Adjusting questions to make them more meaningful to students provides options for recruiting interest by personalizing and contextualizing the content to learners' lives.

Provide Options for Sustaining Effort and Persistence

According to CAST, " feedback that orients students toward mastery and that emphasizes the role of effort and practice rather than 'intelligence' or inherent 'ability' is an important factor in guiding students toward successful long-term habits of mind. " ( UDL Guidelines, Engagement, Research for Checkpoint 8.4 ) In this grade 7 lesson, students work on a problem with a partner by writing the expression as an equivalent addition expression and decomposing the mixed number. A margin note prompts teachers to provide feedback that focuses on students' application of strategies as they work. Offering timely, relevant, consequential, practical feedback and asking students to explain their choices provides options for sustaining effort and persistence .

Provide Options for Self-Regulation

According to CAST, "the ability to self-regulate ... is a critical aspect of human development. While many individuals develop self-regulatory skills on their own, many others have significant difficulties in developing these skills." ( UDL Guidelines, Engagement, Guideline 9 ) In this grade 2 lesson, students share strategies and reason about ways they can combine addends to make an easier problem. Students make connections between the different solutions and their own work, and then they try a strategy one of their classmates used. A margin note encourages teachers to provide feedback that promotes students' belief in themselves. Encouraging students to consider a peer's success and connecting this to the potential for their own success provides options for self-regulation by strengthening students' belief in their own abilities.

How do You Provide Multiple Means of Representation in Math?

The following examples show how Eureka Math² lessons apply the UDL principle of Representation to various lesson components.

Provide Options for Perception

According to CAST, "information conveyed solely through sound is not equally accessible to all learners and is especially inaccessible for learners with hearing disabilities, for learners who need more time to process information, or for learners who have memory difficulties... . To ensure that all learners have access to learning, options should be available for any information, including emphasis, presented aurally." ( UDL Guidelines, Representation, Checkpoint 2 ) In this grade 8 lesson, students factor and use the properties of exponents to simplify numerical expressions and write exponential expressions by using the fewest number of prime bases. A margin note encourages teachers to activate students' prior knowledge of common squares and cubes. Additionally, the margin note suggests displaying the examples in a chart for student reference. Posting the chart provides options for perception by offering alternatives for auditory information and presenting the information in more than one mode.

Provide Options for Language and Symbols

According to CAST, " c lassroom materials are often dominated by information in text. But text is a weak format for presenting many concepts and for explicating most processes. Furthermore, text is a particularly weak form of presentation for learners who have text- or language-related disabilities. " ( UDL Guidelines, Representation, Checkpoint 2.5 ) In this example from a grade 3 lesson , students use tape diagrams to make sense of and solve word problems about liquid volume . Working with a partner, s tudents identify what each part of the tape diagram represents. Then students discuss how the tape diagram helps them find the solution path. Presenting the text-based word problem paired with the tape diagram , which is an example of a visual representation , provide s options for language and symbols by making the word problem more comprehensible . In addition , visual representation s are an example of an evidence-based practice , h elp ful for all students, particularly students with learning disabilities.

Provide Options for Comprehension

According to CAST, " l earning can be  cognitively inaccessible  when it requires the ability to select and prioritize among many elements or sources, and where there are no options for individuals who differ in that capability. One of the most effective ways to make information more accessible is to provide explicit cues or prompts that assist individuals in attending to those features that matter most while avoiding those that matter least . " ( UDL Guidelines, Representation, Research for Checkpoint 3.2 ) In this Algebra I lesson, students use a graphic organizer to highlight the relationships associated with the addition property of inequality and the multiplication property of inequality. Throughout the lesson , students complete each section of the graphic organizer by adding examples . Graphic organizers are another example of the evidence-based practice of using visual representations (IRIS Center 2021) , as they p rovide o ptions for c omprehension by emphasizing key ideas and relationships.

How do You Provide Multiple Means of Action & Expression in Math?

The following examples show how Eureka Math² lessons apply the UDL principle of Representation to various lesson components.

Provide Options for Physical Action

According to CAST , " l earners differ widely in their capacity to navigate their physical environment. To reduce barriers to learning that would be introduced by the motor demands of a task, provide alternative means for response, selection, and composition . " UDL Guidelines, Action & Expression, Checkpoint 4.1 ( provides options for physical action by suggesting alternative ways students can complete their arrays. ) In this grade 3 lesson, students transition from concrete to pictorial representations of the break apart and distribute strategy with arrays by tracing and shading a large array on grid paper. Margin notes in this lesson suggest offer ing alternative materials to minimize fine motor challenge s presented by tracing and shading . Teachers are encouraged to offer square-inch tiles and inch grid paper for completing the array. O ffer ing square-inch tiles and inch grid paper

Provide Options for Expression & Communication

According to CAST, " t here is a tendency in schooling to focus on traditional tools rather than contemporary ones. This tendency has several liabilities: 1) it does not prepare learners for their future; 2) it limits the range of content and teaching methods that can be implemented; 3) it restricts learners ' ability to express knowledge about content (assessment); and, most importantly, 4) it constricts the kinds of learners who can be successful . Current media tools provide a more flexible and accessible toolkit with which learners can more successfully take part in their learning and articulate what they know. " ( UDL Guidelines, Action & Expression, Checkpoint 5.2 ) In this example from Algebra I , s tudents study an animation of a person jumping on an in-ground trampoline and sketch a graph that models the elevation of the jumper as a function of time. S tudents use dynamic features of the digital platform to show key features of functions and their graphs and participate in discussions informally describing those key features. Using the digital tool provides options for expression and communication by allowing students to show what they know in a flexible and nontraditional way.

Provide Options for Executive Functions

According to CAST, " l earning can be inaccessible when it requires planning and strategy development, and where there are no options for individuals who differ in such  executive functions . Young children, older students in a new domain, or any student with one of the disabilities that compromise executive functions (e.g. , ADHD, ADD, Autism Spectrum Disorders) often are weak at planning and strategy development and impulsive trial and error dominates their learning. " ( UDL Guidelines, Action & Expression, Research for Checkpoint 6.2 ) In this example from a grade 5 lesson, students work with a partner to draw a model to solve a division problem involving fractions . Then the class discusses the reasonableness of their quotient. A margin note prompts teacher s to provide guiding questions to support students in planning, monitoring, and evaluating their progress . The guiding questions provide options for executive functions by supporting students with planning, strategizing, and metacognitive thinking as they consider what worked well and what they may do differently next time .

What is the Importance of Universal Design for Learning in Math

So back to our original question, how is a lessons provide options to address the variability of learners. Rather than designing for the illusory average student, Great MindsEureka Math² lesson like the cockpit of a fighter jet? Just as the United States Air Force provided options to address the variability of their pilots, Eureka Math² average ® prioritizes learner variability, recognizing that is a myth and variability is the norm.

Although the concept of UDL has roots in special education, UDL is for all students. When instruction is designed to meet the needs of the widest range of learners, all students benefit. This is especially important since, according to the National Center for Learning Disabilities report The State of Learning Disabilities: Understanding the 1 in 5 , "1 in 5 children in the U.S. have learning and attention issues, but only a small subset are formally identified with a disability in school ... while millions of children with learning and attention issues are not formally identified." The report recommends policy changes, one of which is to "drive innovation for effective teaching and learning." A key aspect identified to accomplish this change is to use UDL to reach every student. As the report states, "Children with learning and attention issues are as smart as their peers and, with the right support, can achieve at high levels" (Horowitz, Rawe, and Whittaker 2017).

Learning Acceleration for All: Planning for the Next 3-5 Years , a recent report by TNTP , an education nonprofit, cautions school systems to recognize and address pitfalls that may hinder their long-term learning acceleration strategy. One of these pitfalls is "centering on the mythical "average" student rather than considering how to plan for high expectations for a diverse set of learners." TNTP recommends that school systems work "in partnership with parents, teachers, students, and community partners to develop a comprehensive education support plan that will provide equitably high-quality academic experiences to all of [their] students." A critical component of a high-quality academic experience for students is a high-quality curriculum that is explicitly designed to attend to the needs of all learners in its instructional design, not just the "average" learner because the average does not exist. Each student arrives to school with their own strengths, areas for growth, and approach to engaging with academic content. School systems can be confident when selecting Eureka Math ² that the curriculum materials were designed to address learner variability from the outset.

Interested in learning more about designing UDL-aligned lessons? Check out these planning questions our writers used to plan for learner variability.

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Great Minds

Great Minds PBC is a public benefit corporation and a subsidiary of Great Minds, a nonprofit organization. A group of education leaders founded Great Minds® in 2007 to advocate for a more content-rich, comprehensive education for all children. In pursuit of that mission, Great Minds brings together teachers and scholars to create exemplary instructional materials that provide joyful rigor to learning, spark and reward curiosity, and impart knowledge with equal parts delight.

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How To Support Math Students With The Universal Design For Learning Principles

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Introducing Eureka Math2 - an exponentially greater math curriculum, written to unlock greatness for every student.

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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American Association of University Women - Equity for All

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American Association of University Women - Equity for All

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This is a great infographic about the disproportionate participation of women in STEM.

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When it comes to ‘innate’ abilities, there’s no evidence whatsoever to support the notion that boys are better at math and science. Yet these limiting stereotypes persist.

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The Future of STEM Depends on Diversity | Nicole Cabrera Salazar | TEDxGeorgiaStateU

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The New Teacher Project - The Opportunity Myth

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The New Teacher Project - The Opportunity Myth

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Infographic raising important ideas around equity and access in public schools.

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To do this, we collected nearly 30,000 in-the-moment student surveys. Using a technology that prompted students in grades six through 12 to answer a few questions at random times during class, we captured a snapshot of their real-time reactions to school. We also surveyed third through fifth graders during the last five minutes of class, and found that elementary students were just as capable as their older schoolmates of providing rich and telling insight into their lives at school.

Across our five partner school systems, we also observed nearly a thousand full-length lessons at all grade levels from K-12, and reviewed almost 5,000 assignments and more than 20,000 individual student work samples. We visited each participating school daily for a week straight at three points in the year, which gave us the chance to see the same teachers and students at the beginning, middle, and end of their time together (and offered a much more comprehensive lens on the learning environment than a single day's lesson could have). These classrooms were not substantially different than the others in their districts, and they represented a wide range: those with new teachers and veterans; those at all age levels; a diverse range of subjects; mixed-ability classes and tracked ones. Four of these school systems were located in states that use standards aligned to the Common Core State Standards; one was not.

To assess the quality of content students worked on, we looked at four elements of every assignment: (1) whether the content in the assignments was aligned to relevant grade-level academic standards; (2) whether the assignments gave students the chance to engage in important content-specific practices, like citing evidence from rigorous texts in literacy, or discussing mathematical ideas using precise mathematical language; (3) whether the assignments gave students a chance to learn relevant content that built their knowledge of the world or helped them see how what they were learning could be applied in the real world; and (4) student performance on both the assignments themselves and against the bar for their grade-level standards.

To study instruction, we observed full-length class periods and assessed (1) whether students were doing what they were asked; (2) whether they were being asked to work on grade-level content; and (3) whether teachers were using instructional practices that gave students the chance to do most of the thinking in the lesson.

We surveyed teachers to capture their knowledge of grade-level standards, their opinions on those standards, and their beliefs about their classroom practices and their students' abilities. We conducted focus groups with nearly 100 teachers and interviewed 24 school leaders at multiple times throughout the year. And we assessed a large set of extant data provided to us by our partner districts on course access, enrollment policies, and district policies on curriculum adoption, among others.

We hypothesized that students' experiences of school were influenced by a confluence of factors-among them, the quality of the work they were doing, the instruction they received, and the expectations of their teachers-and that those factors would interact to have an impact on their academic growth. Taken together with students' in-the-moment survey responses, we were able to triangulate students' perspectives with the classes they were in, the work they were doing and instruction they were receiving, and their academic outcomes.

In addition to amassing this rich data set, we also sat down with a smaller subset of students (more than 50 over two school years), and got to know them. We observed them in class and spoke to them about their experiences, their likes and dislikes, their families, their goals. Just a few of those students are profiled here. While their names and identifying characteristics have been changed throughout this report, their stories help us understand what the data means in the real lives of individual young people.

They also help us understand what real, tangible changes school systems can make-starting tomorrow and over the long haul-to provide more students with school experiences that are meaningful, that honor their aspirations for themselves and their families, and that give them a fighting chance to meet those goals.
For our complete methodology, including further explanation of our analytical approaches and full analysis results, see the Technical Appendix.

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What can 4,000 students teach us about school? Read The Opportunity Myth.