When ‘Careless Mistakes’ Aren’t: Dyscalculia, Math Anxiety, and Learning Strategies That Help

Math anxiety is a common and significant hurdle for many students, especially those with dyscalculia, a learning disability that interferes with math comprehension, computation, and other functions.

Though dyscalculia triggers math anxiety and real, detrimental learning consequences, teachers, parents, and even students with dyscalculia seldom fully understand the nature and breadth of the condition.

The truth is that dyscalculia is a collection of problems stemming from deficits related to several brain processes that compound to overwhelm and impair performance. When teachers understand the complexity of the dyscalculic experience,  they can begin to teach the subject in ways that make sense to the student (and benefit other students in class who struggle with math). With effective and appropriate strategies, teachers can make learning math a positive experience for all types of brains.

Signs & Symptoms of Dyscalculia

Dyscalculia – also known as “math dyslexia”, “math learning disorder”, “specific learning disability in mathematics” and many other names — is characterized by the following difficulties, which result in poor math performance and, often, math anxiety:

• Losing track when counting; using fingers and marks to keep track and count; drawing pictures to reason
• Talking aloud to stay on track
• Trouble with subitizing, or recognizing quantities without counting
• Faulty or inconsistent memory of math facts and procedures
• Insufficient working memory for math (mixes up operations, signs, digits, and ideas; loses track midstream); trouble mentally counting and calculating
• Unconscious number and symbol errors in speech, reading, reasoning, and writing
• Relying on simpler operations (e.g. repeated addition and subtraction instead of multiplication and division, respectively)
• Problems visualizing numbers, shapes, changes in orientation, layouts, and objects in 3-D

[Get This Free Download: Solutions for Common Learning Challenges]

Not all students with dyscalculia will exhibit these difficulties. Even so, dyscalculia goes beyond problems in math class. In fact, it’s best to think of dyscalculia as a syndrome — a collection of characteristics that result from deficits in brain processes involving perception, working memory, processing, and communication. Other frequently observed characteristics of dyscalculia syndrome include difficulty with:

• Telling and keeping track of time (awareness); reading clocks
• Keeping track of and interpreting information on calendars (schedules and dates); planning and organization issues
• Deciphering number sequences (remembering codes, phone numbers, addresses, passwords)
• Interpreting directions (telling left from right, up from down, navigating)
• Visual-spatial processing
• Exhibiting visual memory
• Mastering procedural memory and motor sequencing (tying, dance, sports, learning to ride a bike)

Dyscalculia is not poor math performance due to inattention, illness, insufficient interest, educational gaps, poor instruction, or other environmental causes.

Understanding Dyscalculia: Common Challenges and Examples

All the above difficulties translate to unique challenges for individuals with dyscalculia.

In the classroom

Students with dyscalculia may make errors unconsciously that are misconstrued as carelessness, disinterest, and other negative responses. Their challenges are also often misinterpreted as symptoms of ADHD.

[Read: Developmental Dyscalculia – a New Understanding of Early Warning Signs]

• Perseveration is what happens when the brain gets stuck on a number. Examples:
  • The student finger counts to subtract 3 from 4 and gets the right answer. Still, they incorrectly write down “3” as their answer – the last number they manipulated – without realizing it.
  • The student must expand the fraction 5/6 so that the denominator is 48. They correctly reason that they must multiply the numerator by 8. When they multiply 5 by 8, they incorrectly list the product as 46 instead of 40 – unconsciously retaining the “6” from the original denominator and attaching it to the new product.
• Mixed up operations often stem from poor working memory. Example:
  • The student must multiply 6 by 2. Though they see the “x” symbol on the sheet, their brain immediately adds these numbers instead, and they incorrectly list the answer as “8.”
• Number substitution may originate from poor working memory and perseveration. Example:
  • The student must find the product of 321 x 3. Rather than multiply the numbers in the ones’ place (3 x 1) to start, they incorrectly add them to get 4, and write that number below the answer line. Then, rather than multiply 3 by the 2 in the ten’s place, they multiply it by 4 – unconsciously retaining that number and substituting it.
• Mixing up similar sounding numbers due to poor auditory working memory. (Can also be a form of sound perseveration). Examples:
  • Mixing up “12” with “20” because they both start with the “tw” sound
  • Mixing up “16” and “60” because they both start with “six”
• Mixing up similarly shaped numbers due to visual-spatial ambiguity. Example:
  • The curves of the numbers “2” and “5” may cause some students to confuse them for one another.
• Unreliable storage and retrieval of math rules and procedures. Examples:
  • Flipping numbers: The student must find the product of 52 x 31. The correct procedure is to multiply “1” by “2” first, and then by “5,” but the student reverses the order. (This is also a directional ambiguity problem.)
  • Adding repeatedly to avoid difficulties with multi-digit multiplication, taking longer to compute as a result
  • Failing to remember place value, causing errors in computing

Outside the Classroom

• Difficulty calculating change due and tips in monetary transactions; managing allowance
• Difficulty remembering sports rules and keeping score during play
• Avoiding activities that require strategic thinking (certain types of sports, video games, etc.)
• Impaired processing of rapid visual stimuli (stimuli occurring faster than the brain can process, resulting in feeling lost and struggling to keep up)
• Time blindness, or the inability to accurately perceive the passage of time; punctuality
• Difficulty remembering faces, names, and important facts
• Appearing inconsistent, impulsive, spontaneous, and forgetful

Dyscalculia and Math Anxiety: Teaching Strategies and Classroom Solutions

While dyscalculia presents differently in each individual, math anxiety is understandably ubiquitous. Anxiety is a natural consequence when we are unable to perform as needed or expected. Past negative experiences with math may lead students to predict that present and future instances with math will go badly. What’s more, anxiety might overwhelm the student’s mental bandwidth, making math even more daunting and compromising their ability to meet demands. They might want to avoid math altogether to avoid feeling stressed, frustrated, inadequate, embarrassed, and unsuccessful.

The most effective teaching strategies for dyscalculia emphasize math language fluency – multiple ways of understanding a quantitative idea — and positive learning experiences, which build confidence and deep understanding, and avoid triggering math anxiety.

Teaching Strategy #1: Implement a Universal Design for Learning (UDL)

UDL involves implementing information redundancy in instruction. With UDL, students are given opportunities to access, experience, and demonstrate concepts in a variety of ways (visual, auditory, and kinesthetic). Each student’s learning preference reflects their unique strengths to maximize learning outcomes. Instructional methods can include traditional sources (class lectures, projects, tests, etc.) or creative ways (anything from art presentations, creating videos, verbally presenting information, etc.)

UDL is in line with the “authentic assessment” approach, where the student is the teacher. Through authentic assessment, the student has the opportunity to achieve deep understanding and demonstrate mastery independently.

Teaching Strategy #2: Teach Math Like You Would a Foreign Language

Math is a universal language that should be taught with deliberate attention to symbols, patterns, words, frame, structure, and other parts of math. Make sure to teach and consistently review the following:

• Mathematical terms and vocabulary as appropriate by grade level. (Grade-level math fluency is a prerequisite for learning and advancement.)
• The interconnectedness of symbols, patterns, and shapes
• “Interpreting” and “translating” (e.g. word problems into equations and vice versa); encoding (translation of ideas into speech and writing)

Charts are a great way to visually show mathematical ideas through several iterations and to improve fluency. This equivalent fractions poster (preview shown below, full version available at Dyscalculia.org) represents each concept in multiple forms: with coins, fractions, words, decimals, and percentages. Notice how the half dollar section includes images of the coin, its value as a fraction of a dollar (1/2), the fraction in written form (one half), as a decimal (0.50), and its monetary value ($0.50).

This decimal place value chart (preview below) is a visual tool depicting the language, framework, patterns, and relationships of the base ten  system. The  write-wipe chart organizes information by color and allows students to easily  interpret numbers, convert units, write decimals, and calculate percentages, without a calculator.

Other Math Teaching Strategies

• Reduce visual stimuli and isolate digits; show only one problem at a time to reduce overwhelm
• Allow students to reason aloud
• Color-code related concepts
• Monitor for unconscious dyscalculic errors
• Chunk and simplify information (e.g. don’t use double digits if you don’t need to when testing; divide multi-step word problems into individual ones)
• Have students work in short time intervals
• Reduce the number of assigned problems
• Have students show how to solve problems while identifying key elements, vocabulary, and examples to explain the how and why
• Use visual timers to help with pacing
• Provide visual aids and cues (like charts) to reduce cognitive load, mitigate visual memory weaknesses, and help students “preserve” numbers (search for visual aids on mathisfun.com

How to Reduce Math Anxiety: Positive Teaching Strategies

• Teach students positive affirmations like “I can do math. I’m good at math.”
• Have students jot down their feelings before taking a test (proven to help reduce anxiety)
• Never make a student feel bad about mistakes
• Remind students that dyscalculia is brain-based – and that’s OK
• Teach students that thinking quantitatively is innate to humans – we are all doing math from the day we’re born, we just don’t realize it (a good response to students who say, “I can’t do math!”)
• Help students develop a growth mindset (“I’m not incapable; I’m just glitchy sometimes!”)

Math Anxiety and Dyscalculia: Next Steps

• Self-Test: Dyscalculia Symptoms in Children
• Free Download: Schoolhouse Blocks- a Guide to Building Foundational Executive Functions
• Read: The ADHD Symptoms That Complicate and Exacerbate a Math Learning Disability

The content for this article was derived from the ADDitude Expert Webinar “Quelling Math Anxiety: How to Identify and Effectively Teach Students with Dyscalculia” [Video Replay & Podcast #366] with Renee Hamilton-Newman, M.Ed., M.S.-Sp.Ed. which was broadcast live on August 3, 2021.

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