Tuesday, August 6, 2019

Scaffolding with Automatic Spelling

In my last blog post, I defined educational scaffolding and explained how to use it in the classroom.  Today, I want to focus on how Automatic Spelling uses the scaffolding technique.  It is scaffolding that makes Automatic Spelling so different from other spelling programs.

Automatic Spelling (AS) uses scaffolding in several ways.
*  AS continually repeats what is easy.  (Remember the Easy +1 idea?) Each list contains 7 new spelling words which are repeated 3 times in a grid of 60 words.  That leaves almost 40 words that are review from previous lessons.

*  AS teaches spelling rules, which are repeated in every lesson.  It takes a while, but the students memorize the rules and learn to identify which rules each spelling word follows.

* AS teaches students to identify phonograms.  This helps tremendously in helping students master letter order within a word.  If you have a student who cannot remember whether a word is spelled with an ae or an ea, learning the phonograms will help. (For example, is it baer or bear? We know that bear uses the ea phonogram.)

* AS teaches students to memorize the definitions of homophones so that they can use the word correctly.  It only introduces one of the homophones in a homophone pair or triad to allow students to master that meaning and spelling before learning the other words and definitions with the same sound.  For example, students learn to spell "a location" where and practice it for several days before learning "to put something on" wear.  After they have practiced both words, they start to use them in dictation sentences.  The teacher might read, "Where did I wear that coat?" and the students will be able to use both words correctly.

* AS teaches students how to pluralize, use possessives, and add suffixes with every word possible.  They practice this over and over again until it becomes automatic. Check out this great
suffix game.

Help your student lay a firm foundation in spelling, build upon that foundation, and soar into new heights with Automatic Spelling!

Educational Scaffolding


I was first introduced to the term scaffolding in my education classes in college.  It has shaped the way that I teach.


What is scaffolding? 
A physical scaffold is a series of platforms that you must build one layer at a time.  
An educational scaffold is a method of introducing topics so that they build on each other.  

Students learn best when they add to what they already know.  Andrew Pudewa, the founder of the Institute for Excellence in Writing (IEW), calls this concept “Easy + 1,” in which students do what is easy, then just add one new thing to their papers until that new thing is mastered.


Scaffolding is a wonderful tool that works across the subject areas, works with nearly any kind of teaching method, be it classical, traditional, Charlotte Mason, or even “unschooling,” and encourages growth and knowledge in students with learning delays, gifted students, and every student in between.  Not only that, scaffolding is a natural progression of learning; it is quite easy for trained teachers and  homeschooling parents to implement.

What does scaffolding look like in the classroom? 

I already shared how IEW uses scaffolding (they call it "Easy +1") to gradually increase the dress ups in their papers. In the first paper, a student may need to add an adverb that end in -ly.  When that becomes easy, the student will add the adverb and add a who or which clause.  This goes on until each new dress up, sentence opener, and decoration is added with ease.  You can read more about IEW here.

In math, my daughter learned the multiplication and division facts by practicing what she knew (the ones facts and the twos facts, and just adding two new facts (3x3 and  3x4) on the timed test. When she mastered that timed test, the next timed test tested her on the 1s, 2s, 3x3, 3x4, and now 3x5 and 3x6.  You can read more about the program Kicking It Math here.  (I am not affiliated at all with Kelly Malloy, but I want to be her BFF!)

We do the same for Science, History, Literature, and more.  What do we know? How can we add to that? We know flowers have petals.  What is the purpose of a petal?  We know the story of the Lion and the Mouse.  How is it similar to Androcles and the Lion?

Scaffolding is not rocket science.  It is common sense, but it is one of the most effective teaching techniques I use. Scaffolding helps build synapses in the brain, something that struggling learners desperately need.
Scaffolding does more than just introduce a little information at a time; it forces students to review what they have already learned.  You can’t climb a scaffold without starting at the bottom and ascending one level at a time.  Brain research has shown that review is vital for long term memory storage.

 Some students just can’t make connections between two things without a little nudge.  For those students, parents and teachers can be the nudgers.  Many gifted students enjoy the challenge of finding connections by themselves. Scaffolding works for everyone!

Automatic Spelling uses scaffolding in many ways. To see how my spelling program uses scaffolding, click this link.

You can purchase Automatic Spelling here.

Saturday, June 15, 2019

Treating Spelling Words like Math Facts

My daughter spent last summer mastering the multiplication and division facts. I was so impressed with the simplicity of the program we used.  You can read about it here.

I remember watching her confidence soar while her ability level in math grew.  She could finally understand fractions.  The key to her understanding was math fact mastery.

Spelling... that was a different story.  My sweet girl worked so hard trying to memorize spelling words, but they just would not stick.  Sometimes she did well on a spelling test.  Sometimes she did not. Either way the spelling test did not help her with word retention.  She could not reproduce a spelling word while writing.  It didn't matter what spelling program she used.  She still struggled.  Sometimes even the simplest of words like "what" and "said" caused her anxiety.  She was so focused on the spelling of words, that her thoughts: her beautiful, profound thoughts, stayed inside her instead of on paper where the world could enjoy them. 


I know that spelling and writing are two separate skills.  I had treated them as such for years.  Experts say to allow inventive spelling while children are writing.  You can fix the spelling later.  Experts say to allow children to dictate their thoughts while the parent or teacher act as a scribe.  These are great modifications that I have used in the classroom and with my own children.  But I wanted more for my daughter. 

And then I had a thought,


"What if I treated spelling words like math facts?"



It was such a strange idea.  Spelling is a different skill than math.

But what if instead of numbers grouped together, I taught Elli to group letters together.  Addends and factors became phonograms and spelling rules.  3 x 2 = 6 because it is three groups of two or two groups of three.  The word said = s plus the AI phonogram plus d. 

https://www.teacherspayteachers.com/Product/Automatic-Spelling-Level-1-Lessons-1-24-Final-Copy-Lessons-25-48-Rough-Draft-4577151But still, this was just conceptual.  My daughter had always understood the WHY behind math facts. 

What she needed was consistent practice and gradual introduction of new words. 


Students spend hours practicing math facts.  They use flash cards, written tests, picture stories: whatever works to internalize them.  They need math fact mastery to go on to higher level math.  You can't reduce fractions without an understanding of factors and division.  Math fact memory is necessary.





My daughter after she completed Automatic Spelling Level 1
All my life I've been told that some students are just poor spellers, and it is a good thing that spell check exists.  This is true, but I was not ready to give up.  My daughter was starting to be embarrassed by her struggles.  I thought that she might be able to master the spelling of common words in the same way she learned the multiplication facts:  by learning just a small number at a time and by practicing previous words over and over again.

So I collected words: commonly misspelled words, Dulch words, Fry words, words that used certain phonograms, words that had to be changed before adding a suffix.  Words, words, words.  I showed her what rules each of these words followed.  I pointed out phonograms within the words.  I created a spelling program. 

And she practiced.  And practiced.  And practiced.  And slowly she learned how to spell.  She can write without the hindrance of a spelling block. She can add any suffix to a word and spell it correctly.  She drops Es, changes y to i, and doubles final consonants without batting an eye.




It worked so well for her that I thought it might help other students.  I was right.  More than fifty students have tried this program.  Fifty children who might struggle with spelling otherwise.  Fifty children, some who for the first time believe that they are capable of learning to spell.  Some of these students ask to do spelling as their first subject. They are seeing results.  Your child could, too.


You can purchase Automatic Spelling here.

Wednesday, January 30, 2019

Top Ten Issues Weak Spellers Face Every Day


Note: I am more than qualified to compile this list because I, my friends, am a terrible speller.  I have dyslexia.  I am also a teacher who tries to reconcile spelling issues with teaching methods that work. Welcome to the mind of a terrible speller. 


10. Traditional Spelling Homework.

Copying spelling words can be a mindless activity for poor spellers.  (Not all spellers, obviously.  We will not be talking in absolutes today.) When I copied spelling words I didn’t have to think about the spelling of the word because the spelling of the word was right there in front of me.  I went on autopilot.  (For me, it was a very similar sensation to the feeling you have when you drive somewhere familiar and you zone out for a few minutes, and when you finally zone back in, you look around and think, “I’m already this far?! When did I pass that one landmark?”) When the test came, I couldn’t recall the spelling of the words I copied because the spelling of the words were no longer in front of me.

Cross word puzzles, word searches, and unscramble the word puzzles are busy work.  Personally, I’m great at unscramble the word puzzles because that’s what words look like to me ALL THE TIME. But they don’t help me spell. If anything, they reinforce bad habits.  I can tell you how many letter Is and Es are in the word ExpErIEncE, but don’t expect me to get them in the correct order on my first attempt.  Some students just can’t find the word yellow in a word search sea of letters, and they spend hours trying to find every y, and then make sure an e is next to it, and so on.  When I had to do these kinds of activities, in the back of my mind I was thinking, “I am just wasting time.  I still have to actually practice my words.”  Spelling homework took me HOURS every day.

9. Hours of studying produce little results. 

As I was saying, homework took me hours every day.  I was lucky to scrape by with a C on a test.  Guys, most weak spellers are not lazy.  Usually they work the hardest in the class, and they have nothing to show for it. They just learn differently than the norm.

8. Passing a spelling test does not equal mastery. 

If I did spell a word correctly, I was typically unable to retrieve the spelling of that word in my writing.

7. The amount of new spelling words every week is overwhelming for many students. 

You guys, weak spellers are drowning in new spelling words.  We expect them to learn 20 new words every week, when they usually haven’t mastered the last week’s list, or the week before that, AND SO ON.  We don’t expect a student piano player to play a recital piece after one week of practice.  We don’t expect a student basketball player to master layups in a week. Why do we expect this of our spellers? 

And don’t get me started on the six week unit review tests, in which every complicated word for the last six weeks was required.  The teacher would say, “Oh.  This will be an easy lesson.  You have spelled all these words before.” Dude.  I got most of them wrong, by the way.  And I’ve slept since then.  I haven’t thought about those words for six weeks.  Review lessons always felt like a new lesson: usually the hardest new lesson of the six week spelling period.

6. English doesn’t always follow the rules. 

You say to me,“i before e except after c.”

 “Oh yeah?” I say, “ what about weird?  Huh? Height? Foreign?”

You say to me, “When two vowels go walking the first one does the talking.” 

"Ok, so what about bread? Boa? Field?"

“The silent e makes the vowel say its name.”

“Then why on earth do we pronounce have with a short a?” (P.S. when I found out the answer to this one, I cried literal tears.  I’m not even joking.)

Here’s a truth bomb for ya: Most spelling programs are teaching the WRONG rules. Bam.

5. Learning phonics isn’t enough.

Fonix uloan duz not a gud spelr maik.

4. Homophones. Contractions.

Their, there, they’re.  It’ll be ok. Maybe.

What’s the difference between its and it’s?  I didn’t know until COLLEGE.  College.

3. Suffixes and prefixes. 

AHHH! Why is hurrying spelled with a y, but hurried isn’t?  It was enough to pull my hair out.  And I’ve got very thin hair to begin with.

This struggling speller has improved immensely!
2. Many poor spellers are not great readers.  It’s tough to know how to pronounce though, thought, and through if you can’t remember how to spell them.

1. Bad spellers are some of the most CREATIVE people I know, but spelling inhibits them from getting their thoughts on paper. 
 

Many poor spellers have a lot to say, but they look at a blank page and they have to focus their entire mind on the spelling of each and every word.  By the time they figure out the spelling, or at least a close enough spelling that they can decipher it later, they have forgotten what they were going to say.
https://www.teacherspayteachers.com/Product/Automatic-Spelling-Level-1-Lessons-1-24-Final-Copy-Lessons-25-48-Rough-Draft-4577151


Is there any hope for these weak spellers?  Yes.  I have created a program that addresses these issues. You can read about Automatic Spelling here. You can purchase Automatic Spelling here.

Tuesday, September 11, 2018

Math Fact Automaticity


When Number Sense isn't Enough
My daughter has a great number sense.  She understands what it means to add, subtract, multiply and divide.  She can skip count all the numbers from 1 to 15. Skip counting means to count by a certain number (3, 6, 9, 12, …) But even with all this understanding, she was still struggling to get her math work finished. 

The reason?

She did not have her math facts memorized. 

She could use five or more strategies to solve a math problem, but nothing was helping her recall her math facts quickly.  A worksheet of 20 problems would take her 45 minutes to an hour and many tears to complete.
I love our math curriculum, Life of Fred.  But my daughter needed to sharpen her math facts.

I used an abacus.  We worked with counters.  Base 10 blocks.  Number bonds, ten frames.  We’ve used pictures to help us remember math facts.  Flash cards. Games.  You name it.  I’ve tried it.  Nothing was sticking.
Kicking It to the Rescue
I am happy to report that I finally found something that works for her.  Please understand that memorizing math facts is not a substitute for teaching math reasoning skills, understanding, and number sense. However, at some point children need to know their math facts.  Leigh Bortins, the founder of Classical Conversations, a national homeschooling program that we use, says that,
When the basic facts [of mathematics] are obvious, we have the mental space to investigate the obscure, the unknown and the unfamiliar.”

 

Let me introduce you to my favorite math speed drill program: Kicking It!  I bought Kicking It from teacherspayteachers.com.  The author, Kelly Malloy, was a middle school math teacher who noticed that her students did not have their math facts memorized, and therefore were unable do the fractions, decimals, and pre-algebra problems the class required.  If you don’t know how to divide, you can’t reduce fractions. Kelly vowed that if she ever taught elementary math, she would make sure that her students graduated from her class equipped with basic math facts.  She kept her promise by developing this program. (I do not know Kelly Malloy personally, but if she had a fan club, I would be the president.)
Students earn dog tag "belts" as they
work through the program.

 
The Kicking It Difference
When I taught second grade, I used a math drill program called the Mighty Math Club. It worked fairly well, but students were required to memorize all the ones facts, then when they had mastered the ones, they went on to the twos, and so on.  Each new speed drill had 12 new facts they had to master.  This was overwhelming for some students.

 

Kicking It is different because each test (lettered A-Z) only has two new facts and their reciprocal facts.  For example, In Kicking It Multiplication, the A test has only 1 x 1  through 1 x 12.  (Ones are easy!)  But the B test has 1 x 1 through 1 x12, and two new facts  2x2, 2x3 and its reciprocal fact 3 x 2.  Once that test has been passed, the student goes to test C that has the ones facts, 2x2, 2x3, 3x2, and two new facts and their reciprocals 2x4, 2x5, 4x2, 5x2.  Memorizing the facts just a little bit at a time is so much easier.  Another reason I think Kelly Malloy is a genius, is that she does not always introduce the math facts in order.  Students learn the 9s and 8s facts sometimes before the 3s and 4s.  For some reason, the higher facts take some students a longer time to learn.
 

Three Parts to Kicking It

Part 1: Students are to practice flashcards, introduced in the same order as the A-Z tests. 

Part 2: Students have one minute to practice ring facts.  This consists of 29 math facts that they try to recite and answer in one minute or less. These are printed on colored paper and have belts, similar to karate belts, that they try to earn.  Every time they pass 4 of the timed tests, they get a new “belt” with new facts to master.

Part 3: These are the timed tests lettered A-Z.  Each test has 60 problems. Students work on the same test each day until they can answer all the problems in 2 minutes and 40 seconds or less.  (One minute is preferable, but some children can’t write that quickly).

 

If you want to read more about this amazing program, I highly suggest you go to the source.  Kelly Malloy has an excellent blog post about it.

 
Happily Ever After
My daughter after she earned her First Degree Blackbelt
Multiplication facts 1-9. She has now mastered 1-12.
My eight year old son has a purple belt in multiplication, and my daughter now has passed the entire multiplication program with a third degree black belt in multiplication. She is now working to earn a yellow belt in division. She can look at a math fact, and write the answer without having to think about it.  It is automatic.  Remember that quote from Leigh Bortins? My daughter is now able to focus on things like fractions, factoring, and other harder math skills because multiplication is easy for her.   A two digit by one digit multiplication worksheet with 20 problems used to take my daughter over an hour.  A few weeks ago, she completed  one in just seven minutes.  She told me that this is her favorite math program she has ever used.  “Math used to be hard for me, Mom.  Now I just know the answers.  It’s a nice feeling.”

 

Some modifications that worked for our family:

1. I put the lettered tests in page protectors.  My children use a dry erase marker to write the answers.

2. Instead of using a timer, I used a stopwatch.  I wrote the time it took for my children to solve all 60 problems directly on the test.

3. I allow a test to be passed if they can solve all the problems accurately in under 5 minutes.  My daughter has dyslexia and my son has some anxiety and other special needs, and this worked better for us.  However, I have my children do two tests a day.  First, they complete the test they have been working on.  Then they go back to an earlier test and try to complete it in under 2 minutes and 40 seconds.  My daughter has completed all the tests in multiplication in under 5 minutes, and tests A-O in under 2 minutes and 40 seconds.

4. I take the tests, too.  It makes my children more eager to learn when they see me working beside them.  And let me tell you, passing the test under 60 seconds is hard for me.  I average one minute and eight seconds. To learn more about this process, read my apprenticeship blog post.

Students compare the "Wax On; Wax Off"
concept to memorizing math facts.
5. Several students in our homeschooling community are working through Kicking It. Once in a while we get together to play some math games and a real MMA Sensei teaches some basic martial arts skills to go with the Ninja themed program.

 

Playing Kicking It! math games
I have only used Kicking It! Multiplication and Division, but Kelly Malloy also has Kicking It programs in addition, subtraction, and factors.(I’m excited about the factors program!)

 

If your child is struggling with their math facts, I highly recommend Kicking It!

Are you interested in a Spelling Program that takes a similar approach?  You can read about the spelling program I created here.  You can purchase Automatic Spelling here.

Monday, August 27, 2018

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 10th 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.









Friday, August 24, 2018

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.