At the annual meeting and exposition of the National Council of Teachers of Mathematics (NCTM), a major theme was the access and equity of high quality mathematics instruction for all students in the United States. This included race, ethnicity, gender, socioeconomic status, ESL/ELL students and students who were often referred to as “struggling in math.” Very rarely was the access and equity of high quality mathematics instruction for students with disabilities discussed.

I freely admit that the equity for these other students groups must be a topic of discussion, but so does that same equity for students with disabilities. Students with all disabilities, not just those who “struggle in math.” If we are going to advocate for access and equity, then every student should be represented in the discussion.

NCTM’s Principles to Actions: Ensuring Mathematical Success for All describes their vision of access and equity in this way:

Our vision of access and equity requires being responsive to students’ backgrounds, experiences and knowledge when designing, implementing, and assessing the effectiveness of a mathematics program. Acknowledging and addressing factors that contribute to differential outcomes among groups of students is critical to ensure that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful. Our vision of equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement. (p. 60)

Students with disabilities are clearly lacking from this vision of access and equity. Why? Students with disabilities are just as much a part of the fabric of our national education system as any other “stakeholders.” Why have they been carefully left out of the conversation?

Part of the reason is that learning math for students with disabilities is hard and teaching math to students with disabilities is also hard. There are many obstacles students with disabilities and their teachers face when learning and teaching math. I would list the obstacles, but it is a long list which is not the topic of this post. Just suffice to say that when high quality mathematics instruction necessitates the very skill set with which you struggle the most (communication) then there are obstacles to your access to a high quality mathematics curriculum.

However, I do not want you to despair. At the NCTM conference I went to a session led by Amy Lucenta and Grace Kelemanik of the Boston Teacher Residency. The topic of the session was “Fostering the Mathematical Practices in Students with Learning Disabilities.” Since the Standards for Mathematical Practice (SMPs) are widely considered vital to high quality mathematics instruction, Lucenta and Kelemanik’s presentation appealed to me as a way to allow students with learning disabilities to access such high quality mathematics learning. They did not disappoint.

Lucenta and Kelemanik make the argument that not all SMPs are as important as others. For instance, SMP.1: Make sense of problems and persevere in solving them, they say is the most important. Lucenta and Kelemanik maintain it is the “umbrella” under which all other SMPs become more relevant. This is why they promote problem-based learning regardless of ability or disability. Lucenta and Kelemanik say that the research suggests that students with learning disabilities need mathematics learning experiences that:

- Provide authentic meaningful contexts (SMPs 1 & 4)
- Model learning strategies using multi-sensory techniques (SMPs 5, 1, 2, 4)
- Provide students with opportunities to use language to describe understanding (SMP 3 & 6)
- Provide multiple practice opportunities (SMP 8)

Each pedagogical strategy has attached SMPs, which Lucenta and Kelemanik said were the most closely related. The SMP which is missing from this list is SMP.7: Look for and make use of structure. This SMP may also be the most challenging for students with disabilities who struggle to generalize concepts from one context to another similar, but unrelated context. But did Lucenta and Kelemanik give up on this SMP? Did they give up on the possibility that students with learning disabilities could access this challenging, but valuable mathematical habit of mind? Would I be writing this, if the answer to these questions was “yes”?

No, they modeled an instructional routine (or activity) which used multiple representations of a mathematical story to look for and make use of structure. Lucenta and Kelemanik said that instructional routines could support students with learning disabilities by:

- Teaching specific and generic problem-solving strategies; Multiple and Heuristic strategies
- Giving students opportunities to use language to describe their mathematical understandings
- Providing multiple practice opportunities to help students use their developing mathematical knowledge and build proficiency
- Carefully planning a range and sequence of examples

During the modeled instructional routine, we (role-playing as students) were asked to read short scenarios about a familiar context and relate those stories to graphs that represented the scenarios mathematically. The scenarios were read aloud for “non-readers” and were repeated for students who benefit from understanding through repetition. We were asked to think-pair-share about which graphs matched which scenarios. Then we were asked to re-phrase what previous pairs had just shared. Pairs were encouraged to share in a way that fit their individual communication style (either oral or kinesthetic).

Altogether students would be able to access the content and mathematical practice standard of looking for and making use of structure through this kind of structured teaching and the use of accessibility strategies like these. If you’d like to know more about this instructional routine or the presentation please contact Amy Lucenta or Grace Kelemanik at the Boston Teacher Residency. They are awesome!

The moral of this story is that students with disabilities can and should have access to the highest quality mathematics instruction we can provide and NCTM as an organization should be leading the way!

Was this the connecting representations activity? We just tried it with third graders. Once with the kind of language supports you named (reading it aloud, turn and talk, connect with what others had said, highlighting ideas with colored pens) and once without as much attention to these supports. They definitely made a difference! These seem like important features of that activity that are helpful for all our learners. Thanks for sharing!

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Yes it was!

The kind of supports are key! Thoughtful supports are the most important. Supports that allow access to content and deeper thinking and communication, not supports for quicker answers and procedures!

Thanks for the feedback!

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Reblogged this on and commented:

Thank you to Andrew Gael @bkdidact for giving permission to share this blog post on Access and Equity related to the area of mathematics

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