All students are individuals who can know, use, and enjoy mathematics. These materials empower 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.

Curriculum features that support access

Each lesson is carefully designed to maximize engagement and accessibility for all students. Purposeful design elements that support access for all learners, but that are especially helpful for students with disabilities, include:

Lesson Structures are Consistent

The structure of every lesson is the same: warm-up, activities, synthesis, cool-down. By keeping the components of each lesson similar from day to day, the flow of work in class becomes predictable for students. This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson.

Concepts Develop from Concrete to Abstract

Mathematical concepts are introduced simply, concretely, and repeatedly, with complexity and abstraction developing over time. Students begin with concrete examples, and transition to diagrams and tables before relying exclusively on symbols to represent the mathematics they encounter.

Individual to Pair, or Small Group to Whole Class Progression

Providing students with time to think through a situation or question independently before engaging with others allows students to carry the weight of learning, with support arriving just in time from the community of learners. This progression allows students to first activate what they already know, and continue to build from this base with others.

Opportunities to Apply Mathematics to Real-World Contexts

Giving students opportunities to apply the mathematics they learn clarifies and deepens their understanding of core math concepts and skills and provides motivation and support. Mathematical modeling is a powerful activity for all students, but especially students with disabilities. Each unit has a culminating activity designed to explore, integrate, and apply all the big ideas of the unit. Centering instruction on these contextual situations can provide students with disabilities an anchor on which to base their mathematical understandings.

Instructional strategies that support access

The following general instructional strategies can be used to enhance access for all students to rigorous, grade-level content: 

Eliminate Barriers

Eliminate any unnecessary barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. This requires flexibility and attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.

Processing Time

Increased time engaged in thinking and learning leads to mastery of grade-level content for all students, including students with disabilities. Frequent switching between topics creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding. Some students may need additional time, which should be provided as required.

Assistive Technology

Assistive technology can be a vital tool for students with learning disabilities, visual spatial needs, sensory integration, and students with autism. Assistive technology supports suggested in the materials are designed to either enhance or support learning, or to bypass unnecessary barriers.

Manipulatives

Physical manipulatives help students make connections between concrete ideas and abstract representations. Often, students with disabilities benefit from hands-on activities, which allow them to make sense of the problem at hand and communicate their own mathematical ideas and solutions.

Visual Aids

Visual aids such as images, diagrams, vocabulary anchor charts, color coding, or physical demonstrations are suggested throughout the materials to support conceptual processing and language development. Keeping relevant visual aids posted in the classroom supports independence by allowing students to access them as needed, and is especially beneficial for students with challenges related to working or short term memory.

Graphic Organizers

Word webs, Venn diagrams, tables, and other metacognitive visual supports provide structures that illustrate relationships between mathematical facts, concepts, words, or ideas. Graphic organizers can be used to support students with organizing thoughts and ideas, planning problem solving approaches, visualizing ideas, sequencing information, and comparing and contrasting ideas.

Brain Breaks

Brain breaks are short, structured, 2–3 minute movement breaks taken between activities, or to break up a longer activity (approximately every 20–30 minutes during a class period). Brain breaks are a quick, effective way of refocusing and re-energizing the physical and mental state of students during a lesson. Brain breaks have also been shown to positively impact student concentration and stress levels, resulting in more time spent engaged in mathematical problem solving. This universal support is beneficial for all students, especially those with attention challenges or disorders.

Access for Students with Disabilities

Supplemental instructional strategies, labeled “Access for Students with Disabilities,” are included in each lesson. They are designed to help teachers meet the individual needs of a diverse group of learners. Each  is aligned to one of the three principles of Universal Design for Learning, to provide multiple means of engagement, representation, or action and expression, and includes a suggested strategy to increase access and eliminate barriers. These lesson specific supports can be used as needed to help students succeed with a specific activity, without reducing the mathematical demand of the task, and can be faded out as students gain understanding and fluency. 

The following areas of cognitive functioning are integral to learning mathematics (Addressing Accessibility project, Brodesky et al., 2002), and are indicated in each access support, so that teachers can leverage students’ strengths to address potential barriers or challenges that exist in the learning environment.

• 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 includes tasks that require small muscle movement and coordination such as manipulating objects (graphing, cutting with scissors, writing).

The additional supports for students with disabilities were designed using the Universal Design for Learning Guidelines (http://udlguidelines.cast.org). Each support aligns to one of the three principles of UDL: engagement, representation, and action and expression.

Engagement:

Students’ attitudes, interests, and values help to determine the ways in which they are most engaged and motivated to learn. Supports that align to this principle offer instructional strategies that provide students with multiple means of engagement and include suggestions that, help provide access by leveraging curiosity and students’ existing interests, leverage choice around perceived challenge, encourage and support opportunities for peer collaboration; provide structures that help students maintain sustained effort and persistence during a task, and provide 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 that align to this principle offer instructional strategies that provide students with multiple means of representation and include suggestions that offer alternatives for the ways information is presented or displayed, help develop students’ understanding and use of mathematical language and symbols; illustrate connections between and across mathematical representations using color and annotations, identify opportunities to activate or supply background knowledge, and describe organizational methods and approaches designed to help students internalize learning.

Action and Expression:

Throughout the curriculum, students are invited to share both their understanding and their reasoning about mathematical ideas with others. Supports that align to this principle offer instructional strategies that provide students with multiple means of action and expression and include suggestions that encourage flexibility and choice with the ways students demonstrate their understanding; list sentence frames that support discourse or accompany writing prompts; indicate appropriate tools, templates, and assistive technologies; support the development of organizational skills in problem-solving; and provide checklists that 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 https://www.cast.org/impact/universal-design-for-learning-udl.

References

• Brodesky et al. (2002). Accessibility strategies toolkit for mathematics. Education Development Center. 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

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.