Research Focus: TouchCounts
Nadège’s knowledge in the subject of math was off to a good start. At four years old, she was enthusiastically counting—on her fingers, by pointing at things, and by singing “the numbers song.” That shouldn’t be surprising: her parents are both professional mathematical researchers pretty interested in counting themselves! But like many children her age, she wasn’t counting expertly—she could sequence short runs of numbers in each of these counting systems, but would occasionally drop or repeat one. And when she tried to put them together, chaos would ensue! Her song might reach “seven” just as she ran out of fingers for counting a set of only five objects.
According to Dr. Nathalie Sinclair, mathematics professor in the Faculty of Education at Simon Fraser University—and Nadège’s mother—many diverse ways of knowing come together in children at such moments, poised on the cusp of early numeracy. Cardinality—one’s sense of numbers as things-in-themselves or one’s idea of something like “a dozen”—is based on an earlier experience of ordinality—numbers as they exist in the ordered sequence starting from one. And early learners’ experience of ordinality is very much based on the physical experience of their own bodies in space and time.
When we point sequentially at things to count them off, we are drumming our own sense perception, relating the abstract order of things in the world to a much more physically embodied sense of sequence and rhythm. And when we learn to count on our hands, we encounter our own selves—our own fingers—as our first experience of undifferentiated quantity slowly giving rise to ordered enumeration.
Nathalie’s interests in the role of one’s fingers and gestures in the learning of mathematics—in what learning theorists call embodied cognition—were poignantly focused by having to relearn how to count from scratch, a second time in her life. A decade ago, she lost the ability to read, count and even recognize letters and numbers when a 12-hour surgery saved her life from a brain tumor. After she was released from the ICU, she began a long road of relearning, during which she made the discovery that only through tracing letters with her finger could she reconnect brain awareness of a letter to its physical shape. As a result, she says “I learned to read again thanks to my finger.”
When the iPad began to popularize touch-based interfaces to digital devices, it was natural for Sinclair to start thinking about touch-based counting strategies. As it turns out, Nathalie’s husband—Nicholas Jackiw—is an expert in educational software design for mathematics. (With colleagues in the States and in France, he invented the Dynamic Geometry software paradigm that has revolutionized high school mathematics instruction across the world). Jackiw is also an adjunct professor in the Faculty of Education at SFU.
Sinclair and Jackiw envisioned adopting the technology of the iPad to extend learners’ finger counting “infinitely beyond 10”—into the mathematical empyrean of abstract number—while remaining anchored in the cognitively powerful experience of touch and gesture. At the same time, software could scaffold the experience of finger-counting with a mathematically-enhanced framework that used color, voice and motion to propose or reinforce ways of thinking about number counting and basic arithmetic. Sinclair applied for and received funding from the Canadian Foundation for Innovation for the development of an iPad app. TouchCounts was born.
Development and testing of the app proceeded. Nadège moved from testing to authoring when her parents decided the app might better count aloud in a child’s voice rather than an adult’s. The team worked with and studied toddlers from the SFU daycare on how they used TouchCounts to count; and then with researchers and school communities elsewhere in British Columbia, Ontario and northern Italy to finalize the design and functionality of the app.
TouchCounts includes using tactile gestures to create, add and subtract numbers. This fun counting app is used in-and-outside of classrooms by kids, together with their parents, grandparents and/or guardians and is available for free on the iPad App Store.
Going forward, the team is hoping to “build a whole grammar of gestures for [all] mathematical operations to enable learners to express mathematical ideas in a very tangible, personal way.”