So much of the math we do every day depends on our ability to visualize numbers, quantities, and relationships.
Every time you roll a pair of dice, you don’t count the number of dots to figure out your score. Instead your brain instantaneously recognizes the group of dots on a die and understands it as “4.” This is called subitizing. Most of us take this skill for granted, and it is one of the visual perceptual skills necessary for becoming proficient in mathematics.
For some children, especially those with the math disability, dyscalculia, mentally linking the image of those dots on the die with the symbol “4” does not come easily.
Occupational Therapist (OT) Jennifer Papasodoro and teacher Laura Kent work with students who have visual perceptual limitations, including dyscalculia, which may affect as many as 1 in 20 individuals, according to www.aboutdyscalculia.org. “As we learn more about math and developing number sense, we recognize the importance of visual perceptual skills,” said Kent when I recently met the pair at the Horace Mann School in Melrose.
Last fall, Papasodoro and Kent applied for a Melrose Education Foundation grant to purchase resources aimed at addressing the needs of students with dyscalculia. The workbooks, guides, and DVDs represent work from leading thinkers in the field of dyscalculia, including neuroscientist Brian Butterworth and author and educator Ronit Bird, who emphasize a game-based, visual approach to teaching students with math disabilities.
In the third grade classroom, I observed Papasodoro, Kent, and their students playing Yahtzee. But what the students were actually doing, I learned, was strengthening their subitizing skills.
In another lesson, students were using Cuisenaire rods of varying colors and lengths to help them conceptualize the number 10. In a set of 10 rods, #10 is the longest rod. Students learn different ways to make 10 by putting together shorter rods. In doing this, the students can visualize how by combining 4 and 6 or 7 and 3, you can make 10.
“Efficiency is the key word,” Kent said, describing the goal of the teaching approach. The teaching tools not only help students conceptualize numbers but also use that conceptualization to learn efficient strategies for calculation and understanding, which is essential for all learners as they tackle more complex math problems.
The game-based, hands-on approach “is a huge part of getting kids to buy into doing math, especially if they are struggling with it,” said Papasodoro. In addition, the teaching strategies help the students to problem solve and explain their thinking – a focus of math education currently.
Kent and Papasodoro have seen their students make big strides since the duo began augmenting their teaching practices with lessons learned from the new materials. The students’ ability to fluently add, subtract, and multiply has improved. Scores on assessments have improved. At the beginning of the year, it was a challenge for their students to pick out numbers on a number line. Now, with a stronger understanding of numerical relationships, students are using the number line to help them calculate.
Kent described a recent “a-ha!” moment for one of her students, who smiled at her and announced: “32 is a lot! It is the same as three 10s and two 1s and it is so much more than 16.”
Although targeted at dyscalculic children, the learning materials can be used for any young child developing number sense. “In every first grade classroom, some students have an inherent understanding of numbers and some need to see it in different ways, multiple times,” said Kent, who has shared some of the strategies with first grade teachers.
Papasodoro meets with other OTs frequently to share teaching strategies, lessons learned, and student successes. “It’s amazing: at the beginning of the year, rolling dice and picking out the numbers that were the same was a challenge,” she said, speaking about the students she supports. “Now they are playing Yahtzee.”
Elizabeth Christopher is on the board of the Melrose Education Foundation.