Imagining Math — 4-Year-Old Style
Imagine a 4-year-old. Now imagine a 4-year-old doing math. What comes to mind?
Perhaps you see brightly colored numerals scattered on a rug next to where your conjured child is playing, and you hear the sound of her emboldened voice as she counts, “3, 4, 5, 6.” Maybe you picture an adult lingering nearby asking a question, “How many blue blocks do we have?”
Now imagine math in a preschool classroom. How does your picture change when you move into a formal educational setting? Do you form an image of math readiness leading to success in kindergarten and well beyond as federal policymakers would have you do? What about when you add a touch-screen device, like a tablet or an interactive whiteboard, to the mix? What does mathematical thinking look and sound like now that the materials are digital?
Over the last couple of years, I’ve had the good fortune of having a front-row seat to this kind of exploration as a result of two research projects. The first is CPB/PBS’s Ready To Learn initiative, which is supported by the Department of Education. The second is Next Generation Preschool Math, a collaboration between WGBH, SRI International, and the Center for Children and Technology, that the National Science Foundation has made possible. These two research efforts, the first a summative evaluation and the second an R&D project, seek to understand what happens to young children’s learning—specifically their math learning—when their preschool teachers have new interactive tools at their disposal. It will be several more months before my colleagues and I are able to share official results so, for now, I’ll offer some informal musings, and invite you to share your math thoughts and questions.
- Subi-what? It’s no surprise that the first wave of products in a new medium, such as a tablet, recapitulates products common to an older medium, like a desktop computer. This is why apps that focus on counting and one-to-one correspondence are legion, just as letter recognition was and still is common in literacy apps. These early skill building blocks are extremely important, but they aren’t nearly the whole math story. For example, have you ever heard of subitizing? It’s when a child is able to identify the number of items in a set without having to count, such as quickly identifying the five dots on a single die as “5.” Some of the talented producers at WGBH have been grappling with game mechanics that call for subitizing and not counting, trying to take advantage of the gestural nature of an iPad. It’s a more complex design challenge, but promoting the skill can help a child develop a fuller sense of number.
- The dodecahedron leads the way. Just as Milo required many guides in “The Phantom Toolbooth,” including the mathematical shape with 12 faces when he entered Digitopolis, the interactive realm requires smart people navigating the terrain of young children’s math thinking. These math experts are invaluable to producers and researchers alike as they pull together full learning progressions without over-isolating individual skills, like shape and pattern recognition. Julie Sarama and Doug Clements, for example, have lovely, rich descriptions of preschool and school-age children’s math development. Likewise, Herb Ginsberg, ever mindful of children’s social and cognitive development, doesn’t split apart kids’ emotional relationships from their knack for conceptual math thinking.
- Math, ugh. It’s not uncommon for preschool teachers and parents to carry around negative associations to math. Although that may sound like a “no-duh” statement, it also can point to an opening. Despite what may be longstanding anxiety around math as a topic, otherwise unsuspecting adults engage in math thinking quite regularly. A good example comes from what mathematicians call equipartitioning or creating equal shares, such as dividing a pizza into eight equal slices or passing out six apples to three friends so that each receives two. Although adults may commonly engage in equipartitioning activities, they often do so from a social angle, focusing on the concept of fairness. Calling attention to the mathiness of this concept can help kids’ later learning as it’s a precursor to understanding proportion and more sophisticated number reasoning concepts.
- Angry, um, monkeys? No doubt there is much we can learn from and share with designers working in other cultural and educational contexts. Just as there is an explosion of learning apps in the US, so too are other countries scrambling to create media that support early math learning. Finland, for example, the country that gave us “Angry Birds,” is home to 10Monkeys.com, a math-rich game environment. Like other newly created integrated learning systems, it seeks to build children’s automaticity with certain math skills while mining data on the back end to produce teacher- and parent-facing statistics. Looking at a wide range of interactive productions gives the opportunity to bump up against our assumptions about what it means to “do math” at a young age. What do we think about personalized learning, and how might game design reward collaboration? Or, one that our research teams have come up against repeatedly, what is collaboration when you’re 4, sharing a tablet and trying to convey to an adult who is in your business that you’ve mastered a math concept?
Starting this fall, our Ready to Learn and Next Generation Preschool Math research teams will have much more to say about preschoolers and their teachers’ engagement with math apps and transmedia. Stay tuned for what we hope will be oodles of data and gooey descriptions from Bay Area and New York City classrooms.