I am sure different people of the Natural Math tribe will have different definitions of "Natural." I can share mine.
I am thinking of one of the most advanced, complex, psychologically involved learning tasks humans ever experience in their lives. It is more complicated than any graduate level course you will ever take. Yet the success of people attempting this learning task is almost universal. Can you guess the task?
Hint: people engage in this learning task early in their lives, when they have no prior learning experiences. The task is learning to speak. How is this powerful learning achieved? The features of learning to speak are parts of my definition of "natural":
Math can be like that: a part of our native language. For me, the goal of Natural Math is to collect, distribute and create such natural experiences of mathematics. We need to work with families to support them as units of larger communities of practice. We need to participate and engage babies and kids in math-rich, meaningful human endeavors that are useful, beautiful and fun. From the earliest time, kids should see themselves as co-creators of mathematics. The richness of the mathematical culture has to become available and accessible in a wide variety of communities, in many beautiful and meaningful forms.
"The future is here. It's just not evenly distributed." All the pieces of the natural math puzzle already exist in various "math oases" where families, subcultures, online communities and other groups of people engage with mathematics in ways that are natural for humans. We can put the puzzle together by networking: identifying activities that support natural math, supporting families and communities in finding and developing such activities, and loving one another in the context of mathematics.