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Three class gallery walk on integers problem with @mparhar72 @MPichanick @HazelMcCallionS. pic.twitter.com/339UMZSYif
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— Mr. Oldridge Math (@MrOldridgeMath) October 25, 2013

You may have missed it, if you don't follow math news, but there have been major developments in something called the Twin Prime Conjecture. You may not care about prime numbers, but you should, if you care that your banking data (and any other kind of data is safe). The conjecture is basically that there are infinite number of pairs of primes separate by just one number- for example, 11 and 13, or 17 and 19.
You may have an image in your head of mathematicians working, solitary, alone, crunching numbers, and developing theories that nobody else could possibly understand. In this case, Yitang Zhang's work led to a flurry of collaborative math work. Together, mathematicians around the world worked to refine and push his breakthrough further than ever before.

Here is a quotation from the article:

"For weeks, the project moved forward at a breathless pace. “At times, the bound was going down every thirty minutes,” Tao recalled. By July 27, the team had succeeded in reducing the proven bound on prime gaps from 70 million to 4,680."

To be clear, the "team" here was an fully open and collaborative. They worked in real time, and using their combined wisdom, pushed the project much further than anyone could have imagined.

This matters for elementary (and high school) teachers because we often treat math solely as an individual activity. I myself have memories of sitting in a desk, in a quiet room, textbook open, doing problems in a workbook. We didn't talk math, and we didn't collaborate.

Things have changed since then, obviously, but how much do we see math as an open and collaborative activity in our classrooms? Not enough, I think. It all comes from the class culture. If we are open and truly value student voice in the math classroom, starting from the first day of class, we might be amazed at the culture that develops.

Math IS a social activity. Students learn from each other, sharing strategies and solutions, wondering together about the big ideas in math, scrawling solutions on chart paper, standing and justifying their solutions, and working on bigger projects where we build our understanding together.

Yes, in the end, each student in the end is responsible for having the skills and strategies needed to succeed in math, but together we accomplish so much more than alone.

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