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?


Mathematics and Dyslexia Part I

What do we know about teaching meaningful mathematics to students with learning disabilities, particularly those with profound difficulties learning to read, otherwise known as dyslexia?

Here is a great place to start: a blog post by a mathematician with dyslexia who lists some of the many strengths of people with dyslexia. Here is a quote from the blog:

As I said before, dyslexia comes not only with weaknesses, but with strengths*. Some of these strengths play well into mathematical thinking, such as:

  • Spatial reasoning. Dyslexics tend to be good at thinking relationally in three dimensions. This is great for many areas of math. Topology is one of those. My PhD is in topology.
  • Seeing connections. Progress in mathematical research is made by drawing connections between disparate subfields. Dyslexics often have a strength here also.
  • Thinking in narratives. The way to predict how well a child will do in math is by how complicated a story they can tell. See this ScienceNews article. It makes sense: proofs are the bread-and-butter of math. Proofs are really a lot like stories. Dyslexics are usually good narrative thinkers.

I really didn’t like math at all up until I hit geometry in ninth grade. That’s when math became much easier for me. It may be confusing that moving into more advanced mathematics actually made math easier for me. The key to remember is that my brain works differently from the brains that school curricula were designed for.

*I’m stealing this list of strengths from The Dyslexic Advantage by Eide and Eide.

This epitomizes the concept of neurodiversity, focused on strengths rather than deficits, looking for evidence in the experience of experts, people with disabilities. It is hard to recognize how very ill-suited traditional mathematics education has been for people with dyslexia. For example, I hear frequently about difficulties with retaining memorized facts or procedures. When a child has difficulty in this area, all instruction stops until they are “remediated,” or fixed. The assumption is that you cannot move on unless the facts are mastered. This assumption is dangerous because the student has no access to higher level mathematics, no access to the meaning making of mathematics that might finally connect for that student. No wonder that kids with learning disabilities tend to stall out at about a 5th grade level.

In this post from the website the Dyslexic Advantage, Fernette Eide writes about the four core cognitive advantages demonstrated by dyslexic learners. How does these four strengths matter for learning mathematics?

The Four MIND-Strengths

In our book The Dyslexic Adshutterstock_133874900vantage (2011) we described the results of this investigation, and the four patterns of dyslexia-associated strengths it revealed. With a little tweaking, we used the acronym MIND-Strengths to describe these strength patterns, which are:

M-Strength for Material Reasoning, which is primarily reasoning about the position, form, and movement of objects 3D space

I-Strengths for Interconnected Reasoning, which is primarily the ability to spot, understand, and reason about connections and relationships (e.g., analogies, metaphors, systems, patterns)

N-Strengths for Narrative Reasoning, which is primarily the ability to reason using fragments of memory formed from past personal experience (i.e., using cases, examples, and simulations rather than abstract reasoning from principles)

D-Strengths for Dynamic Reasoning, which is the ability to accurately predict using patterns derived through experience the future or the unwitnessed past

Building on the blog post above, what might these strengths mean in mathematics? How can we leverage these strengths?



Mathematics and Dyslexia Part II

What can we learn from mathematics educators who have dyslexia, or whose children have dyslexia? In a serious of posts a year ago, Paula Beardell Kreig wrote some thoughts about working with her children, who have dyslexia. I recommend reading through both posts.

Here is the first:

And here is the second

What are the implications of what she suggests? How can we build on this work in the classroom?

Beyond Differentiation

The following post includes links from a presentation on October 17, 2016.

A blog post explaining neurodiversity

A great book to learn more about neurodiversity in classrooms: Armstrong, T. (2012). Neurodiversity in the classroom; Strength-based strategies to help students with special needs succeed in school and life. Alexandria, VA: ASCD.

Universal Design for Learning by CAST

Research on links between dsylexia and spatial processing

Blog post by a dyslexic mathematician

The Dyslexic Advantage website


PDF of Differentiation Talk (draft)

Memoirs written by people with learning disabilities referenced in the presentation

Abeel, S. (2005). My Thirteenth Winter: A Memoir. New York, NY: Scholastic.

Arrowsmith-Young, B., & M.D, N. D. (2013). The Woman Who Changed Her Brain: How I Left My Learning Disability Behind and Other Stories of Cognitive Transformation (Reprint edition). Simon & Schuster.

Jr, Jackson. J. T. (2010). Shhhhhhh, I Have Something to Say: The Joe Thomas Story. S.l.: PublishAmerica.

Peel, R. (n.d.). My Dyslexic Journey.  Retrieved from

Rodrigues, J. (2013). High School Dropout to Harvard: A Dyslexia Success Story. CreateSpace Independent Publishing Platform

Young, K. (2012). Smart on the inside: A true story about succeeding in spite of learning disabilities. Highland Park, IL: Writers of the Round Table

Young, S. (2011). How I Learned.

Collections of narratives written by individuals with learning disabilities

Connor, D. J. (2007). Urban Narratives: Portraits in Progress; Life at the Intersections of Learning Disability, Race, and Social Class. New York: Peter Lang Publishing.

Rodis, P., Garrod, A., & Boscardin, M. L. (2001). Learning disabilities and life stories. Allyn and Bacon.


Quick Theory Post #2: Neurodiversity

Neurodiversity grew out of the work of autistic self-advocates, or autistic people who identify as activists. Here is a definition from an interview with a neurodiversity activist you can read in full here.

Neurodiversity, the word, simply means the whole variety of different brain wirings people have…from the different kinds of normal to the different kinds of not so normal. Then there’s Neurodiversity, the movement which is the shocking idea that people with non standard wiring are human and deserve to be treated as such without being “fixed” first.