A couple of years ago, my parents bought a cabin a few miles up Blacksmith Fork Canyon in Cache Valley, Utah. It’s about a 40-minute drive. My dad asked to drive me up there today to see the progress he’s made on the cabin – it’s supposed to snow tomorrow so this would be our last chance for the winter.
We drove on clear roads for some time, but eventually got high enough that the roads were covered in snow and, eventually, ice.
At the first transition from snow to ice, my dad lost control of his truck and we slid around and landed in some trees. The front tires were off the road, but the rest of the truck was at a 90-degree angle to the road.
My dad switched gears to reverse out and get back on our way. The wheels just spun. My dad is very calm in emergencies and, even though my first thought was, “We’re in the middle of nowhere. We are going to die.”, he calmly began telling me what he was doing as he spun his wheels.
He told me that the friction caused by spinning the wheels would melt the snow or ice down until the tires would hit the ground and we would be on our way. So, he would spin the wheels for a minute or two, and then let the truck cool down a bit and let the ice settle a bit, and then spin again.
After he repeated this process over and over for about 15 – 20 minutes, the wheels finally caught and we reversed back on to the road, made up to the cabin. We got stuck one more time, but luckily it was closer to the cabin and some of his neighbors were there with a truck and chains that they could use to pull him out. He calmly explained that if they weren’t there, he would go get his tractor from the cabin and use that to pull the truck out.
The reason I include this story on a math ed blog is because, even though the content is not strictly mathematical, we often talk about the importance of “productive struggle” for our students. The trigonometry book I taught from mentioned that students should be encouraged to regulate their work time and try to keep from “spinning their wheels uselessly.”
This experience taught me a couple of things: First, that spinning your wheels can actually be a productive thing to do: Even when working on mathematics, it can be helpful to dive in and struggle for a while and then take a break to go on a walk, take a shower, or do the dishes. Spinning your wheels and taking a break and then jumping back in can actually help you reach solid ground. Second, I have not had as much experience getting stranded as my dad. So, I can imagine I would spin my wheels for a few minutes and then just give up. But because my dad has had experiences where he was forced to find a way out, he has learned that he just needs to persevere and eventually it will work. So helping our students have experiences where they work hard for a while and reach a solution is important. Third, my dad asked for help and had back-up plans in his mind in case asking for help didn’t work. He suggested a solution to his neighbors, showing them how they could be useful. He also considered other resources available to him, and what he could use if his neighbors were not able to help. So giving our students opportunities to plan for multiple eventualities and to flexibly consider potential strategies is also important.