Ode to a bead string (a non-poem poem)

from The Math Maniac

What is a bead string?
100 beads
Whites and Reds
5+5+5+5+5+
5+5+5+5+5+
5+5+5+5+5+
5+5+5+5+5
From hand and eyes to brain
But also: a caterpillar, a snake,
dog collar and horse bridle
a gun

a gate or a fence

a telephone line
a part of a train
lock for your door
tiny eggs (maybe spiders?)
coins
jewelry (necklace, naturally, or earrings, bracelet, belt)
roller tracks for a made-up truck
beans cooking in a pan
and so much more!

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While reviewing Dreambox Learning, I spent some time thinking about physical manipulatives compared to apps. Apps can certainly have nice features, but physical objects own my heart. I'm not even going to talk about the educational value (see this Hand2Mind note for a summary and further references). The thing we really like is the open-ended flexibility about how they can be used, both mathematically and for creative play.

As an example, the bead string is (maybe?) one of the more limited maipulatives because it is linear and one connected piece. We don't even have one. However, the ideas above were immediate ideas coming from observations of how my kids play and a quick brainstorming session with the little ones.
BTW, we find that a 6 to 9 year old can make any object into a gun, in case that idea didn't make sense to you.

Favorite category of math manipulatives: food! In this case, freshly baked chocolate cake.

Returning to math, one of the cool things about this open play with math manipulatives is that it provides a lot of easy entry points into short math chats. These are fun, in themselves, and also reinforce the observation that math is accessible and all around us.

Manipulatives in Apps
While better than nothing, virtual versions of physical manipulatives always seem to fall short, with the following limitations:

• only one "correct" way to interact with them
• no possibility of combining
• can't take them apart

Perhaps there are also some benefits of virtual objects. In particular, they don't need to obey the law of conservation of mass. Can that, or other advantages, be used cleverly to make up for the disadvantages?

Let me know what you think and tell me where you've seen the best use of virtual manipulatives.