Dyscalculia

Approximately the same number of students have serious reading problems as have disabilities in mathematics; however, more research has been done to date on reading than mathematics (Sousa, 2015).  This pamphlet is intended to deepen secondary mathematics teachers’ understanding of dyscalculia, provide special educators with recent developments in research on dyscalculia, and offer supports for students with dyscalculia.

What Is Dyscalculia?

First discovered by Salomon Henchen, a Swedish neurologist, dyscalculia has been an identified learning disability for the past century (McCloskey, 1992).  Scientists at University College in London have confirmed through transcranial magnetic stimulation (TMS) that dyscalculia stems from malformations in the right parietal lobe of the brain (AAAS, 2007).  The parietal lobe, which lives toward the back of the brain, interprets visual information and processes mathematics.

A mathematics learning disability, dycalculia is characterized by persistent problems with processing numerical calculations, or “what to expect as an outcome of an operation” (Sousa, 2015, p. 173).  This includes conceptualizing numbers, number relations, outcomes of numerical operations, and estimation (Sousa, 2015; Witzel & Little, 2016). 

We know more about reading learning disabilities than mathematics learning disabilities.  However, recent research is closing that gap.

Building on other recent research and longstanding theories about subtypes of dyscalculia, Peake, Jiménez, and Rodríguez (2017) have successfully validated two subtypes of dyscalculia.  The representational subtype consists of deficits in processing quantities.  The verbal subtype involves deficiencies in retrieving number facts from long-term memory.  Furthermore, they have illuminated the possible existence of a spatial subtype.  Peake and colleagues recommend developing evaluation and intervention programs that address each subtype separately.

Representational dyscalculia

• Associating a digit with its quantity (often called subitizing; e.g., the “twoness” of 2 or “threeness” of 3),

• Telling time or direction, or ordering or sequencing events,

• Determining which value is greater or lesser,

• Following sequential directions, sequencing and reversing the order of a sequence, organizing detailed information

Verbal dyscalculia

• Mastering arithmetic facts, especially by counting,

• With spatial orientation, including reading maps and distinguishing left from right,

• Remembering facts and formulas

Supporting Students with Dyscalculia
in Learning Mathematics[i]

(Dennis et al., 2016; Gonsalves & Krawec, 2014;
Sousa, 2015; Witzel & Little, 2016; Witzel et al., 2008)

Foster cooperation, not competition.  Create a classroom culture in which students work together and support each other in learning.  Remove competition from classroom activities.

Incorporate small-group instruction.  A meta-analysis of research since 2006 found strong effect sizes for small-group instruction.  Find ways to incorporate stations that include opportunities to work with small groups of students at a time.

Think trees and forest.  Teach operations and ideas in isolation and systematically draw connections between them as new operations are incorporated together.  This also means using simple enough numbers that students can focus on learning the operation without the complexity involved in less friendly numbers.

Use heuristics.  Heuristics are general techniques for problem solving.  Three Reads Mathematics Language Routine (Fostering Math Practices version; Illustrative Mathematics version) for making sense of word problems, while useful for English Language Learners, can also serve as a heuristic for students with dyscalculia.

Use explicit instruction.  Different from direct instruction (traditional lecture), explicit instruction involves intentionally sequencing problems to illuminate mathematical structure, inviting students to notice and wonder, purposefully fostering students’ making connections between problems, representations, strategies, and ideas.

Embrace students’ use of multiple strategies.  While we want students to learn certain mathematical procedures at each grade level, we also need to encourage students to use strategies that make sense to them.  Recognizing students with dyscalculia may struggle to memorize or retrieve arithmetic facts, we can reduce their anxiety and continue building skill and understanding by accepting and encouraging a variety of strategies.

Use visuals.  Visuals include mathematical representations such as diagrams, number lines, and graphs, as well as graphic organizers, anchor charts, and virtual manipulatives (e.g, Desmos and Geogebra applets).  Explicitly teach the structure of models and connect visuals to mathematical procedures.  Ensure models are available for students to use at any time, even after they are using procedures to solve problems.

Use Concrete-Representational-Abstract sequence to lessons.  This means beginning with enacted examples (using objects or acting out the problem, or contextualizing “naked math” problems), before using pictures, diagrams, and other visual models, and ending with the procedure or algorithm.  It also means explicitly connecting the procedure or algorithm to the ways the objects, actions, pictures, diagrams, and other visual models were used to solve the problem.  Encourage students to continue using concrete, representational and abstract strategies even after procedures have been introduced to reinforce connections between them.

[i] Additionally, supports that have shown value for elementary students are often also valuable for middle and secondary students (e.g., Witzel & Little, 2016; Witzel, Riccomini, & Schneider, 2008).

References

• American Association for the Advancement of Science (AAAS). (2007). The root of dyscalculia found. EurekAlert! Retrieved from EurekAlert! website: https://www.eurekalert.org/pub_releases/
  2007-03/ucl-tro032107.php

• Dennis, M. S., Sharp, E., Chovanes, J., Thomas, A., Burns, R. M., Custer, B., & Park, J. (2016). A meta-analysis of empirical research on teaching students with mathematics learning difficulties. Learning Disabilities Research & Practice, 31(3), 156-168. doi:10.1111/ldrp.12107

• Gonsalves, N., & Krawec, J. (2014). Using number lines to solve math word problems: A strategy for students with learning disabilities. Learning Disabilities Research & Practice, 29(4), 160-170. doi:10.1111/ldrp.12042

• McCloskey, M. (1992). Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44(1), 107-157. doi:https://doi.org/10.1016/0010-0277(92)90052-J

• Peake, C., Jiménez, J. E., & Rodríguez, C. (2017). Data-driven heterogeneity in mathematical learning disabilities based on the triple code model. Research in Developmental Disabilities, 71, 130-142. doi:https://doi.org/10.1016/j.ridd.2017.10.005

• Sousa, D. A. (2015). How the brain learns mathematics. Thousand Oaks: Corwin Press.

• Witzel, B. S., & Little, M. E. (2016). Teaching elementary mathematics to struggling learners. London: The Guilford Press.

• Witzel, B. S., Riccomini, P. J., & Schneider, E. (2008). Implementing CRA with secondary students with learning disabilities in mathematics. Intervention in School and Clinic, 43(5), 270-276. doi:10.1177/1053451208314734