Category: equity in mathematics

Research Breakdown: Teaching Math to SwD during Emergency Remote Teaching

Just uploaded a preprint (before peer review, so not final!) of a study I did this spring with Rachel Schuck, a doc student at UCSB in Special Education. I was working on a research study on UDL with some exceptional special educators. After schools were closed, some of the teachers consented to a series of interviews about their experience teaching during Emergency Remote Teaching (ERT), which is not distance learning, since ERT was unplanned and during a crisis. This first article is focused on teaching math from the perspective of a special educator teaching in a self-contained 3-5th grade classroom. We have a second article which is focused on the experiences of teachers whose students have significant support needs.

Here is the abstract:

“This paper presents a case study of the experiences of a highly experienced special educator named Ms. Z teaching standards-based mathematics during Emergency Remote Teaching (ERT) during the spring of 2020. Pre-COVID, Ms. Z provided her students, all of whom had an IEP for Specific Learning Disabilities and/or Attention Deficit Hyperactivity Disorder, daily opportunities to tackle challenging mathematical problems and taught self-regulation strategies for students to better understand themselves as learners. After the shift to ERT, Ms. Z described “the wall between us” as various digital barriers that made teaching online far more challenging than in person. Challenges included supporting students with productive struggle when not present with them, engaging students in mathematical talk, and creating accessible multi-modal materials. Another barrier was supporting student self-regulation. We analyze Ms. Z’s experience using Universal Design for Learning as the important themes spanned emotional and cognitive engagement, as well as strategic self-understanding. We include recommendations for engaging students with LD and/or ADHD in meaningful mathematical problem solving in ERT. Despite the “walls” in ERT, teachers must create meaningful relationships with students, provide opportunities for students to engage in mathematical talk, create accessible multi-modal materials, and support students to better understand themselves as learners.”

Please read the article for more. Here is just one juicy quotes by this exceptional teacher (fake name Ms. Z), with some of my thoughts that are not in the article. She describes how her first few Zooms in April were taken over by kids:

The first week I started off very just like, the kids wanted to talk to each other. It was hilarious. In one screen, you see somebody having their little cars zooming by and another one, somebody is holding up like five Pokemon cards, just switching through them. And another one, somebody’s got like a family picture. And I’m just like, you guys, you’re supposed to be listening. But they were just so excited to see each other. So we were just doing share outs.

You can see from what Ms. Z says that her students, all of whom have disabilities, wanted time and space to connect with their peers. So much so that they took over the Zoom for an old-fashioned share time. It really bothers me that so many students with disabilities are not being given equal access to synchronous learning on platforms like Zoom. I hear districts and teachers saying that they are not allowed to use Zoom because someone might see a student with an IEP on zoom and know that they have an IEP. Yes, privacy is a concern, but it is inequitable to deny students with disabilities the chance to socialize during a pandemic that is resulting is widespread social isolation and SIGNIFICANT mental health issues. Students with disabilities are already more likely to have anxiety or other emotional disabilities. We need to control privacy risks without discriminating against students with disabilities.

Ms. Z describes “the walls between us” as the barriers that distance and technology have put between her and her students. What walls are you dealing with? Your students dealing with?

Paper citation:

Lambert, R., & Schuck, R. (2020, September 2). “The wall now between us”; Teaching math to students with disabilities during the COVID spring of 2020 PREPRINT.

New article: “Indefensible, Illogical, and Unsupported”; Countering Deficit Mythologies about the Potential of Students with Learning Disabilities in Mathematics

For over two years, I have had a word document on my computer entitled, “Myths in Teaching Mathematics for SwD.” I kept adding bits of writing, particularly when I encountered another myth. Imagine my excitement when Jo Boaler sent out a call for a special issue of Education Sciences on Myths in Mathematics Education. I am so proud to have a paper in this issue, which is amazing and available for free online. (I particularly recommend this amazing piece on dyscalculia by my colleagues Katherine Lewis and Dylan Lane)

My paper:

I decided to focus the paper on students with Learning Disabilities (or specific learning disabilities in reading, writing or math, otherwise known as dyslexia, dysgraphia or dyscalculia). While I wanted to write about a wider range of disabilities, the best research evidence was on this group of learners. I also picked two myths to focus on:

  1. Students with LD ONLY benefit from explicit or direct instruction.
  2. Students with LD cannot create their own strategies in math, and cannot handle multiple strategies.

The first is a major myth that I hear all the time, and the second is a kind of a sub-myth. The assumption that students with LD cannot construct strategies is so pernicious that I decided to include it as a separate myth.

I structured the paper around two things: first a quote written about students with disabilities. This was published in a prominent special education journal in 1998:

“The premise that secondary students with LD will construct their own knowledge about important mathematical concepts, skills, and relationships, or that in the absence of specific instruction or prompting they will learn how or when to apply what they have learned, is indefensible, illogical, and unsupported by empirical investigations.”.
(Jones, Wilson, & Bhojwani, 1998, p. 161)

This quote still shocks me. Having known, taught, been a friend to and a family member or so many people with various permutations of LD, the idea that such learners cannot “construct knowledge” is exceptionally bigoted and wrong. This particular article described constructivism as “ideology” rather than a valid approach to teaching math. In the paper, I try to describe why these myths are themselves “indefensible, illogical and unsupported.” I do not ignore the strong empirical evidence from special education mathematics that students with LD can benefit from explicit instruction, but I present evidence that suggests inquiry instruction as also effective. We also need to consider why we teach mathematics- it is not just to make students into effective computers, but to help them develop life-long identities as mathematical thinkers and explorers. The myth emerges from the assumption that there exists sufficient evidence that inquiry mathematics is NOT effective for students with LD, or that explicit instruction is the only method that is evidence-based. As the National Mathematics Advisory Panel states, “it is important to note that there is no evidence supporting explicit instruction as the only mode of instruction for students [with LD]” (2008, p. 1229).

As I was writing this piece, I checked Twitter and found this tweet:

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Thank you Abby. This tweet inspired me to keep writing, and keep poring through research. If you are more interested in understanding the research divide between math ed and special ed, I would check out another article I wrote with Paulo Tan in Education Sciences (


  1. What myths still need to be unpacked?
  2. What kind of research would you like to see around students with disabilities and mathematics? What specific questions have emerged from your work?


Disability, invisibility, and equity in mathematics (part one)

Disability, invisibility, and equity in mathematics (part one)

A recent post by my friend and colleague Andrew Benjamin Gael rightly critiqued the recent NCTM conference for omitting disability in current calls for equity.  The recent Executive Summary of the Principles to Actions doesn’t mention disability or special education at all.  Andrew asked why, and then went on to describe some recent, powerful work on meeting the needs of students with disabilities using the Mathematical Practices.

As a researcher and teacher educator in both special education and mathematics education, I am constantly confronted with the invisibility of kids with disabilities in mathematics education. Continue reading “Disability, invisibility, and equity in mathematics (part one)”