Accessibility and Mathematics

Disclaimer

I’ve tried to write this post many times. Each time I write the opening sentence, it seems to pale in comparison to the grand scope of what it should encompass. Access and equity is a huge topic, not only in math classes, but in education at large. Often equity is discussed in terms of gender, socio-economic, racial, or sexual orientation. These conversations are also vital, but this post will focus on equity for students with disabilities through access to rich mathematics curricula. However, writing a post about access for students with disabilities in robust math classes is still a daunting task. Since I believe in the importance of this topic I’m going to just begin, though I’ll probably regret how I began once I’ve finished.

Preface

When one considers how to create an accessible math class for students with disabilities it is generally done through deficit thinking. “My students can’t do _____, so what interventions can I implement to fix their deficits?”

At one level, the evolution of deficit thinking in special education stemmed from beliefs that, although some individuals functioned in ways considered “subnormal,” they were still humans and deserved to be educated. A review of the history of the development of programs for children with mild disabilities reveals that, in the early 1800’s, advocates of the child saving theory attempted to determine the etiology of students’ symptoms that resulted in learning and behavior problems.

These psychologists, physicians, and educators developed therapies and instructional interventions designed to improve the educational outcomes and quality of life of individuals with disabilities (Trent, Artiles & Englert, 1998).

Unfortunately, the idea of intervention is inextricably linked to deficit thinking and the belief that students with disabilities are not “normal.” I can’t help but disagree with this. Concepts like neurodiversity and presumed competence provide a much more equitable stance on how students with disabilities should be viewed and treated in the school environment. With this in mind, here are two effective lesson planning guides to increase access to rich mathematics for students with disabilities in your classroom.

Universal Design for Learning

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You may have seen this image before. It tends to punctuate most presentations relating to including students with disabilities in general education classrooms. the reason for this is it is a visual representation of the complex idea of Universal Design.

“Universal Design (UD) is an approach to design that increases the potential for developing a better quality of life for a wide range of individuals. It is a design process that enables and empowers a diverse population by improving human performance, health and wellness, and social participation” (Steinfeld and Maisel, 2012).

The Center for Applied Special Technology (CAST) has taken this idea and applied it to education in the concept of Universal Design for Learning (UDL). UDL “is a framework to improve and optimize teaching and learning for all people based on scientific insights into how humans learn.” According to UDL there are 3 “networks” of learning: engagement, representation, action and expression.

Engagement

  • Provide options for self-regulation.
  • Provide options for sustaining effort and persistence.
  • Provide options for recruiting interest.

Representation

  • Provide options for comprehension.
  • Provide options for language, mathematical expressions, and symbols.
  • Provide options for perception.

Action and Expression

  • Provide options for executive functions.
  • Provide options for expression and communication.
  • Provide options for physical action.

In essence UDL recommends  providing multiple means for students to demonstrate learning. First present information in multiple modalities and mediums to increase perception, comprehension, and communication. Second, engage the students by tapping into their strengths and interests; scaffold persistence through clear goals and objectives, optimizing challenge (zone of proximal development), fostering collaboration, and giving effective feedback. Lastly, allow for multiple means of expression related to classroom products. Include physical action and management of executive functions throughout the demonstration of learning process.

In my classroom this could be as simple as assessing through written, oral, or illustrated answers or as complex as scaffolding the process of an inquiry project using Google Drive. Here’s a great example of a general education high school math teacher revising a lesson plan using the UDL framework.

Accessibility Strategies

The Education Development Center (EDC) provides a toolkit with which to better understand the learners in your room in an effort to plan lessons that avoid obstacles to access while allowing students to engage in rich mathematics.

The goal of this document is to provide an organized list of strategies for making mathematics more accessible to students with disabilities. Standards-based mathematics curricula provide opportunities for students to conduct hands-on investigations, use multiple representations, work collaboratively, and communicate mathematical ideas. The lessons are carefully designed to promote student learning of key mathematical concepts, skills, and processes. However, no curriculum can provide all possible learning alternatives to meet all students’ learning needs. An activity that draws on the strengths of some students may pose challenges for others. For example, a student with strengths in visual-spatial processing may excel at working with geometric representations and rotating figures on the coordinate plane, while a student with difficulties in this area may struggle with those tasks, preferring verbal descriptions to visual representations (Brodesky, Parker, Murray & Katzman, 2002).

The EDC breaks down the strengths and needs of students into 8 categories:

  • Conceptual Processing
  • Language
  • Visual-Spatial Processing
  • Organization
  • Memory
  • Attention
  • Psycho-Social
  • Fine-Motor

Conceptual processing involves connections a student makes between ideas or topics and the metacognitive reflection to solidify any new learning. Language includes describing strategies, explaining reasoning, justifying solutions, making persuasive arguments, both orally and in writing, and learning and using mathematical vocabulary. This also includes receptive and expressive language processing. Visual-spatial processing involves processing visual representations as well as using manipulatives. Organization is another way of saying executive functioning, which is a major contributing factor for the ability to problem solve. Memory includes both working and long-term memory. Working memory is best exemplified when attempting to use mental math. Long-term memory is when a student tries to recall previously mastered skills in unfamiliar situations. Attention involves listening to and following directions, participating in class discussions, and working individually. Students with ADHD will be the most effected in this area, but attentional lapses affect any and all students at some point during the day. Does your mind wander sometime during your work day? Of course it does! Psycho-social includes the social skills required for class discussions, group work, and giving and getting feedback. Fine-motor skills require coordination of the fingers and hands to carry out mathematical tasks, such as using manipulatives or a calculator, which are popular ways to modify lessons for students with disabilities.

A great example of the EDC Accessibility Strategies is its integration into the Contemplate then Calculate instructional routine by Grace Kelemanik and Amy Lucenta.

Conclusion

The most important aspect of the EDC Accessibility Strategies or Universal Design for Learning is that no one strategy will work for every student, every lesson. There is a mix of strengths and needs in any classroom and the more students (with or without disabilities) the more modifications will need to be made. Take just one math task for example. For a task in math class to be successful for all students there are numerous angles for a teacher to take into account. If a student is struggling through one of these accessibility areas then they haven’t yet gotten to the math of the task that they need to learn during the lesson.

Accessibility in mathematics is more than making the print on the worksheet bigger or giving one kid base ten blocks, it is creating a classroom culture when a teacher plans for every student in the room to be successful from the beginning. These are just two ways to do that.

8 thoughts on “Accessibility and Mathematics

  1. Grammar Police: attentional lapses effect… should be affect.

    That said, that list is a treasure trove. When I say “accessibility” most people think strict sensory access. I try to explain cognitive accessibility — but this does it much more succinctly 🙂

    Like

  2. My children both needed academic interventions for their learning differences. One of the most powerful strategies that they learned was to articulate what they themselves needed from an intervention. For instance, when I would fail in getting my son to understand a specific math concept I would then try to explain it in another way. He finally realized that this confused him even more and would tell me to just keep explaining things the same way repeatedly. The more they recognized that they could have a voice in guiding their instruction the more successful they could be. This, or course,not only hinged on whether or not they felt at ease with telling the teacher/tutor/mother how to proceed, but also their becoming aware of what worked for them.
    I’m glad to see you writing about this subject!

    Like

    • Thank you for your comment.

      I believe student self-advocacy in class or in the community is one of the most important topics special educators could focus on. Not enough special education classes allow students the space to advocate for themselves in teacher-centered classrooms. Not every learner is the same and students should be supported in speaking up for their learning needs. This is a skill that will be useful in the world of work!

      Thanks again for sharing Paula!

      Liked by 1 person

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  6. This is an excellent post on a daunting topic indeed. I have heard special education teachers who think of themselves as UDL believers say essentially that students with disabilities who need modifications should not be included in higher-level math classes. I disagree! Thanks for sharing the strategy toolkit, it is super helpful!

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