I’m a real fan of YouTube.  I love watching videos to learn new things; cooking, playing guitar, science, politics, and more.  Most of these content creators teach only by example, and to be honest, most of them are really lousy teachers.  There seems to be this common sense that instruction should be example oriented: 5 ways to peel a banana, 5 heavy metal riffs you need to know, 5 ways gravity brings you down, and so on.  When you think about it though, this is easy to explain; people want to show you what they know, not how they came to know it.  Of course, knowing how you know is more difficult to derive, even as a professional educator.  Frankly, in the guitar videos the instructors just seem like they’re showing off; jerks.

Teaching by Example

One of my favorite instructional descriptions comes from Louis Sachar’s Sideways Stories from the Wayside School:

Mrs. Jewls put 5 pencils on the desk.  “How many pencils do we have here, Joe?”

Joe counted the pencils.  “Four, six, one, nine, five.  There are five pencils, Mrs. Jewls.”

“You got the right answer, but you counted the wrong way.  Listen to me.  One, two, three, four, five, six, seven, eight, nine, ten.”  She put 6 erasers on the desk.  “Now count the erasers, Joe, just the way I showed you.”

Joe counted the erasers, “one, two, three, four, five, six, seven, eight, nine, ten.  There are ten, Mrs. Jewls.”

“You counted right, but you got the wrong answer.”

“This doesn’t make sense,” said Joe.  “When I count the wrong way I get the right answer, and when I count the right way I get the wrong answer.  I just don’t get it,” said Joe.  “I’ll never learn how to count.”

“Sure you will, Joe,” said Mrs. Jewls.  “One day it will just come to you.  You’ll wake up one morning and suddenly be able to count.”

Joe asked, “If all I have to do is wake up, what am I going to school for?”

I’ll let that thought linger.

Teaching by Principle

So, if you don’t orient your instruction by examples, what’s left?  Answer: principles.  Let me be clear, examples aren’t bad, in fact they are necessary, but their purpose should be to support principles, rules, conventions, algorithms, call them what you like.  Principles provide general methods to solve entire classes of problems.  These principles are not always immediately apparent, but they have much more instructional power than examples alone; and when principles are supported by examples, POW, you can hit it out of the park.

Let’s take teaching single digit addition, for example (the paragraph above was the principle, now it’s time for examples).  You might start by telling your students that 2 plus 2 equals 4.  This is an important fact, but it is only one example of single digit addition.  Knowing that 2 plus 2 equals 4 does not help when faced with 2 plus 3.  So, what’s the principle?  Well, I can think of at least two useful algorithms to teach single digit addition.  You probably can think of more, but here are my two:

The first principle we can call “group and count”.  You can use apples (how did we teach this before apples?) or fingers (oh, we had these before apples didn’t we?), or check marks on the whiteboard, or whatever.  Show the students a group of apples, then another group of apples and ask them to count each.  When that is done, push all the apples together and ask them to count the entire group.  This method is universal to addition and teaches both the answer as well as the problem.

The second principle we can call “cheating” (I mean “looking it up”).  Present a sums table and teach how to navigate along the top and side and find an intersection.  This method not only solves the immediate problem, but provides a glimpse into the future: times tables, coordinate systems, laws of commutativity, and more.

In the end, students will memorize 4 as the answer to two plus two, but instruction using principles has value everywhere.  Okay, single digit addition is a trivial example, so let’s look at a common approach to a more complex teaching moment.  You are holding 13 playing cards in your hand and the current bid is 3 spades.  I know, playing bridge isn’t common anymore, but stick with me.  Aunt Nelly tells you to bid 4 clubs.  Got it.  But you could play bridge every day for the rest of your life and never hold those cards hearing that bid sequence again.  Never.  You can see, that in the extreme, examples can be useless.  This is especially true as systems become more complex.

So, how do you find the principles?  

Funny thing, there doesn’t seem to be a principle for finding principles.  Of course, that never seems to stop me from trying.  Since principles can be thought of as ways to address groups of problems, finding a principle might only require putting two like problems side by side and examining common procedures in their solutions.  Of course, this doesn’t always work.  Thank goodness for Google.  Face it, reinventing the wheel is not always necessary.  Countless content principles have been explored and shared online.  If you are struggling to find a principle, the rule is to search.

As I suggested above; teaching by principle alone isn’t much better than only providing examples.  Think of “i” before “e” except after “c.”  All too often, rules have exceptions.  Come to think of it, language arts is full of exceptions.  Of course, ultimately, that‘s what makes literature (and other complex pastimes) so interesting.  Just like examples fail in more complex systems, so do rules.  Keep this in mind when exceptions outnumber the archetypes.  Learning more and more complex systems requires the aggregation of many principles (and examples), but hopefully, by the time a student faces any new content, they have gained fluency in the principles and skills forming the scaffolding for the new material.

The lesson here is to consider if teaching principles could set a better stage for your examples.  If so, derive them, or steal them, and ultimately craft them to create a clear method for their use.  Then your examples will not only teach a concept, but instruct and reinforce a method that students can repeat for success.