These materials empower all students with activities that capitalize on their existing strengths and abilities to ensure that all learners can participate meaningfully in rigorous mathematical content. Lessons support a flexible approach to instruction and provide teachers with options for additional support to address the needs of a diverse group of students, positioning all learners as competent, valued contributors. 

When planning to support access, teachers should consider the strengths and needs of their particular students. The following areas of cognitive functioning are integral to learning mathematics (Addressing Accessibility Project, Brodesky et al., 2002). 

• Conceptual Processing includes perceptual reasoning, problem solving, and metacognition.
• Language includes auditory and visual language processing and expression.
• Visual-Spatial Processing includes processing visual information and understanding relation in space of visual mathematical representations and geometric concepts.
• Organization includes organizational skills, attention, and focus.
• Memory includes working memory and short-term memory.
• Attention includes paying attention to details, maintaining focus, and filtering out extraneous information.
• Social-Emotional Functioning includes interpersonal skills and the cognitive comfort and safety required in order to take risks and make mistakes.
• Fine-motor Skills include tasks that require small muscle movement and coordination such as manipulating objects (graphing, cutting with scissors, writing).

Supplemental instructional strategies that can be used to increase access, reduce barriers and maximize learning are included in each lesson, listed in the activity narratives under “Access for Students with Disabilities.” Each support is aligned to the Universal Design for Learning Guidelines (http://udlguidelines.cast.org), and based on one of the three principles of UDL, to provide alternative means of engagement, representation, or action and expression. These supports provide teachers with additional ways to adjust the learning environment so that students can access activities, engage in content, and communicate their understanding. Supports are tagged with the areas of cognitive functioning they are designed to address to help teachers identify and select appropriate supports for their students. Designed to facilitate access to Tier 1 instruction by capitalizing on student strengths to address challenges related to cognitive functions or disabilities, these strategies and supports are appropriate for any students who need additional support to access rigorous, grade-level content. 

Teachers are encouraged to use what they know about their students’ IEPs, strengths and challenges, and a UDL approach to ensure access. In cases where students may benefit from alternative means of access or support, teachers can draw on ideas from the tables below or visit https://udlguidelines.cast.org for more information. 

UDL Strategies to Enhance Access

The tables below include select examples of the types of supports that are found in these materials. Each UDL principle includes varied levels with suggestions that support ways to increase access to the learning goal, ways to develop or build understanding, and ways to empower learners to internalize learning and executive function.

Engagement
Students’ attitudes, interests, and values help to determine the ways in which they are most engaged and motivated to learn. Supports that provide students with multiple means of engagement include suggestions that support students’ motivation to engage with content, develop effort and persistence, and internalize self regulation.

Provide Access by Recruiting Interest	Provide choice: invite students to decide which problem to start with, select a subset of problems to complete, which strategy to use, the order they complete a task Provide access to a variety of tools or materials Leverage curiosity and students’ existing interests; invite students to name connections to their own lived experiences Use visible timers and alerts to prepare for transitions
Develop Effort and Persistence	Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk Differentiate the degree of difficulty or complexity by starting with accessible values Periodically revisit math community norms and provide group feedback that encourages collaboration and community
Internalize Self Regulation	Provide on-going feedback that helps students maintain sustained effort and persistence during a task Encourage self-reflection and identification of personal goals Provide access to tools and strategies designed to help students self-motivate and become more independent

Representation
Teachers can reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports provide students with multiple means of representation, include suggestions that offer alternatives for the ways information is presented or displayed, develop student understanding and use of mathematical language and symbols, and describe organizational methods and approaches designed to help students internalize learning.

Access for Perception	Present content using multiple modalities: Act it out, think aloud, use gestures, use a picture, show a video, demonstrate with objects or manipulatives Annotate displays with specific language, different colors, shading, arrows, labels, notes, diagrams, or drawings Provide appropriate reading accommodations
Develop Language and Symbols	Support use of vocabulary, mathematical notation, and symbols with charts, pictures, diagrams, tables Highlight connections between representations to make patterns and properties explicit Present problems or contexts in multiple ways, with diagrams, drawings, pictures, media, tables, graphs, or other mathematical representations Use translations, descriptions, movement, and images to support unfamiliar words or phrases
Internalize Comprehension	Activate or supply background knowledge to build connections to prior understandings and experiences Provide access to blank or partially-completed outlines, graphic organizers, or representations, to emphasize key ideas and relationships Maximize transfer and generalization: name connections to previous examples, invite students to identify important details or features to remember

Action and Expression
Throughout the curriculum, students are invited to share both their understanding and their reasoning about mathematical ideas with others. Supports that provide students with multiple means of action and expression include suggestions that empower students with: access to appropriate tools, templates, and assistive technologies, options for the ways they communicate their learning, and resources that facilitate executive functioning. 

Provide Access for Physical Action	Provide independent think time before students engage with others or responses are discussed Ensure students have enough time to complete tasks, provide extra time if needed Provide access to pre-cut materials, assistive tools, devices, or software
Develop Expression and Communication	Offer flexibility and choice with the ways students demonstrate and communicate their understanding Invite students to explain their thinking verbally or nonverbally with manipulatives, drawings, diagrams Support fluency with graduated levels of support or practice Apply and gradually release scaffolds to support independent learning Support discourse with sentence frames or visible language displays
Internalize Executive Functions	Support the development of organizational skills in problem-solving with access to templates, rubrics, and checklists Post visible goals, objectives, and schedules Provide opportunities for self-assessment, enable students to monitor their own progress

For additional information about the Universal Design for Learning framework, or to learn more about supporting students with disabilities, visit the Center for Applied Special Technology (CAST) at www.cast.org/udl.

Accessibility for Students with Visual Impairments

Features built into the materials that make them more accessible to students with visual impairments include:

1. A color palette using colors that are distinguishable to people with the most common types of color blindness.
2. Tasks and problems designed such that success does not depend on the ability to distinguish between colors.
3. Mathematical diagrams are presented in scalable vector graphic (SVG) format, which can be magnified without loss of resolution, and are possible to render in Braille.
4. Where possible, text associated with images is not part of the image file, but rather, included as an image caption that is accessible to screen readers.
5. Alt text on all images, to make the materials easier to interpret for users accessing the materials with a screen reader.

If students with visual impairments are accessing the materials using a screen reader, it is important to understand:

• All images in the curriculum have alt text: a very short indication of the image’s contents, so that the screen reader doesn’t skip over as if nothing is there.
• Some images have a longer description to help a student with a visual impairment recreate the image in their mind.

It is important for teachers to understand that students with visual impairments are likely to need help accessing images in lesson activities and assessments, and prepare appropriate accommodations. Be aware that mathematical diagrams are provided as scalable vector graphics (SVG format), because this format can be magnified without loss of resolution.

Accessibility experts who reviewed this curriculum recommended that students who would benefit should have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams would be inadequate for supporting their learning. All diagrams are provided in the SVG file type so that they can be rendered in Braille format.
 

References

• Brodesky et al., 2002. Accessibility strategies toolkit for mathematics. Education Development Center. Retrieved from https://courses.edtechleaders.org/smi_3/documents/2020/MathAccessStrategies.pdf
• CAST (2018). Universal design for learning guidelines. Version 2.2. Retrieved from http://udlguidelines.cast.org