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.

  • Set challenging puzzles out there
  • Give them enough tools to get started
  • Let them get stuck and work it out, giving a little nudge in the right direction when it looks like their ideas are about run dry, and let them struggle a bit more.

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:

  • First, throwing them into the pool was really successful.  The students were less bored and learned more.  Weaker students gained confidence and realized they could, in fact, figure things out on their own.  Stronger students were less bored.  EVERYONE learned that if they were stuck, there were resources out there to help.  And they learned to use them. 
  • Second, students didn't want me to help them.  Most of them felt really empowered figuring stuff out.  When they asked a question, they wanted me to just answer that question and then take off.  That allowed them to figure things out on their own, which they found much more rewarding.
  • Third, there were big individual differences in how students first approached a task they didn't know how to do.

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: 

  • Write down the question. What is the problem you're trying to solve? 
  • Write down what you know.  Not everything that you know, obviously, but what is given to you in the problem?  What have they given you to work with? 

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:

  • In a classroom, a teacher may pose a challenge because there is something specific they want you to learn.  As I tell my students, each assigned problem is designed to teach you something specific.  It's like an etude or like a piece of music selected for Suzuki instruction: it was selected to make sure you develop one specific skill.  If you know what that is, you know where to focus. 
  • In the real world where the problem isn't 'designed', but just crops up, figuring out why you're solving the problem tells you what aspects of it to focus on and which ones to ignore.  Redesigning a back door for looks is very different than redesigning it for wheelchair accessibility.  If you're really lucky, you may find that you've got a 'problem' but there's no real need to solve it.  You're done!

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.

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