What SLPs Need to Know:
Acalculia

 10 min read

Numbers are everywhere; just look around you now.  We use them constantly, often without noticing. A simple task like telling someone the time requires multiple steps involving language and cognition. In just a few seconds, your brain recognizes digits and symbols (7:00), converts them to a phonological representation (“seven”), and assigns meaning to them (not too late). This mental translation of numbers from one form to another is called transcoding.

So what happens when number processing and math calculations suddenly become a problem? Unfortunately, this is the often overlooked experience of individuals with a brain injury (e.g., stroke, TBI) or neurological disease. Acalculia or acquired dyscalculia isn’t a developmental disorder like you see in children. It’s a new deficit that affects independence in various daily living tasks.

Ardila & Rosselli (2019) proposed two different classifications of acalculia:

• Aphasic acalculia: the result of a language impairment
• Alexic acalculia: difficulty reading numbers or math symbols
• Agraphic acalculia: difficulty writing numbers or math symbols
• Spatial acalculia: difficulty with visuospatial aspects of math, commonly associated with right hemisphere damage and left neglect
• Dysexecutive acalculia: often associated with frontal lobe damage and attention or working memory deficits

Acalculia & Aphasia

People with aphasia can present with a wide range of numerical deficits, including difficulty with counting, transcoding, math symbols, magnitudes, and simple-to-complex oral/written operations (Gonzalez et al., 2020). Single-digit addition is usually the easiest operation, but when double-digit problems or carrying get involved, people with aphasia have more difficulty than age-matched peers (De Luccia & Ortiz, 2016).

Gonzalez et al. (2021) found that individuals with mixed non-fluent aphasia and global aphasia showed the most severe calculation deficits compared to other aphasia subtypes. Individuals with Broca’s aphasia may have trouble with the number syntax (e.g., saying 1005 as 15 or 437 as 43007), whereas a person with Wernicke’s aphasia might have difficulty with lexical understanding (e.g. misinterpreting the number four for six) (Ardila & Rosselli, 2019).

Read more about the importance of numbers in daily life in this article.

In the Gonzalez study, people with aphasia who performed better on language tasks appeared to perform better on basic math tasks, suggesting overlap between language and number skills. This relationship wasn’t consistent across all aphasia types, and performance on nonverbal tasks also predicted calculation ability. Overall, the exact relationship between language and calculation skills remains unclear. What is evident, however, is that math difficulties can make everyday tasks significantly harder than clinicians or patients may realize.

Assessing Acalculia

It can be challenging to identify acalculia because baseline math skills vary across individuals. This also makes it hard to predict recovery. (Benn et al., 2023). There are free cognitive screeners that include very brief numeracy sections. The Oxford Cognitive Screen (OCS) includes more than a single math question, so it might be a better screening option than the Montreal Cognitive Assessment (MOCA) or the Saint Louis University Mental Status Exam (SLUMS), which only have one.

Arithmetic subtests can be found in the following language and cognitive assessment batteries, as mentioned by Cimino-Knight and colleagues (2002):

• Western Aphasia Battery- Revised (WAB-R)($$$)
• Boston Diagnostic Aphasia Examination (BDAE-3)($$$)
• Woodcock-Johnson (WJ V) ($)
• Wide Range Achievement Test (WRAT5)($$)

There are a few numeracy assessments described in research studies, but unfortunately, they are not formatted for easy use in clinical practice:

• EC301 Battery
• Number Processing and Calculation Battery
• Functional Numeracy Assessment

Since none of the readily available assessments are specific to calculation abilities, Semanza and colleagues (2014) designed a tool specifically for calculation abilities, called the Numerical Activities of Daily Living (NADL). Burgio et al. (2022) adapted the NADL into the NADL-Short (see supplementary file 3) for faster administration, which typically takes 15 minutes.

Clinicians can also informally probe different math areas to narrow down what to focus on in therapy (Zamarian et al., 2022), such as:

• Counting: Count items or dots on a page
• Transcoding: Write numbers to dictation and read numbers aloud, using both number words and Arabic numerals
• Basic calculations: Simple addition, subtraction, multiplication, and division problems in both oral and written formats
• Understanding numbers: Compare numbers (greater than/less than) and estimate quantities
• Serial subtraction: Subtract from 100 by 7’s to gauge attention and working memory
• Multi-digit calculations: Observe how the patient sequences steps and organizes their work during more complex equations
• Math word problems: Evaluate reading comprehension and the ability to extract relevant information from text-based problems

Finally, it’s important to ask patients how they used math in their daily lives before their brain injury and how those abilities have changed since. Understanding math use helps clinicians see the real-world impact of acalculia and prioritize meaningful, functional goals.

Keep in mind that patients may not immediately recognize a new math difficulty, especially if numbers weren’t a significant part of their routine (Benn et al., 2023). For some individuals, such as teachers, engineers, construction workers, or scientists, working with numbers is an integral part of their identity. Others may not think of themselves as “doing math” regularly, but numbers are without a doubt woven into their daily tasks, such as cooking, shopping, and time management.

Acalculia Treatment for Adults

Treatment approaches for acalculia vary depending on the subtype and overall goal. Speech-language pathologists can draw from both restorative and compensatory approaches, choosing activities that are meaningful to the patient’s life roles.

Treating Primary Acalculia

Relearning basic number concepts is the first step in treating primary acalculia (Ardila & Rosselli, 2019). Using a number line, drawings (e.g. dots, shapes), or physical manipulatives (e.g., poker chips, blocks, or buttons) can support understanding. The patient can practice counting objects, grouping items, and comparing sets to determine which group has more or less. Once the patient begins to understand number relationships, the clinician can progress to math calculations, gradually increasing their complexity.

Treating Aphasic Acalculia

Number words can be challenging for people with aphasia. Identifying and transcoding spoken number words (“/tu/”), written number words (two), and Arabic numerals (2) is a good place to start. Once the patient has mastered transcoding, the clinician may consider working on arithmetic fact knowledge (single-digit addition, subtraction, multiplication, and division), especially for people with fluent (or Werinicke’s) aphasia (Gonzalez et al., 2020).

Number Therapy

This iOS and Android app works specifically on the communication of numbers.

Clinicians can use a drill-based approach, a conceptual approach, or a combination to improve math fact retrieval (Zamarian et al., 2022). The conceptual approach involves using backup strategies from residual knowledge, like solving a multiplication problem through adding (e.g. 3×5 = 5+5+5). Zamarian and colleagues (2022) referenced a 2003 study that found improvements in trained and untrained multiplication problems in a single subject with calculation deficits following conceptual training.

Patients can advance to more complex procedures that involve double digits, carrying, borrowing, decimals, and percentages (Gonzalez et al., 2020). The clinician can gradually add more language-heavy tasks as appropriate, while incorporating functional concepts like money, time, and measurements. It’s important to keep the patient’s personal goals in mind for person-centered therapy.

Treating Alexic Acalculia

Individuals with alexic acalcuia can perform mental math problems easily, but written problems pose a challenge. If writing skills are intact, patients can write numbers in the air to help recognize them (this is called kinetic writing). Talking about the visual elements of numbers and reconstructing written numbers (e.g., writing an 8 from a 3, or a 4 from a 1) can help patients differentiate numbers from one another (Ardila & Rosselli, 2019).

Treating Spatial Acalculia

A right hemisphere injury, particularly in the fronto-temporo-parietal region, can result in spatial deficits and difficulty with core arithmetic processes. Benavides-Varela and colleagues (2017) found that people with a right hemisphere injury struggled with number comprehension, transcoding, and written operations (especially subtraction and multiplication) compared to a control group of cognitively-intact adults.

Speech pathologists can target these spatially-impaired skills in therapy. If the patient presents with left neglect, clinicians can use the same strategies they would use in reading tasks, such as:

• using a visual anchor (i.e., a bright-colored line) on the left side of an equation or a math problem
• numbering the left and right margins
• finger-tracking to scan the page from left to right
• placing a hand on the left side, or feeling for the edge of the page as a tactile cue

Cues are gradually faded until the patient can use the learned strategies to solve math problems independently (Ardila & Rosselli, 2019). Note that spatial acalculia can impact non-paper-based number tasks as well, such as telling the time on a clock or counting coins. Visual anchors and tactile cues can be applied across multiple contexts to address these functional skills.

Treating Dysexecutive Acalculia

Attention and working memory (holding and manipulating information) significantly influence math performance, so these cognitive skills should be a primary focus of treatment in dysexecutive acalculia. One effective attention strategy is verbalization, which involves saying numbers aloud and talking through each step of a math procedure (Ardila & Rosselli, 2019).

Working memory can be addressed through tasks like backward digit span or serial subtraction. Finally, incorporating metacognitive strategies, such as the predict–perform procedure, can help patients recognize the need for compensatory techniques, which are beneficial for all subtypes of acalculia.

Use the Verbal Working Memory treatment inside the Virtual Rehab Center to work on backward digit span.

Examples of strategies include:

• Reduce distractions to stay focused
• Say numbers out loud to maintain attention and catch errors
• Write out the problem and steps instead of performing mental calculations
• Use a calculator for external support
• Take extra time to process the information
• Check over the procedures and answer to see if it makes sense

Many of these strategies promote self-monitoring to recognize mistakes in real time. It’s also important to encourage self-regulation, or the ability to think flexibly and adapt during the math task, like trying a different approach when one isn’t working. The patient should assess their performance afterwards to increase self-awareness and independence with numeracy.