The past semester, I changed my introductory statistics course as a result of making a more explicit study of how to teach quantitative and formal reasoning skills. In the course of those changes, I saw a lot of really frustrated students. I'll get to solving that problem - I promise - in the second half of this post. But I want to start with talking about why I think frustration is a really good and necessary step for learning.
You're Marooned On a Desert Island. And It's the Hunger Games.
The bottom line of what I learned about 'best practices' in teaching quantitative and formal reasoning skills: let students solve their own problems.
This contrasts with more of the 'common sense' approach to teaching quantitiatve skills: Teach everything explicitly and walk them through it step by step so they don't get scared or frustrated.
You can see the parallel here to the 'jump in the pool' v. 'over-protection' theme here.
Here's what I learned:
There were the students who love a challenge. I had several big football jocks in this group, a couple a real scrappy students who like to argue about their grades, and those students you just love who seem to eat up anything you want to teach them - the harder the better. Those students immediately hunkered down, grins on their faces, took out pencils, and started underlying key things they needed to focus on. They knew how to start. What they needed was resources to succeed.
Where To Start When You're Lost: Pretend You're On a Dessert Island.
Then there are the students who looked lost. They didn't know how to start. It was easy to find them. They were staring at their computer screen with a miserable look on their face.I'd stop by and ask how they were doing. Sometimes I got a wail. But usually they just said they didn't know where to start.
I told them to start where I tell my youngest to start when he's stuck on his algebra homework:
There are two advantages to starting with those steps. First, they make you read the question carefully so you don't miss something. Second, it takes time and lets things stew in the background while you're doing something useful and concrete.
Think a bit more deeply.
While you're still mulling, think a little more deeply. Write down what the goal of solving the problem is. Why is this question important and why were you asked to solve it? This step is important because:
Almost always laying out what you are trying to find out explicitly and what tools you have to solve the problem triggers new ways to combine your resources together.
That may not finish the problem, but it gives you a place to start. And once you've got a start, you can see what isn't working and that gives you a new and much more explict problem to solve.