Visualizing Math: Considerations for students with CVI

Find key takeaways from Tietjen's presentation exploring possible strategies to develop math skills in learners with CVI, along with a summary from the first meeting of the math and CVI study group.

Exploring math and CVI

Matt Tietjen, M.Ed, CTVI, and leader in the field of CVI, discusses the 

  • the implications of CVI on learning math skills,
  • the neuroscience of learning math,
  • why it’s important to bring together diverse perspectives to foster paths of inquiry around math and CVI, and
  • a look at how strategies from the On Cloud Nine math program might benefit some learners with CVI.

Download the transcript. Also, in this video, Tietjen references his previous presentation: CVI and Math Mind.

A path towards unique math approaches for learners with CVI

  • How does math typically develop in the human brain?
  • What unique challenges can CVI present in that development process?
  • What research-based educational/intervention strategies already exist in addressing similar challenges in people not necessarily diagnosed with CVI?
  • How might we adapt, borrow, and apply these research strategies to learners with CVI?
  • What can we learn from presenting case studies of attempting these strategies with students who have CVI? And to what extent can this inform promising practices around CVI and math?

This path of inquiry could then lead to developing new strategies unique to children with CVI and math, which in turn can inform areas of scientific research to more precisely identify how CVI impacts math acquisition and to test the developing promising practices and intervention strategies.

For some individuals with CVI, number sense may not come as naturally and incidentally. Many of my students need intentional, thoughtful instruction and scaffolding to develop number sense.

Matt Tietjen, M.Ed, CTVI, and leader in the field of CVI

CVI and Visualizing Math

Imagery is an important component of how we think with numbers and solve math problems. Visualizing math needs to be intentionally fostered through systematic instruction. For many individuals with CVI, the CVI visual behaviors make it difficult to fully take in the visual world through incidental learning. Individuals with CVI often have difficulty taking an entire visual scene, and often can only visually process one piece at a time. This may mean they are at risk for difficulties with concept imagery. 

Mathematical reasoning develops in the following order:

  1. Concrete: manipulatives to experience the realness of math
  2. Imagery: language to concretize that realness in the sensory system
  3. Computation: apply math to problem solving

(from Bell and Tuley, 2009)

Understanding how we learn and the progression of skills must translate into a systematic instructional approach when working with learners with CVI. Without strong, intentional instruction, CVI accommodations and adaptations only go so far.

The Math Ladder

The purpose of the On Cloud Nine Math Ladder is to “provide a sensory-cognitive mathematical base for life-long success with math and mathematical reasoning” (Bell and Tuley, 2009).

The bottom of the ladder begins with imaging numerals and moves up to fractions.

  • imaging numerals
  • imaging the number line
  • addition
  • subtraction
  • word problems
  • place value
  • jumping
  • carrying and borrowing
  • multiplication
  • division
  • decimals
  • fractions

Tietjen’s presentation discusses the lesson steps for imaging numerals and imaging the number line and offers ideas for CVI considerations and adaptations that include a multisensory approach (tactile, auditory, visual, kinesthetic), and emphasizes the importance of color.

5 takeaways from the Math and CVI discusion

The Math and CVI Study Group hosted its first discussion on December 7, 2021, with 84 participants including CVI families, individuals with CVI, TVIs, and educators. The main focus of the discussion was around this concept of visualizing math.

The answer lies in a wide range of instructional strategies

  • There is no one-size-fits-all approach nor is there a magic bullet.
  • One CVI parent discussed how she uses a customized approach to teach math to her son, which includes an intentional instructional approach for skill-building, along with reducing clutter, use of light, color, manipulatives, and listening skills. This parent also discussed how visual and sensory efficiency skills evolve and change.
  • It’s about daily assessment so we meet the child where they are each day. 

Use the sensory skills that work best for the learner with CVI

Participants shared examples of how their students were able to do the math verbally, tactually, and with other sensory approaches, but visually math continued to be a struggle.  

  • “My kid is processing math verbally—she translates symbols into verbal so she can access them more easily. Visually processing letters/numbers/symbols causes fatigue.”
  • We used manipulatives to master the points on each number. Now the student with CVI is able to visualize the points in her head and does not need the visual/tactile points anymore!”
  • “The On Cloud Nine has been a game-changer for my daughter with CVI, which we individualized for her. To help her visualize and imagine, she has to keep her eyes closed. My daughter says if her eyes can see the room she cannot picture/visualise anything. With her eye shade on, she has developed a mental world called Math Land. She’s on an imaginary boat. Each country in math land is a subject (e.g. money land, measurement land, shape land, word problem land, counting land). We are now at the stage where she is imagining the bridges between the lands—she is in money land and then goes to sit on the bridge between money land and word problem land to visualize a money word problem.”
  • “On Cloud Nine goes beyond just providing accommodations, but offers a tactile/visual/auditory approach and intentional steps on how to imagine and think about math. This makes me think beyond the first step of just trying to declutter and add color for support.”

Color-coding as a powerful compensatory skill

  • Tina, an adult with CVI, shared how instrumental color is when solving math equations. Her vision often becomes blurry, especially with a lot of visual clutter and when there is too much to visually process. If Tina’s working with only black print, she isn’t able to follow the math problem. When each number and symbol has its own color, she’s able to follow the equations. For example, the number 4 is always green and the multiplication sign is always pink. So when she’s not able to see the symbol, she can use color to support recognition. 
  • An educator shared another example for color support: “One of my students uses a color-coded template to do computations. The numbers themselves are black but the boxes where they are written are colored. It was a game-changer.”

Importance of knowing the student’s reliable responses

  • Educators shared questions around how best to support students who have CVI and complex communication needs and/or complex motor needs—how do we know when they don’t understand a concept or are having difficulty interpreting what they see? 
  • Others shared how they used the sensory approach that worked best for the individual with CVI. It’s important to build on their strengths and abilities, and figure out the student’s reliable responses. 
  • Watch Accessible and meaningful learning for students with CVI to learn more about evaluating reliable responses and implementing systematic instruction.

Ideas for math interventions for learners with CVI

  • TouchMath: a multisensory math program that uses the numeral as manipulatives. Several participants shared that they love this math intervention, but may not be fully accessible for learners with complex motor needs. 
  • Numicon: a multisensory approach that uses color and shape to help develop number sense and foster the understanding of connections between numbers. Several participants shared how they are using these manipulatives and instructional strategies with their learner with CVI. 

Individuals with CVI are very capable and have workarounds for so many tasks in life. In order to approach math from a strength-based perspective, we must deeply understand the student’s individualized needs along with how to implement systematic math instruction. And we must explore how multiple strategies, interventions, and multisensory learning, infused with the use of CVI accommodations unlock access to building math skills. 

Stay tuned for registration details for our next Math and CVI study group discussion on February 8 at 3 pm EST. In the meantime, if you have math ideas and strategies that you are exploring for your learners with CVI, feel free to share. Send an email to [email protected]


Bell, N., & Bell, N. (2009). On cloud nine: Visualizing and verbalizing for math. San Luis Obispo, CA: Gander Pub.