Lots of teachers complain that their students don't think for themselves, or don't have perseverance, or need everything spoonfed to them. Students ask for help or just give up at the first sign of difficulty. Seems bad!
Often the solution is to give students problems they don't know how to solve, so they can learn to persevere when they aren't sure what to do. The logic is that persevering when you don't know what to do is a skill, like shooting free throws. If I wanted to get better at shooting free throws a good place to start would be to go out and shoot a bunch of free throws. If we want students to get better at persevering when they aren't sure what to do, the logic goes, we should give students lots of chances to persevere when they aren't sure what to do.
I've done this! That logic above was mine. And the thing about teaching like this is that it's easy to convince yourself it works. In any class there are some kids who already have some confidence in math class. I would see them persevering and say, "look, it's working for some kids, the other kids just need more practice."
I don't think "persevering when you aren't sure what to do" is a skill to practice. I think teachers are better off conceptualizing it as a habit. Students give up easily because they've been given lots of problems they don't know how to do, and they got in the habit of giving up or asking for help right away.
Quick digression. For a long time I was really bad at reminding students of logistical stuff. I finished grading this thing, we have a weird schedule tomorrow, stuff like that. I would make a note to myself to say it but I would forget. The solution wasn’t to practice my reminders in front of the mirror. It wasn’t a skill, it was a habit. I needed to change something in the environment to get into a new habit. I started dropping a slide into my slide deck — I have a slide deck for each unit with a slide for the warmup and a slide with the agenda for the day. I would put a slide for logistics in between. It worked great, and now I often don't need it because I'm in the habit of giving logistical reminders at the start of each lesson.
That's how I think about getting students to persevere when they see a problem they aren't sure how to solve. I don't need to give them practice, I need to make a change in the environment that makes it easier to persevere and build a new habit. In the past I often gave a tricky problem for students to figure out at the beginning of the lesson. That ended up strengthening unhelpful habits for lots of students. Now, I’m much more likely to start with some explicit instruction. This levels the playing field. I do a check for understanding early in the lesson to see if students have the background knowledge they need to tackle the day’s lesson and do a quick reteach if necessary. That explicit instruction does a lot to set students up for success. Then I build gradually on what they know, starting with some problems that might seem simple. Even if those problems are easy for students they build confidence and momentum. Then, after the explicit instruction, some checking for understanding, and some predictable practice, students are in a much better place to try something harder, and to persevere if it doesn't look exactly like something they've seen before.
I don't teach the exact same way every day. Sometimes I start with a problem for students to solve. It depends on the content. There are plenty of times I start with some explicit instruction and students still struggle to work independently. Problem solving in math is hard and requires a lot of different skills, there are no guarantees. The key insight that changed my teaching is to think of perseverance as a habit and not a skill. My job isn't to give students lots of chances to practice perseverance, it's to tweak the environment to make success a little easier and build confidence and momentum toward more challenging problems. For me, and I think for most teachers, we often underestimate the value of a bit of explicit instruction and straightforward, predictable practice to get students going before facing the tough stuff. That's how students, slowly and over time, build more productive habits and become more independent learners.
Is there a succinct way to describe how habits versus skills are learned? Is the idea that a habit has no cognitive component, or a light cognitive component, it's just the environment?