Editor’s Note: Global Math Week begins October 10 and contains events such as a kickoff symposium with short talks by women and men from all over the world describing their own joyous experiences with math. All talks will be archived afterward, find them through the Global Math Project Facebook page. Christopher Brownell, Associate Professor of Mathematics Education at Fresno Pacific University, shares how the Global Math Ambassadors have engaged millions of students around the world in math. And join them for #Globaledchat on Twitter on Thursday, October 11, at 8pm US Eastern time.
Several years ago, a small group of mathematicians, math educators, and teachers got together and wondered aloud about what they could do to improve the image of mathematics around the world. This field, rich with aesthetic, power, utility, and sheer fun, is commonly perceived as something far less interesting or engaging than it could be. The curriculum in mathematics classes are so narrowly constrained that, for many students, it has no sense of pleasure, play, or joy. This subject, which impacts so many other areas, has been portrayed in its worst possible light for far too long.
An Audacious Goal
With more than 1.2 billion elementary and secondary students enrolled in school worldwide, and following on the heels of the recent success of the “Hour of Code” movement put forward by Code.org, the aforementioned group of math-folk decided on a goal of reaching 1,000,000 students in two years. The task? To create engaging mathematical experiences for students of any age from 5 years old to adults, available at no charge and accessible regardless of language or location around the world.
An Exciting Piece of Mathematics
Settling on the best topic ended up being the challenge, but one member of the team, James Tanton, Mathematician At Large for the Mathematical Association of America, had been creating a collection of video classes online around an idea that now is known as “Exploding Dots.” Exploding Dots are a fun (and noisy!) way to introduce young children and adults to the power of a place-valued numeration system, like the one we teach to children and use every day.
The idea is to “explode” dots, which then become a smaller number of dots following specific rules. While the rules can be modified based on the goal of a lesson, a simple introduction has a row of five boxes, an “explosion rule” of two becomes one, and starts with a set number of dots in the first box on the far right, such as two dots as in the example above.
Those two dots “explode” and result in one dot landing in the box immediately to the left of the original dots, in this case, the second box from the right. (While this “exploding” of many to one seems counterintuitive at first, it is well accepted in practice.) In this, two dots in the far-right box can be represented as a single dot in the next box over. Try this exercise yourself on the Exploding Dots website.
For mathematics instructors, you’ll see that we’re building machines using the machine metaphor that “explode” many dots to become a smaller number of dots, just as we might with base-ten blocks or sticks and bundles. Part of the charm and beauty of Exploding Dots is that the machine’s exchange rules are entirely fluid, up to the machine operator. A “machine” may be of any base (see text box for more information on this). The example in figure 1 is, for instance, in base 2. It is just as simple to use base ten, our more common way of writing numbers. Often, when that rule is adopted the real strength of the method is revealed. Furthermore, as in Figure 2, it is possible to provide Algebra students with visualizations of the abstract ideas within that course.
An Auspicious Plan
How do you get such a wonderful bit of mathematics to so many people at once?
In 2016 at the National Council of Teachers of Mathematics conference in San Francisco, California, a campaign was launched to recruit “ambassadors” to the project. These representatives would be the first group, going back to their homes, schools, communities, states, and countries to engage as many people as possible with “15 minutes of joyful and uplifting mathematics.”
A small, web application firm in Canada, Scolabs (Buzzmath in the US), then created the Exploding Dots website. By October 2017, 1.5 years after recruiting ambassadors and within the two-year original timeline, we exceeded our goal of 1 million registered users by more than 75 percent. Presently, nearly 5 million students have engaged in the Exploding Dots experience from all over the world.
What’s Happening Next
Hundreds of teachers have registered their classes and over 96 percent report that Exploding Dots, “has helped my students see math as more approachable and enjoyable.” Three quarters also report that their students are still discussing their experience with global math week last year. Dozens of teachers and other professionals have joined the ranks of the ambassadors, from every continent except for Antarctica. At present, the Exploding Dots website has been translated into several languages and more languages are in process. The week surrounding October 10, 2018 is our second run with Exploding Dots, but we are busy at work planning 2019’s joyful mathematical experience for all.
This year we have set a goal to exceed 10 million users—now that’s a whole lotta dots! You can learn more about Exploding Dots and Global Math Week on our website. Join the fun!
All figures were created by and used with permission of the author.
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