Teaching with the Golden Ratio

The information contained in this post is a compilation of research and lectures delivered over the past year.  Special thanks to Karen Kennedy for delivering the bulk of the information.

I am a choir director and I am a choir director that teaches high school students.  If you teach high school students, you know how much those students love getting their teacher off track.  Unfortunately, this is how choir frequently starts: “Good afternoon class, before we get started, a quick reminder that we sing this Sunday.  Now take out your folders, oh wait, student A? You have a question?”  “Yes, do we need to wear our dresses?”  “Yes, now let’s get started, oh student B? you have a question?”  “Yes, do we need to wear our black shoes?”  “Yes”...and it continues...and goes on...and on...and now I’ve wasted a quarter of my rehearsal time answering questions instead of rehearsing.  Chances are this can be avoided not just in music classrooms but in most classrooms.  Want to know more?  Please take this simple quiz first.

What do pinecones, spiral galaxies, Claude Debussy, and the Parthenon have in common?

A.  Nothing

B.  A lot

If you guessed B, you are correct.  

Let’s try another one: what do these things have to do with classroom management?

A.  Nothing

B.  A lot

If you guessed B, you are once again correct.

Whether we know it or not, our brains are programmed in a way to pace learning and attention, easing into one thing and out of another.  Think about the last time you saw a T.V. show or a movie where the climax came ten minutes after it started.  It does not happen because that’s not how our brains are programmed.  The creators want us to be engaged for the most important part of the plot so they save it for later.  It’s also not at the very end.  It comes approximately two thirds to three quarters of the way through.  More on that in a moment.

There is a phenomenon in math, science, art, music, nature, and many other areas called the golden ratio.  The golden ratio essentially states that a + b is to a as a is to b

Here is a visual representation:

Notice that as you keep using the same proportion, the lengths get smaller in a spiral pattern.  This spiral pattern is used throughout nature.  Clearly, God likes math!  Here are some examples in nature and architecture:

At this point, you are probably right where I was when I first heard about this.  What does this have to do with me?  Stay with me.  I promise you, it will pay off.

In order to hit the golden ratio, you can do some simple math and make a sequence of numbers called the fibonacci sequence.  All you have to do is add the last two numbers of the sequence together to get your next number.  Here it is

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

So 1 + 1 = 2;  1 + 2 = 3;  2 + 3 = 5;  3 + 5 = 8; and so on and so forth.

Wherever you start going back down is the point of the golden ratio of the total added together.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, (the golden ratio occurs here) 34, 21, 13, 8, 5, 3, 2, 1, 1

(first part of sequence total - 143) (second part of sequence total - 89)

143 divided by 89 gives us 1.6067 and the golden ratio is 1.618 so pretty close.  The farther you go in the sequence, the closer you get to the exact number.

So now it’s time for the application to the classroom.  Hopefully I am at the approximate golden ratio of this article because that will mean I have your peak attention!  Our brains are made to focus best at the golden proportion of a time period.  Think about it.  We do not do well when we dive right into a difficult concept without first “warming up” to it.  Our brains work best when we ease into with something that we are familiar with and build towards learning newer, more difficult concepts.  Our attention span also increases as we get deeper into learning and then we ease out of it as we near the end.

Let’s go back to our fibonacci sequence and apply it to the classroom.  Here is how I might use it to teach a choir class

1 minute activity - Warm up #1 - breathing

1 minute activity - Warm up #2 - bubbling

2 minute activity - Warm up #3 - range exercises

3 minute activity - 8 measures that we already know - work on memorizing

5 minute activity - review parts on another section we started yesterday (still familiar material)

8 minute activity - learn a small, new section of a different song

13 minute activity - work on the hardest part of the day (notice this is at the golden ratio)

8 minute activity - sight reading (didn’t do this at the beginning - too difficult)

5 minute activity - memorize a section of music

3 minute activity - announcements (did it at the end - they have no reason to get off track)

2 minute activity - put folders away

1 minute activity - socialize

That covers a 52 minute period.  Obviously you can adjust the times to fit whatever schedule you are on but the concept stays the same across all subjects and time frames.  Be sure to utilize the time when your students brains are most engaged.

I was a little skeptical of this at first but if you take the time to try it out, it really does work.  You also don’t have to deal with lagging attention spans.  It is a fast paced class and students perform well under those conditions.

I challenge you to look for this golden ratio around you.  After I heard about this, I started looking and found the ratio all over the place.  Did you know that 8:00 AM church is at the golden ratio of your weekend?  What are some others?  Leave some examples you’ve seen in the comments section.  I also want to hear if it worked in the classroom.  

Give it a try and see what you can learn!