Math and CVI: Ideas for a multisensory approach

“From the guitar, I was also able to build an internal sense of number lines, and fractions, because I could think of them kinesthetically as the guitar strings and the frets as the intervals. The corresponding musical intervals also helped reinforce thinking in terms of fractions, since all musical intervals can be expressed as fractions as well. The guitar neck laid a foundation so that I could later grasp spatial concepts like points on an X axis and Y axis on a Cartesian graph, which without the help of the guitar neck serving as a kinesthetic-tactile base, would have surely fallen into my aphantasic void. More than once, I was caught playing air-guitar in math class. They mistook it for distraction, when in fact it was my way of grasping the mathematical concepts. 

Music can be a powerful tool to bridge CVIers to understanding many mathematical concepts that usually pull on very visual thinking. Research has shown that internal number lines and such are usually stored in the visual parts of the brain. I suspect that the guitar was the cognitive bridge that allowed me to store my internal number sense in the auditory and tactile parts of my brain.”

We have been working a lot with our 8-year-old daughter, Sam, on number sense and math concepts since our first math and CVI study group meeting. I wanted to share the materials and approaches we are using to learn counting, numerals, sequence, etc.

As with many children with CVI, my daughter is a multi-sensory learner. She requires 3D objects along with a lot of hands-on interaction to build familiarity. 

We started by having her get familiar with jumbo Unifix cubes (smaller ones are a choking hazard), just playing with them and stacking them. 

We then used snack time to work on Math. Snack is super yummy and exciting for her, and we knew it would be important to make math fun, interesting, motivating, meaningful and relevant. She has done some “Snack Math” at school and so I wanted to see what we could do at home. 

We started viewing and tracing the tactile numerals, starting with 1, as Sam is familiar with the phrase “just one.” We used the instructional sequencing steps referenced in Linda Mood-Bell’s book On Cloud Nine (concrete, use manipulatives; imagery, language to help visualize math concepts; computation, apply math to problem-solving): 

• Explored one manipulative (the Unifix cube)
• Traced and viewed the number 1 (sandpaper numeral)
• Used salient feature language [describing visual attributes] (Roman-Lantzy)
• Then she picked one snack item. 

We then increased to 2, and we are working on 3. Slow and steady. 

Sam is using her vision (to see the numbers) and then her pointer finger (to point to the number while she looks away).

She is able to answer the question, “Point to the numeral _____ (1,2,3)” after the series of visualization steps—manipulatives to visualize and feel “one”, tracing to visualize and feel “one” and after she answers the “show me/point to” question, she takes the amount of food she has been working on (i.e., 2 yogurt covered raisins). Note: As Matt Tietjen suggested, when using multiple Unifix cubes, I alternate colors for greater ease in counting and visualizing. 

While doing “Snack Math” Sam is smiling and focused as we learn, and that is so essential. She is having fun! She smiles so big when she gets the answer right. I am so proud of her and excited to teach more, and see Sam showing me all that she knows!

The materials:

• Jumbo Unifix Cubes
• Dowling Magnets Magnetic Demonstration Number Line. (Using the implementation of the number line from On Cloud Nine.)
• Tabletop Magnetic Easel Whiteboard & Washable Blackboard with Chalkboard Design 
• Elite Montessori Sandpaper Numbers. Added velcro to the back so we could get them up & out of lower field on the felt slant board. My daughter has really taken to them—visually and tactually. The girl loves rough surfaces.
• Balck felt slant board with lip at bottom for loading numerals and unifix cubes that was customized for Sam by Perkins. (Can use a felt surface on a regular slant board.)
• Flashlight as a pointer and to gain visual attention
• 3×4 mini muffin pan for ease in displaying visuals and snacks for viewing and counting

“My 12-year-old CVIer benefits from a tactile representation of number lines. She had such a hard time visualizing the number line. And we’ve learned from Matt Tietjen’s presentation that visualizing or imagining math is a part of learning math concepts. When I saw how helpful a tactile approach was for her to internalize and understand a number line, I thought about her challenges with timelines.

She loves history, and we’ve had a long piece of paper with the centuries on it in the kitchen for years. When she learns something new, for example about the Vikings, I show where it occurred on the timeline. After our first CVI and math discussion, I gave my daughter beads and told her each one is one hundred years. She strung them onto a necklace and used her strong verbal and tactile skills to talk through what it meant to have a first century, second century, and so on, and then one hundred, two hundred, three hundred years, and so on. She was very excited to make the connection that had previously eluded her: the fifth century contains the years that are in the 400s. She relies on verbal and auditory skills to memorize things, especially abstract concepts, and the words “fifth century” and “four hundreds” were very confusing. She had also never really understood what the words “twelve-hundred” meant in numbers, or where on the timeline to find a word-heavy number like “sixteen twenty-seven.” 

As soon as we explored a timeline with beads as centuries, I realized she did not know there was the same amount of time between the years 0 CE and 1000 CE as between 1000 CE and 2000 CE. She had based her understanding of the timeline (number line) on the one we had made in our kitchen, which is visual and has more physical distance between 1600 and 2000 than the rest of “time” (we have more historical events to fit into this time period, so it is expanded). Touching the beads, she was amazed to see how recently our country was founded, how long the Roman empire lasted and posed questions about how many years existed before the year 0 CE. 

We have discussed these topics for years but she had nothing to hang the information on—no internal number line. We then spent a week making bead strings that are large enough to feel each century easily that she references now. I can pause a documentary and we take our time touching the timeline beads to find where an event approximately occurred. My daughter is relieved and excited to have this tool to understand timelines. My typically-sighted kid also loved this project.”