If you're going go to the effort of sawing something, you really ought to have the gratification of making it all the way through whatever it is you're working on. Like hammering, sawing requires a combination of good "aim" and force, a balancing act made all the more difficult if the wood in question resists your efforts.
For young children sawing "success" means having small pieces of fairly soft wood available. Our commitment to using scrap wood, however, often leaves that particular material in short supply and explains why so much of our wood bears the faint marks to unsuccessful sawing efforts as children give up without experiencing the feeling of sawing air on that last stroke of a successful cut. Pointing out to the kids, "Look, you're making saw dust," just isn't enough of a reward for all that effort.
The kids aren't the only ones who've been frustrated by this phenomenon. I'd actually come to the point that I was considering spending good money on small scraps of soft craft wood, but last week I had the epiphany that cork is, indeed, wood (the bark of the cork oak), it's soft and we in the Woodland Park community seem to have the ability to produce an endless supply.
Pop them in a vise and even the 2-year-olds are having success.
I love that they're able to successfully saw off "cork cookies," even while working on the technique they'll need before moving on to bigger and better things.
Don't forget your eye protection. Happy sawing!