Using Apprenticeship to learn to solve a Rubik's cube

A Lego covered Rubik's Cube!

In the previous blog post, I explained how I used the Trivium to help me learn to solve a Rubik’s cube. When my son asked me to help him learn, I wondered how I would be able to teach him.  He was only 6 years old, and I knew nothing about the cube.  But after about a month of practice, I was able to solve a 3x3 on my own.  Now I needed to help my son learn. 

The second tool I used to help my son solve a Rubik’s cube is Apprenticeship.  I spent hours learning the steps to solving a cube, memorizing algorithms, and solving the cube, one layer at a time.   By this time, he had already found some strategies to solve the white face by himself.  I let him solve the white face.  Then I showed him over and over again how to solve the second layer.  Finally, he was able to take a little ownership.  I sat beside him while he practiced the second layer.  He asked questions.  When he was able to solve this layer without any help, I showed him the next step.  Over and over again.  We chanted algorithms.  We looked for patterns.  (In the final step to solving a cube, there is a yellow 2x2 square that spins around the top layer as we are moving the cube through the algorithm. It is fun to watch, and if the square disappears, we know that we have not completed the algorithm correctly.)

An apprentice to a blacksmith will not start making nails on his first day.  Instead he will stand beside the master blacksmith and watch him maybe thousands of times.  Gradually the master will start giving the apprentice a little more responsibility.  Eventually the apprentice will be able to make a nail, while the master blacksmith will continue to make horse shoes.  This process is one of my favorite tools for teaching.  It takes a long time.  It takes a lot of work.  But the rewards are infinite. 

Apprenticeship works for more than just Rubik’s cubes and blacksmithing.   I use this tool with my daughter when she studies Language  and Writing.  When we study the English Language, I model how to parse sentences into parts of speech.  We have a series of questions to ask.  For example, the sentence might be: “ Jonny solved a Rubik’s Cube.”  We would ask: Who solved a Rubik’s Cube? Jonny: Subject Noun.  What is being said about Jonny? Jonny solved: Verb transitive.  Solved What? Cube:Direct Object.  What kind of cube? Rubik’s: Possessive Noun Adjective.  When I first exposed my daughter to this series of questions, we started very simply.  The sentences only had two words.  “Suzy sang.”  I told my daughter I would not allow her to say anything.  She just needed to listen to me over and over again.  Who sang? Suzy: Subject noun.  What is being said about Suzy? Suzy sang: verb intransitive.  I repeated this pattern many times.  Tommy danced.  Who danced? Tommy: Subject noun.  What is being said about Tommy? Tommy danced: verb intransitive.  After about the 10^th sentence, my daughter finally said, “Mom, can I do it please?”  And you know what?  She did it perfectly.

I also use apprenticeship when I teach my daughter to write.  I model making keyword outlines, writing from the keyword outline, adding dress ups like adverbs and adjectives, varying sentence openers, etc.  When we first started using Institute for Excellence in Writing (IEW)’s writing program, I wrote most of the assignment myself, with my daughter sitting at my side.  Andrew Pudewa, IEW’s founder, says, “You can’t help your child too much.”

 The teacher in me feels like this is cheating.  It isn’t.  Of course, I do not let my daughter take credit for my work, but I want to model good writing so that students can learn from a master.  Just like in English Grammar, my daughter started out by just observing, then gradually took ownership of her own writing.

This fuzzy picture shows my son's first cube
that he solved entirely by himself!

 

Apprenticeship is a beautiful and effective way to teach. My children learn with me.  They know that learning is a lifelong process because they see me continuing to learn.  My children are better writers, readers, and thinkers because of the way we learn together. 

On Easter day 2017, my six year old son solved his first 3x3 completely on his own.  Later that month he had major surgeries and several complications.  He was sick for months, so he decided to take a hiatus from solving Rubik’s cubes.   He has just recently started to solve them again.  I will continue to sit beside him, cheering him on.

Using the Trivium to solve a Rubik's Cube

My six year old held a Rubik’s cube in his hand.  Turning it slowly, he looked at me.  “Mom.  I want to learn how to solve a Rubik’s cube.”

I could tell he was serious.  This was not a whim of a little boy.  I remembered the promise I made to one of his doctors.

“Help him find things that he can be good at.  Adaptive sports are fine if that is what he wants, but also invest his time in things like music, history, robotics.” 

 Dr. Timothy Brei is one of the most celebrated physicians in his field.  Dr. Brei and my son have something in common.  They both have Spina Bifida.  The Rubik’s cube seemed to be a way to keep my promise to Dr. Brei.  But I knew nothing about Rubik’s cubes. How on earth was I going to teach my son how to solve a Rubik’s cube? The first thing I needed to do was learn to solve a cube myself.

I used two major tools to help my son solve the Rubik’s cube. In this post, I’m going to focus on the first tool: The Trivium.  I will explain how the second tool, Apprenticeship, helped us to solve the cube in the next blog post.

I love Classical Education.  I educate my children classically at home, and we are part of a classical homeschool group that meets once each week called Classical Conversations.  When I first started studying Classical Education thirteen years ago, I thought it was kind of stuffy and dry.  Students learn Latin.  The memorize declensions.  They read old books.  It didn’t sound quite as fun as traditional learning to me.  But I have changed my position on that.  Classical education is not dry.  It is rich.  And the tools of Classical Education can be used to learn just about anything.  To show you how versatile the tools of Classical Education are, I am going to explain how I used the Trivium to learn to solve a Rubik’s cube.  (Not quite as stuffy and dry as it sounds, eh?)

In ancient Greece and Rome, students used the Trivium to learn new skills. Trivium means “three roads”  in Latin.  The three parts (or roads) to the trivium are Grammar, Dialectic, and Rhetoric.  During the Grammar stage, students memorize definitions and facts, with very little concern to meaning. While students can work through all the stages, young children naturally fall into the Grammar stage because they are able to memorize facts without a lot of effort.   Have you ever met a preschooler that can name all different kinds of dinosaurs?  My five year old loves Pokemon cards.  He can tell me the names of each of the characters on the cards, and he can remember how much health and damage each one has.  (I, however, have no idea what that means.  Nor do I care.)  The Grammar of the Trivium, not to be confused with English Grammar, is the basics of the topic you are studying.  Students in the Grammar stage memorize names and dates in History, math facts in Math; they memorize lists in Science such as the five kingdoms of living things. They memorize the list of prepositions for English Grammar. They memorize the states and capitals. Their brains are wired to memorize facts, so classical educators try to fill their long term memory with as many good facts as possible.

To use Grammar  to learn how to solve a Rubik’s cube, I first memorized the colors of the cube: white is always opposite yellow, green is opposite of blue, and red is opposite of orange.  Then I memorized the 7 steps to solving the cube. (White cross, white face, top layer, middle, yellow cross, yellow face, and bottom layer.)  I memorized the notation.  R means turn the right layer clockwise.  R’ means turn the right layer counter clockwise.  I learned how to orient the cube.  Then I started memorizing algorithms.  (I’m probably the only Rubik’s cuber that sings algorithms to herself.) If I have a yellow bar, then I need to use these steps to get the yellow cross; but if I have a yellow hook, then I need to use a different set of steps to solve the yellow cross.  All of this memorization began my journey of helping my son learn how to solve a Rubik’s cube.  While I was memorizing these facts, my son started playing with a 2x2 cube (instead of a traditional 3x3).  The 2x2 uses some of the same algorithms as the 3x3, but there are not as many steps to solve the cube.  This was a great introduction to learning to solve the 3x3.  He also had a pyramid puzzle with 4 faces.  He was able to solve it just by playing with it for a while.  These two simpler cubes helped him to understand the more complex 3x3.

The next stage of the Trivium is Dialectic.  As I said before, learning a new skill can take a student through all the stages, but children naturally fall into this stage around age 10 or 12 to middle school and early high school.  This is the time that students start questioning everything.  They tend to disagree with authority and argue about many things. During the Dialectic stage, students study logic.  They ask questions and answer many.  They use the grammar they have memorized and start to make sense of it.  They see how the facts they memorized fit into the world.

I used Dialectic tools to learn to solve the 3x3 cube.  I started with the memory work I had acquired.  I watched Youtube videos of skilled Rubik’s cube solvers show how to solve a cube step by step.  I practiced each algorithm many times.  I called a few Rubik’s cube solving friends to help me when I got stuck.  We had 5 cubes around the house, so I practiced each step five times before going on to the next step.  I first solved the white face on all five cubes.  Then I solved the middle of all five cubes.  And one day, I finally solved a 3x3 without any assistance.   This process took me about a month.  (I am sure there are many skilled cube solvers that learned to solve a cube in less time than me.)

The final stage of the Trivium is the Rhetoric Stage.  This is when you take the skills you have acquired from the Grammar and Dialectic stage, and you are able to teach what you have learned.  I started  a Rubik’s cube solving club that met at my house.  I was ready to help my son learn to solve a cube. I did use grammar and dialectic stages to help my son learn the cube, but there is also another tool I used to help him. I will explain how I used Apprenticeship to teach my son to solve a 3x3 Rubik’s cube in the next blog post.