Supporting Students with Disabilities
The philosophical stance that guided the creation of these materials is the belief that with proper structures, accommodations, and supports, all children can learn mathematics. Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students. While the suggested supports are designed for students with disabilities, they are also appropriate for many children who struggle to access rigorous, grade-level content. Teachers should use their professional judgment about which supports to use and when, based on their knowledge of the individual needs of students in their classroom.
These materials reflect three key design principles that support and engage all students in today’s diverse mathematics classrooms. The design principles and related supports work together to make each activity in each lesson accessible to all students.
Principle 1: Access for All
This foundational design principle draws from the Universal Design for Learning (UDL) framework, and shapes the instructional goals, recommended practices, lesson plans, and assessments to support a flexible approach to instruction, ensuring all students have an equitable opportunity to learn. For more information about Universal Design for Learning, visit http://www.udlcenter.org.
Principle 2: Presume Competence
All students are individuals who can learn, apply, and enjoy mathematics. The activities in these materials position students to capitalize on their existing abilities, and provide supports that eliminate potential barriers to learning when they arise. Each lesson is designed for a wide range of ability, and all students are given access to grade-level problems. Student competence to engage with mathematical tasks should be assumed, with additional supports provided only when needed.
Principle 3: Strengths-Based Approach
All students, including students with disabilities, are resourceful and resilient members of the mathematics community. When the unique strengths and interests of students with disabilities are highlighted during class discussions, their contributions enhance the learning of all students in the classroom.
Design Elements for All Students
Each lesson is carefully designed to maximize engagement and accessibility for all students. Purposeful design elements that support 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 supports 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 with which to base their mathematical understandings.
Access for All
The following general instructional strategies can be used to make mathematics accessible to all students:
Eliminate any 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.
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 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.
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 such as images, diagrams, vocabulary anchor charts, color coding, or physical demonstrations are suggested throughout the materials to support conceptual processing and language development. Many students with disabilities have working memory and processing challenges. Keeping visual aids visible on the board allows students to access them as needed, so that they can solve problems independently. Leaving visual aids on the board especially benefits students who struggle with working or short-term memory issues.
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, comparing and contrasting ideas, etc.
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, but especially those with ADHD.
Supports for Students with Disabilities
The inclusion of additional supports for students with disabilities offers additional strategies for teachers to meet the individual needs of a diverse group of learners. Lesson and activity-level supports for students with disabilities are each aligned to one of the three principles of UDL, engagement, representation, and action and expression, and are paired with a suggested strategy aimed to increase access and eliminate barriers. These lesson specific supports help students succeed with a specific activity without reducing the mathematical demand of the task. All of the supports can be used discretely and are designed to be used as needed. Many of these supports can be implemented throughout the academic year. For example, peer tutors can help build classroom culture, provide opportunities for teamwork, and build professional collaboration skills while also supporting those who struggle. Other supports should be faded out as students gain understanding and fluency with key ideas and procedures.
Additional supports for students with disabilities are designed to address students’ strengths and needs in the following areas of cognitive functioning, which 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 includes tasks that require small muscle movement and coordination such as manipulating objects (graphing, cutting with scissors, writing).
- Brodesky et al., 2002. Accessibility Strategies Toolkit for Mathematics. Education Development Center. http://www2.edc.org/accessmath/resources/strategiesToolkit.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:
A color palette using colors that are distinguishable to people with the most common types of color blindness.
Tasks and problems designed such that success does not depend on the ability to distinguish between colors.
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.
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.
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.