Shining a Light on Dyscalculia

With reading research and methodology in the current spotlight, educators are learning more about dyslexia. Now, many are asking for the same support regarding math instruction and dyscalculia, which Dr. Honora Wall, founder of the Dyscalculia Training and Research Institute, defines as “a type of neurodivergence: a difference in brain development or function.”

There’s much less research, however, about dyscalculia than there is for dyslexia. In Dyscalculia: From Science to Education, cognitive neuropsychologist Brian Butterworth writes that since 2000, the National Institutes of Health has spent $107.2 million in funding for dyslexia research but only $2.3 million on dyscalculia. Consequently, students with dyscalculia are not getting the support they need, due to the lack of teachers’ knowledge about the disorder. 

Programs and approaches designed for the needs of learners who are dyslexic, such as Orton-Gillingham, Barton, S.P.I.R.E., and Fundations, just to name a few, are readily available. With no equivalent for dyscalculia, educators are scrambling for just the right tools to effectively address the needs of a vulnerable population. The good news is, there are several very concrete ways teachers can support these students.

What dyscalculia is not

It’s not dyslexia with numbers. Dyslexia typically involves difficulty learning how to read, which can interfere with math learning. However, dyscalculia impedes a person’s ability to make sense of numbers and math concepts in ways that are different from dyslexia. 

It’s not uncommon. Research suggests, according to Butterworth, that dyscalculia is just as prevalent as dyslexia. In fact, Butterworth maintains that it’s estimated that 50 to 60 percent of people with dyslexia also have dyscalculia. 

It’s not being bad at math. Studies have shown that babies demonstrate an innate understanding of numerosity, as Butterworth says in his book. Dyscalculia is a learning difference that requires specialized teaching and isn’t just “being bad at math.”

Indicators of dyscalculia

There are several behaviors that can present themselves in learners with dyscalculia. Just as dyslexia and ADHD (attention-deficit/hyperactivity disorder) present themselves on a spectrum, the same is true for dyscalculia. That means that each student brings with them a unique set of strengths and weaknesses. Below are behaviors that are typical for students with dyscalculia. 

Difficulties subitizing and estimating: Subitizing is the ability to “see” small numbers without actually counting them. For example, when rolling a die, a young student with dyscalculia will need to count the dots as opposed to automatically seeing that the number rolled was four.

Difficulties with patterns: Students with dyscalculia may have difficulty putting numbers in order from least to greatest or greatest to least. They also may struggle with skip counting or determining what number would come next in a sequence. 

Loss of previously acquired skills: Research, according to Wall, hasn’t quite determined why this happens, but it is very typical for students with dyscalculia to forget the math they learned, much to the dismay of their teachers. Some lose information quickly, others over time. This is why reference charts and a structured, spiraling curriculum are crucial. 

What kind of teaching do dyscalculic learners need? 

CRA Instructional Sequence: In The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths, specialist teacher Ronit Bird agrees with Butterworth that a Concrete Representational Abstract instructional sequence is an approach that moves students from using concrete manipulatives to representational drawings to abstract numbers when learning new concepts and is a best practice for all learners. Dyscalculic learners will need to experience this sequence multiple times and gradually, when developing new skills and understandings. 

Visualization: Often the transition from the concrete stage to abstract is a bumpy one. Bird suggests that dyscalculic learners be explicitly taught how to picture numbers and operations in their mind’s eye. This is especially true when solving word problems. Drawings, open number lines, and area models are some of the ways she suggests to bridge the concrete and abstract stages. 

Quality over quantity: Bird and Butterworth both recommend limiting the demands on a learner’s working memory, allowing them to focus on the important skills of a task. Providing reference charts, reading directions, and using rubrics are just some of the ways to reduce the load placed on working memory. 

Explicit scaffolding: All learners must have a secure understanding of foundational concepts before building on them. This is especially true for learners with dyscalculia. Making explicit connections to previously taught skills and breaking tasks down into the smallest of steps are essential. This reduces the risk of taking students’ background knowledge for granted.

How to plan instruction

Focus on sets: Butterworth asserts that dyscalculics struggle with operations because of a deficit in the understanding of numbers as sets. Instruction needs to focus on supporting concepts such as counting, one-to-one correspondence, part-whole relationships, and cardinality in the early years. 

Diagnostics: There are assessments typically used by psychologists to diagnose dyscalculia, including the Wechsler Intelligence Scale for Children, KeyMath-3, Wechsler Individual Achievement Test for Math Fluency, and the Feifer Assessment of Mathematics. Educators, however, must first identify which students need additional support and then specifically which mathematical knowledge is in need of intervention. Acadience Math, the Early Childhood Assessment in Mathematics, Universal Screeners for Number Sense, and the Georgia Numeracy Project are widely used resources. 

Feedback: Because a loss of previously acquired skills is a hallmark of the disability, committing mathematical understanding to long-term memory is an arduous process. It is imperative that the information learned be accurate. Wall writes that research suggests that when the brain learns new information, it does not “overwrite” what it has already learned, even if that information is incorrect.

This speaks to the uphill battle that teachers face when having to undo a misconception that a student has committed to memory. In order to avoid this, students who struggle must be given consistent, real-time feedback as they learn. In addition to teacher input, Butterworth recommends adaptive digital platforms and games as great ways to provide feedback consistently.

Manipulatives: Numbers are abstract. Manipulatives make numbers concrete. Using blocks, Cuisenaire rods, ten frames, and counters are just some of the ways students can have hands-on experiences. Dyscalculic learners solidify the concept that numbers are made up of sets of smaller numbers with tactile input from manipulatives.

Joy: Fear of math is a reality for many and is a major obstacle to learning. Years of struggle reinforce math as unenjoyable and a source of anxiety. The frequent use of games modified to students’ current levels of understanding can have a disarming effect on those who experience math aversion. 

There is still much to learn about dyscalculia. When armed with the right information, however, educators can make small changes to their practice that will have a huge impact on the lives of those with dyscalculia.