Cardboard construction is a great way to help a preschooler improve their grip strength and fine motor skills, not to mention the myriad of engineering concepts like geometry and physics. The problem is when you give you little one a pair of scissors, you get one or two cardboard cuts before they give up, because cutting cardboard with little hands is HARD WORK and it hurts. A fun alternative, which is less taxing on the grip, but still challenging is a little Makedo Safe-saw (ages 4+ with adult supervision).
I purchased the Makedo Toolkit from amazon, after having done a lot of research into cardboard construction with a preschooler, and having found nothing else that would really useful. It seemed novel and interesting, however I remained skeptical as to it's effectiveness in a 4-year-olds hands.
It arrived about 30 minutes before quiet time, aka nap time, but I was too excited to wait. I immediately opened it and showed the tools to my son, which included a safe-saw, a scrudriver, and some scrus (not misspelled). As one might think, he grabbed the saw first, which has a little dull spike on the end of the handle for perforating cardboard. I have him an amazon box, and set him loose. The first thing he did was try and saw perpendicular to the cardboard, which didn't work at all. My stomach dropped. I showed him the little spike, and demonstrated poking a whole in the box. He grabbed the saw back, and began stabbing the box repeatedly. Again, my stomach dropped, even more so when his little sister started to get interested in what was happening.
After a little chat the vigorous stabbing changed into small stabs, which was good enough, and he was having fun. I picked up the scrudriver and started screwing in the scrus into the wholes he had made. This too peaked his interest, and for a few minutes distracted him from the stabbing. While he was screwing, I made some perforations in a tight line, then used the saw to break them open. Immediately he wanted the saw back, and started sawing perpendicular to the cardboard, with little effect. Yet again, my stomach dropped, but then I realized he wasn't using the saw effectively, and had I been the one doing the vertical sawing, I too would be having troubles, so I tried to explain. You want to cut at a 45 degree angle to the box, with your shoulders over or in front of the wrist so you can use the weight of your body to push down and cut. This is when the sleepy-angry started coming out. He turned around and humphed. I backed off and told him to do as he pleased. He continued to try and saw the same as he had been before, to no effect and became frustrated, going back to stabbing the box with the nib.
I attempted to help a few times, as he experimented with the saw again, and again without success, but each time got Mr Sleepy-angry. So I let him stab, realizing that he was still trying and stabbing was improving grip strength, which would improve sawing and scissor work. Over time he would be more receptive to learning new techniques, or experiment with them himself. The important part was, he liked and enjoyed doing construction play with the tools, even if he wasn't building anything.
The moral of the story being that when introducing a new skill to a preschooler, a win is as simple as a smile, because the rest will follow in time (especially when My Sleepy-angry is in charge).