I’ve always wondered why the Brits referred to Arithmetic as “Maths” in the plural. Seems I’m not the only one, but the answer is usually a stylistic one. If mathematics implies the plural, then maths is a logical contraction of the word, and a post I saw on LinkedIn today made a good case for considering mathematics in the plural. Peter Flom does a nice job expounding on the beauty and varieties of math, and its pluraility is evidenced by discussion of the term on Wikipedia.
When it comes to deficiencies in visual perceptual development, we tend to place great emphasis on learning difficulties as related to reading. Witness the AOA’s CPG on Learning-Related Vision Problems which has a section on Dyslexia, but no mention of dyscalculia. Yet in Table 4 you’ll note that difficulty with basic operations in mathematics is one of the signs of visual analysis skill deficiency. I like this description from Gayle Zieman, PhD, regarding Dyscalculia: Math is a significantly “right brain” activity involving visual spatial abilities. Conceptualizing math problems involves visualizing the operations. Addition, for example, is a mental operation of “seeing” sets of things being put together. Research has shown that NLD individuals can understand the language and verbal reasoning aspects of a math problem fine, but can’t “visualize” efficiently the relationships between the parts of the problem to actually perform the arithmetic operations. Research has also pointed out that visual perceptual skills have a stronger relationship to math ability than does a person’s general IQ.
Various ODs though the years have noted that visual perceptual abilities, particularly related to visual spatial skills, are essential readiness skills for math. Rosner felt that his Visual Analysis Test, and subsequently the Test of Visual Analysis Skills related more to math performance than any other subject. Although Solan is better known for research related to reading, he also noted the importance of visual perception to mathematics. More recently, Kulp and colleagues have conducted research that visual perceptual ability relates to mathematics achievement. David Mills, PhD, MA, has done a nice job elaborating on the work of Fischer and Groffman involving subitizing and its relationship to mathematical concepts. Here’s a nice paper on applying the principles of visual perception to geometry, with lots of good ideas for therapy procedures. I started thinking more about this after the excellent workshop at the COVD meeting last year presented by Drs. Kneuppel and Montecalvo.
Although reading problems are typically what brings most children to our office, and many have reasonably good computation abilities and only get tripped up when getting to math word problems because of comprehension issues, there are those who struggle with the most basic concepts of math. Many of these children lack the visual readiness tools and math is therefore abstract for them. They need a more hands-on and concrete approach, and an “oldie but goodie” procedure is Cuisenaire Rods. I was reminded of this last week when my son, Dan, was back to tidy up some loose ends in the office before beginning in earnest in the outskirts of Chicago. The timing was good because he got to look in on his niece, Chaya, who was in from Cincinnati to spend the summer with her cousins in NJ. She has a summer workbook from school, and it was clear that some of the math concepts in there were challenging. We’ve had her in to the office daily for a kind of immersion in visual perceptual therapy, and Dr. Dan pulled out the Cuisenaire Rods and they worked like a charm! Here’s a nice YouTube video I found as a review of Cuisenaire Rods in more of a traditional way; another one using Smart Board technology; and yet another YouTube video with a rare sessions recording reminding us to “Get Back” to valuable origins.