This is a guest post by Joseángel Murcia of TocaMates, translated from Spanish by Ever Salazar.

Sand has always been a good place to do geometry. In fact, ancient Greeks used it instead of the “modern” blackboards to show their ideas and schemes. It is also said that Archimedes died while drawing in the sand from the beach, disobeying a Roman order to stop.

At the beach, we can do lots of designs, but today we will focus on two ideas.

Ages two to five

What can we make? Sand polygons
How can we make it? Using a stick, draw a “path”. The kids should follow it. The paths can be curved lines or straight lines (forming polygons), they can be left open (with exit) or closed (to follow indefinitely, around and around).
Why make it? It is about experimenting with polygons, lines and angles. It is about feeling geometry in our bodies.

Five and older

What can we make? Gardener’s curves
How can we make it? We will need two large sticks in the sand, like poles from the beach umbrellas. Use those when sun is down, and they are not necessary anymore. We will also need a rope and another stick to draw the curve. Tie the rope to the two sticks so it has some slack. Pull the rope taut with the third stick, to form a triangle. Now draw with that stick, keeping the rope taut at all times. Changing the distance between the fixed sticks (the focus), we will get different ellipses. What happens if we put both sticks together and have only one focus?
Why make it? Conics (like ellipses) are known from ancient times. Those from the sausages are my favorites!

This post is from a series of everyday life activities to help kids (and grown-ups!) to discover how to look at the world with math eyes. They were published as “Mathematics is for the Summer” in “Today’s Women” magazine.

“GO TO HELL.”

Peter Gray’s book starts with a bang – Peter’s son curses his parents and educators. Peter and his wife are crying: “This time I felt, maybe, I really would go to hell.” What would send him there? The book explores the dire consequences of forcefully educating children.

(Click the images to enlarge them.)

How can we stop being complicit? The book offers several answers to this question, including modeling one’s education after hunter-gatherers tribes. Kids can find the resources to live freer lives within modern tribes, such as techie start-ups, unschooler circles, and maker communities.

One of the benefits of open education is free age mixing, a topic large enough to warrant its own map.

Peter Gray presents a five-part definition of play strikingly similar to math. It is useful for those into game design, experience design, curriculum design, and parenting.

There is a math club activity where students make “star diagrams” out of lists of what is important to them. Here is such a diagram explaining Peter Gray’s five types of play as they relate to math.

“Free to Learn” explores two venues of open education. First, democratic learning communities in freeschools such as Sudbury Valley or Reggio Emilia. Second, a style of trustful parenting and homeschooling called “unschooling” where individual families walk their own paths. Both provide the benefits of open education presented in the diagrams above.

Reading Peter Gray’s analysis of the two methods, the drawbacks are clear. In freeschools, resident teachers do not pursue their professions so that they can help children full-time. This leads to a situation where kids are rarely exposed to the projects of adults. Unschooling families can provide exposure to grown-up work. However, it is harder for individual families to maintain ongoing daily contact with a large multi-age group of kids.

Why not the benefits of both paths without the drawbacks? We need something beyond freeschools, and beyond unschooling. Let’s get to work!